A Refutation of General Relativity

[Guest Zanket]

 

A refutation of general relativity (hereafter "GR"): At A, let a test particle be in free fall near a star. (All drawings are from the particle’s perspective.) At B, let the star be hurled into the particle at an arbitrary velocity v. Special relativity (hereafter "SR") applies to a direct measurement, so the star is length-contracted in the particle’s frame. At C, let the particle instead free-fall to hit the star at v. According to GR, a superset of SR, the star is not length-contracted in the particle’s frame. But B and C are identical situations at impact—GR cannot have it both ways. Then GR is refuted as inconsistent.

 

Drawing B, SR’s prediction, is validated by the muon experiment—a confirmation of SR—in which the whole Earth is length-contracted in the frame of a muon free-falling toward it, and by numerous books on SR: trans-galaxy rocket travel is possible in the crew’s lifetimes only if the whole galaxy is length-contracted in their frame. Then so must be the stars composing it.

 

Drawing C, GR’s prediction, is validated by the book Exploring Black Holes http://www.amazon.com/exec/obidos/tg/detail/-/020138423X/qid=1120352438/sr=1-1/ref=sr_1_1/103-7464968-4419002?v=glance&s=books, pg. 3-22: The general relativistic equation that returns the proper time elapsed of an object free-falling from rest at infinity (or a great distance) toward a Schwarzschild mass (i.e., a spherically symmetric, uncharged, nonrotating mass), is an integration, from a higher-altitude r-coordinate to a lower-altitude r-coordinate, of the equation dT = -sqrt(r / 2M) * dr, where dT is the increment of proper time, sqrt() is the square root function, r is the r-coordinate (Euclidian radius) of the object from the center of the mass, M is the mass in geometric units (same units as r), and dr is the increment of r-coordinate. The proper time elapsed is just the sum of the proper time the object takes to traverse each increment of the r-coordinate at the escape velocity at that r-coordinate. The same integration applies to Newtonian mechanics (GR shares Newton’s escape velocity equation; only the interpretations differ). Then in GR a Schwarzschild mass is not length-contracted in the frame of an object free-falling toward it. When the integration is from r = 2M (horizon) to r = 0 (singularity), the resulting equation is equivalent to 6.57 * 10^-6 (M / MSun) seconds, where M is the mass of the black hole and MSun is the mass of the Sun.

 

Drawing C is alternatively validated by eq. 51 (on pg. 9) of the PDF (Adobe Acrobat) file Exact Solutions of the Einstein Equations. Plug in 2m (horizon) for r2 and 0 (singularity) for r1. This results in 4/3 * m, where m is in geometric units. The mass of the Sun is 1477 meters, which is ((1477 meters) / (c = 299792458 meters / second)) = 4.927 * 10^-6 seconds of light-travel time. Multiply that by 4/3 to get 6.57 * 10^-6 seconds for the proper time it takes an object, having fallen from rest at infinity (or a great distance), to fall from the horizon to the singularity of a point mass equal to the Sun’s mass. This matches the result of the derivation cited above, from the book Exploring Black Holes.

 

Let a particle free-fall from rest at infinity (or a great distance) to a star whose escape velocity at its surface is almost c. The particle reaches the surface at almost c. SR predicts that the star will be length-contracted in the particle’s frame to almost zero length. Were the particle able to pass unimpeded through the star, it would do so almost instantly in its frame (by its clock). (The particle’s minimum velocity while traversing the star is at the star’s surface).

 

GR, however, says that the proper time for the particle to pass through this star is dependent on the star’s mass. The more mass, the more time required, with no upper time limit. This dependency is not because of some black hole strangeness—the derivation is not dependent on any feature of a black hole. The reason is because, in GR, the star is not length-contracted in the particle’s frame. The more massive the star, the greater the r-coordinate at which the escape velocity is almost c. Then the more massive the star, the greater the (uncontracted) diametral distance the particle must traverse to pass through the star.

 

GR is a superset of SR. Then every SR prediction must be equivalently predicted by GR. Because GR disagrees with SR for the same situation (drawings B and C), GR is refuted as inconsistent.

[Tormod]

I have one initial question. How can the drawings be from the particle's perspective when the particle is in the drawing?

[Guest Zanket]

“From the particle’s perspective” should not be taken too literally. It just indicates that the star is drawn as length-contracted if the star is length-contracted in the particle’s frame.

[Erasmus00]

Complete quote of first post removed by Tormod. Please keep quotes short, and only quote the necessary parts.

 

 

What you have done is confused the coordinates in GR. In order to see length contraction you have to create a system of coordinates that reflects the spatial and time dimensions of the falling particle. The standard solution around a spherical mass is the scwarszchild solution, and you can make coordinate transformations from scharzcshwild coordinates (in which the time coodinate is an observer at infinity, and the radial coordinate is derived from the area of spherical shells) to the reference of the observer. If you do this, you lose the spherical symmetry, and you will see length contraction.

-Will

[Guest Zanket]

What you have done is confused the coordinates in GR.

 

Can you please be clear as to which drawing, B or C, you contest? And then tell me what you think is wrong with the evidence I gave that validates the drawing. I cannot figure out that info from your post.

[Erasmus00]

Can you please be clear as to which drawing, B or C, you contest? And then tell me what you think is wrong with the evidence I gave that validates the drawing. I cannot figure out that info from your post.

 

Its not the drawings, its what you claim they demonstrate. You can (and do) have length contraction in general relativity. The situation at C is from an outside observers perspective, at B its from the particles perspective. Your claim that there is no contraction in GR is wrong. It only appears that way because you are using schwarzschild coords, not coords in the instantaneous lorentz frame of the particle.

-Will

[Southtown]

What a conicidence. I was just reading about relativity yesterday, for the first time. I still don't understand the connection drawn between perspective and reality. Is it all just a translation method for interpreting the "coded" observations we make into real measurments? But nevermind me, I find this debate fascinating.

[UncleAl]

A refutation of general relativity

There is no coordinate background in General Relativity. The ten equations that constitute General Relativity are not Euclidean or Newtonian. Special Relativity is not valid in the case of gravitational acceleration. Etc. You have not demonstrated competence in the discipline.

 

There is not a single incidence of disagreement between SR and GR predictions and empirical observations to the extreme limit of experimental certainty at any scale in any venue in 100 years of vigorous looking. Both are self-consistent geometries. They contain no internal errors and no internal contradictions. If you want to trash Einstein then you either you furnish a reproducible empirical falsification of prediction (not bloody well likely) or you reproducibly empirically falsify a founding postulate. The two weak GR postulates are Lorentz Invariance and the Equivalence Principle.

 

http://www.physics.indiana.edu/~kostelec/faq.html

Lorentz Invariance overview

http://www.npl.washington.edu/eotwash/spin1.html

http://www.npl.washington.edu/eotwash/publications/cpt01.pdf

Lorentz Invariance experiment in progress

http://www.mazepath.com/uncleal/qz.pdf

Equivalence Principle experiment in progress.

 

http://relativity.livingreviews.org/Articles/lrr-2001-4/index.html

http://arXiv.org/abs/gr-qc/0311039

http://www.weburbia.demon.co.uk/physics/experiments.html

Experimental constraints on General Relativity

 

http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf

Nature 425 374 (2003)

http://www.eftaylor.com/pub/projecta.pdf

http://www.public.asu.edu/~rjjacob/Lecture16.pdf

http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html

Relativity in the GPS system (weak field)

 

Science 303(5661) 1143;1153 (2004)

http://arXiv.org/abs/astro-ph/0401086

http://arxiv.org/abs/astro-ph/0312071

http://relativity.livingreviews.org/Articles/lrr-2003-5/index.html

http://skyandtelescope.com/news/article_1473_1.asp

Deeply relativistic neutron star binaries (strong field)

 

http://arxiv.org/abs/gr-qc/0306076.pdf

http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP

http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf

http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm

http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm

http://www.trimble.com/gps/index.html

http://sirius.chinalake.navy.mil/satpred/

http://www.phys.lsu.edu/mog/mog9/node9.html

http://egtphysics.net/GPS/RelGPS.htm

http://www.schriever.af.mil/gps/Current/current.oa1

http://edu-observatory.org/gps/gps_books.html

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

More GPS and General Relativity.

[CraigD]

According to GR, a superset of SR, the star is not length-contracted in the particle’s frame.

I believe this statement is incorrect. The theories of SR & GR says no such thing.

 

In SR, the only requirement for length contraction (given by 1/(1-v^2/c^2)) relative to 2 inertial frames is that at least one of them be accelerated. Acceleration in this context means simply mechanical acceleration – change in velocity, as measured in either frame. The cause of the acceleration isn’t important – i.e. it could be due to the force produced by a rocket motor on either the “particle” or the “star”, or due to acceleration produced by gravity. That the acceleration due to gravity can be expressed more generally and accurately with the space-time geometry of GR than with Newton’s Universal Gravitation does not set aside the length contraction described by SR.

 

A suggestion, echoing UncleAl's but with fewer links: when presenting a refutation of a mathematical Physics theory on the grounds it's inconsistent, start with its math and demonstrate the inconsistency algebraically. The math for an example like yours is not very hard, and the math for SR and GR are easily obtained (my link above will do). There’s nothing inherently wrong with using drawings, but are fewer and harder to find that math, and more prone to error and distortion.

[Jay-qu]

but B and C arent the same situation, in B the star is hurled at the particle - what is stopping the particle from also freefalling towards the star from gravity, hence increasing relativistic velocity...

[Guest Zanket]

Its not the drawings, its what you claim they demonstrate. You can (and do) have length contraction in general relativity. The situation at C is from an outside observers perspective, at B its from the particles perspective. Your claim that there is no contraction in GR is wrong. It only appears that way because you are using schwarzschild coords, not coords in the instantaneous lorentz frame of the particle.

 

Then you contest the evidence I gave that validates drawing C. The situation at C is from the particle’s perspective too, as validated by the math I cited, and the example in which I used it. Please tell me how this math is wrong or used wrong in my example.

 

If you want to trash Einstein then you either you furnish a reproducible empirical falsification of prediction (not bloody well likely) or you reproducibly empirically falsify a founding postulate.

 

Can you please be clear as to which drawing, B or C, you contest? And then tell me what you think is wrong with the evidence I gave that validates the drawing. Or do you contest my claim that B and C must match if GR is to be consistent? I cannot figure out that info from your post.

 

I believe this statement is incorrect. The theories of SR & GR says no such thing.

 

I gave validation for SR’s (drawing :) and GR’s (drawing C) predictions. You contest drawing C’s validation. Please tell me what you think is wrong with the evidence I gave that validates the drawing.

 

In SR, the only requirement for length contraction (given by 1/(1-v^2/c^2)) relative to 2 inertial frames is that at least one of them be accelerated. …

 

I cannot figure out how this info relates to the refutation. Can you elaborate?

 

A suggestion, echoing UncleAl's but with fewer links: when presenting a refutation of a mathematical Physics theory on the grounds it's inconsistent, start with its math and demonstrate the inconsistency algebraically. The math for an example like yours is not very hard, and the math for SR and GR are easily obtained (my link above will do). There’s nothing inherently wrong with using drawings, but are fewer and harder to find that math, and more prone to error and distortion.

 

The math for SR (drawing :D is so simple that it’s implied (nobody would understand the post unless they understood the basics of SR). For GR (drawing C) I gave the math, which shows that GR predicts that a mass is not length-contracted in the frame of a particle free-falling toward it. That is all the math of GR needed to validate drawing C. Then I showed that drawing B must match drawing C if GR is to be consistent. The refutation need not be more complex than that.

 

but B and C arent the same situation, in B the star is hurled at the particle - what is stopping the particle from also freefalling towards the star from gravity, hence increasing relativistic velocity...

 

They are the same situation because it is given that the velocity at impact in both B and C is v. In B, the star was hurled to impact the particle at v. Yes the particle would free-fall to increase its velocity after the star is hurled and prior to impact, but it increases to hit at precisely v.

[CraigD]

I (CraigD) said: In SR, the only requirement for length contraction (given by 1/(1-v^2/c^2)) relative to 2 inertial frames is that at least one of them be accelerated.

You (Zanket) said: I cannot figure out how this info relates to the refutation. Can you elaborate?

 

Pleased allow me to elaborate.

 

The essence of your argument, as I understand it, is:

1) According to SR, when the velocity of the sun toward the particle is increased by V, the diameter of the sun as measured from the particle is D1=D0/(1-V^2/c^2), where D0 is the diameter of the sun as measured from the particle before the increase in velocity. This is illustrated in drawing B.

2) When the velocity of the particle toward the sun in increased by V (by gravity, as described by GR), the diameter of the sun as measured from the particle is D2=D0. This is illustrated by drawing C.

3) Because D1 not= D2, SR contradicts GR.

 

The flaw I find in this argument is in step 2, D2=D0. This ignores SR. If step 2 follows SR, D2=D0/(1-V^2/c^2), D1=D2, and step 3 is false.

 

What I mean by “the only requirement for length contraction relative to 2 inertial frames is that at lease one of them be accelerated”, is the equation for length contraction given by SR, 1/(1-v^2/c^2), makes no distinction between a change in velocity of the star toward the particle and a change in velocity of the particle toward the star, nor does it specify how the change in velocity is effected.

 

You are arguing that how change in velocity V is effected determines whether SR applies. Your statements such as “GR is a superset of SR” lead me to suspect you have concluded this because you believe that when GR is used to describe something, SR should not be.

 

Often, it’s correct that “general” theory often supersedes one that is a “special case” of it. For example, Newtonian mechanics give kinetic energy as E=M*V^2, while Relativistic mechanics give it as E=M*c^2*(1/(1 - (V/c)^2)^.5 - 1). The Newtonian equation is a “special case” of the Relativistic one, and should be replace by it in calculations that require such high precision that the difference between them is significant.

 

SR, however, is not a special case of GR in the same sense that Newtonian mechanics is a special case of Relativistic mechanics. SR describes a universe with motion, but without gravity. GR describes a universe with gravity, but without motion. GR and SR combined describe a universe with both motion and gravity. GR does not give equations that replace those of SR. GR requires the equations given by SR. Its equations are derived from them and the addition of new postulates, most significantly the “general equivalency principle” that gravitational force is experimentally indistinguishable from any other, such as centrifugal force.

[Erasmus00]

Then you contest the evidence I gave that validates drawing C. The situation at C is from the particle’s perspective too, as validated by the math I cited, and the example in which I used it. Please tell me how this math is wrong or used wrong in my example.

 

I did tell you why the math was wrong. You are doing it in schwarzchild coordinates, which do not apply to the rest frame of the particle. You need to use coordinates which apply to the rest frame of the particle, then you'll see length contraction.

-Will

[Guest Zanket]

The essence of your argument, as I understand it, is:

 

If you say “to v” rather than “by v”, then it seems that you understand the argument.

 

The flaw I find in this argument is in step 2, D2=D0. This ignores SR. If step 2 follows SR, D2=D0/(1-V^2/c^2), D1=D2, and step 3 is false.

 

Your step 2 refers to drawing C. It isn’t me per se who ignores SR in drawing C. It is GR that ignores SR in drawing C, as evidenced by the math I cited. That’s the inconsistency that refutes GR.

 

What I mean by “the only requirement for length contraction relative to 2 inertial frames is that at lease one of them be accelerated”, is the equation for length contraction given by SR, 1/(1-v^2/c^2), makes no distinction between a change in velocity of the star toward the particle and a change in velocity of the particle toward the star, nor does it specify how the change in velocity is effected.

 

I would put this as, “length-contraction depends only on relative velocity.” And I agree, it doesn’t matter how that relative velocity is attained, whether by the star being hurled into the particle or the particle free-falling into the star.

 

You are arguing that how change in velocity V is effected determines whether SR applies.

 

It isn’t me per se who argues that. In GR’s math, the math I cited, the star does not length-contract in the frame of a test particle free-falling toward it. This disagrees with SR.

 

Your statements such as “GR is a superset of SR” lead me to suspect you have concluded this because you believe that when GR is used to describe something, SR should not be.

 

I do conclude that; see below.

 

SR describes a universe with motion, but without gravity.

 

Agreed.

 

GR describes a universe with gravity, but without motion. GR and SR combined describe a universe with both motion and gravity. GR does not give equations that replace those of SR. GR requires the equations given by SR.

 

I disagree. GR, as a superset of SR, describes a universe with gravity and motion. SR is fully contained within GR. SR is GR, applied to the special case of zero spacetime curvature. Except for the inconsistency I point out in the refutation.

 

When you use GR to make a prediction in a situation in which SR also applies, the prediction should be exactly matched by SR. The GR equations (such as the equation derived from GR that I citied, that shows the proper time it takes a particle to free-fall between r-coordinates) do not come with a caveat that essentially says, “a result from this equation is bogus until you additionally apply SR.” In my original post, I showed that GR and SR make different predictions for the same situation in which SR applies. You say that I am ignoring SR when using GR’s math. But it is impossible to ignore SR using any GR derivation, unless GR is inconsistent.

 

As I understand your disagreement of the refutation so far—correct me if I’m wrong—you disagree with the validation of drawing C, because you think I failed to additionally apply SR to that situation. And I say that that is not required, for GR is a superset of SR. Perhaps we should focus on settling this disagreement as to whether GR is a superset of SR. To that end, the book Exploring Black Holes, pg. 1-1, says (boldface mine), “General relativity—the Theory of Gravitation—describes matter and motion near massive objects.”

 

I did tell you why the math was wrong. You are doing it in schwarzchild coordinates, which do not apply to the rest frame of the particle. You need to use coordinates which apply to the rest frame of the particle, then you'll see length contraction.

 

It is not my math. I took the math right out of Taylor and Wheeler’s book, Exploring Black Holes. And other books and sources agree with them, such as the alternate source I cited. They are the ones who used Schwarzschild coordinates in the derivation. Nowhere will you find a reference in GR books as to a massive object length-contracting in the frame of a test particle free-falling toward it. This is not a concept in GR, and that is confirmed by the math I cited. So when you say that the math is wrong, you are actually agreeing with me that GR is refuted as inconsistent.

[Erasmus00]

It is not my math. I took the math right out of Taylor and Wheeler’s book, Exploring Black Holes. And other books and sources agree with them, such as the alternate source I cited. They are the ones who used Schwarzschild coordinates in the derivation. Nowhere will you find a reference in GR books as to a massive object length-contracting in the frame of a test particle free-falling toward it. This is not a concept in GR, and that is confirmed by the math I cited. So when you say that the math is wrong, you are actually agreeing with me that GR is refuted as inconsistent.

 

No, you misunderstand me. The math is fine, but does not apply to the picture you've drawn. And while you might not find the reference in GR books, (as its an example that isn't elucidating in the slightest) you can work it out yourself. Taylor and Wheeler aren't particularly interested in the special case of length contraction that you are. You've used the formulas they've derived but misinterpreted the results. The math you cited does NOT apply to the rest frame of the particle, which is where you would expect to see length contraction. If you want to find the length contraction, coordinate transform into the rest frame of the particle from the coordinates you are using. Try it, and you'll see what I mean. GR and SR are mathematically consistant.

-Will

[Guest Zanket]

The math you cited does NOT apply to the rest frame of the particle, which is where you would expect to see length contraction.

 

GR’s math I cited is for an equation that returns the proper time it takes a free-falling particle to traverse between two r-coordinates. Were this equation consistent with SR, that proper time would be reduced by length-contraction in the particle’s frame, just as it is for the muon in the muon experiment, a confirmation of SR. Then the derivation must incorporate length-contraction (i.e. it must apply to the rest frame of the particle) to be consistent with SR.

 

GR's math I cited applies to drawing C because it shows that there is no length-contraction of the star in the particle's frame; if there were, then a derivation of the proper time it takes the particle to traverse between two r-coordinates would reflect that, in order for the result to be accurate (consistent with SR).

 

Look at the example I gave in my original post, in which I used the GR equation to make a prediction, and compared it to SR’s prediction, for the star whose escape velocity at its surface is almost c. In the example, the maximum proper time that SR predicts it will take the particle to traverse the star is “almost instantly,” whereas GR’s prediction has no upper time limit; the result depends upon the star’s mass. SR’s result does not depend upon the star’s mass—for any given mass of the star SR’s maximum proper time prediction remains “almost instantly,” and that prediction is accurate for SR. GR and SR are clearly not mathematically consistent in that example.

[Erasmus00]

GR’s math I cited is for an equation that returns the proper time it takes a free-falling particle to traverse between two r-coordinates.

 

And I'm telling you the schwarzschild r coordinate can not be easily interpreted as a linear radius! It is defined by the area of spherical shells. Thats why you don't see the result you are expecting. You need a space coordinate that applies to linear distances in the rest frame of the particle. This is why you are mistaken.

-Will