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Humancafe
Posted on Wednesday, February 01, 2006 - 09:37 am:   

What we think we know, we may know only for here and how, but things may be very different then and far away.

Where are the Pioneers and Voyagers now?

http://www.heavens-above.com/solar-escape.asp

this page is updated continuously
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IVAN
Posted on Saturday, February 04, 2006 - 12:01 am:   

Was Einstein right in using Maxwell's electromotive force 'simultaneity'?

In the Stanford Encyclopedia of Philosophy on Einstein it says:

quote:

Likewise, Einstein faults classical Maxwellian electrodynamics for an asymmetry in the way it explains electromagnetic induction depending on whether it is the coil or the magnet that is assumed to be at rest. (italics mine) If the effect is the same -- a current in the coil -- why, asks Einstein, should there be two different explanations: an electrical field created in the vicinity of a moving magnet or an electromotive force induced in a conductor moving through a stationary magnetic field? To be sure, whether it is the coil or the magnet that is taken to be at rest makes no observable difference, but the problem, from Einstein's point of view, is the asymmetry in the two explanations.


Is it the same to compare the coil or the magnet to be at rest, or in motion? They may be equivalent geometrically, but there is a fundamental difference between such geometrical relationship, which is in close proximity and instantaneous, and that of observational relationship when measuring relativistic velocities, which are at great distances. Can the two compare?

If we are limited observationally by the lightspeed v=c, then we are of necessity forced to observe distant relativistic phenomenon with the modifier sqrt(1-v^2/c^2), but there is no such modifier for relationships which are in immediate proximity to one another. The moving coil, or magnet, are geometrically linked, so the relativity of each is an immediate response; which is unlike if the same relationships were measured over great distances, where the immediate proximity is limited by the velocity of the signal, at v=c. Relativity does not exist in immediate geometrical proximity, whereas it does exist at distant signal dependent observations. So young Einstein, in his comparison, was forcing a relativistic comparison where none exists. And in this, he could not invoke his famous first postulate, that there are no preferred inertial reference frames, because that requires that what is immediate is the same as what is at a distance, as the signal velocity allows the observer to observe moving frames. So the relative movement of the coil or magnet in relation to each other is irrespective of which is the observer, because they are geometrically linked; on the other hand, the observers of distant relativistic motion are not geometrically linked, since their signal is limited by v=c, and of necessity have a time dependence on what is being observed. This is a subtle point, but it shows how we cannot use Maxwell's reference for distant relativistic phenomena. They simply don't match. They are philosophically immensely different from each other.

That scientific thinking had been so deeply influenced by this early youthful error of Einstein, and not nipped in the bud for its error in logic, is a regrettable fact of history. So now we are left with a physics dependent upon a postulate in Einstein's Relativity that is erroneous, since not all reference frames are equal and isotropic; rather, the observer's reference frame, being time dependent on the velocity of light, is always separate, and not equal, to the reference frame of what is being observed. In effect, we cannot assume that what is being observed is the same thing as what is actually happening, since we are left behind by the time dependent velocity of light. The only way Maxwell's example could be employed for relativistic observations would be if there were no time dependent lags, and that the observation were geometrically identical and instantaneous. But if this were so, there would be no need for Relativity, would there?

If the universe has a non-relativistic capability of responding to its geometrical relationships instantaneously, then most of what is now acceptable mathematically in modern physics, in essence, becomes irrelevant, and fanciful. So the preceding statement in the referenced article now makes more sense:

quote:

The one piece of evidence standardly cited for a youthful flirtation with positivism is Einstein's critique of the notion of absolute distant simultaneity in his 1905 paper on special relativity (Einstein 1905c). Einstein speaks there of "observers," but in an epistemologically neutral way that can be replaced by talk of an inertial frame of reference. (italics mine) What really bothers Einstein about distant simultaneity is not that it is observationally inaccessible but that it involves a two-fold arbitrariness, one in the choice of an inertial frame of reference and one in the stipulation within a given frame of a convention regarding the ratio of the times required for a light signal to go from one stationary observer to another and back again.


Indeed, time dependent observations are not the same as geometric related observations, they are not "epistemologically neutral", since the latter are instantaneous, i.e., simultaneous. I further think the universe already is operating at the 'instantaneous' physics, such as illustrated by 'strangeness' in how photons respond to each other, while our modern physics are limited by Einstein's relativistic time dependent observational bias. We had been led astray for the past one hundred years, regrettably.

Ivan

Also see: Brilliant Mind of Einstein
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IVAN
Posted on Saturday, February 04, 2006 - 01:09 pm:   

COMET DUST BALLS?

Deep Impact, science of the Tempel-1 aftermath: http://www.bautforum.com/showthread.php?t=19336

This is on BAUT forums, Space Exploration, where there's a very nice discussion on the evidence being gathered from the Deep Impact on comet Tempel-1. My thought was expressed here:

quote:

Comet rethink?
Of course, Tempel-1 deep inpact is only a sample of 'one'. But there seems to be enough evidence that perhaps comets are not 'dirty iceballs' anymore, in fact have little water, and are more like dirty 'dust balls' instead.

I've long had a notion (if any had followed my past posts) that comets are little solar region 'vacuum cleaners', gathering molecules and dust on their way out into the colder regions, and letting them loose again into the inner regions of the solar system. At this time, I'm not sure we really know what comet tails are made up of, but they should turn out as de-pressurized dust particles from comets in the hotter inner regions; in the outer colder regions, the process should be opposite, where they gather particles; hence, they don't shrink into nothing over time, but remain replenished. This is not the same as now theorized, that comets are remnants of the early solar system's formation; rather, they are cosmic entities in their own right. Will comets turn into asteroids eventually? Hard to say, but probably not.

BTW, this is perhaps more ATM for now, but as more data comes in from the outer solar system, we should get a better fix on why comets do what they do, and are fluffy dust balls rather than ice balls. (However, for dust to be more attracted on the comet's mass in outer regions might mean something that had been debated on ATM, that G is greater out there than here, but that's a line of reasoning which is not crickey to discuss here.) One way to confirm whether or not comets are distant solar system scrapers is to tally what loose dust and molecules constitute 'empty' space out by the Kuiper belt and beyond.


Insofar as to why I thought G is greater in the outer solar system (not mentioned in the BAUT post above), it can be found here: Short Summation of variable mass in variable G, dated 4 August, 2005, where I then said:

"This would mean that far ranging comets, those with highly elliptical orbits, would be seen to gather material of dust , water molecules, gases, very far out in the solar system's hypo higher G, and shed that same accumulation on their return trip back into a much lower G domain of the inner solar system. Hence, closer to the Sun they would gas out, or at least drop a few dust balls."

Ivan
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Ivan
Posted on Saturday, February 04, 2006 - 01:36 pm:   

Newton's "GM = rv^2" is a short form

F = GMm/ r^2, and we know F = ma
F = M*(Gm/r^2), where a = (Gm)/ r^2

F = M*(Gm)/r^2 = mv^2/ r

netted out: GM = rv^2

This was discussed here: http://www.bautforum.com/showthread.php?p=438344#post438344
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IVAN
Posted on Wednesday, February 15, 2006 - 09:32 pm:   

'ANTIGRAVITY' PROPULSION? - Space.com article

Does Dr. Felber's 'exact solution' to Einstein's theory of gravity reveal a new possible source of 'antigravity propulsion'? It does sound intriguing. However, upon reading the paper immediate references to "as seen by a distant observer" and "in the inertial frame of an observer far from the interaction between the source and payload... calculated exactly for relativistic speeds of both the source and payload..." leaves me wondering if we're not back to the old relativistic conundrum: Can we transpose what is 'observed' mathematically onto what is happening for the 'observed'? In effect, are we once again using Schwarzschild 'black hole' event math to extrapolate relativistic gravity for 'particles' on the event horizon? And is this observation nothing more than what is observed from the observer's reference frame, and not what is happening in the observed's reference frame? Of course, this begs the question as to how we get to 57.7 percent of light speed in the first place?

Interesting idea, worth a good read, but also worth taking with a grain of relativistic salt. The answer is out there...
:-)
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IVAN
Posted on Thursday, February 23, 2006 - 09:39 am:   

SR Null and Void

Just tell it like it is... no clothes.

...or take me to the Ritz, in no time!

Either massage time, or distance, and you've got it. :-)
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marc
Posted on Friday, February 24, 2006 - 07:20 pm:   

HUBBLE OUTTA THIS WORLD

http://hytaipan.home.comcast.net/hubble640.html

...may not work on slow dial up...
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ng71
Posted on Sunday, February 26, 2006 - 11:31 am:   

RELATIVITY DISPROVED?

quote:

Originally Posted by clj4

This is clearly not the case, this concept (which belongs to Ritz) has been refuted experimentally multiple times in the past 100 years. You have been given ample proof in another thread, you are simply reopening the same discussion

http://www.bautforum.com/showthread.php?t=36020

using an experiment (Sagnac) this time.
Here is one of the many refutations of the 'c+-v'.

http://imaginary_nematode.home.comca...echer_1977.pdf

Here is one of the many correct explanations of the Sagnac experiment:

http://www.mathpages.com/rr/s2-07/2-07.htm


You just opened another identical thread and you got plenty of explanations here:

http://www.physicsforums.com/showthread.php?t=112002



(bold mine)

The 'refutation' of Sagnac experiment may be spurious, in that it involves 'renormalizing' relativistic proper Time, where the difference in 'travel time' is adjusted. In effect, we have time factor=(1-v^2/c^2)^1/2 in one direction, while we have time factor=(1+v^2/c^2)^1/2 in the counter direction. If you make 'proper Time' variable, you get around the fact that it will take less time in one direction and more time in the counterdirection. Or, as the paper referenced says:

quote:

Of course, the result represents the time difference with respect to the axis-centered inertial frame. A clock attached to the perimeter of the ring would, according to special relativity, record a lesser time, by the factor y = (1-(v/c)2)1/2, so the Sagnac delay with respect to such a clock would be [4Aw/c2]/(1-(v/c)2)1/2. However, the characteristic frequency of a given light source co-moving with this clock would be greater, compared to its reduced value in terms of the axis-centered frame, by precisely the same factor, so the actual phase difference of the beams arriving at the receiver is invariant. (It's also worth noting that there is no Doppler shift involved in a Sagnac device, because each successive wave crest in a given direction travels the same distance from transmitter to receiver, and clocks at those points show the same lapse of proper time, both classically and in the context of special relativity.)



Once you adjust Time, you get the relativistic effect desired. How can it be claimed to falsify the experiment, if the experiment is designed, using relativity, to achieve invariant results? The only clue you get something is variant (in Sagnac experiment) is in the Doppler lightshift.

That said, I stand to be corrected if I got it wrong.

Feb. 24,2006: http://www.bautforum.com/showthread.php?t=38545
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IVAN
Posted on Tuesday, February 28, 2006 - 09:19 pm:   

~1G per 1AU? --Discussion

HYPOTHETICAL ATOMIC MASS AS A GRAVITY AND ENERGY FUNCTION, PER THE AXIOMATIC EQUATION: With Implications for the Pioneers 10 & 11 Acceleration Anomalies.

This is the paper that cannot be listed on the Discussion page of Wiki's "Pioneer Anomaly: Talk", due to a restriction on "original research" within the parameters of discussion, which is understandable, if not regrettable. A link to here would have nicely complimented, why a variable inertial mass per a variable ~1G per 1AU matches closely the Pioneer Anomaly.

By "coincidence"? Hubble Constant and Pioneer Anomaly (by coincidence?) share a common value: at = ap /c . Why is that? Could it be that variable G in deep space (where it may be 5 orders of magnitude than Newton's "universal" G on Earth) causes gravitational redshift of cosmic light, so the "coincidence" is not?

Ivan
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Anonymous
Posted on Thursday, March 02, 2006 - 09:08 pm:   

Explanation for the phenomena of cheese-shift:

"Aaron's proton mass times (deep dish) cheese pizza C-space, divided by Aaron's C, equals deep dish 4 cheese mass for a pizza, or cheese molecules."

Using this research I believe it is possible to construct a pizza in such a way as to completely eliminate occurences of cheese-slide, where the cheese and all toppings fall off the underlying crust.
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IVAN
Posted on Thursday, March 02, 2006 - 09:13 pm:   

PIONEER 10 & 11 ANOMALY, something else:

In their paper "Study of the anomalous acceleration of Pioneer 10 and 11" by Anderson et al (see PDF at http://arxiv.org/PS_cache/gr-qc/pdf/0104/0104064.pdf ), the authors mentioned on pg. 40 that (per Fig.17) there seems to be an apparent annual/diurnal periodicity in the signal received from Pioneers; this signal has a sinusoidal oscillation term of about 1.6E-8 cm/s^2 amplitude per year. The measurement batches illustrated seem fairly consistent from year to year, except some batches appear longer than others. What comes to mind is that Earth, as the preferred reference frame from which the signals are received, is affected locally by the main solar reference frame, so that gravitationally the Sun acts as a kind of gravitational amplifier, or lense, through which the Pioneer signal must pass when Earth is opposite the Sun. The signal received while Earth is on the far side of the Sun is 'lensed'. while on the near side it is not. The regularity would support this, though known math may not. Also, the irregularity of the annual batched data is puzzling, unless the plane of ephemeris is somehow responsible for how the signals are received. Puzzling...

Ivan
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Ivan
Posted on Friday, March 03, 2006 - 08:06 pm:   

Anon, is that new and improved 4D cheese pizza same as Shrodinger's pizza? Open the oven door, and there it is... or open the door and it's not there? :-)
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Ivan
Posted on Sunday, March 05, 2006 - 03:47 pm:   

Dark Energy and Dark Matter by Sol Aisenberg, Ph.D, show Big Bang may not be so.

Someone else who sees Newton's G as possibly variable over great cosmic distances. His academic credentials are much stronger than mine. :-)

Ivan

Here are some links to my math, BAUT forums, showing how variable mass works in a variable G universe: http://www.bautforum.com/showpost.php?p=450372&postcount=215
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Ed Chesky
Posted on Sunday, March 05, 2006 - 08:21 pm:   

In the 1990s, landmark research showed that quantum computers would be able to crack any code, except ones generated through quantum cryptography.

I would concur with that asessment, however, I suspect it would be possible to construct a program to run on a quantum computer that was capable of using the technique I have been exploring with regards to Pi, using primative tools, to abstract via a duplicatable algorythm data from an infinte data set. This premise is related to some concepts I have been exploring with regards to spooky action at a distance, multi-dimentional, multi-universal theory and time that could only be proven with the development of quantumn computers and related technology.

I note that I now use the irrationality of Pi and its representation in non-Euclidian space as it applies to the solution of the billiard problem, trisection of the angle and squaring of the circle as proof of concept for that premise.

I also note that C. A. Laisants work in this area, along with a host of others, mirrors my own and that this point of overlap likely indicates a next step along the path to understanding the field that makes up quantumn mechanics and its application to being able to build and control quantum processes necessary to develop the quantumn computer. Much like other geometry was used to develop the current generation of computer technology that we are using. It thought that by understanding this point of overlap along with Pi and the related genration of geometric shapes that I feel were we will begin to understand how to make use of quantum mechanical devices.

As best I can explain it, what I see is the visualization of a circle, that via an algorythym, is intersected at various points that have meaning in terms of solutions to complex mathmatical problems. With pi represented by the circle and its irrationality serving as a infinite data source.

These mathmatical expressions are viewed by me in terms of geometric figures that are generated by the interaction of curves and shapes with pi. This allows for the genration of solutions to geometric problems, as I discussed earlier. Hence my premise and belief that it is has application to quantumn mechanics and quantumn computing.

My Best

Ed Chesky
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Ed Chesky
Posted on Tuesday, March 07, 2006 - 06:31 am:   

Ivan,

over the last few days I have revisited my trisection problems and found that they inolve the use of conic sections and curves constructed with compass and ruler. On my webpage I have on problem illustrated with a hexegon depicted in yellow and a triangle depicted in blue.

If you add a couple of lines to the hexegon it turns into a cube. Hence the relationship I have been exploring with trisection and solid geometry.

http://pg.photos.yahoo.com/ph/edwardchesky/album?.dir=/66d7&.src=ph

Ed Chesky
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IVAN
Posted on Wednesday, March 08, 2006 - 11:51 pm:   

BLACK HOLES REVISITED

Ed, I came across this page on calculating black holes with the Schwarzschild radius equation: http://library.thinkquest.org/C007571/english/printcore.htm which is:

R_s = G 2 M/ c^2

This equation was easily derived from matching kinetic energy with gravity potential, viz. E_k = 1/2 mv^2 and U_g = GMm/R, which making v=c, you get the resulting:

1/2 mc^2 = G Mm/ R, which reduces to the above: R_s = 2GM/c^2, as derived by Schwarzschild.

Story has it that he penciled this quickly while in the trenches during WW I, and then sent it on to Einstein, who approved of it. Regrettably, Schwarzschild died in that war, so a great mind was lost due to humanity's incrediblde appetite for idiotic pursuits, like lobbing bombs at each other like a bunch of stupid school kids. (We used to play this game when children, throwing stones at each other's lines of led soldiers burried behind little soil barricades, until someone's stone threw high and hit one of the combatants in the head, then this escalated to throwing stones at each other rather than the led soldiers... plus ca change, plus c'est la meme chose.) Such is war.

Anyhow, I found it interesting that if we substitute M with solar mass, which is M=1.989E+30 kg, and use the usual values of G and c, the resulting black hole R radius for our Sun is something like R_s = 2.948 meters. Pretty darn small! But if so, that the Sun has a tiny black hole (as once proposed by Stephen Hawkins), then it doesn't take much to hold together such a large solar mass, does it?

Cool pictures in your 'trisection revisited' above. Thanks!

Take care, cheers, Ivan
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Ed Chesky
Posted on Thursday, March 09, 2006 - 10:28 pm:   

Thanks Ivan,

I found the link you posted very interesting and keeping with my thoughts on the subject.

I am still working on a number of ideas and concepts with regards to the geometry I have been exploring and its relationship to gravity and quantumn physics and predictive analysis and cryptology.

I hope to have more to post.

My Best

Ed Chesky
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Ed Chesky
Posted on Friday, March 10, 2006 - 08:48 am:   

The Ontology and Cosmology of Non-Euclidean Geometry

http://www.friesian.com/curved-1.htm

A very good article on the relationship of non-Euclidean geometry to the Theory of General Relativity.

For ages geometrists have been exploring the aspects of non-euclidean space and how that space looks and how forces would act in it from the perspective of geometry.

Those explorations have touched upon math, science, physics and religon because they deal with an attempt to visualize and illustrate principles and relationships that are central to what constitutes the nature of the universe and reality itself.

The website above raises and discusses certain issues related to this point.

Ed Chesky
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Ed Chesky
Posted on Friday, March 10, 2006 - 02:12 pm:   

One note on the solution to the trisection problem in the website above. It involves a unorthodox manipulation of the compass that I don't quite understand but suspect is related to the irrationality of Pi as used in the Quadrix of Hippias. It is different to my solution which inovles cubic geometry and the relationsip between planar geometry and the generation of a hypercube.

Interesting but exciting.

Ed Chesky
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Ed Chesky
Posted on Friday, March 10, 2006 - 03:42 pm:   

Once, many post ago, Ivan you considered the ramefications of a star drive and whether or not countries like North Korea or Iran should be allowed access to such technology.

Even Dr. Hawking feels we are close to understanding the principles behind quantumn gravity.

What we have done here is to focus our thoughts on the trisection of the angle, the aximatic equations, Newton, Einstien and all the rest and exlpore all the ramifications of such work and breakthroughs in geometry, math, physics and religion as they echoed down the ages.

For me that also included the teachings of Jesus Christ and the realization that we are close to a breakthrough in physics that follows where math and geometry lead us.

When or where that will occur I do not know. All I know is that I am certain is that breakthrough will be on the same plane in terms of impact on the human race as the development of the atomic bomb.

I still recall the the words of Oppenhiemer, when he looked upon the atomic mushroom cloud and said I have become Shiva destroyer of worlds.

Fundmental research can not be classified by the Government, however the application of such research can and is routniely classified.

We are exploring some of the fundmental principles of creation and the structure of the universe with the simplest and most complex of tools every created the Human mind and the compass and ruler. With these tools we have done much to force open a window that looks out on the tapestry of creation itself. A occurance that for better or worse I sure will be recorded in history some where.

Sometimes I have to go to Church to sit and think about the implications of what we are and have done.

With control of gravity comes the migration of the human race into the universe.

I have a feeling that history will look back on these days and say it was at this point that the begining of the migration of the human race to the stars began.

For me it has been a long journey back from a dark place close to the point of death where reality itself become questionable back into the light of sanity, reason, the world and life.

Along the way I have learned many things about limits, god and what we can, as imperfect being understand.

As i write this Dr. Hawking one of the greatest minds of our world lives close to death. He holds Newton's old chair. I suspect even he is puzzeled by the relationship in the geometry of the trisection of the angle and billiard problem and is frustrated because he is almost out of time.

Life is very short and even a 100 years is a small bit of time. In a movie I recall it was said the brighest candles burn the fastest. I am not fast and my journey will take me some time to complete, but even I can see that we are moving down the same path in terms of understanding as Dr. Hawking and that we owe a great dept to him and that when his light flickers out I will light a candle in rememberence of him, his life and his work.

Ed Chesky
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Ivan
Posted on Friday, March 10, 2006 - 06:27 pm:   

On Mintz, trisecting the triange.

Hi Ed, I haven't figured out how he did that, but probably some technique related to yours, I'd imagine. Also, when I looked at your illustrations, I did wonder how you picked the radius of the compass, though I could easily see how connecting the circle instersections yielded the desired results. Thanks for sharing it.

Ivan
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Ed Chesky
Posted on Saturday, March 11, 2006 - 07:25 am:   

Ivan

In doing some more research it can be shown that a plane passing through the midpoints of opposite edges (perpendicular to a axis) cuts a cube in a regular hexagonal cross section (Gardner 1960; Steinhaus 1999, p. 170; Kasahara 1988, p. 118; Cundy and Rollett 1989, p. 157; Holden 1991, pp. 22-23). Since there are four such axes, there are four possible hexagonal cross sections. A hexagon is also obtained when the cube is viewed from above a corner along the extension of a space diagonal (Steinhaus 1999, p. 170).

What I did was identify points from the interection of the circles where a hypercube is begining to be formed within the limits set by an angle. These points of interesection allow for the trisection of the angle that set the limits for the problem set.

It is related to the geometry of the hypercube which is an expression and graphical representation A non-euclidian object where it intersects our space. Which computer models have shown would be represented by a complex configurations of vertices and edges. What I belive I have shown is an aspect of the hypercube and way to use it to solve complex problems such as the trisection of the angle and billiard problem. hence my research into multidimentional space.

The following link discusses this very subject and from its discussion you begin to see the relationship bewteen my solution to the trisection of the angle, multidimentional theory and the geometry that Hawking and Einstien were pndering as it relates to general relativity.


http://members.fortunecity.com/templarser/mathex8.html

Ed Chesky
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IVAN
Posted on Saturday, March 11, 2006 - 11:21 am:   

TIME DILATION AND RELATIVITY

In J.P. Norris et al paper "Detection of Signature Consistent with Cosmological Time Dilation in Gamma-Ray Bursts", the authors make a case for why Time Dilation is the cause of stretched signal wavelengths observed from distant cosmic GRBs. However, the dimmer redshifts understood as a factor of stretched 'time' may be no more than time 'appearing' to slow for redshifted wavelengths. The observed 'stretch' ratio of ~2 in the spectrum wavelets does not prove Doppler recession, though it does show light redshifts. This non-relativistic way of seeing it means that yes, the wavelengths for dimmer redshifted signals are stretched, so each peak and trough of the wave is farther apart, but this may be a natural phenomenon of what happens when light is stretched over great cosmic distances only, and not a time variable. If deep space gravity, much greater than our known on Earth, is what causes redshift, and if it is not a Doppler effect due to imagined expanding universe, then it is completely natural that the waves would be stretched over cosmic distances. And if so, what we see here is not what took place there at the source. But it does not prove time dilated, merely that the waves were stretched. Observationally, yes, it would appear as if time dilated, but nothing like this happened in real terms, only observational terms. We see an illusion of time dilation only, if there is no Doppler like universal expansion.

Here is an example of how this works: http://www.cs.sbcc.cc.ca.us/~physics/flash/relativity/relatvisticclocks.html
You'll see that it takes a longer time for a 'tick' of a clock to catch the longer distance the light had to travel. However, this is contradictory to Einstein's second postulate, since now the light registered at the clock is less than c, relatively speaking, as per the third and fourth frame in the example.

This is one more Relativity conundrum, that either light is always a v=c, or for the observer in the case above (moving with clock), is it less than v=c, which violates the second postulate but 'proves' time dilation. They can't have it both ways. Once again, Relativity has a serious flaw in it, and the perceived 'time dilation' for GRBs is no more than an observational illusion due to the stretched wavelengths of distant cosmic signals reaching us. Neither Doppler space expansion, nor time dilation, are proved by Norris et al's paper.

Ivan
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IVAN
Posted on Saturday, March 11, 2006 - 11:59 am:   

DARK ENERGY CUM MASS?

In this NewScientist.com article Three cosmic enigmas, they claim dark energy and dark matter may be two sides of the same coin. Is this justifiable?

I think of dark matter as merely a function of gravity G, where it is orders of magnitude greater in deep cold intergalactic space than in the inner solar system. Out there, it is in the order of G=~3E-6 m^3 kg^-1 s^-2; that is its 'cut off' level, except for a black hole where G=c. For the hottest solar surface, G = ~4E-15, for E=c^3=10X+24 j; so that is the lowest level it can go before it fails to hold molecules together gravitationally, hence the solar wind. That lowest G can be seen as 'dark energy' of sorts; while higher deep space G can be seen as 'dark matter' causing flat rotational curves for galaxies. The article says:

quote:

"Dark energy stars and black holes would have identical external geometries, so it will be very difficult to tell them apart," Lobo says. "All observations used as evidence for black holes - their gravitational pull on objects and the formation of accretion discs of matter around them - could also work as evidence for dark energy stars."


Yes and no. Perhaps identical geometries, but for very different reasons. What we call 'neutron stars' may be no more than very high G stars only. By this reasoning, galactic black holes may be where all em lambda cancel, within the Schwarzschild radius, so maximum G results. I think a serious rethink needs to be called for here by our astronomical experts.

Ivan
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Ed Chesky
Posted on Saturday, March 11, 2006 - 05:17 pm:   

Here is a quote from the French mathematician C.-A. Laisant (1904): "I hope that, by the these few examples, I have succeeded in showing you that we can easily enlarge the field of investigations which the brain of a child is capable of pursuing much more than is generally imagined. To arrive at this result, a bit of material, which is very simple and infinitely variable, is nessary, as you have seen.

The very first element of this material is graph paper, a wonderful instrument which should be in the hands of anyone who does mathematics (whether in their living room, the common room of an asylum, or even all the way to the Ecole Polytechnique and beyond) and in general, anyone who does science. But above all, it is a wonderful instrument from a pedagical point of view, to give little children their first notions of form, size and position, without which this initiation is nothing but a sham."


Ed Chesky
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Ivan
Posted on Wednesday, March 15, 2006 - 06:29 pm:   

Cold stars and cold worlds:

I had earlier postulated, per the Axiomatic Equation, that gravity 'constant' G in the vicinity of cool stars would be greater than here as known for our inner solar system, on Earth where it is 1G at 1AU. Here is anecdotal evidence that this may be so: Icy Super-exsolar-planet. What this shows me, in theory, is that the small brown dwarf sun has a much higher G in its system, so that any planets there should exhibit characteristics of higher G. If substantially higher than here, then even planets that would have been gas giants in our solar system may become solid hard worlds, as all the gas collapses to the surface. This is merely hypothesis, but it may be so, for cold stars, per the Axiomatic. If true, then such cold planets should also exhibit greater spin.

Ivan
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Ivan
Posted on Saturday, March 18, 2006 - 11:37 am:   

BBC's Ice Layers record comet creation

quote:

"The normal outgassing of the comet has been modelled by different people as coming from bare ice on the surface to subsurface ice that migrates through pores to escape, or from 40-50m below the surface," Deep Impact's chief scientist Mike A'Hearn told the BBC News website.
"I think it is clear from what we have here that the ice that is subliming is within the upper metre. Whether it's 5cm or 20cm below, I wouldn't want to say; but it's not below the top metre. That rules out a lot of the models."


I would tend to agree, that 'outgassing' is from subsurface ice migating to the surface, rather than from top centimeters, though new thinking seems to support the latter.

My view is that cold space, such as out beyond the gas giants, is more gravity dense than for inner solar system, so comets out there pick up stuff and become more (gravitationally) compacted. When they fall back into the warmer regions closer to Earth, this compacted stuff becomes 'decompacted' and released as fine grains, the cometary tail. Its composition, if so, must be of all materials it accumulated over the eons, going back and forth from a cold region to warm in its highly elliptical orbits. Some comets go much further out there, stay there longer, so may have more spectacular tails when they come towards the Sun,

Ivan
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IVAN
Posted on Wednesday, March 22, 2006 - 07:32 pm:   

BIG BANG 'INFINITY' IN ALMOST NO TIME!

The big bang's 'smoking gun'

I don't know what they're smoking there, but this article was not written to amuse little children, but is actually believed by grown scientists, many of whom have Ph.Ds. Go figure, 'inflation' from a small marble sized ball (of infinite density?) to the present visible universe! Poof! In a trillionth of a second!

How deep can ignorance get before they realize that cosmic light redshift has nothing to do with space expansion? There was no Big Bang, or anything remotely like it. Massive G in intergalactic space slows light into redshift. By the time it is redshifted down to the CMB, it's virtually worthless for observational purposes, too diffused. But they'll be silly all their lives, no use arguing with fairytales.
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Ivan
Posted on Thursday, March 23, 2006 - 08:46 pm:   

These were my last posts on BAUT forums. If their ears are closed, like this thread, then there is nothing I can say. Until there is empirical data of a variable G, then truly there is nothing I can say.

Ivan/NG 71
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Ed Chesky
Posted on Thursday, March 23, 2006 - 10:00 pm:   

Ivan,

Your postings and the responses to them is why I stick to geometry. Its hard for someone to deny you did something when its depicted in black and white on a piece of paper.

The argument over variable G will go on for a long time to come.

What I saw in completing my geometric work was, as I have said previously, the interaction of a multi-dimentional construct with our reality.

The hyper cube and the geometry I did are all related to this. The geometry is but a poor depiction this aspect of reality in terms that our limited minds can grasp.

In my mind its as if I caught a glimpse of all of creation with all the aspects of the hypercube representing the Core of the Universe, God in other words. Perfect in design extending in multi-dimentional space and interacting with our reality in ways we are only begining to understand.

I have pushed geometry as far as I am able to and now its up to the next generation to build upon this work. Its part of the body of knowledge and part of the discovery process.

Your work, my work and the work of countless others will one day release mankind from this solar system and unlease it upon the universe.

How and when that will happen I do not know.

But when it does people with study the history of it and look back on these days and wonder where the inspiration came from that free'd us from this rock.

My Best Ed Chesky

http://www.thenewbiblecode.co.uk/thekey.html

PS the above is a link about a new bible code that involves geometry. Whether or not you believe in this stuff it is an interesting read, from a geometric perspective. :-)
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Ed Chesky
Posted on Friday, March 24, 2006 - 07:43 am:   

An interesting website that finds that in working with a Hypercube that one of its multidimentional aspects is linked to the modius strip.

http://www.maa.org/editorial/knot/tesseract.html


I note that C. A. Laisants work in the late 1800's in his trisection problem was built upon work that came from Mobius.

http://www.physlink.com/Education/AskExperts/ae401.cfm

I have included a link that talks about the mobius strip.

At this stage we are just beginning to explore aspects of multidimentional space.

These concepts can be traced in geometry back 3000 years each building upon the other adding to the body of knowledge

My Best Ed Chesky
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IVAN
Posted on Saturday, March 25, 2006 - 10:42 am:   

GRAVITOMAGNETIC TEST

Towards a new test of general relativity

Dr. Martin Tajmarr of Austria, and Dr. Clovis de Matos of Netherelands, built an experiment to test the magnet Barnett effect, a variance of a Faraday's 1861 test for electromagnetism, here done with superconducting spinning plates, to test for a gravity equivalent. This is constructed as an another test for Einstein General Relativity, though the results seem to invalidate it somewhat. It says:

quote:

Although just 100 millionths of the acceleration due to the Earth’s gravitational field, the measured field is a surprising one hundred million trillion times larger than Einstein’s General Relativity predicts. Initially, the researchers were reluctant to believe their own results.


After long study and much debate, they decided to go public with their find.

If you look at their original paper "Gravitromagnetic Barnett Effect": http://xxx.lanl.gov/abs/gr-qc/0012091 you'll notice that in their original experiment design the rotating mass was cylindrical, whereas in the article it is a rotating superconducting ring. This is significant, because per the Axiomatic Equation, when all lambda of electromagnetic energy cancel on a point, it cancels leaving only gravity. This is achieved in a quasi-cylindrical or spherical rotating energized mass, so all ambient energy focusses on a center where the lambda cancel (as happens at the center of spiral galaxies), and there gravity is no longer modified by e.m. energy, so it reasserts itself at its highest order. The ring construction means the energy is not diffused by its physical mass molecules, so it shows up in the hollow center. In galactic centers this appears as a so-called black hole. What would make this experiment more interesting, in my mind, is if it is performed in a vacuum so that air molecules do not diffuse this effect, and the result should be intensified. However, neither the article nor the paper referenced make it clear they did this. But if it were proven true, then it would be one more evidence favoring the Axiomatic Equation. And if that is so, we're on our way to modifying gravity and using it as a constant accelerating force for future propulsion systems. (Thank you Mr. 'Moto!)

Does Ajma-Matos experiment disprove Einstein's GR? I think the question is irrelevant, since many real observations such as cosmic light redshift (non Doppler effect, no space expansion, but very high intergalactic-space-gravity redshift), Pioneer Anomaly, galaxy flat rotation curves, etc., already disprove it.

Ivan
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Ivan
Posted on Saturday, March 25, 2006 - 10:44 am:   

Ed, thanks for the great 4 dimensional cube references. It is a real mind bender, I love it!

Imagine that we can actually image geometrically what is inherently a mathematic interrelationship in 4 dimensiions. Cool indeed.

Ivan
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Ivan
Posted on Saturday, March 25, 2006 - 12:29 pm:   

Newton's Gravitational Equations derived from Kepler's?

In his delightful easy read book, "Five Equations that Changed the World", Michael Guillen, Ph.D., shows how Newton used Kepler's simple orbital equation T^2 = constant x d^3 to derive equality between Moon's orbital centrifugal force and gravitational attraction, by substituting T^2 in the equation for Centrifugal Force = (constant x m x d)/ T^2. This turns into:

Moon's Centrifugal Force = (constant x m x d)/ (constant x d^3), where T^2 in centrifugal equation was replaced with (constant x d^3), so you are left with the centrifugal-gravitational equivalence of F = new constant x m / d^2.

Of course, the "new constant" was Newton's G, which is 6.67E-11 m^3 kg^-1 s^-2, and the final result is F = GMm/d^2, where G is Newton's gravitational constant, M major mass, m is minor mass, and d is distance. Of course, everybody knows this, but it was nice to see it derived thus from Kepler's orbital equation. :-)

I think what intrigues me about this is how a purely geometrical relationship, as discovered by Kepler, can turn into a usable equation for gravity, the equation that gets our space probes out into space. But for now, until we better understand G, it still remains a purely mathematical expression.

Ivan
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Ed Chesky
Posted on Saturday, March 25, 2006 - 12:53 pm:   

Thanks Ivan

I have included a couple of links to websites that talk about mobius resistors.

The operation of the mobius resistor could be the first step to making use of a multi-dimentional effect.

As I have tried to illustrate with geometry the mobius strip is related to a complex expression of pi, which in turn is related to an aspect of the hypercube.

All I have done is add one more piece to the understanding of the gemontry of multi-dimentional space. Like Dr. nash it will take others to build upon this to come up with a better understanding of the nature of space time and gravity.

My best

Ed Chesky

http://mathworld.wolfram.com/MoebiusStrip.html

http://www.explorepub.com/articles/summaries/12_6_harezi.html

http://www.rexresearch.com/davis/davis.htm
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Ivan
Posted on Tuesday, March 28, 2006 - 09:53 pm:   

Hi Ed, thanks for your references to Mobius Strips above, especially the R.L. Davis: Noninductive Resistor, which will be useful in future 'gravitomagnetic' air and space ships. These early ships will be powerded by sequenced, on a platform, vacuum spheres of spinning rings generating gravity and axial electric fields against which pilot and passengers will need to be shielded. The 'noninductive resistor' using the Mobius Strip principle is one way to cancel out this electric effect, so only gravity effect will experienced by those riding the ships. Otherwise, they occupants would be fried, a bad thing. Later they'll perfect the system so shielding will be deflected to the hull, but initially we won't know how to do that. Baby steps, but eventually the stars! :-)

Cheers, Ivan
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IVAN
Posted on Tuesday, March 28, 2006 - 10:56 pm:   

A FUNNY THING HAPPENED ON THE WAY TO MASS.

When I first formulated the Axiomatic Equation, where I converted solar energy and planetary kinetic energy into proton mass, using the hybrid Quantum equation: E = hc/ (lambda*proton mass) = f(1-g)c^2, which worked out in Watts (rather than customary Joules), the units of small g, which is the proton gravitational constant 'g', the result worked out as "kg s^-1", which I thought odd, but left it alone. Later, when I found a way to convert this g to Newton's G for gravity, the equation used, G^2=g(c^2)(pi^2), had the same g in Volts, viz., "V m^2 s^-1". This led to a conundrum, so I left it in the paper on the Pioneer Anomaly as units "unresolved", and left it at that. I didn't give it much thought, until one day recently I thought there was an odd relationship to which I had been earlier blind. It seems that perhaps this is a way to convert kilogram mass into length and time. Both are "mass", but where one is in Volts, the other is in kilograms. In fact, they are both in units of length, or more specifically volume m^3, and velocity, m s^-1. Here how I think it really looks.

In terms of universal SI units which are length, mass, and time, Volts are expressed as V = W/A, or Watts over Amperes, where A = N/m, or Newton's per meter. This means that Volts are therefore the same as V = W/N/m.

Taking these values at their universal length, mass, and time, they work out as follows:
W = m^2 kg s^-3, N = m kg s^-2, and A = m kg s^-2 /m = kg s^-2.
So taking V = W/A, we get V = m^2 kg s^-3/ kg s^-2, which reduces to: V = m^2 s^-1.
Now, (in my above for g) V m^2 s^-1, (because V = m^2 s^-1) the g from the gravitational Newton's G conversion equation, is really V^2 (Volts squared), which is also "m^4 s^-2". But the Axiomatic Equation's g (in the f(1-g)c^2 right side of the equation) came out as kg s^-1. This is the "unresolved" part. Where can this go?

If we equate the two, here is what we get: m^4 s^-2 = kg s^-1

And if this is worked out for kg, we get: m^4 s^-1 = kg

But this is a 'hidden' value for perhaps volume and velocity, such as: m^3 (m s^-1) = kg.

The m^3 is volme of mass, and m s^-1 is its velocity. That's more strange than the "unresolved"!

If we keep in mind that the Axiomatic Equation was first worked out in Watts, or J/s as power from the Sun, then the kg s^-1 made sense, but later I revised it to Joules, so the resulting g was now in kg. (I suspect either way works, since mass is treated as m=1, as kg/kg, or dimensionless.) If so, then the above in Joules makes (more) sense, since it reduces to kg = m^3 m/s^2, which means "volume times acceleration". I suppose this is truer to what kg represents (as a gravitationally derived value for mass), but the prior, in Watts, where "volume times velocity" worked, that seems to be closer to some alternate description of mass in kg. I have always entertained a 'pet' theory that all mass at 'rest' is actually traveling at lightspeed c, from some perspective of the universe, but since we're all at c here already, it looks like it's at rest. Strange idea, but it would seem to fit into an idea of volume times velocity, where what we think of as mass here is really no more than volume at c. Think of it as a strange kind of Machian concept, where the rest of the universe is modifying us here. Is this crazy? It in truth leaves me in stiches!

Therefore, I must leave it once again as "unresolved", but thought it funny enough to show it here. Stay tuned... until my next "brain bubble" does something with this again. :-)

Ivan

[edidted 3/29/06, to correct typo on "volume time" velocity or acceleration (not length) in original]]
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Ivan
Posted on Saturday, April 01, 2006 - 04:19 pm:   

In part answer to Le Chef in his Pizza-Spaghetti (in 'miscellaneous' thread, March 30, 2006, post). In his paper "What the Global Positioning System tells us about Relativity", Tom Van Flandern addresses the issue of GPS verifying Relativity. As to whether it is LR, SR, GR, that best answers to the 'time dilation' adjustments necessary for synchronizing time on the GPS, it seems all three are involved nearly equally. The distinction may be perhaps better defined, however, in this quote from his:

quote:

Richard Keating was surprised in 1972 that two atomic clocks traveling in opposite directions around the world, when compared with a third that stayed at home, showed slowing that depended on their absolute speed through space -- the vector sum of the Earth's rotation and airplane speeds -- rather on the relative velocities of the clocks. (italics mine)


This is the defining moment, that perhaps it is not 'time' that is being dilated here, but rather that all atomic oscillations, and photon wavelengths, are naturally dilated while traveling through a gravitational field; in effect, the de Broglie wavelengths are 'dilated', not time itself, and the preferred relativistic reference frame is thus a gravitational field. This is proved by the fact that Earth's spin becomes the preferred reference frame in Keating's traveling atomic clocks, as GPS illustrates through necessary time adjustments. So whether it is LR/SR/GR may be moot if in fact it is AR, or 'actual relativity', of moving bodies within a gravitational field, so that both light and atomic oscillations slow. Time had nothing to do with it, same time, but oscillations and wavelength did.

What does that do to the theorized aging of the Twins, in their famous paradox? In fact, one would have to assume that genetic DNA replicant chromosomes age at the same rate of dilated atomic oscillations, which may or may not be a justifiable assumption. Rather difficult to falsify, but that is the only way to prove that this aging as theorized actually happens. Actual Relativity may not work as simply as that. In fact, it may work in reverse, where the dilated oscillations break down chromosomes faster, so instead of aging less, the traveling twin goes into the twighlight zone, and ages like in Shelley's mirror, faster.

BTW, regarding universal balance, the Standard Model is largely polulated by subspecies, including nutrinos, which emanate during beta decay. Only the proton, electron, and isotopically the neutron (subject to beta decay releasing electron and anti-nutrino), are the building blocks of atoms. The rest is detritus of smashed atoms, important, but not the building blocks of matter.

Ivan
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IVAN
Posted on Saturday, April 08, 2006 - 11:02 am:   

ANOTHER FUNNY THING ON THE WAY TO MASS - II

Let us postulate the following, both known and unknown. If we take (the above) in Volts to kilograms, we had shown: V m^2/s = kg, where Volts were in m^2 per second, then we can derive the following:

Let assume (per Axiomatic) that mass kg = V m^2/s = m^4/s^2 so that kg is also:

m^2/s*m^2/s = kg m^3*m/s^2 = kg m^3*a = kg

Now, let's move this kg at velocity v:

m^3*m/s^2*m/s = kg*v m^3*m^2/s^2 = kg*v*s m^3*v^2 = kg*v*s

Then separate out the v^2, which is what we want:

v^2 = kg*v*s/ m^3 v^2 = kg*m/s*s/ m^3 v^2 = kg/m^2


Then we can say by making v^2 = c^2 = kg/m^2 (for when mass kg is moving at v) and substituting mass m^3*m/s^2 = kg, we get:

E = mc^2 v^2 = c^2 = (m^3*m/s^2)/ m^2 E = m^2/s^2

which is c^2, times mass, as an expression of Energy (for moving kg*v), which is also, if a leap of logic, in principle same as m^3*a = kg, or "volume times acceleration is mass", we can by extension say "mass times acceleration is force", as in Newton's F = ma, so that kg*a times velocity becomes:

E = kg*m/s^2*v or E = kg*a*m/s E*s = kg*a*m

which becomes another expression of Energy:

F*v = kg*a*v= E in Watts? or in Joules?

Still "unresolved", but interesting., e.g.:

F*v = kg*a*v =E m*kg/s^2*m/s = kg*m/s^2*m/s E = m^2*kg/ s^3

It looks like Watts takes it, for now... But if taken, as per above, where E*s = kg*a*m, then we're back to Joules again... Puzzling.

Energy is "force times velocity", or "accelerated mass at velocity", both the same!

Can this have implications for why v^2 in KE = 1/2 mv^2 leads to (work) energy? But is this work in Joules or Watts? It could be either way, depending upon how it is measured.

It may also show why F = ma as an accelerative force, and why kilogram inertial mass is always equivalent to its gravitational mass acceleration. Something to consider. Could it also be the link between gravitational acceleration and Energy, or why energy modifies G? If they are interactive in how E = kg*a*v, then it may be possible, for conservation of energy is not violated if gravitational energy and eletromagneticf energy are taken as a whole product, though inversely proportional as per the Axiomatic Equation. Of course, this is all predicated on the conversion equation from proton mass gravitational 'constant' to Newton's G gravitational 'constant', as per equation: G^2 = g(1)c^2 pi^2, where Volts squared equals kilograms, and mass = 1.

More to ponder, more questions than answers at this point. But whether work or gravity or electromagnetic energy, it is all Energy! Does this validate V^2 = kg?

Ivan
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IVAN
Posted on Sunday, April 09, 2006 - 11:50 am:   

FUNNY THINGS ABOUT MASS - III

Energy is always energy, but mass is different, in principle:

m^3*a = kg is gravitational mass

V m^2/s = V^2 = kg is electromagnetic mass

kg = kg is universal energy mass

kg/kg = 1 is universal mass (m = 1)

Whether or not these musings have merit, I do not know, but their interrelationship as shown in the equations above is interesting enough to give further thought. Perhaps we never thought of it this way before, that there are different kinds of mass, such as shown by the Axiomatic Equation. It will need to be tested and verified, of course. But if it should prove that gravity G is variable and inversely proportional to electromagnetic radiant energy, then we would need to rethink the physics of our universe, from cosmology to the quantum level. Cosmic light redshift then becomes a natural non-Doppler gravitational effect, where deep space high gravity has a refraction effect affecting both light redshift and gravitational lensing; and energy conservation at the quantum level has a new twist, if gravitational mass is different from electromagnetic mass, because the proton-neutron strong force is an extreme gravity effect, while charge duality is an electromagnetic effect. These two are interactive, combined in the atom. If it proves so, then our knowledge of the universe will prove infinitely greater than we understand today, with a new energy dividend that will propel future gravity assist engines at immense accelerative velocities unimagined now, if mass is different.

Ivan
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Ivan
Posted on Friday, April 14, 2006 - 09:15 pm:   

A Funny Thing about 'Infinite' Mass - IV


quote:

F*v = kg*a*v= E



It occurred to me while looking at this equation for Energy that there may be something hidden here that addresses Einstein's accelerated mass a v->c, where as mass velocity approaches the speed of light it grows in mass, until at v=c it is infinite. But is it?

This has been tested in cyclotrons where an electron or proton accelerated to near light speed does indeed 'appear' to have gained mass, since it takes progressively larger doses of energy to keep accelerating it. However, this is done with stationary magnets accelerating the particles. But what if the magnets were themselves moving with the particles, so that the magnetic accelerative force is not F but F*v instead? This may be difficult, if not impossible, to do in real life, but it would appear that if this F*v = mass*a*v, then E remains the same, and mass kg is not growing as now believed. This would mean that, in theory, as the particle accelerates and the force pushing it is keeping up with it, F*v, then it will take less energy to keep accelerating it than when the F was stationary. Though F*v may be testable and falsifiable only at very low velocity, for example, it should yield enough result to show that the particle's mass is not growing as expected. Rather, it is the force needed to propel it at higher velocities that is growing. And this is a fundamental difference from what Einstein's equations predict. Furthermore, it also means that, in theory, the lightspeed limit velocity c can be violated, if F*v itself is continuously accelerated to v=c (though we have no way of doing this today), where the particle's velocity would be accelerated beyond v=c.

None of this is doable yet, but even at low velocity F*v moving magnets pushing particles in a cyclotron, we should see the result as stated, that it takes less force to accelerate a particle already in motion than predicted by Einstein. The end result would be a falsification of the idea that the accelerated particle is gaining mass. In fact, its mass remains unchanged.

Has anyone done this in any cyclotron. I wonder?

Ivan
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IVAN
Posted on Saturday, April 15, 2006 - 06:58 pm:   

ON A SIMPLE UNIVERSE

I had gotten myself in hot water on another forum, trying to show how perhaps the current theories of the universe are more simple than we had made them, arguing that the Relativistic interpretations are unnecessarily complicated. It may have been no more than a tempest in a teapot, but I had to back paddle pretty quick with a lesson in humility. Of course, they were right and I was wrong, in my ranting polemics, and my non de guerre "nutant gene 71" got properly trounced.

In fact this is turning out to be a highly interesting discussion worth looking at, despite my off topic remarks, for which I am humbled. This thread on the BAUT forums can be found at: Theoretical Physics Reviewed, a discussion on the works of Carel van der Togt, of the Netherlands.

Privately, I still think the universe is a simple place, though I am in no way qualified to prove this. I think that there are easier explanations for certain phenomena than the relativistic ones, though the currently held theories too offer a good explanation. But to me they are overly complex mathematically. I would simplify it as such, without having any proof this is so:

1. Dark matter is no more than higher G gravity in intergalactic space, why it cannot be found.

2. Higher G in intergalactic space naturally shifts distant cosmic light to the red, a (dark matter) gravitational redshift.

3. Atomic clocks will slow while traveling in any gravitational field, a natural phenomenon unrelated to slowing 'time'.

4. Aether drift, along with Mercury's (low G mass) precession, are merely momentum transfer phenomena.

5. Gravity G is very low near hot stars and progressively higher far from them.

I can't prove any of this, but intuitively this appears right. For me to argue this, I will be shown a fool, so cannot do so, not without years of scientific training. But this is how I see the universe, as a rather simple place, for the record, how I see it in my mind's eye. Of course, I could be totally wrong.

Ivan
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Anonymous
Posted on Sunday, April 16, 2006 - 10:17 am:   

Archive Freedom, read this:

The history of science teaches that the greatest advances in the scientific domain have been achieved by bold thinkers who perceived new and fruitful approaches that others failed to notice.  If one had taken the ideas of these scientific geniuses who have been the promoters of modern science and submitted them to committees of specialists, there is no doubt that the latter would have viewed them as extravagant and would have discarded them for the very reason of their originality and profundity.  As a matter of fact, the battles waged, for example by Fresnel and by Pasteur suffice to prove that some of these pioneers ran into a lack of understanding from the side of eminent scholars which they had to fight with vigor before emerging as the winners.  More recently, in the domain of theoretical physics, of which I can speak with knowledge, the magnificent novel conceptions of Lorentz and Planck, and particularly Einstein also clashed with the incomprehension of eminent scientists.  The new ideas here triumphed; but, in proportion as the organization of research becomes more rigid, the danger increases that new and fruitful ideas will be unable to develop freely.
 Let us state in a few words the conclusion to be drawn from the foregoing. While, by the very force of circumstances, research and teaching are weighted down by administrative structures and financial concerns and by the heavy armature of strict regulations and planning, it becomes more indispensable than ever to preserve the freedom of scientific research and the freedom of initiative for the original investigators, because these freedoms have always been and will always remain the most fertile sources for the grand progress of science.

Nobel Laureate Louis de Broglie,  April 25, 1978

SEMINAL ideas will take much hard work and persistent fight with vigor to change any errors in science.
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ad gnostic
Posted on Thursday, April 20, 2006 - 06:55 pm:   

E= mc2 -- not so Atomic Energy, big boy.

For all you Einstein lovers, no whining. The rest of you, weep on what you read, loud sobbing allowed.

Dissident View of Relativity Theory
You been had! :-)

yours, ad gnostic
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Ivan
Posted on Friday, April 21, 2006 - 10:35 am:   

Dissent on Dissent?

Thanks ad gnostic for posting. I had seen this report before, and don't know if I agree with it entirely. It seems the author, though a PhD (in physics?), bases his dissent on a violation of Einstein's second postulate, that light is a constant velocity in a vacuum at c, but per his it is somehow variable. This leads to the conclusion that Pioneer Anomaly is due to this variable c, where the em signal is affected on its return trip from the probes. However, he gives no further detail on this. I think that c is not of consequence here, but that gravity is, a variable Newton's G. Of course, until we can measure such in the outer solar system, we don't know, and the jury on Einstein's is still out.

Cheers, Ivan
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Anonymous
Posted on Friday, April 21, 2006 - 09:47 pm:   

I have looked at the postings on this site and while I am not qualified to judge them from a physics perspective, its clear the one of the posters, Ed Chesky, while recovering from something, demonstrated a degree of brilliance in the area of predictive analysis and geometry that is clearly remarkable to say the least and is on par with that of the most advanced predictive models run on super-computers.

That madness and great genius is related is a fact, but couple that to brain damage and exposure to a toxin of some sort and we have something that pushes the edge of human understanding of what a human being is capable of doing.

I have looked at Ed's geometry and like he said its hard to argue with. His solution to Al Hazen's Billiard Problem is astounding in it simplicity. With a few twists of a compass and lines drawn from a straight edge he has surpassed the work of an Oxford Don.

Why he is not held up by the media, academia and the rest for public recognition and reward is beyond me and begs the question of the existence of a conspiracy on the part of someone or someone’s. This is something I don’t believe in personally but many others do.

I note, however, that an autistic boy is given official recognition and flown down to NASA to demonstrate his skill and ability to perform phenomenal mathematical functions. In technical terms he is known as and idiot savant.

Why Ed languishes outside state, federal or academic service is beyond me, but rather raises the question if the Bush administration is truly suppressing the truth and punishing its opponents using the tools of economic power as many have said.

A retired psychologist.
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IVAN
Posted on Saturday, April 22, 2006 - 12:21 pm:   

RE Kinetic Energy:

In mine above (Apr. 14, 2006) I said, regarding accelerating mass:

quote:

This has been tested in cyclotrons where an electron or proton accelerated to near light speed does indeed 'appear' to have gained mass, since it takes progressively larger doses of energy to keep accelerating it. However, this is done with stationary magnets accelerating the particles. But what if the magnets were themselves moving with the particles, so that the magnetic accelerative force is not F but F*v instead? This may be difficult, if not impossible, to do in real life, but it would appear that if this F*v = mass*a*v, then E remains the same, and mass kg is not growing as now believed. This would mean that, in theory, as the particle accelerates and the force pushing it is keeping up with it, F*v, then it will take less energy to keep accelerating it than when the F was stationary. Though F*v may be testable and falsifiable only at very low velocity, for example, it should yield enough result to show that the particle's mass is not growing as expected. Rather, it is the force needed to propel it at higher velocities that is growing. And this is a fundamental difference from what Einstein's equations predict. Furthermore, it also means that, in theory, the lightspeed limit velocity c can be violated, if F*v itself is continuously accelerated to v=c (though we have no way of doing this today), where the particle's velocity would be accelerated beyond v=c.


I think this is testable, where the cyclotron accelerator magnets are rotated in the direction of the accelerating particle. This would test for the relativisitc mechanics based on kinetic energy: Ek = mc2(y-1), where y=1/(1-v2/c2)1/2. If the co-rotating magnetic accelerator idea is right, we should find that the real mass of the particle is not changing, only the force needed to accelerated it is changing relative to the stationary magnet accelerator, and that the velocity of the particle is commensurate; which means the particle's velocity, not affected by any increase in mass, can theoretically exceed Einstein's limit of v=c.

Ivan
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Ivan
Posted on Sunday, April 23, 2006 - 01:17 pm:   

NO MASS, LENGTH, NOR TIME TRANSFORMATION IN THE REAL WORLD?


quote:

In another profound assertion, which goes directly to the heart of unraveling the mystery of E=mc2, they state: "We have proposed our own aetherometric analysis of these type of experiments, where it it shown that the experimental velocities of massbound charges are predicted by a theoretical model that does not take recourse to any of the Lorentz transformations. That means— no time dilation and no relativistic mass increase with acceleration of inertial mass. The inertial mass of a system is only a measure of its rest energy, unlike what SR proposes it is."


This is from: Breaking Through Editorial: The Einstein Myths— Of Space, Time, and Aether
(Originally Published July-August, 2001 In Infinite Energy Magazine, Issue #38) by Eugene F. Mallove, Sc.D.

Also see: http://www.aetherometry.com/
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Le Chef
Posted on Tuesday, April 25, 2006 - 06:37 pm:   

Pisa cake, easy as pi, no cheese :-)

nz302.jpg
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Ivan
Posted on Wednesday, April 26, 2006 - 12:30 am:   

Cassini-Huygens (2005)
Cassini's Sixth Flyby of Titan: Tweaking the Tour, by Emily Lakdawalla, April 15, 2005

This news is a year old, and perhaps entirely anecdotal, but Titan's Cassini-Huygens mission may be yielding some information on the gravity-inertia problem for the outer solar system, at about 9.5 AU from the Sun. There seems to be an anomalous relationship between atmospheric density and thruster behavior, in that the thruster had to "fight harder" when encountering Titan's atmosphere.

It says:

quote:

"The Titan-A flyby in October of last year was our very first opportunity to swoop down and sniff the atmosphere. We did it on purpose, going down to about 1,200 kilometers [750 miles]. We turned the Ion Neutral Mass Spectrometer [INMS] in the direction of the spacecraft motion and literally sucked particles into a mass spectrometer, analyzing what the upper atmosphere of Titan was like. At the same time, we also took the information from the thrusters about how hard the spacecraft had to work fight the atmosphere. The answer was, ‘harder than we thought.’ At 1,200 kilometers they were fighting at 6% capacity."

Six percent may not sound like much, but when that number was extrapolated to a lower altitude, the navigators found a problem. "At 950 kilometers they’d be fighting at over 106% capacity. If you’re over 100%, you’ll tumble the spacecraft," Ray said.


At first read this seems innocuous enough, but upon deeper reflection, we may be witnessing something that would happen if the inertia-gravity relationship was different there, where G is nearly 10 times (per Axiomatic) that of what we know on Earth. This would translate, hypothetically, into molecules of atmosphere numbered as expected, and as measured, but that the density of these molecules is greater than expected, causing the thrusters to work harder. This could be indicative of a greater G cum inertial mass in Titan's 9.5 AU distance from the Sun. But is G 9.5 times that of Earth's? Still unknown. The article further says:

quote:

"In the end, we flew by at 1,200 kilometers and we were using 6% of the thrusters. If it scales exactly the way we think it should scale, no matter who says what about density, then we wouldn’t be able to fly by at 950 kilometers. Of course, there’s several questions. Did the thrusters actually see a higher density, and the instruments are giving a lower density? Or are the thrusters seeing something and interpreting it incorrectly and taking action that they don’t need to take? Maybe it’s just a flight software problem. It could be any number of things.


So they look for alternative explanations, software or something else, but the answer may be as plain as the thrusters readings give, that density there is greater than an equivalent atmosphere at a lower G. Anecdotal for now, but interesting, and puzzling. But if so, is it only 2 or 3 times greater, as the article thinks, or a great deal more?

Ivan
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Ivan
Posted on Saturday, April 29, 2006 - 04:20 pm:   

MORE ON FUNNY MASS - V

I write in my above (April 9, 2006):

quote:

Energy is always energy, but mass is different, in principle:

m^3*a = kg is gravitational mass

V m^2/s = V^2 = kg is electromagnetic mass

kg = kg is universal energy mass

kg/kg = 1 is universal mass (m = 1)



Taking that "a" in acceleration as "gravitational mass" we mean that G is involved. So let's explore that:

m^3 (Gm/r) = kg, where F = G(m1/r)(m2/r) = Gm1m2/r^2

Now, let's consider (per Axiomatic) that G is variable at 1G per 1AU, so that for any distance from the Sun, G'/G is the ratio encountered in AU'/AU. If so, per equivalence of gravitational and inertial mass, as G'/G grows, so does m'/m grow in units of kilograms, kg. So think about: if inertial mass has equivalence to gravitational mass, then any change in G becomes amplified by this equivalence; my take on it is that G'/G becomes f(m^2), per this relationship, as the two factors of inertial mass and gravitational mass play on each other per some function. The function for local mass then becomes m = (m'/m)^2*m. This is not to say that local kg for local G' is this, since it is only increased by the amount of change in G', but that in terms of "our" kilograms, because of the double effect of equivalence, they are compounded at the rate of squared.

Conversely, in terms of local kg, when m^2 is considered, the gravitational G is likewise affected, where it is the converse of squared, so it becomes its "square root". This translates into the funny mass equation, whereby m^3*a = kg becomes "volume times acceleration" (or gravitational potential Gm/r=a, for each m1 and m2) so that it should read as: m^3*(G'/G)^1/2*(Gm/r) = kg*, which now reflects the equivalence adjustment for gravitational mass cum inertial mass.

The question that remains is: is this new kg in Earth kilograms, or in local kilograms? I think it is Earth kilograms, as this adjustement to mass is not kg' in local terms, but our Earth kg for local mass m'. If this is true, then variable G is a very strange and funny thing to recon with.

Ivan

Ps: Is it not strange that below <1, the 'squared effect' is in taking the square root, while above >1 it is in making it squared? Somehow, it harks back to the original idea behind the Axiomatic, that zero*infinity=1.

*(edited to fix error, and add Ps. IA)
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Anonymous
Posted on Monday, May 01, 2006 - 01:07 am:   

What are you people on this thread smoking??!

Among all the nuts this Ed guy takes the cake. All he posts are complete nonsense.Any math graduate from a reputable university knows that.

And he cracks Al-Queda's codes and predicts earth quakes. Does he wear a cape and sleep upside down in a bat cave under Gotham city too? Yeh, right. Only one thing the dude says is credible: he suffers brain damage.
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Anonymous
Posted on Monday, May 01, 2006 - 08:09 am:   

Well you know,

It hard to argue with the fact that he despite brain damage Ed makes deans list, has presidential citations for breaking codes, completely documented in black and white, and did break Al Qaeda's command code.

Under the freedom of information act a copy of his statement to DSS a investigator about about a network in the Ryadh compound is available.

Sometimes, the truth hurts both sides.

Autistic men can perform analytic feats beyound that of computers that is a fact.

One autistic man is brought down to NASA to lecture and perform mathmatical functions. He out performs all computers.

Having worked with Ed I have seen his abilites at predictive analysis that go off the chart, its similiar to the same thing that an autistic individual can do.

The problem is Ed was also trained by DOD, which we all think was a grave mistake, in terrorism, religion and weapons of mass destruction and studied the network of Osama. He is verified expert in small arms, explosives and qualified sniper. DOD used his talents at predictive analysis for a long time like NASA uses the autistic man.

When he got laid off we, and I mentor Ed from time to time and calm him done when he gets irritated, have verified the fact that he has built a religous based network of some type similiar but much more extensive than that of Waco.

We have to assume the worse because our testing shows his functional IQ is 130 to 140 and in geometry is 150 plus, it was off our testing scale.

He was also trained by DOD in improvised weapons explosives, assisnation techniques clandestine communications techniques, has a exceptional functional memory can read a 1200 page book in 4 hours with an 80 percent retention rate and has spent 26 years reading all of our national security secrets.

All in all its comnplete mess because he is a verified genius that somebody tried to poison, and using a skill at predictive analysis built a religous based network from inside a secure facility.

In sum he is one of the most dangerous men on the planet.
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Anonymous
Posted on Monday, May 01, 2006 - 08:48 am:   

It gets worse,

In debriefing Ed,

I have confirmed that he did find a backdoor into our nuclear planning and intelligence system while serving at Joint Analysis Center Pacific.

His skills at network reconstruction allowed him to find a backdoor that could be exploited into these systems.

In the event Ed falls into the possession of a government other than the United States it is likely that he could assist them in penetrating the command and control system of the United States Military.

The closest we come to another genius like Ed that was verified was a man from CT that penetrated the security of several major insurance companies and drove them to the edge of bankrucy while looting them.

He built a network of agents and infiltrators that penetrated the insurance company for a cash profit motive. In Ed's case he penetrated our national defense systems, nuclear fire control and planning systems and we are not sure of what he did with the data or what system is still secure.

Now consider that and what Ed did and why we all agree its best to leave him alone keep him happy and just what DOD was using all those years to break codes.

To date all he has done is build a system to protect himseelf our of a misplaced sense of fear. It is very simliar to what the guy in CT did when he almost brankrupted seven insurrance companies.
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Le Chef
Posted on Monday, May 01, 2006 - 09:41 pm:   


quote:

What are you people on this thread smoking??!



That's how new progressive irrational genius ideas get beaten into acceptable publishable shape.
nz089.jpg
"Any math graduate from a reputable university knows that."

Welcome to the mainstream!
:-)
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Anonymous
Posted on Monday, May 01, 2006 - 10:52 pm:   

"Welcome to the mainstream!"

It is true that sometimes unconventional ideas get rejected by the mainstream because they are too far ahead of their times. But 95% of the time they are rejected because they are just, well,wrong and some are outlandishly stupid to boot.

If you work in a patent office you would know how many crackpot ideas you have to reject each day. Of course the people being rejected would not think of themsleves as crackpots. They no doubt think there is a conspiracy against them by the "mainstream"

I don't dismiss ideas simply because they aren't mainsteam. But what I find here are not even ideas. They are just incoherent gibberish. Hence the question: what are you guys smoking?

Consider this gem from our autistic genuis with IQ 150:

"I am close to being able to double the cube as well as square the circle using this same application of the irrationality of Pi."

Or how about this?


"Its a very difficult concept to verbalize and its difficult for my to frame it due to brain damage in terms that I can readily convey. But through the application of this curve what I believe I have done is indicate that it is possible to define an equation that allows for the extraction of data from an infinite data set. In this case that data set is represented by the Irrationality of Pi.

The application of this equation to quantum mechanics is I feel a way to deal with the random factor that is a manefestation of quantum theory"

I challenge any of you new age scientist here to explain to me what the hell does that mean, or is it just the semi-conscious rambling of a stoned mind?

Ed Chesky is no Galois here, if you don't know who Galois was do a google search.

I see on top of being an assasin, an unparalled mathematician, a master code breaker, a predictor of earthquakes and "the most dangerous man in the world" now Ed manages to bifurcate into other anonlymous characters too, including a "retired psychologist" who said he was not competent to judge Ed's physics and math yet somehow managed to conclude Ed's "predictive ability" is on par with the best super computers. I wonder what does a psychologist know about sismology and super computers. Nice try. You need help man.
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Anonymous
Posted on Tuesday, May 02, 2006 - 02:35 pm:   

The record speaks for itself in terms of predictive ability.

As to the rest the free expression of ideas is what this board is about.

As to Ed. Well considering he has spent 26 years with access to all Soviet Weapons Programs, PRC weapons programs and our weapons programs and command an control computers. He is either locked up, paid off or goes to work for another nation and turns his talents to destroying the United States.

Not a lot of choices out there are there.
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Anonymous
Posted on Tuesday, May 02, 2006 - 03:36 pm:   

For small minds

I for one love the diagrams

http://pg.photos.yahoo.com/ph/edwardchesky/album?.dir=/66d7&.src=ph

As to the rest, well everyone has the right to their ideas
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Anonymous
Posted on Tuesday, May 02, 2006 - 10:31 pm:   

"As to Ed. Well considering he has spent 26 years with access to all Soviet Weapons Programs, PRC weapons programs and our weapons programs and command an control computers. He is either locked up, paid off or goes to work for another nation and turns his talents to destroying the United States.

Not a lot of choices out there are there."

More amusing tall tales.

If "Ed" is such a deadly genuis why don't they simply kill him, like make it look like an acident? It's not like they haven't done it before. Remember Gerald Bull?

Ed would be a smashing success writing spy thrillers for TV. LOL

Nice graphics from the link. But what do they prove? Nada, nil, zero.

To solve the trisection problem with compass and ruler means coming up with a recipe that works for ARBITRARY angles. Any highschool kid with sufficient patience can trisect a number of special angles like those produced by "Ed".

To save you further troubles it has been proven that such a general recipe doesn't exist.

That's right, it has been MATHEMATICALLY PROVEN LONG TIME AGO that this cannot be done. Google up Galois like I told you before.For essentially the same reason the billard problem is not solvable with compass and ruler(it has NOTHING to do with Pi being irrational. Pi shows up in squaring the circle.It is impossible because Pi is TRANSCENDENTAL)

There is a BIG, BIG difference between not being able to produce a solution and coming up with a proof that no solution exists; any "mainstream" math student knows that.Interesting that this simple fact somehow eludes our math genuis with IQ 150.So don't waste your time coming up with any more alleged solutions. They are all wrong aprior.


There are other ways to trisect angles using special curves like the conic sections. But the ancient Greeks figured that out centries ago.





A skeptical small mind
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Anonymous
Posted on Wednesday, May 03, 2006 - 02:00 am:   

skeptical,

Don't need to be cruel. Whatever keeps the man happy..A little self indulgence hurts no one..
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Anonymous
Posted on Wednesday, May 03, 2006 - 02:34 pm:   

Yes trisection using curves is quite possible, and a man with an ability to trisect them time after time demonstrates a unique ability to process information. Its clear he has talent at processing information that may be related to autism.

The fact that he can trisect angles does not by itself prove a universal formula but an ability to perform complex geometric problem solving.

Again a link to autism would be consistent with this.

What other capabilites this individual has in terms of processing information and data is unknown at this time.

Very interesting and Anonymous's ravings above do indicate that trisection using conic sections is possible. This, however, begs the question of Ed having an unique ability to perform complex operations that may be related to a configuration of his brain. Similar to that of the "Rainman"

If so it is logical that he could have been exploited by DOD for his information processsing gifts.

Pity he is not willing to be studied at a major university which could measure and chart his capabilities.

We in the UK have a long history of working with such gifted people and I would love to have him at my university.
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Anonymous
Posted on Wednesday, May 03, 2006 - 03:02 pm:   

The human mind is more complex than we can imagine.

That someone can trisect angles and perform abstract geometries we can explain by virtue of a quirk in the brain.

Religion is outside of logic and moves into the releam of faith.

Hatred on the side of religion and science clouds many things.

Both science and religion are powerful tools for a person that is skilled in both.
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Ivan
Posted on Wednesday, May 03, 2006 - 07:59 pm:   

Some Postcripts on M-Theory and Gravity, and Super Massive Black Holes (SMBH).

(These are from private correspondense, on how the Axiomatic Eq. fits into modern physics theory, but will not divulge names unless they request it.)

This is Re Gravity, as a possible variable Newton's G:
I'm not a scientist (actually, I'm a mainstream stockbroker with a major Wall St. firm), so it may be out of character for me to delve into the mysteries of astrophysics. But I got there in a roundabout way through philosophical discussions, so what you see is several years of gravitating (no pun intended) about these ideas. Mostly from reading hundreds of science papers and articles, several books, I too came to the conclusion that Big Bang is a bad and untenable idea. So I set off, with my limited highschool math, to explore an idea first conceived as a philosophical question on the nature of what reality is made of. The eventual findings (described on my BAUT posts) is where this finally took me, to what I called the Axiomatic Equation, which shows an inverse relationship between radiant EM energy and the gravitation 'constant' G. The SMBH idea that emerged from this is mere speculation on my part, since I can't think of how to falsifiably test for it. I also think that cool stars, where EM radiance is low, such as brown dwarfs, should have more gravity per mass density; the so called neutron stars should fall in this category too. If you follow the paper, you should see that EM lambda for our solar system works out to be l=1.32x10^-15 meters; this could mean that for other stars, if cooler (lower E) and thus of longer wavelength (longer lambda), the proton (and neutron) mass should be greater than our ~1.67x10^-27 kg. This is the only way these super gravity stars, or gravastars, can make sense. By extension, this also implies that whatever mass exists in a SMBH, its gravitational power is immense, perhaps the maximum it can go. The way this works out in the (simplified) math is as follows:

G^2 = gc^2 , where G is Newton's gravitational 'constant', and little g is proton gravitational 'constant'; so if g goes to its max of g=1, then you get G^2 = (1)c^2, so that G = c (approximately)

What this means, conceptually, is that the ratio of attraction between masses, which is what Newton's G represents (leaving SI units aside for now), is equivalent to the speed of light; if so, then anything inside the SMBH becomes invisible to us. In fact, it is visible only by the radiation all nearby matter and stars give off at their very high velocities, so we see intense radiation of x-ray and radio waves from the galactic center.

What I think happens at the SMBH is that as matter falls in, remember matter is really just energy confined within an atom, it gets chewed up by the intense gravity and 'recycled' into basic proton-neutron proto-matter which is spat out the axials (it can't go any other way because of immense spin, so the axis is the path of least resistance), to re-seed the universe with new matter. That's why I think the second law of thermodynamics does not apply to a whole system like our universe, because matter gets recycled. Then it gets interesting if this new proto-baryonic matter is of very high gravitational density, because (before it gets modified by star radiant EM) it will clump under this immense gravity when there is enough of it, and combust into a new star. That new star is what breaks entropy. But I can't go into any kind of detail about this on BAUT because they would close the thread, IMO.

So the basic Axiomatic Eq. says E = hc/(lambda)(prot m) = (1-g)c^2, and when this E is maximum, g goes to zero, and mass simply cannot hold together (it actually happens at a number above zero, and may be the cause of solar wind origin in very hot solar corona); and conversely if g goes to its max 1, then E becomes zero. This is another way to show the same (gravity conversion Eq.) where at either extreme, something happens. But what really makes it interesting is that if 'gravity G for baryonic matter' is so much greater in deep intergalactic space than here within our Earth region, it may be gravitationally red shifting distant cosmic light as it travels through space into the Hubble constant. If so, then NO BIG BANG!, since the red shift is a non-Doppler effect, no expanding space (illusion only), and no need for an original start of when it all began. The other dividend of this, if it proves true, is that if EM and G are somehow inversely proportional, it may be subject to our manipulation. And if we can do that, then we're on our way towards a new physics of manipulating gravitational energy which is inexhaustible and accelerative. That has huge potentials.

In the end, all this rests on whether or not we find evidence that G is different from what we postulated it to be on Earth, and that it is not a universal constant but a (well hidden) variable instead. That's why in the past I called for a dedicated test for inertial-gravitational mass in the outer solar system, and I'm not the only one saying this as mainstream (ESA et al) is calling for this too. So what happens to GR? It is interesting with many good observational successes, but it may not be the best way to understand what is really happening to light red shift, or to SMBH and neutron stars, or why the gas giants have such great atmospheres. In effect, GR would have to be rewritten to accomodate a variable G; or it gets scrapped altogether, since you get the same relativistic results by measuring for red or blue shifts of light. Of course, that makes modern physics look bad, so expect resistance to this new idea, even if the empirical evidence proves it right, and research funding politics may keep it buried for some time, which is too bad. But not my concern, since I'm not a scientist whose livelihood depends on this. I just stumbled on something interesting.

So let me think on your points mentioned, and I'll write some more later. I think I should leave a trail of 'bread crumbs' on how all this came together for me, which I may do at some point on the Humancafe forums, maybe under "Ivan's great works" thread. :-)

Cheers, Ivan

Ps: in the paper on Pioneer Anomaly I explain how mass is not kilograms but kg/kg = 1, though the kg units are conserved. I'm still working on that, since I think it is something important to understanding mass in a variable G scenario, which we never had to consider before in a universal constant G universe. However, I don't know if any of this is any good, not until we find real evidence for a variable G.


And also on this, Re M-Theory:
I've thinking about this M theory. And also on this in your last note:

See, here you immediately assign the deep space gravity to a Baryonic Matter function, and then go on to say that the Hydrogen molecules can bind easier in this environment. How can 'all' of  "Dark Empty Space" have this remainder of atomic mass, and where did the Hydrogen come from? Now, as I said earlier, I DO NOT DISAGREE that it (the gravity) is there, BECAUSE IT IS. This is the reason I was intrigued by your work, because you are saying it is there, it's just how it gets there that is the real difference.

And yes, it is good to have a discourse with someone whose mind is open enough to consider that maybe we hadn't got it all right yet. :-)

I think there is something I need to clarify first. I do not think space itself creates gravity. Rather, I think of any baryonic matter in space where radiant EM energy is low will become subject ot very great gravity, at least much greater than we know here, living close to our hot star. Let's if I can explain this better.

The key is how the atom forms and the four basic forces: Electromagnetic, strong force, weak nuclear force, and gravity. The way current physics theory has it, according to the Standard Model, the first three forces are unified, but the last, gravity, doesn't quite fit in. From little I know of M theory, or QTF, is that gravity generates infinities, so sensible results become meaningless. (See: http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html ) These unwanted infinities were later removed through Strings, or M-Theory, but it remains a largely fanciful and untestable theory, not falsifiable, nor of predictive value. So for now, in my opinion, it is a fabrication of curiosity, which is fine with me. But I think where they missed the boat, was in combining the first three, so that everything became definable as particle theory, which then included gravity as particle theory, gravitons. I suspect this is wrong. Here is my thinking on it.

I think that EM particle and wave energy belongs on one side; while gravity belongs on another. Not even considering variable G here, but the stuff we know now. The way the Axiomatic (Quantum) equation works out, when gravity is included into it, is that gravity and electromagnetic energy are opposed forces. There are no graviton particles, because it is not unifiable with the other three forces. So if these are in two camps, gravity and EM energy, then how do the forces fit in? I suspect, without having all the necessary math and theory behind it, that the nuclear strong force is in the same category as gravity; and that the nuclear weak force is in the same category as electromagnetic energy. So nutrinoes, electrons, positrons, isotopes beta decay, photons, are all in that category; while on the other side we have nucleus mass, strong force, proton and neutron mass, and from their interactions with EM energy, there is a 'remainder' gravity, what we experience. So my vision of how the atom is built is of necessity different from what is now part of the Standard Model. But I don't know how all this works, except that the model painted by combining the Quantum and Energy equations seems to look like this: gravity and EM energy are inversely proportional by some function. Of course, this is not how it is understood today! So to make it a viable alternative to Standard, we need to find evidence of this inverse proportion, which would show up in a variable G, as the Axiomatic predicts.

So given this conceptual scenario, it is not space per se that is deep gravity (as I had said perhaps without realizing how this is misleading), but that when an atom is in deep space far from EM radiant energy, that atom exhibits greater gravity. If we think of the atom as a strong force (gravitational) force held together, and when in the vicinity of hot EM radiant energy it 'captures' that energy (as a standing wave of light), then the atom is formed. The Quantum restrictions on photon energy is well defined, but when it falls outside the norm, other things start to happen. One of these anomalous events is the forming of isotopes, which are then subject to radiation decay. The other thing is that if the EM energy is too low, hypothetically for now, the atoms retain much more of their gravitational component, so they exhibit great gravity. I think this is what we see in neutron stars (I read that new measurements of 'neutron' stars shows they are not magnetically neutral). If the EM energy is too great, the gravitational remainder (if the standing wave of EM energy is too hot), gravity is too low to keep matter together, and it flies apart. I think this is what we see in the solar wind (notice how it actually accelerates away from the sun, which may be an energy function of combined kinetic energy, solar energy, and too low gravity). Otherwise, what we see as baryonic matter is all very nicely balanced, since this is what survives the test of time. I also read that the Strong force is unique in that it attracts more strongly as you move the protons and nuetrons further apart! Think about that a moment, since it really is counterintuitive, unless we are dealing with the gravity of space. Then, pulled appart means less 'hot' energy and more 'strong' gravity, and it makes sense. So this is another reason I think the Strong force belongs in the gravity camp. But the whole key to all this is to move beyond the Bohr model of the atom, which is okay for use in chemistry, but to see that it is more than merely dual charge acting on the electron and proton, and that in fact the very strong gravity holding the nucleus together is modified greatly by the presence of the electron, and that what is 'left over' is the gravity we experience.

So M-theory may not be directly addressed by this new model of the atom, though I do not now it well enough to say this for sure. What I think is happening in deep space is that baryonic matter there exhibits a greater 'remainder' gravity force, since EM energy is weaker, and that this greater gravity is what is now being called Dark Matter. If so, then light traveling the cosmos naturally redshifts (gravitationally) due to the greater gravity of all the molecules in intergalactic space. And this is why I think the Big Bang is dead: there is no Doppler expansion going on al all, a mere optical illusion.

As far as how stars are born, or galaxies form, I still don't know. I suspect deep space gravity (for molecules there) may at some point be great enough, given enough mass accumulated, to trigger critical mass and star combustion. Once enough stars are in a vicinity to form a potential galaxy, then will find within their collective mass a center where the EM cancels on a point, and that starts the Black Hole around which they will eventually form a spiral galaxy. But how can we test for this? I don't know, so leave it as a curiosity only.

So in yours:

I think what you 'may' have done is shown how, by including the 'g', gravity can be included in GR in a more realistic way, even though it may very well be variable. Getting the scientific world to understand that, is a whole other story.

I agree, but don't know how to fix GR, of even if it needs fixing. Let me think on this some more, and look forward to more of your ideas.

Cheers, Ivan

No great revelations, just some postscripts.
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Ivan
Posted on Thursday, May 04, 2006 - 09:26 pm:   

Photon-Graviton Duality by Ingo H. Leubner

This is an interesting parallel development, which uses the same equation as was first used in the Axiomatic: E = hc/ lambda. Though we may come to different conclusions, since it invokes an origin Big Bang universe, which goes from expansion to eventual contraction, unlike the Axiomatic which dispenses with this, since redshift of distant cosmic light is seen as a great gravitational effect; it nevertheless is a worthwhile good read. I think where we may connect , possibly, is how light photons have a gravitational component, which may explain (in Axiomatic) how radiant EM energy interacts with the 'remainder' force of gravity in the atom, or its inertial mass.

Ivan
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Ivan
Posted on Sunday, May 07, 2006 - 12:39 pm:   

M = L^3 / T^2

23 Dec 1998 (see orginal above by date)
Derivation of the Space-Energy Equivalence
With the increasing interest in zero-point energy
and similar concepts, itΥs natural to wonder how
much energy space might contain. A formula for the
space-energy equivalence may be derived as
follows: The universal gravitational constant (G)
is an expression of the relationship between space
and mass. Fundamentally, G is the space-mass
equivalence. Expressed dimensionally, G=L^3 / MT^2
where L=length, M=mass, and T=time. Bringing the
quantity to unity, it can be written M=L^3 / T^2
and simplifying, M=rC^2 where C=the speed of light
(L/T) and r stands for a radius (L). Substituting
M into the mass-energy equivalence (E=mC^2) yields
E=rC^4 where E=energy. Thus, the total amount of
energy contained in a volume of space defined by a
given radius is equivalent to the radius times the
speed of light to the fourth power. Written in
dimensionally balanced form, the space-energy
equivalence is E=rC^4 / G.
Nelson Zink mailto:zink@newmex.com


This was the second entry into the original People's Book, now archived, which gives an algorithm for Space-Energy. Notice how similar it is to the above post on Mass -V (April 29, 2006):
This translates into the funny mass equation, whereby m^3*a = kg becomes "volume times acceleration" (or gravitational potential Gm/r=a, for each m1 and m2) so that it should read as: m^3*(G'/G)^1/2*(Gm/r) = kg*, which now reflects the equivalence adjustment for gravitational mass cum inertial mass.


Mass as kilograms is a function of m^3*r/s^2, or in using Nelson's terms, M = L^3 / T^2.

Are we on the same page here? This is another expression for Energy as E=rC^4 /G, which is space-energy as it affects mass, no matter what G is found to be away from Earth's known 1G. What is different, per this reasoning, is that the acceleration m/s^2 is contained within the distance r, so that it becomes r/s^2, as the radius of mass.

Ivan
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Le Chef
Posted on Thursday, May 11, 2006 - 09:42 pm:   

RELAVAUTISTIC MASS -- it's not what you think!

These guys have the right idea, mass does not change with velocity.

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

It was a David McBane virtual reality trick, not related in by blood to McEinstein, who invented this great virtual Mc2Cheese Burger = pure Energy. You get more cheese!!!

nz161.jpg

Not conn-fused enough? Then try this: Does light in a box have mass?

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

le Chef :-)
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Ivan
Posted on Wednesday, May 17, 2006 - 11:08 pm:   

ZERO POINT ENERGY DRIVES research for future space propulsion mentioned in these pages.

I think they're on the right track, that perhaps Heim Quantum Theory for Space Propulsion, or the NewScientist article Take a leap into hyperspace, and also Physical and Numerical Modeling for Advanced Propulsion Systems are pointed right.

This last paper, on Advanced Propulsion Systems, is from a book titled "Recent Trends in Aerospace Design and Optimization", Editors: Biju Uthup, Santhosh P. Koruthu, R.K. Sharma, Pankaj Priyadarshi (SAROD -2005, Hyderabad), of which I have read the works of Dr. Sharma (I have a copy of his book explaining an alternate to space ether, using Sharmans, though I disagree with it). However, this last paper calls for 61 Tesla to make it work, which at this point we still cannot achieve. At least they're trying, not accepting the finality of present day physics. Until we can unlock the secrets of gravity, and use it as a contained force (not merely planetary slingshots for spaceprobes), physics is not there yet.

I feel that the idea expressed in the latter, especially sections 3.2 to 3.5, (3 Field Propulsion) may have some promise, as they parallel my idea where all energy canceled down to below the Planck lengths (as happens when all lambda cancels on a point), there should become evident a release of gravitic energy.

Here is a page with a more comprehensive list:
http://www.borderlands.de/Links/NewSpacePropulsion.pdf

I suspect that it is all much simpler than the GR math used. If we could contain a light gas in a partial vacuum vessel and spin it at high speeds, with an external energy source turning the gas to plasma, the self canceling effect of energy on a point, even if only some nanometers across, should yield a tremendous release of gravitic energy, if Axiomatic is right.

Ivan
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Ivan
Posted on Sunday, May 21, 2006 - 01:53 pm:   

PLASMA PHYSICS, why stars form from ionized space dust?

(source taken from BAUT forums posts: http://www.bautforum.com/showpost.php?p=746815&postcount=10 )

This is a quote from the paper by Hannes Alfven and Per Carlqvist, pg. 8, sect. 1.3.6; Ionizing Process; Interstellar Clouds and the Formation of Stars (1997): http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1978Ap&SS..55..487A

I suspect there is a problem here, in that:

"In an extreme case the plasma may consist of heavy negative particles (dust) and less massive, positive particles (positive ions) contrary to ordinary plasmas with light negative and heavy positive particles."

This may be an inserted demand from the authors to make a fit for why space dust plasma can condense into star forming fusion, by reversing the normal charge of plasma particles.

I suspect that positively charged particles, represented by proton mass, are always the more massive, while negative charged particles, represented by electrons, are always less massive. The answer to why space dust plasma comes together in force to combust lies not in their charges, but in their space gravity G, which out there is some 50,000 times greater than our known Newton's G in the vicinity of our planet Earth. The charges involved are incidental, more likely how electromagnetic energy modifies mass, where the positive charge of the wave's magnetic field 'connects' with the positive charge of proton mass, while negative charge remains at a distance around this proton as a negative charged electron. This implies, however, that gravity acts conversely to electric charge, in that like charge goes with like charge, as opposed to electromagnetic where like charges repel. Here is how the authors see it, pg. 14, II.5:

1. Consider first an intersellar cloud of 100 solar masses... The temperature of the cloud is T = 10-10^2 K...The number of atoms present in the clouds is ~10^+59 ... we find that an electric current of I ~ (5x10^12)-(2x10^13) e.m.u = (5x10^13)-(2x10^14) A has to flow through the clouds in order to produce a considerable compression effect.

The normal distribution of atomic mass in deep space is estimated at 1 atom per cubic centimeter, whereas they have this a 100 times normal distribution. This may be too high. Also, the T they estimate may not be correct, unless taken as a total temperature for the whole cloud. There is still no justification why this interstellar cloud should merge into combustion, given these numbers, though the other numbers for once this merging starts may in fact be close to what happens. The upshot of all this is that it takes very great gravity G to cause plasma clouds in deep intergalactic space, where G is 10X^-6 strength (vs. 10X^-11 strength here), to combust into fusion star formation. Otherwise, the above linked paper is fascinating, but may not be the right answer to star formation.

Ivan
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Ivan
Posted on Wednesday, May 24, 2006 - 10:07 pm:   

ENERGY AND MASS INTERRELATIONSHIP

Here are some interesting papers dealing with the Energy and Mass interrelationship. They all take the point of view that electromagnetic energy is responsible for inertial mass, and gravity. This is contrary to what the Axiomatic Eq. says, that electromagnetic energy and gravity are inversely proportional, so that inertial and gravitational mass are defined (inversely) by the amount of energy received. Nevertheless, they are interesting in that they reach back towards more fundamental values of mass as opposed to post relativity definitions of mass. The early works up until Einstein's description of relativistic mass focussed more on the electron mass, as the papers show. It should be noted that the real key is proton mass, as it is modified by electromagnetic mass, if the Axiomatic is right.

I think Sarin is on the right track, almost, except he can't see how proton mass, both inertial mass and per equivalence gravitational mass, are byproducts of the remainder strong force of the proton as modified by electromagnetic energy. Still, he is closer than the Standard Model with its Bosons, quarks, colors and spins, all of which must be parameter 'adjusted' to fit. His idea of the proton mass (neutron mass is a hybrid of the proton, charge neutral, subject to decay) as a function of electromagnetic radius is on the right track for the H atom, for our region of space; this radius may be different elsewhere.

"Nature and Quantization of the Proton Mass: An Electromagnetic Model" by G. Sarin
http://arxiv.org/ftp/physics/papers/0512/0512108.pdf

Mentioned in the above is the paper: "The Equivalence of Magnetic and Kinetic Energy" by Carel van der Togt
http://www.paradox-paradigm.nl/%5CVan_der_Togt_equiv2ckw.pdf

On page 2, van der Togt takes the liberty to 'substitute' Qe with We as 'electrostatic energy', which may or may not be crikey (where the electrostaticc energy of a charged sphere We = Qe2/ 8pi e0Rc, pg. 3), don't know, which leads him to equate magnetic energy with kinetic energy. Again, there is no awareness of the role strong force plays in defining inertial mass, so we see everything only through an electromagnetic lens. If modified strong force is remainder gravitational, hence inertial mass, then less energy would mean higher inertial mass; while very high energy, such as close to the Sun's third planet, means exceptionally low inertial and gravitational mass. We can use chemical propelled rockets to get off Earth's surface, but will need to use gravity-assist propelled spacecraft to launch from very high G planets. On all gas giants, with chemical rockets, once you land you can't get off.

Another interesting paper, from its history perspective, is "Did 20th century physics have the means to reveal the nature of inertia and gravitation?" by Vessilin Petkov
http://alcor.concordia.ca/~vpetkov/inertiagrav.html

Petkov looks mainly at the early attempts to define electron mass, as the 'origin of inertia', with a caveat, IV:

"If it turns out that the strong interaction does contribute to the mass, we will face a major crisis in physics - it will not be clear what compensates the negative contribution to the mass that originates from the strong interaction."

Again, 'negative contribution' may be mistaken labeling, since strong force properly defined adds a 'positive' contribution, as is its charge, negated by the negative charge of the electron shell. This positive charged proto-gravitic force is what captures the electron, largely neutralizing it with dual charge, and nearly neutralizing it gravitationally, except for the small remainder Newton's G. That's how the Axiomatic sees it. If so, then 'relativistic mass' is merely an artifact of observation, or force, applied from a 'stationary' observer, or force. Petkov also says, I:

"Therefore, the classical electromagnetic mass theory does say not only a word, but offers a detailed mechanism explaining the origin of inertia and mass of charged particles: it is the UNBALANCED repulsion of the volume elements of the charge of an accelerating electron that gives rise to the electron's inertia and inertial mass."

That's right. Howevever, the 'unbalanced' remainder of inertial mass is what's left over from the proton's modified strong force. Einstein's relativity did us no special favors, and now we must start over again.

It will take some work to show all this in algorithmic language, but I think it is doable. Except, I'm not ready for this.

Ivan
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Ivan
Posted on Thursday, May 25, 2006 - 11:08 pm:   

FOR THE RECORD, on the New Physics.

For the record, why do I post these references to papers on physics, or some of my ideas on mass and energy? It is not to show that I am right, since I have no assurance my ideas are right or not. But I list them so that in the event we do in fact discover that gravity is not a universal constant, as now assumed, but instead is a variable, then a whole new approach to physics will be demanded. My purpose here, should this come to pass, is to show how mass and energy interact to form the atom, the basis for how this new gravity physics will evolve. I do not know if any of this is right or not. However, when I see the gas giants atmospheres, or the thick atmospheres of moons at distant AUs from the Sun, or what the Pioneers are doing, or how comets start gassing out from as far as Jupiter's 5 AU where it is still very cold; these are telling me something else is going on out there. They are clues that perhaps we got gravity wrong, and the universe works on a different level than postulated, and later defined mathematically with General Relativity; that perhaps it is all much simpler than we think. Going further out beyond the solar system into flattening galaxy rotation curves, or type Sn1a Gamma ray bursts anisotropic redshifts, or dark galaxies bending light with their gravitational lensing; we have to start with the premise that we should reexamine our assumptions. Perhaps the universe is not expanding, that their was not origin to space-time in some phenomenal Big Bang, that perhaps our curve fitted observational cosmology may have it all wrong. This does not invalidate the spectacular mathematics that yielded our current cosmological theories, including branes and strings, but nor does it validate it if the observations keep coming back with anomalies that require more ad hoc fitting to make sense of them. Then it gets tricky, because if we are making so many adjustments, and call on reasonable minds to make so many amends to reason that what had been thought of as science begins to look more and more like philosophy, if not fiction; the basic premises on which these elaborate theories are built become open to criticism. Reasonable men and women have the right to reject what they feel is wrong, even if they are not equipped mathematically to refute theory, nor to present a whole new theory in their place. There comes a point where the mind rebels against such constrictions and refuses to be fooled, because they see them as absurd speculations. I think we reached this level in modern physics today, where the theories are so fantastic that ordinary reasonable men laugh, cannot take them seriously even if very intelligent and skilled professional people do, because the ordinary reasonable person is no fool. And when the evidence finally comes in, the foolish ones will be those who built such incredibly elaborate constructs to explain what in the end was quite simple. To my mind it is already simple, we just cannot as yet see it.

When I see articles like this, for example, "Distant gamma-ray bust may be in a class of its own" (NewScientist, 24 May, 2006), what appears mysterious to most for me falls instantly into place. For example: "They say the event, called GRB 060121, resembles a short GRB in terms of the range of radiation it emits but lies farther away than all known short GRBs. It appears to lie 12.7 billion light years from Earth. But this is not entirely certain because the spectrum of its "afterglow" – produced by shockwaves from the burst heating up surrounding gas – shows features that could also place it at a distance of 10.1 billion light years." In a variable G universe, there is nothing strange here. As the gamma radiation passes through different levels of gravity density in deep intergalactic space, it will appear to be more redshifted in very high G regions, and less redshifted in lower G regions, dependent upon the amount of gases and space dust there, so that it could show up as both. Different wavelengths will have different responses to these conditions, which is confusing in a universal G scenario, but understandable if G is variable, and greater than here in deep space. The mystery of all these observational puzzles become more easily resolved, if a variable G is correct.

We need proof that G is not a universal constant, not the anecdotal evidence but science dedicated to finding out for sure. Of course, if it is found out, then many things change. The atom as now understood will need revision, perhaps right down to the Quantum level. Astrophysics will need to be rewritten, to accommodate a variable G. The interrelationships between electromagnetic energy and gravity will have to be explored, with a possible dividend that it could be a usable energy, accelerative and inexhaustible power. The Standard Model may be simplified from its 20 adjustment parameters and 18 'elementary' particles to something more usable. Where does that leave Einstein's Relativity? Probably it will kill it, leave it merely as a mathematical curiosity, since the math involved in describing a variable G universe is much simpler. There is no need for geodesic tensors, same as there will be no need for the Higgs boson, these are artifacts of mathematical constructs, correct within their own formalism, but inapplicable to real conditions. Time 'appears' to slow, same as atomic clocks slow traveling through gravitational fields, but this is merely illusion created from how light redshifts. Only what is usable should survive, the rest will be permanently shelved onto the dusty racks of history. The new physics sciences will be more direct, understandable to reasonable men without investment of years of study, and will be taught at the secondary school level much as Newtonian physics is today. The final blow will fall on the expanding universe and its big sibling, the Big Bang. If light redshifts naturally over cosmic distances due to gravitational redshift, then Doppler expansion is wrong. The universe may yet prove to be isotropic and homogenous, but at a much greater G than we had suspected, since we live in one of those privileged low G bubbles of space, being close to a hot star. But we need proof, or else none of this is any good. Either a variable G is fantasy, or it is real. Only when we know for sure can we go to the next level of research, and open up the field in ways we had not imagined.

So I write this only in anticipation that we will find it is so. The Pioneer Anomaly becomes understandable in a variable G, so are the gas giants, so is the thick atmosphere on Titan, while our Moon has almost no atmosphere; even Enceladus has a small atmosphere, a moon the size of Arizona, if Newton's G is so much higher at great AU distances from the Sun. Comets in their highly elliptical orbits contract in the high G of the outer solar system, and release internally when closer in as visible cometa, not because of the Sun's warm glow, since it is still very cold at Jupiter's orbit, but because they are expanding from inside as they hit lower G. Flat rotation curves for galaxies or galaxy clusters make sense then. The black hole, so called, at each galactic center makes sense, if all ambient electromagnetic energy cancels there, and maximum G, inversely proportional to the very high energy surround the black hole, is revealed; nothing escapes it, not even light, as it recycles matter into positive charged proto-hydrogen spat out the axii at near light speed. Cosmic light redshift becomes easily understandable as deep space gravitational effect on the photons passing through the 'heavy' atoms scattered through intergalactic space. Even momentum transfer to the rings of gas giants, or Mercury's very low G responding to the Sun's surface rotation, all start to fall into place, as does the planetary plane; they are all momentum transfers. Same with the composition density of planets, and rings, where those closer to hot energy sources will collect 'heavier' particles of matter, while those further away will collect 'lighter' particles of water ice. It all falls into place. Perhaps even why spaceprobers landings on Mars (1.5G) and Titan (9.5 G) hit harder than expected, if their inertial mass increased. But it also remains an unknown until proven so.

Finally, I present these papers listed in the pages of this forum, and its other ideas, as guideposts to where future research will need to go. Once we find evidence of a variable G, there will be much work that will need to be done. Some of this work will be done by the authors mentioned above, and some by people who are now unknowns. But those whose vision can leap beyond the historically deleterious effects of Einstein's Relativity will be the first to see it, while others will remain 'puzzled' trying to understand what had just happened. That is the way of the world, and that is how science takes its giant leaps forward. It is not merely on the shoulders of scientific thinkers and giants of the past, but also on the giants of the future. It will take open minds who had not fallen in love with the incomprehensible physics of today to have the vision of that future. But for now, we do not know. Yes, Newtonian physics with a constant G works, but it may not be telling us the whole truth.

I leave this here for the record.

Ivan
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Ivan
Posted on Monday, May 29, 2006 - 01:33 pm:   

NEUTRON STARS NOT SO DIFFERENT FROM BLACK HOLES IN PRINCIPLE?

http://www.space.com/scienceastronomy/060529_compact_jets.html

This short article on Space.com reveals something very interesting, in that the jets shooting out the axii of black holes also appear in a neutron star, though much fainter. This is not unexpected, if Newton's G is orders of magnitude greater for neutron stars than Earth's known 'universal constant' G, though lower than for black holes, as the intense gravity for mass crunches matter back into its primordial proto-hydrogen state, shooting out the dual axis as the path of least resistance, at nearly light speed. Interesting.

Ivan
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Aladim
Posted on Wednesday, June 07, 2006 - 04:03 am:   

Hello,

As I see the main interest here is gravity.

Like my teacher from highschool said :

"We don't know why the objects are attracting each other.If they were repulsing (I guess this is the opposite word for attraction in English) each other , again some kind of harmony will exist."

The reason I am writing the words of my teacher is that in my openion it is absolutely correct abstract statement which I won't forget.
But if a repulsion was on the place of gravity , I guess that the universe will be screwing up (I guess this is the right word in English) instead of expanding like in our case . And the most interesting part is the trajectories of the moving objects .
If someone can imagine this oppposite situation I think that the answer for the explanation of the gravity will be in his hands .

I think that the mankind likes a lot to see all kinds of objects and for me this is the reason for the "big bang" theory , which is a critical moment in today's science . It is not sure that this is the thing ,
big bang ......ha-ha-hey-hey.

What banged the something and where was the nothing(vacuum)?
Why the bang had acceleration <0> 0 .

I am not sure that explained something.It is like question just becouse I was wondering 2-3 day what to post here and was not sure about anything.
These are easy even dumb questions but I think that there is no joke.

Bye for now.
1.4.1.1.4.0.
Peace
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Ivan
Posted on Wednesday, June 07, 2006 - 06:22 pm:   

BABY STEPS TOWARDS A VARIABLE GRAVITY G?

Seeds of doubt are sown in "Gravity's dark side" from PhysicsWeb.org, June 2006 issue, brought to my attention by a Ph.D. scientist friend.

These may be only 'baby steps' and a rather roundabout way to get to the obvious, that so called 'dark matter' is regular baryonic matter in a higher G region, far from hot sources of radiant energy. Not there yet, but moving in the right direction. 'Dark energy', so called, is just gravitational redshift of cosmic light passing through the 'dark matter' higher G regions of space, making 'expansion' unnecessary. Hang loose, it gets more interesting now. :-)

My take on this is here: http://www.humancafe.com/discus/messages/70/166.html

Cheers, Ivan
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Ivan
Posted on Wednesday, June 07, 2006 - 06:37 pm:   

Thanks for posting, Aladim, and Welcome!

In yours:

quote:

What banged the something and where was the nothing(vacuum)?
Why the bang had acceleration <0> 0 .



The Big Bang was 'assumed' as a conclusion from space observations that all cosmic light coming to us from all directions is (Doppler) redshifted with distance, so that space is expanding, which means it must have had an origin; that origin was then assumed to have been from a moment in time, some 13.7 billions years ago, when a sudden burst of energy expanded within nanoseconds into the first moment of space-time, and then continued to expand since then into what appears to be the Hubble constant. Ad hoc it appears to be, but that's the cosmology we get today. How did something start from nothing? What is it expanding into? Some more space-time that does not exist? All unanswered questions, which may not have an answer.

Your teacher brought up an interesting idea: where is the counter-balance to gravity? It may be radiant electromagnetic energy, or there may not be any, so gravity by itself violates some sort of conservation law. But if you have more on this, to expand on your idea, please feel free to share it here, if you wish. (You might look at my link in the post above, skip through the math if you wish, the text is sensible in itself. :-) )

All the best, cheers, Ivan
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Aladim
Posted on Thursday, June 08, 2006 - 06:15 am:   

http://physicsweb.org/articles/news/7/7/9

An interesting field for thinking is the light pressure.

It exists so every , movement in the universe is not only becouse of the existence of the gravity.


My intuition is telling me that the light is the reason for the gravity . It is every where and it pushes everything it reflects and pushes another thing . So here we must mention the black holes.
They eat gravity and light , as I know from the abstract papers . For me the science nowadays is too abstract .

E=m.c`2 => c`2=constant=E/m => if E is changing and m is changing , but in my openinion it works only if we take the whole universe as one body .
The semiconductors are working becouse of the theory but who knows what is in the "dark" holes.


I think that the real formula must be "close" to E/m=constant and here we don't have to speak about the speed of light if we think in this way.

The gravity changes the trajectory of the light.
The light changes the trajectory of the bodies with it's pressure.So they work both in every moment.They are making the bodies to move (not only gravity ).
Maybe the right formula is close to the Einstein's formula but the gravity must be in it too .

The vacuum in the space is very big but the particles are there . They are moving together . If the photon exists as a partical it is absolutely possible to have an inertia , which we can measure with an "impossible" machine.

If the guys are right (http://physicsweb.org/articles/news/7/7/9) when they slow down the speed of the light ,????????where is E or m to compensate.

Two possibilities for the photon :
1->m=constant
2->E=constant

I became abstract here so I want to mention :
Einstein was thinking in an easy way and we must talk and write without thinking if we want to make something real and clear .

The formula for every scientist , from buddah's point of view is something like:

Write , speak and at the end - think,but be a good man all day every day .

The mind can work like a vector . The start point is not the most important one . The importance is in the direction ( always must be for good purpose )

Maybe E is constant not c .

Cheers
Aladim from schz T.M.
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Aladim
Posted on Thursday, June 08, 2006 - 06:17 am:   

Want to mention:
I am 24 years old engineer , not a scientist.
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Ivan
Posted on Friday, June 09, 2006 - 12:36 am:   

Dear Aladim,

RE: E / m = c^2

I've been thinking about this for a long time, never quite really happy with any explanations I found. I like your idea just fine, as evidenced in your article referenced, that light speed c is not necessarily a constant. It can vary immensely under some circumstances, and get refracted such as in a lens, for example. "Light pressure" may have something to do with gravity, but I worked it out differently.

So here is my solution, somewhat intuitive perhaps. If we think of light 'attaching' itself to an atom, in a two dimensional form on a plane, then it is analogous to the area of a circle: pi r^2. Now think of light not as a (geometrical) representation of a sine wave, but rather as a percussion wave that (nearly flat from great distances) hits the atom with each photon, so the plane of entry is actually perpendicular to the direction of the source. What you get is an area of photons connecting with the atom (perpendicularly) at pi r^2, but in the case of light, the result is pi c^2. I had worked out (in my referenced paper above) that the conversion for proton to proton gravitational constant 'g' into Newton's gravitational (mass attraction ratio) 'G' is: G^2 = gc^2 pi^2, where the nuclear gravitational strong force remainder (what is left over after light modifies it) is what represents G, per this conversion.

Now, remember our Sun is the dominant light source for us here on Earth, being the closest and hottest such source. Solar photon energy, at all wavelengths, is what dominates energy on Earth. So as photons stream from our solar light source, it continuously connects with each atom's nucleus, both the proton and neutron, to modify its otherwise inherent Strong force (equal to 1 by convention), into the remainder we measured for the proton, which is g = ~5.9x10^-39 (commonly dimensionless, but it can also be in Volts), which then translates into Newton's G (for us on Earth) into about ~7.3x10^-11 m^3/ kg s^2 (vs. Newton's G = 6.67x10^-11 as measured, due to other factors, such as internal Earth's energy, where higher E translates -inversely- into lower G). So we may be looking at how light modifies each atomic nucleus into the matter we know, covered by a 'trapped' photon which is now its electron shell (atoms have dual charge internally, but are mostly charge neutral otherwise, unless ionized), which together combine into E = mc^2. This may be the source of how Energy 'E' is responsible for what we experience here, per equivalence as 'm', once it goes through this process. (On Earth, this works out (for one kg of mass) as E = 9x10^+16 Joules.) In effect, this is the theoretical basis for the Axiomatic Equation I wrote, for this E value; but Einstein's equation was missing the 'g' component (remainder) from its atomic mass. The mass, at least here on Earth, is consequently a very small inertial value (per equivalence principle), but it could be much greater if the E is smaller. So if our Sun were a (cool) brown dwarf, for example, atomic mass (for same volume of matter) would be orders of magnitude greater than what we know here as the 'one kilogram'. Because we assumed G to be a 'universal constant' we never had to cope with a variable mass value for kilograms. As explained above, with the conversion eq. for Newton's G, this may have been a monumental oversight, since mass (per equivalence) may be modifiable with E, and consequently with c^2 as well.

So in yours:

quote:

I think that the real formula must be "close" to E/m=constant and here we don't have to speak about the speed of light if we think in this way.


The 'constant' E/m may be, even if 'c' is different, except the 'm' would adjust for either a higher E (closer to Sun) or lower E (intergalactic space) regardless of what 'c' is doing (it may slow or accelerate through higher or lower G regions, for example, which would give it a 'lensing' effect as it passes by large bodies). Remember mass is mass, in that the volume of the atomic matter had not changed, but its value can change, per the equivalence principle, if G changes. In my above, in a higher G (intergalactic space) the mass would command a higher equivalent version of our Earth's kilogram value. There's your 'dark matter'. The 'hole' at each galactic center is this same at its maximum, I believe.

If this is confusing, here is something more. If c varies, meaning it is not always a universal constant as posited by Einstein in his Special Relativity, then the E will fall with slower c (meaning it is 'cooler' and redshifted). Less total Energy, and the mass, per equivalence with inertial mass, would reflect a greater Newton's G. I think this is what so called 'dark matter' is all about. So getting back to your E / m = c ^2, it is essentially correct, if the 'm' is known in advance, which on Earth is one kilogram; but this may be different elsewhere in space. If it is greater out there, in the low E regions of intergalactic space (same 1 kg volume of matter, but the kg value is greater), then the 'dark matter' puzzle is solved. All that is happening far from hot stars is that E is low, G is high, and the same matter per volume acts as if it had higher inertial mass (why Pioneers are slowing, or galaxy rotation curves flatten). If inertial mass is greater, due to greater G, then its gravitational attraction increases, which violates the inverse square law for gravity. The reason we never saw this before, I suspect, is because we figured out the whole universe with a constant G, so all our mass assumptions of distant bodies are off, though the calculations are consistent, so it works mostly well (with some exceptions, like density of atmospheres, or how hard landers hit upon entry, etc.), so we never had a clue something was wrong.

And if we could find a way to duplicate the very powerful energy produced by our solar companion, bottle it somehow, we might have a key to modifying atomic G in the lab. To do that, young engineer, will be the prize of the millennium!

BTW, I think this is doable, but it requires a trick to contain (or cancel?) c^2 on a point. Remember the 'hole' at the galactic center? :-)

BTW2, I think all 'redshift' of distant cosmic light is gravitational, as it passes through the very high G regions of intergalactic space, which is BIG. My hunch is G out there is about 10X^-6 (at about 'cut off' wavelength of orange light for the photoelectric effect, if using Axiomatic Eq*), or five orders of magnitude greater than on Earth. I worked out the numbers, and it seems to approximate Hubble's constant for nearly one kilogram of matter (one atom of hydrogen per cubic centimeter stretched) over the distance of light years necessary to redshift at 1z, if G is that high out there. Of course, if so, you know what that means: that Doppler expansion of space is a no go, bad idea, and Big Bang is bust. It never happened!

Cheers, Ivan

*(see this page, "Posted on Sunday, May 07, 2006 - 03:53 pm:   
‘BREAD CRUMBS’ TRAIL – a Chronological Anthology, for how this worked out. Scroll down to #22 & #29. Links there give more detail; you may need Netscape or MS Explorer to get full access to the linked pages, or the symbols are all screwed up. #32 talks about light redshift in deep space at Hubble constant.)

CAVEAT LECTOR: This is not physics as it is now understood, and will not be unless we find definitive evidence that Newton's 'universal constant' G is in fact a variable as described by the Axiomatic Eq.
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Anonymous
Posted on Friday, June 09, 2006 - 10:13 am:   

http://www.msnbc.msn.com/id/13070896/

The above link is a discussion of the effort by scientists to explore the concept of multi-dimentional space as it relates to a unified field theory and gravity.

The interactive diagram is a geometric dipiction of that space.

It is similiar to what I glimpsed when exploring the geometric constructs I made at the intuitive level.

Lacking the words and concepts I did my best to try and expain what I saw when I trirsected the angle and depicted the Billiard problem. It is related to a non-Euclidian geometry.


Hope this aids the discussion

Ed
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Ivan
Posted on Sunday, June 11, 2006 - 02:26 pm:   

SPACE-TIME AND GRAVITATION

Thanks Ed, for that article on multi-dimensional space as a unified theory and gravity. I think the idea of multi-dimensions of space have an origin in space-time, which is a manifold of three dimension of space volume with time as an additional dimension. If you read through the above links, you'll get some idea of the evolution of this idea. Often, because it is intuitively incomprehensible for us to think in four or more dimensions, the manifold is collapsed into lower dimensions, so that the four dimensional space-time is collapsed into three dimensional space, which we do understand. Or three dimensions can be collapsed into "flat land" of only two dimensions, for illustration. The article refers to these extra dimensions beyond our plane as "branes", also called String Theory, where space has these planes of dimensions. I am not totally comfortable with this, besides that I understand it dimly, because I see them as an "artificial reality" created by the constructs of the math using manifolds, which then translates into geodesics and tensors, and finally branes. Is it real? Or is it an artificial artifact of mathematical construct? Until we can prove this theory, falsifiably, the extra dimensions may only exist on paper, or in computer models, but may not be where we're really at. We know there are three dimensions, and we know time exists as a measure of change in this three dimensional universe. The rest of it, if we wish to believe, fine. I reserve judgment until we can test for it.

Gravitation may be much simpler than this mathematical construct, and may in fact be a natural elemental condition of reality, that "empty" space if full of gravity. Atoms then respond to this condition by being attracted to one another's "gravitation" as observed, per the ratio of attraction called Newton's Universal Constant G. My humble suspicion on this is that the "ratio of attraction" is not a universal constant, and rather is defined by the electromagnetic energy (light) and the atom's nucleus (proton) that results in a substantial modification of this "space gravity" function to where it is exceptionally weak here, but may be exceptionally strong elsewhere (neutron stars, black holes) so that we have only known of one dimension of gravity (here on Earth); it may already be different at Mars and beyond. This, however, a different G, is fasifiably testable, unlike the multidimensional space of branes and strings. The math is wonderfully fun, but the reality may be much more mundane, if this is so.

Keep us posted if you find anything on Gravity Probe-B, the "frame dragging experiment", I'd love to see the results!

Ivan
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Aladim
Posted on Tuesday, June 13, 2006 - 04:31 pm:   

Hello,

While I was reading the posts here I saw a post that helped me to remember the words of a friend of mine.

The post:
Richard Keating was surprised in 1972 that two atomic clocks traveling in opposite directions around the world, when compared with a third that stayed at home, showed slowing that depended on their absolute speed through space -- the vector sum of the Earth's rotation and airplane speeds --rather on the relative velocities of the clocks.

Now what I want to mention here.
I know from him that in the university his teacher said that if we rotate a gyroscope with the same speed in two opposite directions ,
in the first direction the resulting force will be less than the resulting force in case we rotate it in the other direction.
I told him that I think it happens becouse of the gravity force and the rotation of the earth and he answered me that the teacher said :
"The scientists still don't know why it is happenning"

I don't know is it true that the resulting force is different for two different directions and don't know do the scientists know the reason , but reading the post I've found something similar between these two experiments.

If you know something about the difference in the resulting forces becouse of the differnce in the direction of the rotation
please post some information.

Bye for now.

P.S. I think that the gyroscope is a beautiful tool for understanding gravity.
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Ivan
Posted on Tuesday, June 13, 2006 - 11:32 pm:   

GYROSCOPE effects.

Interesting idea, Aladim, on gyroscope's variant behavior, similar to Einstein relativity (Keating) traveling clocks in Earth orbit, when flying in opposite orbital directions. We know atomic clock oscillations vary with their velocities in orbit traveling through a gravitational field, where in opposite directions they will either slow more, or slow less, relative to a 'stationary' clock on Earth, i.e., in relation to their 'absolute speed through space'. This is the adjustment necessary for the Global Positioning System, the kind of GPS I use in my car's navigation system for when I am lost. If time were not adjusted, I'd get really lost! But otherwise it is accurate within a meter of my location, mostly, unless there are tall buildings around to deflect the satellite signal. I can't drive fast enough to throw it off, nor is my car equipped with a gyroscopic navigation, but the GPS satellite is gyro stabilized, I think. But I was never convinced that the 'absolute speed' is not merely a 'momentum transfer' from Earth's rotational mass to the traveling clocks, or gyros. I would think that gravitational transfer, which would translate into momentum transfer, might have something to do with it. I often wondered about this and the orbital precession of Mercury, being so close to the Sun, where this precession is most evident, but it declines (in proportion to the inverse square law) for all the other planets, so even Earth has some of this 'precession' effect, though very slight. It was the 'inverse square law' decline that made me think of gravitational momentum transfer in the first place. However, for this to work, Mercury's mass must behave as if it were lighter (per its volume density) if it moved as much as one arc second per century (I think), and be measurable. (I never did the math, but if my hunch is right, Mercury's 0.4 G equivalent inertial mass may fit right in.)

When I was a kid, I had two gyroscopes which locked together on their axis. I discovered if I spun one gyro clockwise, and the other counterclockwise, and then attached them together on their axis, the gyroscopic torque disappeared or was highly minimized (if the two rates of spin were not equivalent), which was always puzzling to me. I know the math describing torque (sort of know it) but I always took that to be merely a description of the forces involved, not really an explanation of what those forces actually are. But the two counter-gyro experiment led me to think that this 'torque force' was something transferable from one gyro to another, and hence why they canceled. But as to how or why gyroscopes would behave differently in opposite orbital directions, that is another puzzle again. Very interesting, maybe some more reading on this matter is required. Do you have any references, maybe some science papers that discuss this issue?


Here are some interesting readings from Wikipedia, always a nice place to start: :-)

Gyroscope

Ring laser gyroscope

Fibre optic gyroscope

Quantum gyroscope

Control Moment Gyroscope (CMG)

Is the Gravity Probe-B merely a highly polished version of a CMG experiment? Could that 'frame dragging' of (warped) space-time be but another version of 'momentum transfer' of planet's spin? I'm looking forward to seeing their results, can't wait! :-)

Cheers, Ivan
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Aladim
Posted on Wednesday, June 14, 2006 - 01:29 am:   

Ivan,

I have some nice books.50% of them can be downloaded through this link http://jazma101.multiply.com/journal/item/104.
I'll check in my collection for something that can help .

P.S. I can say for your navigation system that you can buy one MEMS(I guess) gyroscope chip from Analog Devices , Sony ...... take a microcontroller and using the adc your navigation system will work even in tunnels (if you use two axis gyro ). :-)
Gyros are great :-) .

P.S.2.
http://en.wikipedia.org/wiki/Image:Einstein_gyro_gravity_probe_b.jpg

It is a nice one.
I want to mention here that when you watch through a sphere the up/left corner converts into down/right corner.
It is very close to the Mobius strip.
It is a tricky part.
The planets are "spheres".
If the light comes from the backside of a planet becouse of it's gravity as I know it flips (they call it lens effect).So here is some sort of Mobius "flip" ( not Mobius loop/strip ) with a lot of "light" planes .Infact we have mobius loops and it is possible to see a lot of things flipped , but we must be far away from the planet and the planet must have large mass and little size.
I mean that it is possible the lens effect(for the light)to exist in a lot of cases.
I guess that a recursive experiment , using optical fibers or something like this will give some nice results but it will cost a lot of time,money and imagination.
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Anonymous
Posted on Wednesday, June 14, 2006 - 02:57 pm:   

Aladim,

Very nice work. You have identified a possible link to Mobius's Work, which I have also been exploring in advanced geometric concepts.

I believe that your ideas on light may at some level be related to the concept that AL Hazam was working with when he came up with his Billiard Problem. This particular problem was solved mathmatically by an Oxford Don, who translated that problem into a form that could be solved and depicted on an X / Y coordinate system. I have done a similar thing with compass and ruler as part of an exploration of the nature of the hypercube.

Again good work. You have opened a line of inquirery into experiments that may one day add information into the body of knowledge that the human race is amassing

Ed

Just as a note, while I lack the education and ability to express these concepts in terms of mathmatics due to a brain injury, I can draw them using geometry. The ability to do so is linked in my opinion to a way I process data as part of the way I have to compensate for the brain damage I have sustained. The processing center of my brain that deals with higher level math concepts was damged as a result of military service and what I used do be able to do with numbers and math I no longer can. By way of compensation the area of my brain that processes spatial information and geometry has taken up for those mathmatical parts that were damaged.

In a way I view it as compensation from God, like all such gifts its a double edged sword.
Being able to do it, but no having the ability to prove it mathmatically is very frustrating, but I have come to accept it.
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Humancafe
Posted on Wednesday, June 14, 2006 - 09:38 pm:   

Mobius Strip references.

These were brought to our attention by Ed Chesky, in prior posts above:

http://www.physlink.com/Education/AskExperts/ae401.cfm

http://www.rexresearch.com/davis/davis.htm

http://mathworld.wolfram.com/MoebiusStrip.html
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vlaladim
Posted on Wednesday, June 28, 2006 - 11:17 am:   

Hello guys,
http://physics.umbc.edu/Faculty/shih/Uncertainty_2.pdf

The interesting thing here is :

"There is no physical correspondence in classical
electromagnetic field theory, and more importantly, the physics behind the concept seems nonlocal."
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vlaladim
Posted on Wednesday, June 28, 2006 - 11:20 am:   

Please take a look at the other publicatins in :

http://physics.umbc.edu/Faculty/shih/
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Ivan
Posted on Sunday, July 02, 2006 - 02:24 pm:   

VENUS VS. EARTH ATMOSPHERES: Earth's atmosphere spins 'counterclockwise', while Venusian atmosphere spins 'clockwise', if viewed from their northern poles.

Data: Per Venus Data Sheet: http://www.space.com/scienceastronomy/solarsystem/venus-ez.html , Venus's mass is 82% of Earth's mass, given its diameter is 95% of Earth's. Venus is approximately 72% distance from Sun of Earth's distance. Also Earth spins in one ~24 hour day, while Venus has nearly no spin at -241 days of rotation for 225 Earth days orbit. NASA Venus data fact sheet: http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html

ESA's Venus Express confirms Venus atmosphere spins 'westward': http://www.space.com/scienceastronomy/060627_venus_vortex.html The animation in the article shows double vortex at south pole. By contrast, Earth's atmosphere spins 'eastward', so the two planets are dissimilar in their atmospheric spins, in that Earth's jet-stream defines our atmospheric spin. Venusian atmosphere spins 'as if' it were 'dragged' by Sun's spin, in the manner Mercury is 'dragged' in its precession by the transfer of momentum of Sun's spin; contrary to Earth's atmosphere which is in the direction of planet's spin. Both atmosphere, therefore, spin for opposing reasons. What does this mean?


Analysis: When I first theorized planetary spin ratios (see Jaszz* spin, July 28, 2004 - March 2, 2005) where I calculated spin ratios vs. planetary zero-point-gravity (ZPG) and zero-point-heat (ZPH) I concluded, tentatively, how these two, heat and variable gravity, are indicative of how planets spin. My goal was to show that within the orbits of a given planet's (variable) G and its relative interior 'black body' heat, there is a close relationship to how planets exhibit spin. The major anomalous planet within this model was Venus, so it never fit, except as a 'balanced' planet where its ZPH was so close to ZPG that the planet in essence had virtually not spin characteristics (it spins slightly retrograde at -241 days 'spin' per 225 days orbit). The 'spin ratios' were worked out on Sept. 25, 2004 (per above link) so Venus came in exceptionally close to its predicted SR. However, atmospheres were not addressed at the time.

Astronomers had ignored the possibility that Newton's assumed 'universal constant' G may not be a constant, but is a variable with distance from the Sun, as per the Axiomatic Equation, which showed up on a graph (Oct. 4, 2004, in Jaszz 'planetary spin' link ) so that Newton's G is relative to astronomical units (AU) at the rate of approximately 1G per 1AU (with minor adjustments for planetary interior heat). Venus at about 0.72 AU should exhibit about 0.72 G, which translates its inertial mass ratio (per Equivalence to G, see Oct. 9, 2004 ) to be Venus's local G mass = 6.25e24 (local) kg, vs. Venus (Earth's G) mass = 4.87e24 kg as now calculated, or about 78% of what it should be if G were constant, vs. 82% of Earth mass, as assumed now. But if this 78% is divided by the 95% diameter difference, we come back to 82% mass as measured.

Another calculation, though rough, is if Venus's diameter is 95% of Earth's (assuming roughly same planetary composition), its mass should be on the order of 5.67e24 kg (5.97e24 kg x 95%) vs. the now calculated (constant G) Venus mass of 4.87e24 kg. This implies roughly 16% greater density for Venus than Earth's planet density (5.67e24 kg divided by 4.87e24 kg). If we take the (variable G) calculation for Venus mass = 6.25e24 kg and multiply it by 84% (to account for ~16% greater density), we get 'density adjusted' mass = ~5.25e24 kg, which adjusted for 5% diameter difference is reasonably close to ~4.99e24 kg (vs. 4.87e24 kg). This may imply that astronomers had miscalculated Venus mass and density all along by using a constant G, and that in fact Venus is about 16% denser than Earth's mass, while it resides in an orbit of 0.72 AU, in a variable G of about 0.72. If so, then Venus's atmosphere is denser by comparison to its Earth equivalent, while residing in a weaker 0.72 G, and thus more susceptible to momentum transfer from the Sun's rotational moment of inertia. Therefore, if so, Venus's atmosphere (largely made up of heavy gases) should respond better to the Sun's spin ratio (in the absence of its planetary spin) and move as observed, clockwise (in response to Sun's spin) rather than counterclockwise, as viewed from the northern pole. It may also be implied that, given Venus's greater heat (nearly equivalent ZPH and ZPG) the planet's 'oceans' are airborne, which explains its very high density atmosphere and lack of liquid oceans. The atmosphere is Venus's 'ocean' in gas form.

Conclusion: Venus may not be as anomalous a planet as we think. All planets respond to the Sun's spin, though by the inverse square law, which makes it noticeable at Mercury (with measurable precession) it becomes negligible for the outer planets. (All planets revolve around the Sun in the same direction as its spin, while their atmospheres revolve around the planet is the opposite direction from Sun's spin, except for Venus.) The Sun's rotational transfer of moment of inertia to Venus's atmosphere may be a perfectly normal event, given its atmospheric density is higher, while it resides in a low inertial equivalent G, so the atmosphere is swept up by this momentum transfer to mimic the Sun's spin (clockwise rather than counterclockwise as for most other planets). This is a rather exciting process of discovery, if correct, because it means the variable G concept is better suited to understanding planetary behaviors than a constant Newton's G. It also is exciting because it better explains, with higher density, why Venus's atmosphere is so radically different from our own. In lighter G but heavier density, where molecules are less drawn to planet's surface as weight, Venus's 'ocean' is entirely airborne. This is a very exciting process of discovery in our planetary physics, when a variable G is applied, because it better explains why Venus's atmosphere spins the 'wrong' way, as it should.


Ivan

*(JASZZ stands for "j_-alexander-stransky-zpg-zph" - who early worked on this 'silly' idea.) :-):-):-)
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Ivan
Posted on Saturday, July 08, 2006 - 03:15 am:   

Different dimension of gravity?

Well, at least they're looking, knowing something is wrong with Newtonian-Einsteinian gravity. But like looking for love in all the wrong places, they fail to understand that gravity is in the atom. How the atom is formed, as an interaction between its nuclear strong force and its electromagnetic energy modifier, the remainder is gravity. And, surprise, surprise, it's different out there! :-)
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Ivan
Posted on Tuesday, July 11, 2006 - 10:39 pm:   

Inching closer towards the Black Hole.

In NewScientist article: Earliest black holes bent the 'laws' of physics, the article mentions this:

quote:

This might be because the black hole "swallows" the radiation generated as the hole gobbles up the matter around it, preventing a destructive explosion.


I see it a little differently, that 'black holes' are a function of canceled radiation on a point, so the extreme gravity generated there (per Axiomatic Eq) keeps it all together, so explosion is in fact impossible. Nor do I see black holes as a function of collapsed stars, since this is rendered nonsense when galactic center 'black holes' represent the mass of billions of suns. How did all those suns form and collapse in one place in such a short time? Silly! Especially true if this one is only about 1 billion years old, by Big Bang recconing, which itself is nonsense anyway. Modern astrophysics is at this point still a non-science, and will remain thus until we find how gravity is different out there. We're inching closer, but not there yet.

Ivan
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Ivan
Posted on Tuesday, July 18, 2006 - 09:49 pm:   

THE GREAT BIRTH AND DEATH OF GRB RADIATION

I have this idea, that the great Gamma-Ray Bursts we register in our satellite observations of the cosmic sky is actually two things, but we now do not see it this way. We know from observations where GRBs occur, since launching NASA's Compton Gamma Observatory put in orbit in 1991, that these GRBs are not from within our Milky Way Galaxy but come from very great distances in all directions of the cosmos. Earlier theories going back the the 1960-70s where these cosmic radiation bursts were first discovered (accidentally by the Vela spy satellites monitoring possible nuclear bomb tests), invoking Einstein's famous E = MC^2, it was calculated that they had to be close in within our galaxy, if the inverse square law of distant radiance was taken into effect, or else the mass would have been too large. However, with later works by Bohdan Paczynski, Stan Woosley, Meszaros, Cavallo,Goodman, Sehmi and Piran , and Sir Martin Rees, Royal Astronomer, it appeared that the only way these bursts could contain such power is if they were concentrated on a narrow beam pointed towards us. For this reason, though perhaps there are more such bursts per year, we only detect one out of 500 of those in any time; and since they fade so quickly, within a matter of seconds to days, they are extremely difficult to study and pinpoint. Some are "long bursts" while others "short bursts" of varying intensity, generating in excess of 1E^45 Joules of energy. All very mysterious, such immense energy, and thus far registered at immense distances from our Galaxy, on the order of billions of light years away. Why do they happen? What are they? Why so far away?

What bothered me first was that they were all so far away. This did not make sense to me. In the common parlance of current cosmology, they are far away because they happened long ago, sometime in the early universe after the Big Bang creation. But since I do not subscribe to this line of thought, in my thinking that cosmic light redshift is due to intense intergalactic gravity rather than Doppler expansion, no such 'creation' of the universe fits my hypothesis. Therefore, it must be from some other cause that accompanying 'afterglow' redshifts as observed. If gravity is the cause of distant light redshift, the logical conclusion must be that what causes GRB is gravity sensitive, meaning that the resulting collapsed massive star, or other cause, for the creation of a 'black hole' after a supernova is the phenomenon directly related to the redshift. In effect, if great gravity results after the event causing a GRB, then that same gravity is what holds the light back gravitationally, so as this gravity acts on the light, it 'slows' it down in the form of redshift. I am assuming two things here, one is that supernovae and GRB are related, and two that light traveling through space is as Einstein described it, a constant velocity of ~3E^8 m/s, so that any retention on this velocity shows up as altered wavelengths of light, or redshift. So our measurements of how far away these bursts occur may be off, if gravity is in fact holding back the light from the afterglow. An extreme case is where light is reduced to no wavelength, as from within a black hole, so it is invisible; while on the other extreme is light of such high wavelength, such as gamma and above, that travels unrestrained in intergalactic space. I suspect GRBs are of the latter, while the visible light their observable afterglows, something caused by the GRB's interaction with surrounding space gas and dust remaining from the explosion, is a phenomenon restrained by the resulting great gravity remaining after such a supernova. So GRBs may not be as distant as we now think, but could be much closer in, but retained by the great gravity remaining after the event. Just my opinion at this point, since we do not yet know with certainty that gravity's G can be different for different regions of space.

The second aspect of these bursts is the "long and soft" burst versus the "short and hard" bursts, which may be due to two unrelated events. My suspicion, and at this point it is all it can be, as most of theory regarding GRBs must be, is that one grouping results from supernovae, which is an effect of exploding dying stars. But the other grouping may be from birthing stars, so their observable results are different. According to Wiki's Gamma ray burst, the current theory is that these result from collision of dense magnetostars, or from collisions of material falling into black holes, or from the death of a massive short-lived star within the distant birthing galaxy of new stars. I am uncomfortable with that idea. Though I think the 'death stars' will generate such a burst of energy as they go supernova and explode, which may account for one type of GRB, I do not believe these collapsed stars, or colliding stars, making 'black holes' are really what is happening. Especially given that these GRBs seem to show up in young galaxies made up of newly formed stats, or nursery galaxies. So the time sequence is suspicious. Why aren't they happening now closer to us? Rather, I suspect that some of these bursts are actually the first birthing of a galactic black hole, which may come in stages, where the newly formed stars are arranged such so all their ambient light find a common point, where these wavelengths of light cancel, and start the 'explosive' burst of radiation resulting from a newly formed black hole. This makes more sense, as these are happening in birthing galaxies, and whatever interaction results from this black hole birthing, then manifests as super powerful jets of electron-positron energy thrown off that event. As to whether such birthing causes long or short bursts, at this point, I cannot know. This would require further observation. But I do think that in addition to stars dying and giving off intense Gamma radiation, stars birthing will also give off such radiation, but only when their combined energy is sufficient to cause the birthing of a new galaxy, what will accrete around the newly formed black hole. Of course, this is all predicated on the Axiomatic Equation's hypothesis, that where light cancels, gravity becomes extreme. If this is shown in the future that gravity is resultant inversely to the electromagnetic energy received by the baryonic mass there, then a complete absence of EM energy, such as where it cancels on a point, should release total gravity. Conversely, where the star energy is too great, where it is burning up its heavier atoms, then the EM reaches a breaking point where gravity no longer holds the star together, it goes nova, and then in a supernova explodes to seed the universe with these newly created heavier elements.

My universe is a simple place. Gamma-ray bursts are redshifted from inception by the very great gravity they leave behind, either in the form of a ' cold' dead star, or in the gravitationally extreme black hole, so these hold back the light; because light always travels at a constant velocity, the result is a redhsift to a longer wavelength. But this is not to say that redshift means the event is at great distances, merely that at present we have no idea how far they are, though there are other ways to measure distance. One such method is discussed in "An Alternative View of SN1987A", where the 'light echo' is used to determine distance (see sections 8-16 for description). However, this may not yet have been done for GRBs, since the paper only talks about one specific supernova, SN187A. The second simplicity is in that if stars give off Gamma-ray bursts in their death throes, as they are about to die and cast off their newly generated heavy elements into the cosmos, which gives off a short and powerful radiation burst, which I suspect is the short one. The long burst, I suspect, is the newly created black hole type. A similar burst may be given off in the event where a star is birthing, not in the individual star's birthing necessarily (though this may happen as a result of intense gravity pulling together space molecular gas with such force that it ignites fusion), but mainly in the birthing of the newly formed galaxy around a newly formed black hole. That black hole's creation, a function of canceled light on a point within the ambient star generated energy, creates a massive gravitational event, with its radiation burst signature. Then, the black hole will shine like a light beacon out into the cosmos with its electron-positron jets shooting out both ends of its axis, which is what we register here as quasars. But that initial black hole event may cause an excessively powerful burst, which fades over the days, while a supernova event may be short lived, except for the afterglow surrounding the exploded star. In either case, the events are short lived in that they soon cease to affect the ambient gases released by the event, so their 'afterglows' fade quickly. All we can really observe at this time, except for the Gamma-ray burst, is the light coming from these afterglows, so we are only getting half the picture. In the future, should our instruments be better equipped to measure the actual gamma radiation, then perhaps we will have a better fix on this. But it is not technologically feasible yet, since Gamma rays are at too high a frequency to be examined with current technology. So in my simple universe, stars give birth, are announced to the cosmos as new galaxies with a newly birthed black hole, and then at the ends of their lives, they once again announce their death to release all their creation of elements into the cosmos, all this is done with Gamma-ray bursts. Rather nice system, if this is so.

I think we should look for simplicity rather than complexity in our universe, since it already all worked itself out with extreme economy, as a very simple place. Rather than confuse the universe with extremely complex theory, we should look for this ultimate Occham's razor at work. So no need for star collisions, or magnetostar collisions, nor neutron star collisions, nor colliding black holes, to cause Gamma-ray bursts, but the simple birthing and dying of stars. The proof of it all is that it is understandable by simple minds like ours. In fact, the fact that we are here and born of the materials of the stars, shows how much work the universe had already done to make itself simple. It is really all elementary. :-)


Ivan
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Ivan
Posted on Friday, August 04, 2006 - 10:33 pm:   

UNIVERSE IS BIGGER AND OLDER THAN HUBBLE CONSTANT SAYS?

Here's something interesting, the Big Bang is being pushed back, and out, now 15.8 billion light years.

http://www.newscientistspace.com/article/dn9676-big-bang-pushed-back-two-billion -years.html

Of course, it could also be that "there was not Big Bang" at all, just a figment of our Hubble induced, Doppler redshift imagination. If redshift of distant cosmic light is from other causes, such as "gravitational redshift" due to very high gravity G in deep intergalactic space, then the univere is much much much bigger and older than anything we can imagine. Imagine it infinite? Big Bang is dead.

Ivan
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Ivan/timelight
Posted on Sunday, August 12, 2007 - 03:42 pm:   

On the 'instaneousness' of light photons traveling through space.

Nebula NGC 2392.jpg
Hubble's Nebula NGC 2392 (interactive)

"What is the universe like for a photon?" - tangential discussion, where the OP asks:

quote:

How does the universe appear to a photon ? I understand that light is not subject to time (meaning time doesn't flow at light speed) therefore :
-does zero time mean zero distance ? to a photon, is the universe all in one point ?
-does zero time means zero change ? to a photon, is the universe always the same ?
-if I was a photon, would take me zero time to reach the other side of the universe or would it only appear that way to an outside observer while a "clock" is still somehow ticking for me ?



This is an aside for the above discussion on BAUT forum, as to what does a photon of light 'experience' as it travels from its source (not a discussion in which I participated). But I think the question merits examination, because the relativistic nature of light at constant velocity c, per Einstein's second postulate of SR, makes it an interesting phenomenon in the universe's constitution.

First of all, a photon can appear to be at two separate places at the same time. This is true both in the case of gravitational lensing, where the background image magnified by large foreground mass will appear in multiple images around it, as well as distant light seen from two places simultaneously. So it is not merely the life of one photon, but a multiple version of itself. This is also why the double split experiment with light will yield spectrographic lines, a very useful tool in astronomy and physics. Light, as a continuous stream of photons, does not exist at any one point as that photon alone, because it can be split, so that the photon must carry with it 'information' able to reach beyond its particular existence, in a kind of 'spooky action' at a distance effect. What comes to mind is that when a photon of light is released from its source, it travels not as a S-wave, nor a particle per se, but in fact as a P-wave; so that anywhere along that wave, from any direction in space, there will be information locked inside that wave, traveling at light c, in 360 degrees, or some portion thereof if blocked. This means, of necessity, that intercepting the P-wave anywhere along its perimeter will show up as a photon of light, or act like a particle, hence if intercepted simultaneously at different places along the wave, multiple photons can be seen simultaneously.

Why is this significant? Whether or not 'time' exists for a photon is nearly irrelevant. From a relativistic point of view, if light c is used as a unit of measure, then time does stand still, and distance traveled per unit of time is one. In effect, 1t*c=d, or c=d/1t, or 1t=d/c. But how relevant is this? What is more relevant is the 'information' carried by this equation, that at any moment of time photons carry information about the state of energy along the circumference of the P-wave anywhere along that circumference. That is important, because if you intercept that circumference anywhere along its curvature, you get a unit photon, no matter from what angle it is viewed (as long as it is not obstructed but visible). This may be the 'spooky action' light carries with it, that what is 'information' anywhere along that curved P-wave is available instantaneously on any other point of the wave, so in effect, along that wave time does stand still, or it is instantaneous. But this is along its curvature only, not in the line of sight where that same photon experiences the same parameters of time and travel as does anything else, which is why distance is measurable using light. Its relativistic features can be distilled fully by its wave-shift, either red or blue, if gravitational redshift is eliminated, though for cosmic light that is false. So what a photon carries in itself is as true in our line of sight as it is at 90 degrees from it, if along the P-wave carrier, which translated means seen from anywhere in the universe such light is visible, it will show the same. Now, this is discounting the Big Bang idea of an expanding universe, since light traveling from 13.7 billion years ago is likewise traveling in every direction simultaneously, which is what we see when looking back 13.7 billion light years. Therefore, 13.7 billion light years in the opposite direction from where light visibility fails us (the assumed origin of Big Bang) there is another observational 13.7 billion light years, should anyone there be able to use their telescopes to see the same. More interesting still is that that same observer 27.4 billion light years away from us would see the same thing! Information along the P-wave was not lost, though it is 180 degrees away from us.

Relativistically, time is standing still for us, observationally speaking, when we look back 13.7 billion years, because we are seeing an event 13.7 billion light years away as it happened then, if t *c=d, then so is c=d/t, light distance traveled per second. Consequently, using light along any distance gives us a t=d relationship (if c=1 is applied), a kind of 'time machine' to observe phenomena that took place at some point in time. However, this is a trick of light, because in using light c as distance, from whatever reference frame we wish, adjusted for relativistic factors, our measuring rod is defined by (assumed) constant velocity, which of necessity 'freezes' time for us anywhere along the line of sight. This is by definition, since we equated c=d=t, and any distance measured in light years, or light seconds, gives us both time and distance of the observed. But that information exists all along 360 degrees of the P-wave, if unobstructed to line of sight, simultaneously anywhere in the universe. From a photon's point of view, this is by far more relevant than whether or not its time is standing still. In fact, along the curved line of information in its P-wave, time does stand still, but only along the curvature of the wave. The photon will reveal its carried information anywhere in the universe from any angle simultaneously, which means its time may be simultaneous, but obviously not its distance. What is intriguing about this information is that perhaps in some future time, we will be able to access it, so that no matter where we are in relation to the signal generated, the reader will get that information simultaneously, which means there would not be the time delay of light traveling at c=3E+8 m/s, but information would be accessible tangentially along its P-wave in no time at all.

But this is still far off into the future, because other than at very short distances where we find 'spooky action' for polarized light, we do not know how to 'read' it along its full P-wave circumference. Theoretically, it should be possible. Tongue in cheek here, but if you want to talk to someone 13 billions light years away, no problem, just 'hitch' onto a light signal coming in 360 from 6.5 billion light years away, and use it as a pathway for instant communications. :-) "Can you hear me now?.."

Ivan
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Ivan/bleep
Posted on Tuesday, August 14, 2007 - 12:52 am:   

What the bleep do we know?"

I'm watching "What the Bleep do we know" and it is interesting, but packaged to fill your brain with (unsolvable) conundrums. It appears about 80% fantasy and imaginary ideas about the world, or our place in it, in how the brain processes information, with about 20% scientific substance. These conundrums are easily resolved if one thinks of the universe as already 'processing' all this information in terms of itself (what I called 'interrelationship' in my philosophy, see ch. 2-5) and we are merely 'observers' within it. So reality does exist, but on its own terms, not ours. We know this intuitively because we cannot change it in our minds, except at some very low level through self healing, but reality persists upon being itself. What we observe is then just that 'interrelated' totality of existence where all possibilities that exist are defined by all the other possibilities that exist, and the end product is the universe as it is, for itself. Catch a wave of light, and it appears a particle, observed simultaneously in two places, big deal! It's in the wave. The fact that we can interact with it, really in our brains and bodies, is something quite magical indeed. Can 'time' go backwards? Only in our mathematical imagination. So who are we? We're lucky. :-)

Anyway, it's fun watching it, but very low level philosophy, more entertainment for me than a challenge. In fact, I used a Quantum Mechanics equation, de Broglie's, E=hf, matched up with a relativistic equation, Einstein's, E=mc2, to show how within our solar system Newton's gravity G changes with distance from the Sun, very close to what the Pioneer Anomaly shows... but what the 'bleep' do I know?

More to the point, how is my ratatouille doing? I'd better go and check, since my brain is telling me it's almost ready. :-)

I'll watch the rest of it, but gotta eat first, more bleepin' important for now.

Ivan-bleep

[Ps: somewhere about three quarters into this flick I realized that the authors were purposefully blurring the difference between subjective and objective reality, so I lost interest and fast fowarded it to the end, a bore, but that was my choice, :-) it's just modern day mythology, low level pop philosophy, no big deal but fun otherwise, entertaining.]
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Anonymous
Posted on Tuesday, October 09, 2007 - 01:17 pm:   

The following geometric solution to a complex problem is posted in the hope it may assist others in the quest to expand the frontiers of human knowledge.

Whether or not this is a solution to this problem is open to debate. To prove it one way or the other would take much work by a mathematician or team of mathematicians. On the surface it appears to be reasonable solution to the problem presented.

If it found to be incorrect it is the closest solution to this problem to have been found to date and as such still offers something in terms of contributing to human knowledge.

Regardless of all of this it is an elegant proposed solution to a problem that is breathtaking in its simplicity.

Posted for the man that created it by a friend.

It was a labor of a lifetime.

billiardproblem3.jpg
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Anonymos
Posted on Wednesday, October 10, 2007 - 10:08 pm:   

Below is a copy of the same diagram created using the GeoGebra version 2 geometry software program.

The Program is freeware that allows the user to construct compass and ruler constructions.

The software package confirms creation of a perfect isosceles triangle using only compass and ruler
within the confines of the Billiard Problem

652.png


Attached below are the geometric construction steps for the problem

Given two points on a circle draw an isosceles triangle with the lines joining these two points as base
and a point on the circle as apex.

Construction:

Given the radius of a circle C with radius r.
Points A and B are given.

With A as center draw circle C1 with radius r. This would cut the given circle at points A1 and A2.
Select the point, which makes B lie in the arc.
That is select A1 so that A1 B A is an arc of the given circle.

Draw circle C2 with A1 as center and radius r. This circle passes through the center of C.
[Proof: A1 is on C and thus the distance between the center of C and A1 is r. Hence the circle with A1 as center
and radius r passes through the center of C.]

Draw another circle C3 with B as center and radius r. This circle cuts circle C at B1 and B2.
Select B1 such that B1 A B is an arc of the circle.

Draw a circle C4 with B1 as center and r as radius. This circle also passes through the center of C.

Call the center of C as point X.

Call the intersection of circles C2 and C4 other than X as Y.

The quadrilateral AXBY has sides AX, XB, BY, YA of length r.

AB is a diagonal.

XY is the other diagonal.
Let the intersection of AB and XY be Z.

Consider the triangles AXY and BXY. These are mirror image of each other along XY as AX = BX = r
and AY = BY = r. XY is common. Hence angle AXY = angle BXY.

The triangles AXZ and BXZ are congruent. AX = BX = r; Angle AXZ = Angle BXZ; side XZ is common.
Therefore AZ = BZ. Z is a mid point of AB. Angle AZX = Angle BZX = 90 degrees.

Thus the line XZ is a perpendicular bisector of the line AB.

Extend the line XZ to intersect C at T1 and T2.

The triangle A T1 B is an isosceles triangle. So also the triangle A T2 B.

QED.
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Ivan/golden mean
Posted on Wednesday, October 10, 2007 - 10:28 pm:   

Is this the Golden Mean?

Ed, you're briliiant! Looking at it visually, it looks like you found the Golden Mean ratio again, where those points intersect inside the triangle, about 1: 1.619 ratio, as per the Egyptian pyramids:

250px-Mathematical_Pyramid.svg.png
A regular square pyramid is determined by its medial right triangle, whose edges are the pyramid's apothem (a), semi-base (b), and height (h); the face inclination angle is also marked. Mathematical proportions b:h:a of and and are of particular interest in relation to Egyptian pyramids. (interactive)

I'm only doing a visual on it, a relationship of areas above and below the point, but it looks right! :-)

Ivan
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Anonymous/Problem Solved
Posted on Thursday, October 11, 2007 - 10:42 pm:   

Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains the important problem known as Alhazen's problem. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point.

This leads to an equation of the fourth degree.

This eventually led Ibn al-Haytham to derive the earliest formula for the sum of fourth powers; and by using an early proof by mathematical induction, he developed a method for determining the general formula for the sum of any integral powers. This was fundamental to the development of infinitesimal and integral calculus.[21]

While Ibn al-Haytham solved the problem using conic sections and a geometric proof, Alhazen's problem remained influential in Europe, as later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l'Hτpital, Isaac Barrow and many others attempted to find an algebraic solution to the problem, using various methods including analytic methods of geometry and derivation by complex numbers.[1] Mathematicians were not able to find an algebraic solution to the problem until the end of the 20th century.[15]

http://en.wikipedia.org/wiki/Ibn_al-Haytham#Geometry

They said it could not be done, they laughed at him, ridiculed him and then with a few twists of a compass he solved the problem.

The United States Military Intelligence Corps Hall of Fame is missing the picture of one of the Greatest Code Breakers in History.

From the desk of the Former Commander, National Ground Intelligence Center, Colonel USA (RET)

I served with him in peace and war. He never let us down.
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Anonymous
Posted on Monday, October 15, 2007 - 06:12 pm:   

The following is a graphic depiction of the trisection of 90,180,270 and 360 degree angles.

The accuracy of the trisection is confirmed by the GeoGebra version 2 Freeware software application.

This solution is tied to the generation of a dodecahedron.

A link to a math site that discusses the dodecahedron is attached.

http://mathworld.wolfram.com/Dodecahedron.html

This trisection solution is tied to the solution to Alhazen's Billiard Problem posted above.

That solution was created by a Master Cryptographer that has been recognized by some of the most powerful military personnel in the world as one of the most brillient analysts in the United States Deparment of Defense. This analyst is reponsible according to official DOD records for development of new cryptographic systems, decryption of Soviet era codes and signals intelligence, leading to the resconstruction of Soviet/WARSAW Pact war plans, Iraqi Bath Party Intelligence Networks in support of Operation Iraqi Freedom and a host of other military operations around the globe.

The dodecahedron itself is a highly advanced and complex geometric object. Included in its makeup is the Golden Ratio, as discussed by another previous poster.

This solution can be reproduced and independently validated.

But for the current President of the United States, former director of CIA, and former Secretary of Defense this master cryptographer would still be serving his nation in the Global War on Terror. Instead he has moved into the private sector where he has made a comfortable life for him and his family.

Anonymous

Trisection Cardinal Angles
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ANON
Posted on Monday, October 15, 2007 - 09:13 pm:   

Even though it is impossible to trisect general angles, there are some exceptions to this rule. An exception is angles that are multiples of nine. For example, one could trisect an angle measuring 90 degrees, such that the angle measure of each new angle is 30 degrees. Another way that the University of Wisconsin – Green Bay defines angles that can be trisected using a compass and straightedge is as “surds” or “numbers that can be expressed as combinations of rational numbers and square roots”. Therefore, it is possible to trisect angles of certain degree measures using only a compass and straight edge; but in general angles cannot be trisected using this method.

The following is posted not to detract from the diagram above but to support its findings.

The generation of a hexagram as a result of this effort marks new ground in the study of this problem. Along with that of the Billiard Problem posted above. The linkage to the Golden Ratio in this discovery is extremely interesting.

What is depeicted here is a simple elegant way of trisecting surds,or “numbers that can be expressed as combinations of rational numbers and square roots."

Again the linkage to the dodecahedron and hypercube as an outgrowth of this is fascinating and well worth exploring.

ANON
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Anonymous
Posted on Monday, October 15, 2007 - 09:24 pm:   

The following diagram more clearly indicates the linkage between the generation of a dodecahedron and the trisection of cardinal angles or surds.

Trisection Cardinal Angels3
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Ivan/dodecahedron
Posted on Tuesday, October 16, 2007 - 01:01 am:   

Dodecahedron image, from Wolfram's math.

DodecahedralGraph_700.gif
(interactive)

Thanks Ed, Ivan
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Anonymous
Posted on Tuesday, October 16, 2007 - 02:14 pm:   

Attached below is clarification of the linkage between the trisection of the angle to the surds and the generation of a hypercube.

The squared depicted in the diagram below is a result of the trisection of surds.

Its dimensions are linked to the dodecagon in the diagram. The square through further geometric work can be expanded to replicate a cube and from there the hypercube.

Trisection Cardinal Angles3
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Hypercube Link
Posted on Tuesday, October 16, 2007 - 03:35 pm:   

The first stage of depicting the linkage to the hypercube is posted below.

The cube in the diagram appears distorted due to the limits of a 2 dimentional display.

Trisection Cardinal Angles4
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Anonymous Light Speed
Posted on Wednesday, October 17, 2007 - 05:01 am:   

It is clear from the diagrams above that a linkage to the hypercube has been established. The hypercube itself is linked to the Theory of General Relativity and the speed of light. As this geometry is explored it is important to look back at this theory and its key concepts to constantly test them for validity. Such is the scientific method.

Statement: "The speed of light c is a universal constant, the same in any inertial frame".

This postulate is the nub of special relativity, and much of the content of these pages is concerned with exploring its paradoxical consequences, starting with the next page, The Paradox of Special Relativity. Amongst other strange consequences, the postulate implies that the time dimension behaves in many ways as if it were an imaginary spatial dimension. Watch this 4D spacetime hypercube rotate (47K GIF movie).

Measuring speed requires being able to measure intervals of both space and time: speed is distance travelled divided by time elapsed. Inertial frames constitute a special class of spacetime coordinate systems; it is with respect to distance and time intervals in these special frames that the speed of light is asserted to be constant.

In general relativity, arbitrarily weird coordinate systems are allowed, and light need move neither in straight lines nor at constant velocity with respect to bizarre coordinates (why should it, if the labelling of space and time is totally arbitrary?). However, general relativity asserts the existence of locally inertial frames, and the speed of light is a universal constant in those frames.

In 1983, the General Conference on Weights and Measures officially defined the speed of light to be
c = 299,792,458 meters/second ,
and the meter, instead of being a primary measure, became a secondary quantity, defined in terms of the second and the speed of light.




The Principle of Special Relativity
Statement: "The laws of physics are the same in any inertial frame, regardless of position or velocity".

Physically, this means that there is no absolute spacetime, no absolute frame of reference with respect to which position and velocity are defined. Only relative positions and velocities between objects are meaningful.

It is to be noted that the Principle of Special Relativity does not imply the constancy of the speed of light, although the postulates are consistent with each other. Moreover the constancy of the speed of light does not imply the Principle of Special Relativity, although for Einstein the former appears to have been the inspiration for the latter
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Quantum Gravity Geometry
Posted on Thursday, October 18, 2007 - 05:36 am:   

Quantum geometry
From Wikipedia, the free encyclopedia

In theoretical physics, quantum geometry is the set of new mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at very short distance scales (comparable to Planck length). At these distances, quantum mechanics has a profound effect on physics.

Each theory of quantum gravity uses the term quantum geometry in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions, minimal possible distance scale, and other effects that challenge our usual geometrical intuition. More technically, quantum geometry refers to the shape of the spacetime manifold as seen by D-branes which includes the quantum corrections to the metric tensor, such as the worldsheet instantons. For example, the quantum volume of a cycle is computed from the mass of a brane wrapped on this cycle.

In an alternative approach to quantum gravity called loop quantum gravity (LQG), the phrase quantum geometry usually refers to the formalism within LQG where the observables that capture the information about the geometry are now well defined operators on a Hilbert space. In particular, certain physical observables, such as the area, have a discrete spectrum. It has also been shown that the loop quantum geometry is non-commutative.

It is possible (but considered unlikely) that this strictly quantized understanding of geometry will be consistent with the quantum picture of geometry arising from string theory.

Another approach, which tries to reconstruct the geometry of space-time from "first principles" is Discrete Lorentzian quantum gravity.

http://en.wikipedia.org/wiki/Quantum_geometry
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Fifth Dimension of Gravity
Posted on Thursday, October 18, 2007 - 07:08 pm:   

http://theory.uchicago.edu/~smaria/lisa.pdf

A very good briefing on the multidimensional aspect of gravity.

It takes the concept of gravity to the fifth dimension.
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Ivan/zeropoint grav
Posted on Thursday, October 18, 2007 - 10:59 pm:   

Zero-point Energy and Quantum Gravity at the Planck Scale.

400px-First_Gold_Beam-Beam_Collision_Events_at_RHIC_at_100_100_GeV_c_per_beam_recorded_by_STAR.jpg (interactive)
Ultra-high-energy collisions of particles in a particle accelerator, gold ion collision on the RHIC, Brookhaven


Thanks Quantum Geometry, and Anon-Light Speed, for interesting ideas. In the Wiki on Zero-point Energy it describes this as:

quote:

In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. The concept was first proposed by Albert Einstein and Otto Stern in 1913. The term "zero-point energy" is a translation of the German Nullpunktsenergie.


Planck's formula for this zero-point energy is: E = 1/2 h-bar times frequency, where h-bar is Dirac's constant defined as h-bar=h/2pi, and where the Quantum field theory says every point in space is the space vacuum infinite zero-point energy. However, this is not clear if this energy is the same as electromagnetic energy or space vacuum gravitational energy. So the question remains as to whether Quantum gravity, which one would expect emanating from this zero-point, is the same thing as zero-point energy, as an attracting force, or something different, as a repulsive force. For example, from same article, the Gravitation and Cosmology describes it as:

quote:

In cosmology, the zero-point energy offers an intriguing possibility for explaining the speculative positive values of the proposed cosmological constant. In brief, if the energy is "really there", then it should exert a gravitational force. In general relativity, mass and energy are equivalent; either produces a gravitational field.


Is this energy absurdly large, of near infinite proportions, or something closer to zero, like the cosmological constant? It says further:

quote:

One obvious difficulty with this association is that the zero-point energy of the vacuum is absurdly large. Naively, it is infinite, but one must argue that new physics takes over at the Planck scale, and so its growth is cut off at that point. Even so, what remains is so large that it would visibly bend space, and thus, there seems to be a contradiction. There is no easy way out, and reconciling the seemingly huge zero-point energy of space with the observed zero or small cosmological constant has become one of the important problems in theoretical physics, and has become a criterion by which to judge a candidate Theory of Everything.


But if it is closer to the cosmological constant, approximating the Hubble constant for expanding space (if it is truly expanding as observed), then this means at the Planck length zero-point becomes a repulsive force rather than gravitationally attracting. What a dilemma! What is happening at the Planck length?

Can we even imagine what the geometry at the Planck scale, which is L = 1.616E-35 meters, if this tiny space packs the energy scale of around 1.22E+19 GeV, which is an absurdly high number. However, when I figured space vacuum energy, I came up with an even more absurd number, where E = 116.1E+40 KeV (same as 116E+26 GeV, for comparison, even higher than Planck's), which is also in Joules as E = 186E+24 J (about 2pi times mc^3), all very large numbers. How can so much energy be packed into a space so small, where Heisenberg's uncertainty principle operates, and still make sense in terms of physics, or geometry? I think this is the most exciting part of the Quantum gravity vis a vis Zero-point energy quantum field of discovery, because the understanding of this powerfully obscure point may in fact be the key to unlock the Theory of Everything. The answer may very well be a Quantum physics mechanism operating at the Planck's length, which might mean that gravity at this zero-point equivalent length is perhaps enormous, and that Quantum gravity is extremely powerful there. How powerful? It would approximate galactic 'black hole' proportions, where the gravity equivalent energy is of those high orders of magnitude for E shown above, anywhere from 1.2E+19 GeV (Planck's) to 1.2E+28 GeV (mine). What is happening here?

First of all, we know theoretically that at the Planck scale of the Compton wavelength (about 4 Χ 10-13 meters), the Schwarzchild radius is at about the Planck length (1.616E-35 meters). We also know the electron radius is about 3 x 10-15 meters (much larger than Planck length), and that at these miniscule dimensions the quantum theory uncertainty principle applies, or as this John Baez article says:

quote:

We can then work out how big a black hole we need for its Compton wavelength to equal its Schwarzschild radius! This sort of black hole will have mass about equal to the Planck mass, and radius about equal to the Planck length.
What does this mean? Well, remember that the Compton wavelength of a particle is the length scale at which quantum field theory becomes very important in describing it. So the Planck length is the size of a black hole for which quantum field theory becomes very important. Hawking has predicted that black holes of any size emit radiation due to quantum-field-theoretic effects - the bigger the black hole, the less radiation. His calculations treat the black hole classically and only use quantum field theory in treating the electromagnetic radiation. For a black hole about as big as the Planck length one would expect this approximation to break down drastically.



Now putting together the above, if we interpret the Schwarzchild radius equivalent to the Planck length, when employing the Compton wavelength of the electron, which means at the Planck scale we get 'black hole' type gravitational energy equivalence (not as radiant electromagnetic energy but as gravitational energy), then where the electron energy ceases to operate on such a small scale, a vast reservoir of gravitational energy results. But why don't we see this in our experimental evidence? There may be two reasons for this: 1. We do see it as a 'micro black hole' created in the Large Hadron Collider when gold ions collide, at least for some fraction of a picosecond; and 2. We do not see it evident in the Casimir force, or van der Waals force, because we are taking these measurements within the all powerful solar energy in which our planet resides, which includes all wavelengths from infrared to microwave to gamma, and to nutrinos, so we never effectively shield our experiments from these solar rays. Therefore, the only time we get clue to these enormous gravitational 'black hole' like forces is when either the uncertainty principle kicks in the Planck length, where light energy becomes disoriented and ineffectual, or in a gold ion collisions on the RHIC, both of which approximate what happens at the Planck length's Schwarzchild radius. The other time we see this enormous gravity is from astronomical observations of galactic black holes, though this is still undermined as to whether these are 'naked singularities' or spinning. Work done on Zero-point energy by Haisch and Rueda seems to indicate that the QM zero-point field is filled with a near infinite energy, or to quote:

quote:

The zero point field can be thought of, roughly speaking, as a superposition of electromagnetic waves with random phases and directions, with a power distribution proportional to the cube of frequency, i.e., 1/2 h-bar times frequency per normal mode. Since this spectrum diverges, that implies that there is an infinite amount of energy at every point in space (as does conventional QM for different reasons), a cutoff frequency on the order of the reciprocal of the Planck time is often introduced in principle. Planck's constant then appears as a scale factor for quantum fluctuations in the zero point field.


Where does this 'cube of frequency' reside in the Planck scale, or does physics simply break down at that point? We cannot isolate ourselves sufficiently from the Sun's powerful energy output to test it here, so all that is left over from this immensely powerful gravitational zero-point force is the very weak Casimir force, for example. And this is the dilemma, in my opinion, as to why we are unable to confirm this immense energy locked inside the space vacuum, because it is not the same space vacuum that exists inside a galactic black hole, nor the same which exists for a picosecond in a Relativisitic Heavy Ion Collider, nor can we go outside our galaxy to test for the space vacuum density out there. This is where we are stuck at present, and why I think Quantum gravity, which exists at the Planck scale, has proven so illusive.

Now, there is one other dilemma, and that is the cosmological constant, which approximates the Hubble constant for 'dark energy' expansion of space. I'll be brief, because this discussion deserves another long explanation, but here is what I think is happening. The vast cosmic distance through which light must pass on its way to becoming observed by our instruments on Earth is filled with space vacuum zero-point gravitational energy. This means space gravitational Newton's G is orders of magnitude greater than on Earth (about 5 orders greater) which has the effect of gravitationally redshifting light by the time it comes out of the long well of space to arrive here. Because this redshift approximates the Hubble constant, and is currently understood as a Doppler like expansion of inter galactic space, we then conclude (erroneously in my opinion) that there exists a 'dark energy' pushing space apart. There is the added factor that some believe the vacuum energy may be reversed to repel instead of attract (leading to all sorts of inventive ideas of levitation, though none work), and that this repelling force is what causes 'dark energy'. For this reason, some have theorized that the cosmological constant is the same as the zero-point energy, where it approaches zero rather than of high magnitude, such as evidenced in the Casimir force. However, I believe this is wrong logic, and there is no space expansion, nor is the Casimir force a very weak force, nor can it be reversed into a repelling force. In fact, I suspect that if the Casimir force were measured at the Kuiper belt or beyond, where G is much higher than here, it would prove to be a greater force. Or, put another way, if we could measure for zero-point energy out there, where electromagnetic energy density is very low, and G very high, we would discover it to yield a higher reading than on Earth. In effect, the reason we have a weak operating space vacuum force here, at about the cosmological constant, for our experimental evidence, i.e. Casimir, is because we are in a very low G region of space. And the coincidence of the Hubble constant being equivalent to this very weak reading is misunderstood, of necessity because of this high solar energy and low G, but it also is coincidental with generating a light redshift for very great intergalactic distances with the difference of G being so much higher out there.

So what do we have here, as it applies to Quantum gravity? At the Planck scale, Quantum gravity is very great, or equivalent per radiant electromagnetic energy at about the level of E = mc^3. But because we cannot enter the Planck length with our instruments, nor can we exit ourselves from the powerful solar influence under which our space vacuum exists in Earth's region, we are forced to conclude that this Quantum gravity either does not exist, or is very weak. In fact, I suspect it is extremely powerful, more like what we see around the galactic 'black hole', and this immense gravitational energy can at present only exist for an extremely short period of time, in picoseconds. If we ever manage to shield the experimental space vacuum from the Sun's powerful energy density output, we could then find a way to tap into this immense Quantum gravity. But for now, it exists only theoretically inside the Schwarzchild radius of the Planck length, or what shows in RHIC for picoseconds.

I suspect the answer to these dilemmas are very simple. All we need do to tap into the very high gravitational energy of the space vacuum is to cancel out completely all the electromagnetic energy present here, the Sun's, and thus recreate the same very high energy of the Quantum zero-point at the Planck scale.* Then we could recreate in the lab this...

329px-BlackHole.jpg

... and use it. :-)


Ivan

*[This will require great deal of experimentation to test for best effects, but my intuition hunch is that such elimination of solar energy can be achieved, where all lambda of energy cancel, in a perfect sphere filled with a partial vacuum of ionized gas put into very fast spin, which will recreated conditions necessary for a continuous Planck-scale micro-black-hole at its center.]
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Le Chef
Posted on Sunday, October 21, 2007 - 01:29 pm:   

Einstein's GR on trial?

"Ladies and gentlemen of the jury, drop that ball-and-chain GR" says judge.

nz374.jpg

Dump Einstein and General Relativity, and go with Humancafe's G-flat.

Variant gravity makes more sense, and lighter on the feet too. :-)


le chef 'lite'
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Ivan/Riemann field
Posted on Wednesday, November 14, 2007 - 07:13 pm:   

We live in a 'snowflakes' universe?

Here's an interesting paper, mostly math, unifying the standard model and gravity, using the E8 Lie algebra principle bundle connection, a kind of 'interrelationship' of the strong force, electroweak force, and gravity. The paper has the grand name of "An Exceptionally Simple Theory of Everything" by A. Garret Lisi, 6 Nov. 2007: http://arxiv.org/abs/0711.0770

I read it with great interest (with about 5% comprehension!) looking for where the 'interconnectedness' of all that is can be simplified into a unitary theory. I can't say I found it, and though it uses Cartan subalgebra, including Lie algebra, which are self enclosed systems, almost by definition they are meant to be self contained. I failed to find the connections to anything other then their internal parts, however. For example, what predictions does this theory make in the real world, or universe? Also, if gravity is taken as a constant, which it appears so, then should we find evidence that this is not so outside our orbital region, then this unified theory applies only to that region, and not the universe as a whole. So some unanswered questions, in addition to it being all 'Greek' to me. Math way beyond what I can handle. :-) But the graphics are pretty.

snowflake.jpg (pg. 19: Fig. 3: The E8 root system)

Of course, if that doesn't impress you, here's some text:

quote:

1. Introduction

We exist in a universe described by mathematics. But which math? Although it is interesting
to consider that the universe may be the physical instantiation of all mathematics,[1]
there is a classic principle for restricting the possibilities: The mathematics of the universe
should be beautiful. A successful description of nature should be a concise, elegant, unified
mathematical structure consistent with experience.

Hundreds of years of theoretical and experimental work have produced an extremely
successful pair of mathematical theories describing our world. The standard model of particles
and interactions described by quantum field theory is a paragon of predictive excellence.
General relativity, a theory of gravity built from pure geometry, is exceedingly elegant and
effective in its domain of applicability. Any attempt to describe nature at the foundational
level must reproduce these successful theories, and the most sensible course towards unification
is to extend them with as little new mathematical machinery as necessary. The further
we drift from these experimentally verified foundations, the less likely our mathematics is
to correspond with reality. In the absence of new experimental data, we should be very
careful, accepting sophisticated mathematical constructions only when they provide a clear
simplification. And we should pare and unite existing structures whenever possible.
The standard model and general relativity are the best mathematical descriptions we
have of our universe. By considering these two theories and following our guiding principles,
we will be led to a beautiful unification.

1.1 A connection with everything

The building blocks of the standard model and gravity are fields over a four dimensional base manifold. The electroweak and strong gauge fields are described by Lie algebra valued connection 1-forms,..




The paper gets more interesting with the math, but in the end, it still leaves the reader puzzled, especially as to what predictions these internalized interrelated components of subalgebra are supposed to predict.

My advice to readers, if you are not familiar with terminology, is to liberally access the Reference.com page and keep looking up the terms, which will keep you busy, if you have nothing else to do. :-)

http://www.reference.com

Gravity is intergrated on pp. 25, 26, 29, as part of a topolgy without free parameters, but it is a manifold which can stretch but not break, as per Cartan isomorphic subalgebra and Riemann manifold, i.e,:

quote:

"The Riemannian geometry of general relativity has been subsumed by principal bundle geometry | a significant mathematical unification. Devotees of geometry should not despair at this development, as principal bundle geometry is even more natural than Riemannian geometry. A principal bundle with connection can be described purely in terms of a mapping between tangent vector fields (dieomorphisms) on a manifold, without the ab initio introduction of a metric."




Just read on. I just hope that when math is created to explain 'interrelationship' on a cosmic scale, it is a lot simpler than this! "Exceptionally simple"? I don't think so. :-) But great paper!

Have fun, Ivan

[Ps: there's a You-Tube animation about this TOE, which is fun: http://www.youtube.com/watch?v=-xHw9zcCvRQ - compliments of my physicist friend Robert B.]
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aladim
Posted on Monday, November 19, 2007 - 06:39 am:   

Hi,
In a post above there was written
"In this depiction the sides Of the Cuve are equal But due to the limits of a 2 dimensional display Appear distorted"
Sorry if my question is stupid , but I cannot understand so I am asking.
What you mean with "due to the limits of a 2 dimensional display Appear distorted"
what you mean with limits of a 2 dimensional space, as I can understand this is the reason for the "distortion" but still cannot understand "the limits". If you explain me I will be thankful.

Are the plane and the "2 dimensional space" different things, i guess no :-) ...For me it sounds stupid but I really cannot understand those "limits".
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ANON ANON
Posted on Thursday, November 22, 2007 - 07:20 am:   

http://en.wikipedia.org/wiki/Perspective_(graphical)

Aladim the link above talks to the concept of perspective as it applies to images. This should help you begin to understand.
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Aladim
Posted on Thursday, November 22, 2007 - 08:28 am:   

I know what is perspective , I was studying Math enough and geometry and trigonometry were my favourite :-) ... still cannot understand why in a post above the word CUBE is used...
It looks like that the object third side is longer than the two infront of us ( not in the perspective view but in a real 3D )...

Infact I cannot understand why you decided that it is a cube - this is the thing that I cannot understand ... all the geometrics are 100% clear for me
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ANON ANON
Posted on Thursday, November 22, 2007 - 08:51 am:   

In the computer program the length of all sides of the cube are equal as is the area of the sides. As to why it looks distorted it is a function of flattening the object.
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Aladim
Posted on Thursday, November 22, 2007 - 09:15 am:   

LOL - now I understand , thank ya ... I'll continue thinking it
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Anon Anon
Posted on Thursday, November 22, 2007 - 09:56 am:   

wscg.zcu.cz/wscg2002/Papers_2002/E37.pdf

A Method for Obtaining the Tesseract by Unraveling the 4D Hypercube

The link above illustrates the same distortion effect in the diagrams of the cube posted above.
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Ivan/E8 root system
Posted on Thursday, November 22, 2007 - 10:52 pm:   

E8 is neat! - for you geometry lovers. :-)

e8plane2a.jpg
Visualizing the E8 root system (interactive)

[Compliments of my friend Robert B., PhD physics]

This E8 system connects with the earlier post on Lisi's paper.


Cheers, Ivan
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Circle Squaring
Posted on Tuesday, February 05, 2008 - 10:46 pm:   

get-attachment.jpg

The above is a Geo Gebra generated solution to the generation of a circle with the same area as a square. This is a variation of the circle squaring problem from antiquity. The Geo Gebra software package confirms generation of a circle and square that match in terms of area. In the diagram both are 4 CM in area each.

This approach to circle squaring differs from that of the ancient problem in that it starts with a square and then generates a matching circle.

Regardless of the inverse of the approach this is a great breakthrough in geometry that has yet to be fully explored.
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Re Circle Squaring
Posted on Thursday, February 07, 2008 - 06:50 am:   

I have used the Geo Gebra software package to replicate the approach depicted above. I have confirmed that by using it that with compass and ruler is is possible to construct a circle that matches a square in area but not the reverse a square that matches a circle in area.

This begs the question of why this works. It also opens a door into areas that touch upon the basic structure of reality.

It clearly shows a linkage at the geometric level between the circle and the square at some fundamental level.

I think this linkage is what the ancients were trying to determine with regards to the circle squaring problem of antiquity.

This is a highly interesting bit of geometry
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Algebraic Proof
Posted on Thursday, February 14, 2008 - 10:32 am:   

Below are the steps and begining of a algebraic solution to the circle squaring depicted above and verified by computer.

If this algebraic solution independently confirms the accuracy of the computer solution we have proof of the integrity of this geometric construct.

1. Point A (3.0, 0.0)

2. Point B (3.0, 1.0)

3. Circle c has center A with B on the circle, with radius 1

4. Point C is the intersection of Circle c on the X-axis to the left of the center A. Hence (2.0, 0.0)

5. Circle d has center C with A on the circle, again with radius 1.

6. Point D is the intersection of Circle c on the X-axis to the right of the center A. Hence (4.0, 0.0)

7. Circle e has center D with A on the circle. The radius is of course 1.

8. Point E is the intersection of Circle c and Circle e above the X-axis. This could be solved by solving the two quadratic equations corresponding to Circle c and Circle e. These would give 2 points. Select the one with positive value for the Y-axis.

9. Point F is the positive Y-axis intersection of Circle c and Circle d.

[By symmetry, the X-coordinate of E is 3.5 = (3 + 4)/2. Similarly the X-coordinate of F is 2.5 = (3 + 2)/2. The Y-coordinate of these points satisfy the equation 0.52 + y2 = 1 and thus y = &#8730;0.75 = (&#8730;3)/2. Point E is (3.5, (&#8730;3)/2 ) and Point F is (2.5, (&#8730;3)/2 ).]

10. Draw a square with side CD in the first quadrant. The area of this square is 4. This square is C, D, G, and H in the anti clockwise direction.

11. Draw the diagonal of the square DH. This would pass through the Point B. This diagonal is called segment g.

12. Draw the diagonal CG of the square. This also would pass through Point B. This diagonal is called segment i.

13. With Point E as center draw a circle to pass through Point A. This circle would pass through Point F also as the distance between Points E and F is 1.

14. With Point F as center draw a circle to pass through Point A. This circle would pass through Point E as the distance FE is 1.

15. Point l is the intersection of circles with centers E, and F. By symmetry, the X-coordinate of Point l is the same as that of Point A, that is, 3.0.

16. Draw Circle q with Point l as center to pass through Point B. This is Circle q.

[What are the coordinates of Point l? The X-coordinate is the same as that of Point A, 3.0. To calculate the Y-coordinate observe that the Y-coordinate of Point l is twice that of Points E and F. Thus l is (3.0, &#8730;3 ). What is the radius of Circle q? The segment lB is a radius of the Circle q. The Coordinates of B are (3.0, 1.0) Thus the radius of Circle q is ( &#8730;3 – 1 ). ]

17. Point J is the intersection of Circle q with line GH close to Point G.

18. Point K is the intersection of Circle e with the X-axis away from A and is (5.0, 0.0).

19. Point L is the intersection of Circle k with Circle e away from the Point E.

[What are the coordinates of Point L? Consider the triangle FEA. The side FE is of length 1 as Point E lies on Circle p with center at Point F. The Points E and F lie on Circle C with center A and hence side FA and side AE are of length 1. The triangle FEA is an equilateral triangle and angle FEA is 60Ί. Consider the triangle AED. Already we have shown that the length of side AE is 1; length of side AD is 1 as D lies on Circle c with A as center. As Point E lies on Circle e with center D, the length of side ED is also 1. Thus triangle AED is also equilateral giving angle AED to be 60Ί. Consider triangle DEL. Side DL is of length 1 as L lies on Circle E with center D. Side DE (i.e. side ED) is already shown to be of length 1. Side EL is also of length 1 as L lies on Circle k with E as center. The fact that triangle DEL is equilateral implies angle DEL is 60Ί. Adding the three angles, EFA, AED, and DEL gives the angle FEL to be 180Ί. Since FEL is a straight line, the Y-coordinate of L is the same as that of F and E that is (&#8730;3 / 2).

To find the X-coordinate of Point L, consider triangle DLK. Angle ADE is 60Ί. Angle EDL is 60Ί. Angle ADK is 180Ί. Hence angle LDK is 60Ί. Sides DL and DK are of unit length as Points L and K lie on Circle e with center D. Hence triangle DLK is an equilateral triangle. The side DK is horizontal and thus the X-coordinate of the apex L is the average of the X-coordinates of D and K, giving the value 4.5. Accordingly, the Point L is (4.5, (&#8730;3 / 2)). ]

20. Point M is the intersection of Circle p with diagonal DH.

21. Point N is the intersection of Circle k with diagonal CG.

22. Point O is the intersection of Circle e with the vertical side DG and thus the Point O is (4, 1).

23. Point P is the intersection of Circle d with vertical side CH and is (2, 1).

24. Point Q is the intersection of Circles p and q to the left of Point l.

25. Line j is a line through Points A and B and thus is x = 3.

26. Line l connects Points M and l.

27. Line m joins Points l and N.

28. Point R is the intersection of line l with Circle q.

29. Line n joins Points R and E.

30. Point S is the intersection of line m with Circle q to the left of the center of Circle q.

31. Line r joins Points S and F.

32. Point V is the intersection of Circle q with line j above the center of the Circle q.

33. Point T is the intersection point of line n and diagonal CG. [Verify the coordinates. Are the coordinates close to the ones given by the program (3.772, 1.811)?]

34. Point Z is the intersection of line n with Circle k.

35. Point U is the intersection point with coordinates (4, 0) which coincides with Point D.

36. Point G1 is the intersection point with coordinates (2, 2) which coincides with Point H.

37. Point H1 is the intersection point with coordinates (3, 1) which coincides with Point B.

38. Area of the square CDGH is 4.

39. Point W is the intersection point of Line j with side GH of the square and has coordinates (3, 2).

40. Point A1 is the intersection of Circle q with side GH of the square.

41. Segment s connects Points A1 and N. [Is the length of this segment close to 1.508?]

42. Point B1 is the intersection point of ??? with coordinates (3.775, 1.82) given by the computer.

43. Circle t with center at Point B and passing through Point B1??? Computer gives the equation t: (x – 3)2 + (y – 1)2 = 1.273.

44. Area of Circle t is 4.

45. Type “Area=4” on top of Circle t.

46. Segment a1 connects Points J and M. Computer gives segment length as 1.508.

47. Point C1 is the intersection point of Circle t with the vertical side of the square CH. The coordinates of C1 given by the computer are (2, 1.523).

48. Point D1 was a free object with coordinates (1.537, 2.065).

There seems to be no more steps.

[Develop algebraic equations and see if the area of the Circle t is in fact 4.]
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Re Algebraic Proof
Posted on Thursday, February 14, 2008 - 02:37 pm:   

The information posted above is the begining of a algebraic proof with regards to the geometry depicted above.

It is clear from reviewing the above that this geometry pushes computer technology to its limits.

In reviewing the above a Doctor in computer science has said that in the computer field we have 'Numerical Analysis' which is concerned with errors in computations due to finite precision of practical computers. The above could be due to the finite size of the computers used or it could possibly be that there is no finite relationship between square root of phi and the operations that are involved in this procedure.

To determine which is the case exceeds current computer technology.

I note that the mind that produced this geographic solution is one of the finest cryptographics experts ever produced by produced by the United States Department of Defense.

It is clear from this work that the United States Government, Department of Defense and Private Industry in the United States has failed to recognize the ability of this mind or place it in a position commesurate with its abilities.

It is clear that this mind coupled to the skills and training that 24 years in the clandestine services is capable of many things.

Given the fact that this mind has been given access to high speed computer networks, satelight communication systems, scientific and technical databases one has to wonder what exactly it has been up to for the last 7 years and just what the Bush adminstration has been faced with for the last 7 years.
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Ivan/Vitruvius
Posted on Friday, February 15, 2008 - 09:50 pm:   

Leonardo Squared the Circle! -- Da Vinci’s Secret Solution in the Vitruvian Man Decoded


Vitruvius1.jpg
Vitruvius, the square the circle Golden mean man


quote:

Leonardo uses the Roman architect Vitruvius’ archetypal proportions of the human body and the Golden Ratio to “solve” his day’s great squaring of the circle problem – to greater than 99.8% accuracy. For all practical purposes, Leonardo’s solution, encoded in his Vitruvian Man, is definitive. His solution is also ingenious, previously undiscovered and elegant in its simplicity. (A geometric solution of 100% accuracy is not possible because the underlying mathematics involve Pi, the infinitely repeating decimal places of which, p = 3.14159265..., defy the drawing of perfectly measured geometric shapes.)
...




Our hat is off to Ed and Mohideen for their efforts to solve this great historical problem. Pi is transcendental, and though it may be solved analog, it defies digital numerical resolution, itself a 'transcendental' problem of mathematics.

Thanks to Ed for above article reference.

Ivan
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ALgebraic Proof II
Posted on Wednesday, February 20, 2008 - 06:39 pm:   

The following is an algebraic analysis of the cricle squaring problem posted above. This solution and analysis so far prove that the geometric solution posted above takes the solution of the circle squaring problem to the farthest limits possible. It also demonstrates that the problem, while defying a perfect numerical solution due to the transcendental nature of Pi, clearly shows a linkage at the most fundamental level to other complex geometric problems.

That this solution may have value in developing algorithms for use in advanced computer applications is also clearly indicated. In terms of what may be accomplished with regards to this solution is a potential exponential enhancement of complex problem solving applications. Both potential Military and Civilian applications for this work exist.

I note the geometric work produced above was produced by one of the best cryptographers ever trained by the United States Department of Defense.

He did it using only compass and ruler, freeware and a home computer.


1. Point A (3.0, 0.0)

2. Point B (3.0, 1.0)

3. Circle c has center A with B on the circle, with radius 1

4. Point C is the intersection of Circle c on the X-axis to the left of the center A. Hence (2.0, 0.0)

5. Circle d has center C with A on the circle, again with radius 1.

6. Point D is the intersection of Circle c on the X-axis to the right of the center A. Hence (4.0, 0.0)

7. Circle e has center D with A on the circle. The radius is of course 1.

8. Point E is the intersection of Circle c and Circle e above the X-axis. This could be solved by solving the two quadratic equations corresponding to Circle c and Circle e. These would give 2 points. Select the one with positive value for the Y-coordinate.

Consider the triangle AED. Side AE is of length 1 as A is center of Circle c and E is on Circle c. Side DE is of length 1 as D is center of Circle e and E is on Circle E. Side AD is of length 1 as A is center of Circle c and D is on Circle c. The triangle ADE is equilateral with side of length 1. The length of any perpendicular from a vertex to the opposite base of an equilateral triangle is (&#8730;3 / 2) times the length of a side. Hence the perpendicular from point E to the X-axis coinciding with side AD is (&#8730;3 / 2). The coordinates of point E are (3.5, (&#8730;3 / 2)).

9. Point F is the positive Y-axis intersection of Circle c and Circle d. An argument similar to the one made for point E gives the coordinates of point F as (2.5, (&#8730;3 / 2)).

10. Draw a square with side CD in the first quadrant. The area of this square is 4. This square is C, D, G, and H in the anti clockwise direction.

11. Draw the diagonal of the square DH. This would pass through the Point B. This diagonal is called segment g.

12. Draw the diagonal CG of the square. This also would pass through Point B. This diagonal is called segment i.

13. With Point E as center draw a circle to pass through Point A. This circle would pass through Point F also as the distance between Points E and F is 1.

14. With Point F as center draw a circle to pass through Point A. This circle would pass through Point E as the distance FE is 1.

15. Point l is the intersection of circles with centers E, and F. Consider the triangle FlE. Arguments similar to the triangle AED give the height of l to be (&#8730;3 / 2) above the horizontal line EF which itself is at a height of (&#8730;3 / 2) above the X-axis. Thus the Y-coordinate of point l is &#8730;3. The X-coordinate read from the diagram is 3. Hence the coordinates of point l are (3, (&#8730;3)).

16. Draw Circle q with Point l as center to pass through Point B. This is Circle q.

[What is the radius of Circle q? The segment lB is a radius of the Circle q. The Coordinates of B are (3.0, 1.0) while that of l are (3, (&#8730;3)). Thus the radius of Circle q is ( &#8730;3 – 1 ). ]

17. Point J is the intersection of Circle q with line GH close to Point G. Let the coordinates of point J be Jx and JY. The length of the segment lJ is given by &#8730;(( Jx – 3)2 + (JY - &#8730;3)2) which is ( &#8730;3 – 1 ). Taking the squares we get: (( Jx – 3)2 + (JY - &#8730;3)2) = ( &#8730;3 – 1 )2. We know from the fact that J lies on segment GH, the value of JY is 2. Substituting this value, we get: ( Jx – 3)2 + (2 - &#8730;3)2 = ( &#8730;3 – 1 )2.

( Jx – 3)2 + (4 + 3 – 2x2x&#8730;3) = (3 + 1 – 2 x1x&#8730;3)

( Jx – 3)2 = -7 + 4x&#8730;3 + 4 – 2x&#8730;3

( Jx – 3)2 = 2x&#8730;3 – 3

( Jx – 3) = &#8730;(2&#8730;3 – 3)

Jx = (3 + &#8730;(2&#8730;3 – 3)).

Thus the coordinates of point J are ((3 + &#8730;(2&#8730;3 – 3)), 2)

18. Point K is the intersection of Circle e with the X-axis away from A and is (5.0, 0.0).

19. Point L is the intersection of Circle k with Circle e away from the Point E.

What are the coordinates of Point L? Consider the triangle FEA. The side FE is of length 1 as Point E lies on Circle p with center at Point F. The Points E and F lie on Circle C with center A and hence side FA and side AE are of length 1. The triangle FEA is an equilateral triangle and angle FEA is 60Ί. Consider the triangle AED. Already we have shown that the length of side AE is 1; length of side AD is 1 as D lies on Circle c with A as center. As Point E lies on Circle e with center D, the length of side ED is also 1. Thus triangle AED is also equilateral giving angle AED to be 60Ί. Consider triangle DEL. Side DL is of length 1 as L lies on Circle E with center D. Side DE (i.e. side ED) is already shown to be of length 1. Side EL is also of length 1 as L lies on Circle k with E as center. The fact that triangle DEL is equilateral implies angle DEL is 60Ί. Adding the three angles, EFA, AED, and DEL gives the angle FEL to be 180Ί. Since FEL is a straight line, the Y-coordinate of L is the same as that of F and E that is (&#8730;3 / 2).

To find the X-coordinate of Point L, consider triangle DLK. Angle ADE is 60Ί. Angle EDL is 60Ί. Angle ADK is 180Ί. Hence angle LDK is 60Ί. Sides DL and DK are of unit length as Points L and K lie on Circle e with center D. Hence triangle DLK is an equilateral triangle. The side DK is horizontal and thus the X-coordinate of the apex L is the average of the X-coordinates of D and K, giving the value 4.5. Accordingly, the Point L is (4.5, (&#8730;3 / 2)).

20. Point M is the intersection of Circle p with diagonal DH.

The equation for Circle p is (x – 2.5)2 + (y – (&#8730;3)/2)2 = 1. The equation for diagonal DH is x + y = 4. Substitute x = 4 – y in the equation for the circle to get

(4 – y – 2.5)2 + (y – (&#8730;3)/2)2 = 1

(1.5 – y)2 + (y – (&#8730;3)/2)2 = 1

y2 – 3y + 2.25 + (y2 – (&#8730;3)y + 0.75) = 1

2y2 – (3 + &#8730;3)y + 3 = 1

2y2 – (3 + &#8730;3)y + 2 = 0

y2 – ((3 + &#8730;3)/2)y + 1 = 0

The above equation is of the form a y2 + b y + c = 0 where a = 1; b = – ((3 + &#8730;3)/2); and c = 1. Now b2 = (3 + &#8730;3)2/4 = (9 + 6&#8730;3 + 3)/4 = (12 + 6&#8730;3)/4 = 3 + 1.5&#8730;3

b2 – 4 a c = 3 + 1.5&#8730;3 – 4 = 1.5&#8730;3 – 1.

-b = (3 + &#8730;3)/2

-b + &#8730;( b2 – 4 a c) = (3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)

(-b + &#8730;( b2 – 4 a c)/(2a) = ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2

Just for verification the computed value of y is 1.815078974491474905777150744918 and x is 2.1849121025508525094222849255082. These coordinates seem to match with the figure. The x coordinate has the expression 4 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 that is

(8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2

y = ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2

x = (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2

21. Point N is the intersection of Circle k with diagonal CG. The figure is symmetrical about the vertical line AB and thus the y coordinate of point N is the same as the y coordinate of point M. The equation for the diagonal CG is x = y + 2. Hence the x coordinate of point N is 3.815078974491474905777150744918. The position of N in the figure seems to correspond with these values.

The expressions are:

y = ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2

x = (4 + ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2

22. Point O is the intersection of Circle e with the vertical side DG and thus the Point O is (4, 1). Point O has no role in deciding the solution.

23. Point P is the intersection of Circle d with vertical side CH and is (2, 1). Point P has no role.

24. Point Q is the intersection of Circles p and q to the left of Point l.

Equation for Circle p is (x – 2.5)2 + (y – (&#8730;3)/2)2 = 1.

Equation for Circle q is (x – 3)2 + (y - &#8730;3)2 = ((&#8730;3) – 1)2.

Let us shift the origin to the center of Circle q to simplify the equations. Let w represent the new horizontal axis and z represent the new vertical axis.

w = (x – 3). Therefore x = (w + 3).

z = (y - &#8730;3) giving y = (z + &#8730;3).

Substituting for x and y, we have:

Equation for Circle p is (w + 3 – 2.5)2 + (z + &#8730;3 – (&#8730;3)/2)2 = 1.

(w + 0.5)2 + (z + (&#8730;3)/2)2 = 1

w2 + w + 0.25 = 1 - (z + (&#8730;3)/2)2

w2 + w = 0.75 - (z + (&#8730;3)/2)2

w = (0.75 - (z + (&#8730;3)/2)2) – w2

Squaring the above equation we get,

w2 = ((0.75 - (z + (&#8730;3)/2)2) – w2)2 Equation for Circle p in w and z.

Equation for Circle q is w2 + z2 = ((&#8730;3) – 1)2 giving

w2 = ((&#8730;3) – 1)2 - z2

Substituting for w2 in the equation for Circle p we get

((&#8730;3) – 1)2 - z2 = ((0.75 - (z + (&#8730;3)/2)2) – (((&#8730;3) – 1)2 - z2))2

((&#8730;3) – 1)2 - z2 = ((3/4-(z2 + Ύ + z &#8730;3)) – (((&#8730;3) – 1)2 - z2))2

((&#8730;3) – 1)2 - z2 = ((3/4-z2 - Ύ - z &#8730;3) – ((&#8730;3) – 1)2 + z2)2

((&#8730;3) – 1)2 - z2 = ((-z2 - z &#8730;3) – ((&#8730;3) – 1)2 + z2)2

((&#8730;3) – 1)2 - z2 = (-z2 - z &#8730;3 – ((&#8730;3) – 1)2 + z2)2

((&#8730;3) – 1)2 - z2 = (- z &#8730;3 – ((&#8730;3) – 1)2)2 Since (-a)2 = (a)2 we get

((&#8730;3) – 1)2 - z2 = (z &#8730;3 + ((&#8730;3) – 1)2)2 Switch LHS and RHS to get

(z &#8730;3 + ((&#8730;3) – 1)2)2 = ((&#8730;3) – 1)2 - z2

3z2 + 2z(&#8730;3) ((&#8730;3) – 1)2 + ((&#8730;3) – 1)4 = ((&#8730;3) – 1)2 - z2

4z2 + 2z(&#8730;3) ((&#8730;3) – 1)2 - ((&#8730;3) – 1)2 + ((&#8730;3) – 1)4 = 0

The above is a quadratic equation in z in the form of ax2 + bx + c = 0 where

a = 4; b = 2(&#8730;3) ((&#8730;3) – 1)2; and c = - (((&#8730;3) – 1)2 - ((&#8730;3) – 1)4) c is negative while the value (((&#8730;3) – 1)2 - ((&#8730;3) – 1)4) is positive.

b2 = 12 ((&#8730;3) – 1)4

4ac = -16 (((&#8730;3) – 1)2 - ((&#8730;3) – 1)4)

b2 – 4ac = 12 ((&#8730;3) – 1)4 + 16 (((&#8730;3) – 1)2 - ((&#8730;3) – 1)4) = 16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4

The variable y is directly proportional to z. From the figure it is seen that Circle p intersects with Circle q at two points and Point Q has the higher y coordinate. Accordingly we choose the higher value of z.

z = (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))/2x4

= (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))/8

We substitute the above value of z in w2 = ((&#8730;3) – 1)2 - z2 and calculate the value of w.

w2 = ((&#8730;3) – 1)2 - (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))2/64

w = ±&#8730;(((&#8730;3) – 1)2 - (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))2/64)

For the Point Q which is to the left of the center of Circle q, the w-coordinate is negative. Hence, we select the negative value of w.

From the values of w and z we get:

x = 3 - &#8730;(((&#8730;3) – 1)2 - (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))2/64)

y = &#8730;3 + (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))/8

Let us check the numerical values of x and y now.

For simplicity we perform computations to six digit accuracy.

((&#8730;3) – 1)2 = 0.535898

x = 3 - &#8730;(0.535898 - (-2(&#8730;3) 0.535898 + &#8730;(16 . 0.535898 – 4 ((&#8730;3) – 1)4))2/64)

((&#8730;3) – 1)4 = 0.287187

x = 3 - &#8730;(0.535898 - (-2(&#8730;3) 0.535898 + &#8730;(16 . 0.535898 – 4 . 0.287187))2/64)

2(&#8730;3) 0.535898 = 1.856405

16 . 0.535898 = 8.574368

4 . 0.287187 = 1.148748

x = 3 - &#8730;(0.535898 - (-1.856405 + &#8730;(8.574368 – 1.148748))2/64)

&#8730;(8.574368 – 1.148748) = 2.724999

x = 3 - &#8730;(0.535898 - (-1.856405 + 2.724999)2/64)

(-1.856405 + 2.724999)2 = 0.8685942 = 0.754456

x = 3 - &#8730;(0.535898 – 0.754456/64)

0.754456/64 = 0.011788

x = 3 - &#8730;(0.535898 – 0.011788)

&#8730;(0.535898 – 0.011788) = &#8730;0.52411 = 0.723954

x = 2.276046

Geogebra gives the value of 2.276. We proceed to compute the value of the y-coordinate of Point Q.

y = &#8730;3 + (-2(&#8730;3) ((&#8730;3) – 1)2 + &#8730;(16 ((&#8730;3) – 1)2 – 4 ((&#8730;3) – 1)4))/8

y = &#8730;3 + (-2(&#8730;3) 0.535898 + &#8730;(16 . 0.535898 – 4 . 0.287187))/8

&#8730;(16 . 0.535898 – 4 . 0.287187) = &#8730;(8.574368 – 1.148748) = &#8730;7.42562 = 2.724999

y = &#8730;3 + (-2(&#8730;3) 0.535898 + 2.724999)/8

2(&#8730;3) 0.535898 = 1.856405

y = &#8730;3 + (-1.856405 + 2.724999)/8 = &#8730;3 + 0.868594/8 = &#8730;3 + 0.108574 =

y = 1.840625

Geogebra gives the value of 1.841.

The expressions for the coordinates of Point Q are verified.

25. Line j is a line through Points A and B and thus is x = 3.

26. Line l connects Points M and l.

Point M has the following coordinates – relabeled with subscript M:

xM = (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2

yM = ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2

Likewise the coordinates of Point l are copied below:

xl = 3

yl = &#8730;3

The equation for Line l is:

y = yl + ((yM – yl)/(xM – xl))(x – xl)

Substituting the values, we get:

y = &#8730;3 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) (x – xl)

27. Line m joins Points l and N.

28. Point R is the intersection of line l with Circle q.

Shift the origin to the center of Circle q.

w = (x – 3). Therefore x = (w + 3).

z = (y - &#8730;3) giving y = (z + &#8730;3).

Substituting for x and y, we have:

Equation for Circle q is w2 + z2 = ((&#8730;3) – 1)2

Equation for Line l is:

(z + &#8730;3) = &#8730;3 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) (w + 3 – xl) Since xl is 3, on simplification we get

Equation for Line l is:

z = ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) w

Transferring z to the RHS in the equation for Circle q gives

w2 = ((&#8730;3) – 1)2 - z2

Substituting for z in the above equation results in

w2 = ((&#8730;3) – 1)2 - ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2 w2

w2 (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2) = ((&#8730;3) – 1)2

Therefore,

w2 = ((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2)

w = ±&#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

The point R is to the right of the center of Circle q and thus we choose the positive value, giving

w = &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

From the figure it is clear that for a positive value of w the corresponding value of z is negative. Thus

z = - ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) w

= - ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

Since x = (w + 3), the x coordinate of Point R is

xR = 3 + &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

Likewise the y coordinate of Point R is

yR = &#8730;3 - ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

For verification of the equations, let us first calculate the value of

&#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2)) which is common to both the coordinates.

Again we verify to six digit accuracy.

((&#8730;3) – 1)2 = 0.535898

&#8730;(0.535898/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

(3 + &#8730;3) = 4.732051

&#8730;(0.535898/ (1 + (((4.732051/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

4.732051/2 = 2.366026

&#8730;(0.535898/ (1 + (((2.366026 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

&#8730;(1.5&#8730;3 – 1) = 1.264150

&#8730;(0.535898/ (1 + (((2.366026 + 1.264150)/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

(2.366026 + 1.264150)/2 = 1.815088

&#8730;(0.535898/ (1 + ((1.815088 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

(1.815088 - &#8730;3) = 0.083037

&#8730;(0.535898/ (1 + (0.083037/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

(3 + &#8730;3)/2 = 2.366026

&#8730;(0.535898/ (1 + (0.083037/( (8 - (2.366026 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

&#8730;(1.5&#8730;3 – 1) = 1.264150

&#8730;(0.535898/ (1 + (0.083037/( (8 - (2.366026 + 1.264150))/2 – 3))2))

(2.366026 + 1.264150) = 3.630176

&#8730;(0.535898/ (1 + (0.083037/( (8 – 3.630176)/2 – 3))2))

(8 – 3.630176)/2 = 2.184912

&#8730;(0.535898/ (1 + (0.083037/( 2.184912 – 3))2))

2.184912 – 3 = -0.815088

&#8730;(0.535898/ (1 + (0.083037/( -0.815088))2))

0.083037/( -0.815088) = -0.101875

&#8730;(0.535898/ (1 + (-0.101875)2))

(-0.101875)2 = 0.010379

&#8730;(0.535898/ (1 + 0.010379)) = &#8730;(0.535898/1.010379) = &#8730;(0.530393) = 0.728281

xR = 3 + &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

xR = 3 + 0.728281 = 3.728281

Geogebra gives the value of 3.728. Hence x-coordinate of Point R is verified.

yR = &#8730;3 - ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

yR = &#8730;3 - ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) 0.728281

(3 + &#8730;3)/2 = 2.366026

yR = &#8730;3 - (((2.366026 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) 0.728281

&#8730;(1.5&#8730;3 – 1) = 1.264150

yR = &#8730;3 - (((2.366026 + 1.264150)/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) 0.728281

(2.366026 + 1.264150)/2 = 1.815088

yR = &#8730;3 - ((1.815088 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) 0.728281

(1.815088 - &#8730;3) = 0.083037

yR = &#8730;3 - (0.083037/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) 0.728281

(3 + &#8730;3)/2 = 2.366026

yR = &#8730;3 - (0.083037/( (8 - (2.366026 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) 0.728281

&#8730;(1.5&#8730;3 – 1) = 1.264150

yR = &#8730;3 - (0.083037/( (8 - (2.366026 + 1.264150))/2 – 3)) 0.728281

(2.366026 + 1.264150) = 3.630176

yR = &#8730;3 - (0.083037/( (8 – 3.630176)/2 – 3)) 0.728281

(8 – 3.630176)/2 = 2.184912

yR = &#8730;3 - (0.083037/( 2.184912 – 3)) 0.728281

( 2.184912 – 3) = -0.815088

yR = &#8730;3 - (0.083037/-0.815088) 0.728281 = &#8730;3 - (0.083037/-0.815088) 0.728281

yR = &#8730;3 – (-0.074194)

We need to modify the equation for yR. We chose the negative sign for the expression other than &#8730;3 expecting the rest of the expression to be positive. Since the rest of the expression is indeed negative, the equation for the y-coordinate of Point R is modified as below.

yR = &#8730;3 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

With the corrected expression,

yR = &#8730;3 + (-0.074194) = 1.657857

Geogebra gives the value as 1.658. The y-coordinate of Point R is also verified.

The coordinates of Point R are:

xR = 3 + &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

yR = &#8730;3 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3)) &#8730;(((&#8730;3) – 1)2/ (1 + ((((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1))/2 - &#8730;3)/( (8 - ((3 + &#8730;3)/2 + &#8730;(1.5&#8730;3 – 1)))/2 – 3))2))

{This particular verification has taught us a very important lesson. When we use symbols alone without the aid of the geometric figure, we are forced to carry the ± for every square root in the expression. Such ± makes it impossible to reduce the following equations. Having a figure for the solution resolves the choice between the positive and negative values of a square root and permits the progress of the derivation. We believe this is a demonstration of – A picture is worth a thousand words.}

29. Line n joins Points R and E.

30. Point S is the intersection of line m with Circle q to the left of the center of Circle q.

31. Line r joins Points S and F.

32. Point V is the intersection of Circle q with line j above the center of the Circle q.

33. Point T is the intersection point of line n and line m.

34. Point Z is the intersection of line n with Circle k.

35. Point U is the intersection point with coordinates (4, 0) which coincides with Point D.

36. Point G1 is the intersection point with coordinates (2, 2) which coincides with Point H.

37. Point H1 is the intersection point with coordinates (3, 1) which coincides with Point B.

38. Area of the square CDGH is 4.

39. Point W is the intersection point of Line j with side GH of the square and has coordinates (3, 2).

40. Point A1 is the intersection of Circle q with side GH of the square.

41. Segment s connects Points A1 and N. [Is the length of this segment close to 1.508?]

42. Point B1 is the intersection point of Line n and segment s.

43. Circle t with center at Point B and passing through Point B1. Computer gives the equation t: (x – 3)2 + (y – 1)2 = 1.273. This is the desired circle with area equal to the square.

44. Area of Circle t is 4.

45. Type “Area=4” on top of Circle t.

46. Segment a1 connects Points J and M. Computer gives segment length as 1.508.

47. Point C1 is the intersection point of Circle t with the vertical side of the square CH. The coordinates of C1 given by the computer are (2, 1.523).

48. Point D1 was a free object with coordinates (1.537, 2.065).

There seems to be no more steps.

[Develop algebraic equations and see if the area of the Circle t is in fact 4.]
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Quantum Geometry
Posted on Thursday, February 21, 2008 - 03:24 pm:   

Quantum Computation as Geometry
Michael A. Nielsen,* Mark R. Dowling, Mile Gu, Andrew C. Doherty

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

School of Physical Sciences, The University of Queensland, Queensland 4072, Australia.

The unclassifed work posted above in the open unclassified domain has potential application to designing circuit paths for quantum computers. If verified this work would give the nation state that is able to bring online a quantum computer a advantage much like the development of the atomic bomb did.

This geometry was developed by one of the greatest cryptographers produced by the United States Department of Defense.

If verified this work, its application to quantum computing and resulting algorithms would be among the most classified data within the United States Department of Defense.

The cryptographer that produced the geometry depicted above has been the target of at least three verified asassination attempts including poisoning by an organophosphate based Neurotoxin produced by the old Soviet Union. He is currently is studying for an advanced degree within the United States.

He is willing to work as a consultant to the United States government, DOD and NSA should those agencies, pending the departure of the current president from office, see fit to offer him work comensurate with his demonstrated skills.

Having spoken to this cryptographer I know that is opposed to working with the current administration on philosophical grounds.
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Ivan/simply elegant proof
Posted on Friday, February 22, 2008 - 12:36 am:   

An elegant proof of Squaring the Circle, as presented by Mohideen Ibramsha?


180px-Squaring_the_circle.svg.png (interactive)
Squaring the circle, in principle

All of the above on Squaring the Circle is using the original idea of a triangle and compass geometric solutions, and quantum computations, with brilliant results. Though in theory this is impossible, there is nevertheless centuries of effort to prove that it is possible. One such proof, which is incredibly simple to follow, is by Mohideen, with whom Ed and I had been corresponding by email. Here is his proof:

Theorem: Given a method to draw a circle in area equal to a given square, it is possible to draw a square in area equal to any given circle.

Proof:
Let the given circle have a radius r.
The area of the circle is Pi*r2
The side of a square of equal area is sqrt Pi* r.

We achieve our goal if we find a procedure to multiply the given radius by sqrt Pi.

Since we are given a procedure to draw a circle of equal area given any square, let us draw a square of side 1 with area of 1. The circle of equal area has a radius of 1/Pi. (this should be 1/sqrt Pi? - this may be a typo in original?)

Let the center of the circle of unit area be O. Draw a triangle AOB where AO is the radius of the circle of unit area, OB is a side of length 1 and AB is the other side.

To get the square with area equal to the circle of radius r, extend OA to OX such that OX is equal to r. Draw a line through X which is parallel to AB. Extend OB to intersect this parallel at Y. Consider the triangles AOB and XOY. These are similar triangles. Hence the ratio OB/OA is the same as the ratio OY/OX. By construction OB/OA equal sqrt Pi. Therefore OY equal sqrt Pi times OX, that is sqrt Pi * r. The area of a square with OY as side is pi*r2. The required square is the square with OY as a side. QED.

When I examined this, I found one possible typo, but otherwise it appears sound. Here is how I would restate it, given that the above has a final solution as the area of both the circle and square is 4, I could reformulate the above Theorem in that same manner:

1. If Pi* r^2 = s^2, where the left side is the area of the circle, and right side is the area of square with s = side, then

2. if circle radius r = s/sqrt Pi, we get:

3. Pi*r^2 = Pi * (s/sqrt Pi)^2 = s^2*Pi/Pi = s^2

4. Therefore, Pi*r^2 = s^2, or for any number in "s" as the side of a square, there will be an equal area in the circle, where radius r = s/sqrt Pi.

5. So if per above, s = 2, then area = 4 for both the circle and square.

6. End of proof.

I believe this will work for any number in "s", but it does not compute numerically exactly for the same reason Squaring the Circle had always been illusive, that Pi is a transcendental number. So I leave this here, as elegant as it is thanks to Mohideen (and a long tradition of Indian mathematical genius), and to Ed for all his work with compass and ruler, for others to visit and comment.

Thanks Ed, Mohideen, very interesting posts on this illusive centuries old puzzle. We may be closing in one Squaring the Circle.


Ivan
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RE: A simply elegant proof
Posted on Friday, February 22, 2008 - 08:31 am:   

QUANTUM COMPUTATION USING GEOMETRIC ALGEBRA

The University of Texas at Dallas

http://www.utdallas.edu/~cantrell/matzke.pdf

The link above is supplied by a student at the University of Texas at Dallas

We stand at the cusp of a breakthrough in Quantum Technology.

Some of the greatest minds in history have explored the problem of circle squaring. Da Vinci is one. Each effort to solve this problem has brought us closer to understanding the nature of Pi and its application to efforts in various fields.

Fundamental research can not be classified. The above material uses thousands of years old efforts to develop the solution posted above.

Much like E=MC2 is open and in the public domain the solution posted above opens a door to potential creation of quantum logic paths.

It is the culmination of several thousand years of work and as Ivan said it is elegent in its simplicity.

The transcendental nature of Pi poses a number of challanges for those of us who labor within the field of computer science and cybernetics.

This work opens lines of inquiry that were not thought of before because of the findings that the problem depicted above was impossible to solve. By demonstrating a linkage to other geometric constructs what the authors of the solution above have done is clearly indicate that quantum computation using geometric algebra does work and can be applied to highly complex problems, allowing us to solve these problems via alternative pathways.


As Ivan said it is a simply elegant proof
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Riemannian Geometry
Posted on Sunday, February 24, 2008 - 07:11 am:   

Posted by a Student of Mathmatics in Russia

Riemannian Geometry is characterized by a inherent symetry. The solution depicted above to the squaring of the circle appears to reflect aspects of Riemannian Geometry and Reimannian manifolds, multidimentional non-euclidean constructs.

If true this solution could have application to string theory and other problems.

I am reviewing the work and I am corresponding with associates on the matter. I will post my findings later. I have a friend in India and China I will speak to as well.

It may be that as others said a "door" to other possibilites has been opened by this work.

It is too early to say one way or the other.
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Riemann Geography II
Posted on Sunday, February 24, 2008 - 02:14 pm:   

In mathematics, the Riemann sphere is a way of extending the plane of complex numbers with one additional point at infinity, in a way that makes expressions such as

1 / 0 = &#8734;
well-behaved and useful, at least in certain contexts. It is named after 19th century mathematician Bernhard Riemann. It is also called the complex projective line, denoted .

http://www.answers.com/topic/riemann-sphere?cat=technology

The information posted above is provided to illustrate what the cryptographist who has pushed the Circle Squaring problem to its limits has touched upon with regards to Riemann Geometry.

If we explore the equations and geometry posted above we begin to see a possible linkage to the Riemann Sphere.

I am a student at the Technische Universitδt Dresden. If verified this geometric work could indeed hold applications to quantum computing and existing computer architecture.

It is clearly a work of genius. The question now is verification. Indeed this work also has potential industrial, academic and military applications.
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Riemann Geometry III
Posted on Sunday, February 24, 2008 - 02:36 pm:   

Intial results of the verification process with regards to this approach to circle squaring indicate a high degree of probablity that this solution to circle squaring has pushed the limits of the problem to infinity.

Initial computations indicate that using this technique a circle theat is 3.9999 to 4 is generated with regards to this problem. Numerical truncation and software limitations are being examined to determine if the solution can be pushed to 3.999infinity. If so what has been achieved is indeed a breakthrough in the field of geometry.

It is clear from this work that the federal government of the United States and the United States civilian private sector has discrimated against, passed over for promotion and actively worked to suppress the mind that created this work.

Georgetown University Faculty Member
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Mathmatical Findings
Posted on Monday, February 25, 2008 - 08:23 pm:   

Mathmatical analysis indicates that the geographic solution to the squaring of the circle posted above has a high degree of internal coherance and demonstrates a previously unidentified mathmatical relationship to Pi.

At present this geometric construct pushes computer ability to validate its degree of precision to the limits of its technology. Truncation of numbers and approximations used in silicon based computer processors are incapable of determining the degree of precision displayed in this figure.

That a previously unidentified mathmatical relationship exists within this figure and Pi has been proven. However much more research and effort is necessary to fully explore what has been found.

In sum this geographic solution is without peer and pushes the edge of what was thought possible to its limits
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Aladim
Posted on Thursday, February 28, 2008 - 04:42 am:   

Can you post a bigger image showing the "squaring of the circle", so we will be able to discuss it easily?

P.S.
Or give a link :-)
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Circle Squaring 2
Posted on Saturday, March 01, 2008 - 12:06 am:   

Repost of Feb. 05, 2008 entry, on Circle Squaring, with expanded graphics

[Please note this is a poor quality pict, so scroll down to Mar. 6, 2008, for better resolution and larger one.] - Ivan

985.jpg



quote:

The above is a Geo Gebra generated solution to the generation of a circle with the same area as a square. This is a variation of the circle squaring problem from antiquity. The Geo Gebra software package confirms generation of a circle and square that match in terms of area. In the diagram both are 4 CM in area each.

This approach to circle squaring differs from that of the ancient problem in that it starts with a square and then generates a matching circle.

Regardless of the inverse of the approach this is a great breakthrough in geometry that has yet to be fully explored.



Aladim, I hope this image helps, but if not, perhaps Ed and Mohideen can help me find a better original, since I seem to have lost the copy I had. Or else someone else can update image, by uploading with the image format, per "help" tab below, or give link to another site with image.

Thanks, Ivan
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Ivan/inverse square
Posted on Saturday, March 01, 2008 - 12:31 am:   

Is the square of integers the inverse of the square root of its fraction?

270px-Cake_fractions.svg.png
1/2 is sqrt 'inversion' of 1/4

Here is what I mean by this question:

10^2 = 100, whereas its fractional inverse would be sqrt 1/100 = 1/10, where in both cases the result is higher.

This works for any number as integers and their inverse fractions, where the inverse of squaring the number works as the square root of its inverse fraction.

I mention this in reference to multiplicative inverse where each integer x has its inverse 1/x. But more importantly, this inverse relationship also exists in how the squaring of a number is affected by the 'squaring' of its inverse number; except that in the inverse number it is not squaring that gives the same effect, but its 'inverse' which is the square root. So if a energy density is let's say 4, which is 2 squared; then its inverse would be 1/4 to become 1/2, then it needs to be the sqrt 1/4. Now in both cases the energy density is higher after either squaring its who integer value, or square rooting of its fractional value. Because one is the inverse fraction of the other, the process of squaring becomes reversed for the fraction to cause the same effect, in that the fraction must be square root instead: x^2 = 1/sqrt x ... so they're related.

I don't know if this makes sense, or even why I say this, but it's been on my mind.

Ivan
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Algebraic Proof III
Posted on Sunday, March 02, 2008 - 07:54 am:   

The following Algebraic proof of with regards to the squaring of the circle is provided for discussion.

What this proof does is confirm that the solution to the problem posted above reflects an alternative method for the determination of the value of Pi.

The method of circle squaring posted above takes the accuracy of the problem to the limits of Pi. In effect pushing the accuracy of the solution of the problem to an infinately small degree of error.

The resulting applications of this solution has been discussed previously.

It has potential applications to the fields of quantum computing, computer system architexture design and possible application to string theory development


1. A (0, -1)

2. B (0, 0)

3. Circle c has center A with radius 1. x2 + (y + 1)2 = 1

4. C (-1, -1)

5. Line a is through points C and A and is y = -1.

6. Point D is the intersection of Circle c with Line a. There are two points on Line a intersecting with Circle c: (-1, -1) which is Point C and the other point (1, -1) is Point D.

7. Circle d has center at Point D with a radius of 1. (x – 1)2 + (y + 1)2 = 1

8. Circle e has center at Point C with radius 1. (x + 1)2 + (y + 1)2 = 1

9. Point E (-0.5, (&#8730;3)/2 – 1)

10. Point F (0.5, (&#8730;3)/2 – 1)

11. Make a square with CD as the base. The corners are C, D, G, and H. Side CD is segment b; DG is segment f; GH is segment g; and HC is segment h.

12. Diagonal DH is segment i. x = -y

13. Diagonal CG is segment j. x = y

14. Circle k is with Center F and passes through Point D. It has a radius 1. (x – 0.5)2 + (y + 1 – (&#8730;3)/2)2 = 1

15. Circle p has Center E and passes through Point C with radius 1. (x + 0.5)2 + (y + 1 – (&#8730;3)/2)2 = 1

16. Point l is the intersection above X-axis of Circles k and p. Point l is (0, (&#8730;3) – 1). The other point of intersection Point J coincides with Point A and is (0, -1)

17. Circle q has center at Point l and passes through Point B. The radius of this circle is the difference between the Y-coordinates of Points l and B and is equal to ((&#8730;3) – 1).

x2 + (y - ((&#8730;3) – 1))2 = ((&#8730;3) – 1)2

18. Point K is the intersection of Segment i and Circle p. Point L is the opposite point of intersection between the diagonal and the circle.

Equation for Circle p is (x + 0.5)2 + (y + 1 – (&#8730;3)/2)2 = 1

Equation for Segment i is x = -y

Substituting for x in the equation for Circle p we get:

(-y + 0.5)2 + (y + 1 – (&#8730;3)/2)2 = 1

(y2 – y + 0.25) + (y2 + 2 (1 – (&#8730;3)/2)y + (1 – (&#8730;3)/2)2 ) = 1

y2 – y + 0.25 + y2 + 2 (1 – (&#8730;3)/2)y + (1 – (&#8730;3)/2)2 = 1

2 y2 + (2 - &#8730;3 – 1) y + (1 – (&#8730;3)/2)2 +0.25 – 1 = 0

2 y2 + (1 - &#8730;3) y + 1 + Ύ - &#8730;3 – Ύ = 0

2 y2 + (1 - &#8730;3) y + (1 - &#8730;3) = 0

2 y2 - ((&#8730;3) – 1) y - ((&#8730;3) - 1) = 0

The above is a quadratic equation a y2 + b y +c = 0 where

a = 2; b = - ((&#8730;3) – 1); and c = - ((&#8730;3) - 1)

b2 – 4ac = ((&#8730;3) – 1)2 + 8 ((&#8730;3) - 1) = 3 + 1 – 2 &#8730;3 + 8 &#8730;3 – 8 = 6 &#8730;3 – 4 = 2((3&#8730;3) – 2)

For verification, 2 (3 &#8730;3 – 2) = 6.392305

Positive root is (-b + &#8730;(b2 – 4ac))/2a = ( 0.732051 + 2.528301)/4 = 0.815088

Hence K(-0.815088, 0.815088)

The negative root is (0.732051 – 2.528301)/4 = -0.449063 giving L(0.449063, -0.449063)

Geogebra gives K(-0.82, 0.82); and L(0.45, -0.45). Verified.

xk = -(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4

yk = (((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4

Point L is of no interest to us.

19. Point M is the intersection between Circle k and diagonal CG in the 4th quadrant. The point of interest, Point N is the intersection point in the 1st quadrant.

The equation for Circle k is (x – 0.5)2 + (y + 1 – (&#8730;3)/2)2 = 1

The equation for diagonal CG is x = y.

Substituting for x in the Circle k equation, we have:

(y – 0.5)2 + (y + 1 – (&#8730;3)/2)2 = 1

(y2 – y + 0.25) + (y2 + 2 (1 – (&#8730;3)/2) y + (1 – (&#8730;3)/2)2) = 1

(y2 – y + 0.25) + (y2 + (2 – &#8730;3) y + (1 + Ύ - &#8730;3)) = 1

y2 – y + 0.25 + y2 + (2 – &#8730;3) y + (1 + Ύ - &#8730;3) – 1 = 0

2y2 + (1 – &#8730;3) y + (1 - &#8730;3) = 0

2y2 – ((&#8730;3) – 1) y - ((&#8730;3) – 1) = 0.

The above is of the form ay2 + by + c = 0 where

a = 2; b = – ((&#8730;3) – 1); and c = - ((&#8730;3) – 1).

The solution to the above equation is the same as the one found in step 18.

xN = (((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4

yN = (((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4

Point N is (0.815088, 0.815088)

Geogebra gives M(-0.45, -0.45) and N(0.82, 0.82)

N equations are verified.

20. Line l is the line through Points K and l. Point l is the center of Circle q.

Coordinates of Point K are:

xk = -(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4

yk = (((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4

Point l is (0, (&#8730;3) – 1).

The equation for a line through two points (x1, y1) and (x2, y2) is given by

y = ((y2 – y1) x + (y1 x2 – y2 x1)) / (x2 – x1)

We map Point l as (x1, y1) and Point K as (x2, y2).

The equation for Line l is:

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1)) x + (((&#8730;3) – 1) (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))) / (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)

For verification we calculate the values of the symbols in the above equation to six digits accuracy.

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1)) x + (((&#8730;3) – 1) (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))) / (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)

y = (((0.732051 + &#8730;(2((3&#8730;3) – 2)))/4 – 0.731051) x + (0.732051 (-(0.732051 + &#8730;(2((3&#8730;3) – 2)))/4))) / (-(0.732051 + &#8730;(2((3&#8730;3) – 2)))/4)

y = (((0.732051 + &#8730;(2(5.196152 – 2)))/4 – 0.731051) x + (0.732051 (-(0.732051 + &#8730;(2(5.196152 – 2)))/4))) / (-(0.732051 + &#8730;(2(5.196152 – 2)))/4)

y = (((0.732051 + &#8730;(2(3.196152)))/4 – 0.731051) x + (0.732051 (-(0.732051 + &#8730;(2(3.196152)))/4))) / (-(0.732051 + &#8730;(2(3.196152)))/4)

y = (((0.732051 + &#8730;(6.392304))/4 – 0.731051) x + (0.732051 (-(0.732051 + &#8730;(6.392304))/4))) / (-(0.732051 + &#8730;(6.392304))/4)

y = ((3.260352/4 – 0.731051) x + (0.732051 (-3.260352/4))) / (-3.260352/4)

y = ((0.815088 – 0.731051) x + (0.732051 (-0.815088))) / (-0.815088)

y = (0.084037 x + (0.732051 (-0.815088))) / (-0.815088)

y = (0.084037 x + (-0.596686)) / (-0.815088)

y = (0.084037 x - 0.596686) / (-0.815088)

y = (0.596686 - 0.084037 x) / (0.815088)

y = 0.732051 – 0.103102 x

The above six-digit accuracy equation suggests that we could arrive at a simpler equation by expanding the terms.

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1)) x + (((&#8730;3) – 1) (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))) / (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1))/ (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x + (((&#8730;3) – 1) (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) / (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1))/ (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x + ((&#8730;3) – 1)

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1))/ (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x + ((&#8730;3) – 1)

Let z = (((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4. Then the equation becomes

y = ((z – ((&#8730;3) – 1))/ (-z)) x + ((&#8730;3) – 1)

y = ((&#8730;3) – 1) - ((z – ((&#8730;3) – 1))/ (z)) x

y = ((&#8730;3) – 1) - ((1 – ((&#8730;3) – 1)/z)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/z) x

Substituting for z, we get:

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x

Rechecking

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(5.196152 – 2)))/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(3.196152)))/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(6.392304))/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + 2.528301)/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/(((1.732051 – 1) + 2.528301)/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/(((0.732051) + 2.528301)/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((0.732051 + 2.528301)/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((3.260352)/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/(3.260352/4)) x

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/0.815088) x

y = ((&#8730;3) – 1) - (1 – (1.732051 – 1)/0.815088) x

y = ((&#8730;3) – 1) - (1 – (0.732051)/0.815088) x

y = ((&#8730;3) – 1) - (1 – 0.898125) x

y = ((&#8730;3) – 1) – 0.101875 x

There is discrepancy in the coefficient for x. We review the earlier computation from the colored equation below.

y = (((0.732051 + &#8730;(6.392304))/4 – 0.731051) x + (0.732051 (-(0.732051 + &#8730;(6.392304))/4))) / (-(0.732051 + &#8730;(6.392304))/4)

y = (((0.732051 + 2.528301)/4 – 0.731051) x + (0.732051 (-(0.732051 + 2.528301)/4))) / (-(0.732051 + 2.528301)/4)

y = (((3.260352)/4 – 0.731051) x + (0.732051 (-(0.732051 + 2.528301)/4))) / (-(0.732051 + 2.528301)/4)

y = ((0.815088 – 0.731051) x + (0.732051 (-(0.732051 + 2.528301)/4))) / (-(0.732051 + 2.528301)/4)

y = (0.084037 x + (0.732051 (-(0.732051 + 2.528301)/4))) / (-(0.732051 + 2.528301)/4)

y = (0.084037 x + (0.732051 (-(3.260352)/4))) / (-(3.260352)/4)

y = (0.084037 x + (0.732051 (-0.815088))) / (-0.815088)

y = (0.084037 x + (-0.596686)) / (-0.815088)

y = (0.084037 x -0.596686) / (-0.815088)

y = (0.596686 - 0.084037 x ) / (0.815088)

y = (0.732051 – 0.103102 x )

The discrepancy persists. Hence we retrace further.

y = (((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4 – ((&#8730;3) – 1)) x + (((&#8730;3) – 1) (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))) / (-(((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)

y = ((((0.732051) + &#8730;(2((3&#8730;3) – 2)))/4 – (0.732051)) x + (((&#8730;3) – 1) (-((0.732051) + &#8730;(2((3&#8730;3) – 2)))/4))) / (-((0.732051) + &#8730;(2((3&#8730;3) – 2)))/4)

Comparing with the reduction performed earlier we find that the second copying of 0.732051 was typed wrongly as 0.731051 and that error was carried through. Hence the correct equation for Line l is:

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x

21. Point O is a point of intersection between Circle q and Line l. The other point of intersection, Point P is of interest.

The equation for Circle q is:

x2 + (y - ((&#8730;3) – 1))2 = ((&#8730;3) – 1)2

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x

Substituting for y in the equation for the circle, we have:

x2 + (((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x - ((&#8730;3) – 1))2 = ((&#8730;3) – 1)2

Rearranging the terms shown in color we get:

x2 + (((&#8730;3) – 1) - ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x)2 = ((&#8730;3) – 1)2

As the colored terms cancel each other, we get:

x2 + ( - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) x)2 = ((&#8730;3) – 1)2

x2 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 x2 = ((&#8730;3) – 1)2

(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 ) x2 = ((&#8730;3) – 1)2

x2 = ((&#8730;3) – 1)2/ (1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

x = ± ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

The point of interest P has a positive X-coordinate and hence we take

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

Using the above value for x, the value of y is

y = ((&#8730;3) – 1) - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

Interchanging the colored terms we get:

y = ((&#8730;3) – 1) - ((&#8730;3) – 1) (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

Removing the common factor out

y = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 ))

Verification:

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(5.196152 – 2)))/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(6.392304))/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + 2.528301)/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/(((0.732051) + 2.528301)/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((0.732051 + 2.528301)/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((3.260352)/4))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/(0.815088))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – (0.732051)/(0.815088))2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – 0.732051/0.815088)2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (1 – 0.898125)2 )

x = ((&#8730;3) – 1) / &#8730;(1 + (0.101875)2 )

x = ((&#8730;3) – 1) / &#8730;(1 + 0.010379 )

x = ((&#8730;3) – 1) / &#8730;(1.010379 )

x = ((&#8730;3) – 1) / 1.005176

x = (0.732051) / 1.005176

x = 0.728281

y = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(5.196152 – 2)))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(5.196152 – 2)))/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(3.196152)))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2(3.196152)))/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(6.392304))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(6.392304))/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + 2.528301)/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + 2.528301)/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – 0.732051/((0.732051 + 2.528301)/4)) / &#8730;(1 + (1 – 0.732051/((0.732051 + 2.528301)/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – 0.732051/(3.260352/4)) / &#8730;(1 + (1 – 0.732051/(3.260352/4))2 ))

y = ((&#8730;3) – 1) (1 - (1 – 0.732051/0.815088) / &#8730;(1 + (1 – 0.732051/0.815088)2 ))

y = ((&#8730;3) – 1) (1 - (1 – 0.898125) / &#8730;(1 + (1 – 0.898125)2 ))

y = ((&#8730;3) – 1) (1 – 0.101875 / &#8730;(1 + (0.101875)2 ))

y = ((&#8730;3) – 1) (1 – 0.101875 / &#8730;(1 + 0.010379))

y = ((&#8730;3) – 1) (1 – 0.101875 / &#8730;(1.010379))

y = ((&#8730;3) – 1) (1 – 0.101875 / 1.005176)

y = ((&#8730;3) – 1) (1 – 0.101350)

y = ((&#8730;3) – 1) 0.89865

y = (0.732051) 0.89865

y = 0.657858

Point P is (0.728281, 0.657858)

Geogebra gives O(-0.73, 0.81) and P(0.73, 0.66)

The coordinates of Point P are verified. The corresponding equations are:

xP = ((&#8730;3) – 1) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 )

yP = ((&#8730;3) – 1) (1 - (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4)) / &#8730;(1 + (1 – ((&#8730;3) – 1)/((((&#8730;3) – 1) + &#8730;(2((3&#8730;3) – 2)))/4))2 ))

22. Line m is a line through the Points P and F.

23. Point Q is the intersection in 1st quadrant between Circle q and segment g that is side GH of the square. The other point, Point R in the 2nd quadrant is of interest.

Geogebra gives Q(0.68, 1) and R(-0.68, 1)

24. Segment n is the line joining Points R and N.

25. Point S is the point of intersection of Segment n and Line m.

Geogebra gives S(0.78, 0.82)

26. Circle r has center at Point B and passes through Point S. This circle is the result.

27. The area of this circle is calculated to be 4.

28. This area is recorded.

The value of radius r is of interest to us. It should be equal to 2/(&#8730;&#928;). From this equation we get an algebraic equation for &#928;.
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Ivan/square-circle
Posted on Thursday, March 06, 2008 - 06:21 pm:   

Best graph showing Squaring Circle, thanks to Mohideen Ibramsha, and Ed's works.

get-attachment.jpg

I hope this helps, since the earlier copy came out poorly, but higher definition here. Thanks Mohideen!

Ivan
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Ivan/elegant proof2
Posted on Friday, March 14, 2008 - 12:01 am:   

Proof that Squaring-Circle is possible with absolute certainty. :-)


This is a followup of the above Squaring Circle posts, particularly the one on Feb. 22, 2008, above which said:

If Pi* r^2 = s^2, where the left side is the area of the circle, and right side is the area of square with s = side

Which when reconfigured gives us r=s/sqrt pi, so that

Pi (s/sqrt pi)^2 = s^2, which proves the cicle can be squared

whereby s^2 = s^2.


This 'elegant and simple proof' is marred however by the fact that pi is a transcendental number, so the numeric values between circle and square, though perfectly fitted, would nevertheless still show a slight variance between the two.

But there is an even more elegant way to get around the fact that numerically Pi is transcendental: make s = pi

Now the equation reads:

Pi*(pi/sqrt pi)^2 = pi^2

so all that remains is Pi^2 = pi^2

Therefore, in this case only, there is absolutely no way for this equivalence to fail numerically, though we really may never know the values of both sides, except they are equal! :-)


Ivan
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Ivan/pi day
Posted on Friday, March 14, 2008 - 08:38 pm:   

3.1415926535 8979323846 2643383279 5028841971


_44491967_pyrm_getty_203.jpg
Pi is found in Great Pyramid at Gaza

BBC:

quote:

Life's work

One of the most endearing and enduring qualities of humans is that we're so often sure that we can find the answer to any problem if we just try hard enough. For 3,500 years, humankind has attempted to solve the puzzle of pi, also called "squaring the circle", calculating the exact ratio of a circle's circumference to its diameter. However, no matter how hard anyone tries, they find only a new approximation.

In ancient Greece, the great mathematician Archimedes worked tirelessly to discover the ratio, uncovering only a few digits of accuracy. When he tried to stop a Roman soldier from blundering over his work by shouting "do not touch my circles" he was unceremoniously murdered.


... Pi to die for! Of course, we're getting closer all the time. Hmmm... if you add the first 5 decimal numbers together, you get a number divisible by ten... hmmm...I wonder... if all the numbers succeeding added together brings 9 to the next zero digit?* ... What if we sum to infinity all the numbers that follow? Nahh.... can't lose sleep over this... there's lots of nines!... even some zeros too.... each latter 9 is closer to zero... ZZzzzzzz.

Back to Pi, which the Japanese had now calculate to over a trillion digits.

Have a Happy Pi Day! :-)

Ivan

*(this in principle is a variation of Zeno's paradox, 1/2 + 1/4 + 1/8 +...=> 1, where 3.14159 =>> 3.14160 etc. if each future decimal number is - in infinite summation - no more than one half the former, so that for example 3.141592653589 =>>> 3.141592653590 etc., where 9 goes to a number divisible by 10, eg. the next 'zero' as an infinite summation)

Also see: How to Build a Pyramid - Archeology Magazine
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Ivan/time math
Posted on Saturday, April 12, 2008 - 01:54 am:   

Time in a relativistic variable G universe.


6a00d8345157c669e200e54f8dfa208834-800wi.jpg
Salvador Dali clocks (interactive image- G time dilation)

Time is a mathematical concept. From when our very distant ancestors first marked days on a stick with a notch, we had invented time. Today time as a concept has been refined to nanoseconds, or 10^-9 seconds, with a still smaller Planck scale time of t = 5.4x10^-44 seconds. This gets time down to the Quantum level of Planck mass. However, in theory, it need not stop there, mathematically, because we can assign any unit of measure we wish to time, if there is a need. There should be no limit to how we can define time mathematically. In Einstein's relativity, time became a variable unit of measure, so that Time dilation became a workable variable unit of measure, from any observer's given perspective whether at rest or in motion, where the ticking of time is affected by the observer's frame of reference. In effect, without getting into relativity math, if time is seen as a unit of light speed, we might say t = d/c, which is a variation of t*v=d where v=c. So at rest we can say d=1, which then makes t=1/c, which then defines time in terms of light speed as a unit of c. However, if this is taken further to where c*t=c*1/c, we arrive at v=c as time t=1. (Conversely, if we define d=0 for the observer traveling at v=c, then t=0.) Not very useful, but it is merely another way to assign the unit of measure to time, whereby the observer traveling at light speed c sees all time as essentially standing still at t=1 (or t=0). Whether or not this actually happens for the observer, since for that observer time is ticking away same as before, even if traveling at v=c, is another matter. But time can be defined as 'standing still' if we wish to define it as such mathematically. For the observer 'left behind' at rest frame, time would indeed seem to have 'stopped' at v=c, in a relativistic sense.

200px-Time-dilation-001.svg.png400px-Time-dilation-002.svg.png

Observer at rest sees time 2L/c, while moving observer sees time>2L/c in time dilation.

So the time formalism in relativistic time dilation works out to be a function of delta time as: c85a497c5735f0b8fe3859ffd3c4ec43.png which is a far more complex derivation of the time unit of measure than a primitive 'notch on a stick'. In fact, this time dilation had been tested satisfactorily enough to be used in our GPS satellite systems to correct for relativistic time drift, so we know it works. Atomic clocks traveling around the Earth's gravitational mass will tick faster than those left behind on the planet surface (which is contrary to the Twins Paradox, where time is slower for the accelerated twin, except it is correct per Equivalence of slowing in an accelerated reference frame), though this may be more a factor of gravitational blue shift (it ticks faster in a low gravity field) than time speed, though it is perfectly valid to call it "accelerated time" from a mathematical formalism point of view. Time is whatever we wish to make it, as a mathematical concept, where clocks run faster in a weak gravitational field but slower in a stronger gravitational field (or slower in an accelerated frame). This is known as the gravitational time dilation. Tick tick tick is whatever we want it to be.

The complication of atomic clocks working slower in a greater gravitational field in the relativistic sense may not necessarily mean 'time' slows down, nor that atomic (oscillations) time 'speeds up' in a weak gravitational field. In effect, it may not be Time that changes but how we measure the atomic oscillations that changes. However, since this change in atomic clock oscillations mimics Einstein's relativistic time dilation, we work on the assumption that "time slows down" in the presence of a stronger gravitational field. In the same way light will red shift (slowing oscillations) coming out of a gravitational field, as was proven by the Pound-Rebka experiments (1959-1965), where Earth's gravitational red shift came out to be within a fraction of a percent of Einstein's prediction, viz. 2.5x10^-15 (over a 22.5 meter distance on Earth), so will atomic oscillations 'red shift'. However, the point here is that this may be a function of how atomic oscillations are affected, and not necessarily a function of time, though the two are matched by Einstein's relativistic math as being equal. But if the unit measure of time is not adjusted relativistically, then the faster or slower atomic oscillations do not define time as different, merely as different oscillations due to gravitational effects. Time would not change, only the measurement of time using relativistic terms would change, so that the conclusion would be if the unit measure of time is adjusted for relativistic effect, time would be changed with it, to slow down in a gravitational field. But if not, then time is a constant, and the only change, same as in GPS, is to adjust for how atomic clocks behave in a gravitational field.

But now what would happen in a variable G universe where the gravity 'constant' Newton's G is much greater in deep space, some 5 or 6 orders of magnitude greater, as to how the unit of time is defined mathematically? Current astronomical thinking has time adjusted for an expanding universe (where it slowed as of the 'inflationary period' of the Big Bang), since Newton's G is believed a universal constant. But if G is so much greater in space, and the distant light red shift observed is a function of a very long line of sight deep well of gravity from which this light reaches us (which means it is gravitationally red shifted, but no Doppler space expansion), so that it is red shifted at the Hubble constant z, then either time would have to be slowed down dramatically to relativistically adjust for this red shift, or the other option is to keep it as a constant and not adjust it relativistically for the greater gravity, so there is no slowed time. This is now a conundrum, because either way can work, though the latter is perhaps more true to a mathematical concept of time as a constant unit of measure, rather than adjusting it to fit the observed gravitational red shift. So which time is the 'proper time'?

There is no easy answer, because time can be whatever we wish to define it mathematically. Again, if we default to how atomic clocks work in a gravitational field, and use their relativistically changed unit of time, then it will read one way; whereas if we use a standard 'rest frame' unit of time to measure changes recorded through a greater gravitational field, we will read it another way. Which choice works better? That depends upon what we wish to measure. If we wish to measure time without adjusting it for the gravitational time dilation, then we should use a constant measure; but if we wish to measure time as a function of its gravitational time dilation, then we should use its relativistic time. It is really a matter of definition, as to which definition of time as a mathematical concept makes more sense to use in cosmological distances, as to how those distances affect light red shift. In one respect, time is a constant but gravity is a variable, and there is no space expansion (light redshift is a function of deep space high gravity); but in the other context, relativistic time is a variable and G is a constant, so there must be space expansion. However, which is true? This, alas, will be the great question to be answered in cosmology over the coming decades. I have my answer... I go with variable-G.

Of course, until we measure for Newton's G and its equivalent inertial mass away from Earth's known 1G, we are left guessing. So for now an expanding universe out of a Big Bang is how we see cosmology. But is it true? The answer to this conundrum may be a simple as a notch on a stick. Which is right?.. Time will tell.

300px-Velocity0_70c.jpg (interactive)
Doppler light shift for source traveling at v=0.7c, higher frequency on right, lower on left.


Ivan

Also see:
Something about light and time…
Quantum Entanglement
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Ivan/gravity time?
Posted on Wednesday, April 16, 2008 - 07:16 pm:   

Einstein's universe: dilated time as gravity idea.

Here's an interesting read on a physics student's idea that gravity is 'time dilation':

Basics of gravitation by W. Jim Jastrzebski

The idea is simple: the reason gravity acts as a pseudo-force is because of Einstein's General Relativity time dilation. However it starts to look shaky when he says:

quote:

Since for a particle at rest v = 0 then from (2) dm/dx = dm0/dx = 0. If it were also dc/dx = 0 we would have dE/dx = 0 and our dE/dx = 0 would fail as a candidate for gravitational force acting on the particle and E as a candidate forpotential energy of a particle. In teories of gravitation in which dc/dx = 0 it would be the end of our calculations. Luckily in the real world the light ray bends in the vicinity of a material object twice as much as it would be required by curvature of space and so it means that around materal objects speed of light changes and it better be dc/dx = - g/2c because otherwise energy (1) couldn't be potential energy.


So in the proof which follows it begins to look a little bit circular, in that the reason Newton's gravitation appears to be an attractive force (though he shows why it really is energy 'repulsive' force) is because of time dilation, but the reason we get time dilation is because of gravity.

Alas, it makes for a fun quick read, if anyone is interested. There is a discussion on BAUT, though as ATM its time is limited. See: Einstein's universe, if interested in the discussion that had followed.

Ivan
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Outta this world
Posted on Saturday, April 19, 2008 - 11:37 pm:   

Einstein was soooh cute!


einstein-on-bike.jpg (interelative)
Albert Einstein, Rock Star

Here are some 20 things bet you didn't know about ol' uncle Albert:
1  Who invented relativity? Bzzzt—wrong. Galileo hit on the idea in 1639, when he showed that a falling object behaves the same way on a moving ship as it does in a motionless building.
2  And Einstein didn’t call it relativity. The word never appears in his original 1905 paper, “On the Electrodynamics of Moving Bodies,” and he hated the term, preferring “invariance theory” (because the laws of physics look the same to all observers—nothing “relative” about it).
3  Space-time continuum? Nope, that’s not Einstein either. The idea of time as the fourth dimension came from Hermann Minkowski, one of Einstein’s professors, who once called him a “lazy dog.”
4  But Einstein did reformulate Galileo’s relativity to deal with the bizarre things that happen at near-light speed, where time slows down and space gets compressed. That counts for something.
5  Austrian physicist Friedrich Hasenφhrl published the basic equation E = mc2 a year before Einstein did.
6  Never heard of Hasenφhrl? That’s because he failed to connect the equation with the principle of relativity. Verdammt!
7  Einstein’s full-time job at the Swiss patent office meant he had to hash out relativity during hours when nobody was watching. He would cram his notes into his desk when a supervisor came by.
....

You can read it all here, all 20 of them with more links inside: http://discovermagazine.com/2008/mar/20-things-you-didn.t-know-about-relativity

Outta this world! :-)
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Circle Squaring
Posted on Wednesday, April 30, 2008 - 03:40 pm:   

As of this date a mathmatical analysis of the geomtetric construct relating to circle squaring performed by Major Edward A. Chesky, USA (RET) has been performed.

Analsys of the construct has revealed that the construct takes the circle squaring problem, using only a compass and ruler technique, to a level of accuracy never seen before. A previous effort by Da Vinci involved a complex integration of geometric properties to take the problem to a 99.8 percent degree of accuracy.

Major Chesky's solution takes the problem to a 99.99235 percent degree of accuracy and has also resulted in the development of a new equation for the determination of the value of Pi.

Further more, the geometric constuct above has raised a number of questions regarding whether of not a geometric construction for a alegebraic equation is the expression invariant of the relationship between the RHS and LHA of the algebraic equation. This construct has also opened the door to further research within the field of algebra.

The full details of this analysis will be published in appropriate Journals and credit will be given to all parties who contributed to the verification and analysis of this solution to the Circle Squaring problem.
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Ivan/space physics
Posted on Saturday, May 24, 2008 - 12:30 pm:   

What's in between 'space' or inside the SMBH?

256px-Magnetic_rope.png (interactive)
Birkeland current description- Wiki

Here is a part of an email I sent to a party who is an enthusiast of cosmology, in our private correspondence, name is left out:

Okay R____, I think we're getting somewhere here.  RE yours:
IF, you say that the SMO (Super Massive Object) is either a Compact Core Object (Which would mean it has some kind of 'physical surface' ie; Huge star like entity/Neutron/Quark (There is a guy who has a "Neutroid" theory) OR that the SMO is "White Hole" 'spewing' electrons/protons as the Jets, Then that is not a "Real Black Hole".
 
1. How do those 'jets' make the SMBH for the new galaxy it is supposed to be making?
2. How does your model explain the Voids between the galaxy clusters?
3, How does "Space" get here in the first place, and what is it made up of?

Most definitely the whole BB shebang is nonsense, so scratch any ideas of some grapefruit sized compact pre-time ball of plasma inflating suddenly into a whole universe 13.7 billion years ago.  That's just stupidity at the highest mathematical level.  So no Big Bang, and the universe's dimensions are unknown, age unknown, and that brings us down to what is happening inside galaxy centers.  Are they SMOs or SMBHs or SGMOs?

Okay, we only have distant observations to account for what is holding the galaxy together gravitationally, since it obviously does not fly apart, and interior gravitational dynamics show very high gravity activity, fast spin around the central galactic core, x-ray generation out axial poles, and a halo in most of them.  So what's going on?

What does that add up to?  First of all, there is not enough self-gravitating mass at the galactic center to account for the super gravity evident there, so something must exist at its center that is of exceptionally high gravity.  We cannot see past all the swirling dust and stars around the center of our own Milky Way to know.  Observing other galaxies at all angles gives us a clue, that a super massive gravity center does exist, and it may have an 'event horizon' from which no  light escapes, so it is 'invisible' to us, except for the polar jets of high energy.  We seem to think  those are positive charged jets, which escape out the axial line at near light speed, which itself then creates strong magnetic fields for the galaxy.  (We may in fact live in an electric universe, but it is not well defined as to what that means.)  The very powerful gravity of the galaxy center is not understood at present in any other way than a 'black hole', and it may be a 'super massive object', but if so, what is it made of?  Not neutron stars, since those exist independently.  

So my conclusion on this, since we can't get there to find out, is that we use whatever knowledge we have of local conditions and apply the physics there.  When I mentioned earlier Matusmoto's hot plasma simulation, there were characteristics of 'self-gravity' at the center of the spinning hot plasma.  That dovetails into what I realized from how works the equation made up of Louis de Broglie's quantum equation, E=hf, and Einstein's (really Thomson's) equation of E=mc2, but these were incomplete.  To make it work, I had to assume something, that e.m. energy and gravity are counter opposite forces, not complimentary but opposite, in the same way n* 1/n=1 are opposites.  The atom then becomes m=1, and E becomes n, and gravity becomes 1/n, per the Axiomatic equation's reasoning.  So that we get the full thing (not including magnetism, which is treated separately as another function of e.m.), looking like this:

1)  E=hf become E=hc/ (lamda*proton mass)  .... this is on the left side of Axiomatic, a quantum equatiion 

where the lambda is 1.32E-15 m, and proton mass is 1.67E-27 kg, and the whole thing works out for E=9E+16 Joules
(BTW, lambda 10^-15 m is about range for neutrinos)


Then on the right side we get the gravity equation portion, using proton-to-proton gravitational constant g, so that:

2)  E=mc^2 becomes E=(1- g)c^2

where m= kg/kg = 1 always ... using Earth based kilograms, but those are different per Equivalence in other G regions


When E => 0, look at what happens in the equation:

3)  0 = hc/ 0*proton mass = (1-1)c^2  ... where at no e.m. energy lamda disappears and proton gravity goes max to 1,

At that point, where there is no lambda (because it all cancelled out, which can ONLY happen when all lambda converges on a point from a spinning ambient hot-plasma sphere, as Matsumoto's simulation shows), the gravity goes to its maximum value, which I worked out using a conversion equation from proton-proton g to Newton's G:

G^2 = g c^2 pi^2  so that if g=1, you are left with:

G = (1)^1/2 c pi, which means G=c  (pi drops out on a point, since there is no sphere anymore) and that is what this interaction of quantum (left side equation) with gravity (right side adjusted) becomes at a galactic center, where you have Newton's G go to 3E+8 m^3 kg^-1 s^-2, so it 'eats' all the light it can, and it becomes invisible.  What's there?  We don't know...

Now is there an event horizon to such a point of maximum gravity?  Sure there is, but what's inside it?  Is it super massive matter, or is it empty of matter?  That I can't know until we duplicate this process in a lab, the way Matsumoto did, and start to study the science behind this phenomenon.  Then, and only after a lot of lab testing, can we understand what this means.  Guessing at what's in the black hole is good for storytelling and philosophy, but it is not science.  For that, we need to examine real evidence.  One of the evidenced energies coming out of Matsumoto's simulation of spinning hot plasma was magnetic fields mimicking the sun's surface; the other was polar jets of high particle energy. So we have the tools (in theory) to test this hypothesis, but we haven't done so.  Why not?

I think the answer is that we're stuck with Einstein's GR explaining the whole universe as if it were some giant space-time geometric reality, with gravity as a universal constant 'warping' space.. It's silly.  That is holding us back, and then led to stupid ideas like BB.  If we can get away from Einstein's long enough to observe what the variable factors of gravity (NOT a universal constant) are in relation to quantum energy, we will get one step closer to understanding both the universe and galactic black holes, including 'dark matter', which is just invisibly dark higher G space dust and gas very far from hot stars and galaxies.  Then it all falls together into a real theory, rather than that silly nonsense about expanding space and 13.7 billion blah blah stuff. ... SR is ONLY useful for observational purposes, has nothing to do with how works the universal physics, except as an observational tool to measure using light c.

 We need real science done once more, and Einstein's GR/SR is not the right path.  In fact, he led us astray for about a century, and we're way off track...

... where to look for this stuff on Humancafe:  

1)  Variable G:  http://www.humancafe.com/discus/messages/6/23.html#POST300

2)  Modern Universe in G-flat (really curved):  http://www.humancafe.com/discus/messages/88/475.html?1194407574

3)  Matsumoto's experiment:  http://www.humancafe.com/discus/messages/88/475.html#POST4550  (see Feb. 15, 2008 post)

4)  Deep Space gravitational redshift at 1z:  http://www.humancafe.com/discus/messages/88/185.html#POST3594
(where intergalactic space is 5 or 6 orders of magnitude greater than Newton's G on Earth)

5)  Index of gravity related research at Humancafe:  http://www.humancafe.com/discus/messages/294/294.html#POST3939


Okay, that's all for now!  Can this explain 'voids' between galaxy clusters?  Not any more than to say they're empty! ... It's just the space in between things, full of gas and energy, but at much lower density than Earth's atmosphere, where space density is about one atom per cubic centimeter.  What's in between those atoms?  Well... what's in between molecules of gas on Earth?  It's empty, no molecules in between molecules, so what's to explain?  It's like asking how could the universe exist? ...who knows!


Ivan

___________________________________________________________________________

Ps: Four things stand out that can make this variable G scenario a real possibility, what one we should look for in future space missions, as per Humancafe forums with reference links:

1) Pioneer Anomaly is the square root of distance whereby G increases with distance at the rate of about 1G per 1 AU, per Equivalent higher G: http://www.humancafe.com/discus/messages/6/23.html#POST300

2) Titan's atmosphere for a small moon (at about Saturn's 10 G), smaller than Mars and Mercury, has an extensive nitrogen atmosphere ten times taller than Earth's: http://www.humancafe.com/discus/messages/88/475.html#POST4696

3) Deep space gravity, if about the 'cut off' wavelength for photoelectric effect, yields inter-stellar space about 5 or 6 orders of magnitude greater than Newton's G (universal 'constant'), so distant intergalactic light redshifts at about 1z gravitationally coming out of a deep well line of sight, not Doppler 'expansion': http://www.humancafe.com/discus/messages/88/185.html#POST3594

4) The Boltzmann constant shows the difference between space Earth orbital Newton's G' = ~7.24E-11 m^3 kg^-1 s^-2 and Earth's measured G = 6.67E-11, if the Earth's interior heat is approximately 2500 Kelvin, so it adjusts accordingly: http://www.humancafe.com/discus/messages/88/185.html#POST3173


All of the above stemming from the Axiomatic Equation, and more, see June 25, 2007 post: http://www.humancafe.com/cgi-bin/discus/show.cgi?tpc=88&post=3950#POST3950

There is enough reason to believe we should look for the evidence, though the trick is to get past the Equivalence in G for kg'/kg we will encounter.
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An elegant universe
Posted on Tuesday, June 23, 2009 - 12:37 pm:   

The Universe is elegant - backlit rings of Saturn


20090110APODnewrings_cassini.jpg (interactive -BBC video)
Audio slideshow: Splendour of Saturn


This is pure elegance as it should be, simple.


[Note: If you click Rings of Saturn- Wiki image above, you will notice a rings 'distortion' over the planet's surface area. Is this a 'gravitational lensing' effect? In the enlarged version, you can see Earth as a tiny blue dot within the rings, about 10 o'clock.]

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