Freethought & Rationalism Archive

Ted Hoffman · 10-04-2002, 02:26 AM

[ October 04, 2002: Message edited by: Intensity ]

Answerer · 10-04-2002, 02:40 AM

So whats the conclusion?

Jesse · 10-04-2002, 03:50 AM

Quote:

Intensity I agree with your objection that the GR, based on the rubber sheet analogy, violates the causality principle, but what about when one thinks of a photon of light travelling through space (in a geodesic) and having its path being "bent" by potential wells? Does that also violate the causality principle?

Tom Van Flandern In the geometric interpretation, it does because there is no force to induce change in the motion. In the field interpretation of GR, it depends.

Consider the Earth�s orbit around the Sun � clearly a curved path through space, and a geodesic path at that. Now choose two points along the orbit and stretch a taut rope between them. That is obviously a shorter path than the geodesic path. Now ask a relativist to explain how that can be. You will get a purely mathematical answer; e.g., �the geodesic path is an extremum in space-time�. But you are unlikely to get anyone to address the physics of this simple example.

I think I remember enough about GR to see what's wrong with this statement--"shortest path" does not mean that spatial distance is minimized, but that spacetime distance is minimized. In flat space the spatial distance between two points with coordinates (x1, y1, z1) and (x2, y2, z2) would be (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2...that's just the pythagorean theorem. The analogue of this for the spacetime distance between two events (t1, x1, y1, z1) and (t2, x2, y2, z2), where the t-coordinates stand for "time", would be (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2 - (t1-t2)^2. This spacetime distance is usually called "proper time", but I'm calling it spacetime distance here to make the comparison with ordinary spatial distance more clear. In both SR and GR, spacetime distance is seen as more fundamental than spatial distance, because spatial distance depends on your choice of reference frame while the spacetime distance between two points is invariant in all reference frames.

Once you realize that you're using spacetime distance instead of spatial distance, there is nothing very technical about the notion that the geodesic is the "shortest path." Shorter really does mean shorter--the spacetime "length" of a geodesic is the shortest of any path. Actually, to be technical the geodesic is the extremal spacetime distance, so there are occasional situations where there is no shortest path but there is a longest one, and that would be the geodesic. But I believe that in the example Van Flandern brings up above, the geodesic would indeed be the shortest path in terms of spacetime distance. I am not sure why he thinks that "you are unlikely to get anyone to address the physics of this simple example"--the answer seems pretty simple, he was using spatial distance when he should have been using spacetime distance. Maybe you could ask him about this next time you talk to him (but if you do, don't use 'spacetime distance' unless you explain what you're talking about, since it's not the usual terminology).

edit: actually, immediately afterwards Van Flandern made this comment:

Quote:

The geodesic path between two points in space at a certain initial speed is the one for which the smallest amount of proper time elapses. If the body deviates too far from a straight line, the elapsed proper time at that speed will be greater because the distance is greater. But if the exact straight line path were taken, the elapsed proper time would not be a minimum because that path goes through a stronger gravitational potential (e.g., closer to the Sun) than an almost-straight line that curves enough to keep a greater average distance from the Sun. So the geodesic path is the one where the elapsed proper time (not the �distance� is a minimum.

So he obviously understands that it's proper time (what I called 'spacetime distance') and not spatial distance that's supposed to be minimized along geodesics. So what exactly did he find troubling about the fact that a "taught rope" stretched between two points in an orbit is shorter than the curved orbit in terms of spatial distance? I don't understand the point of that comment.

[ October 04, 2002: Message edited by: Jesse ]

Ted Hoffman · 10-04-2002, 05:09 AM

Jesse,
Nice response, only problem was, you launched into a criticism before reading the whole post - you retreated gracefully though after realizing your error. Overzealous, are you? Or is it just raw impatience?

Being one who has denigrated this guy so egregiously, dont you think you its only proper that you say something concerning what you think regarding the disparaging links you provided? The GPS thingy, Einstein "jiggering" the equations, that he doesn't understand GR maths etc? Or are we still too ignorant to voice an opinion even after getting TVF's side of the story?

And Steve Carlip's affirmative comments concerning FTL speeds being possible? TVF's thesis (in the link I provided) DOES falsify SR doesnt it? (I expected Steve Carlip to repeat the argument about TVF using post hoc conclusions to make predictions or something to that effect)
Dont you think all these issues that arose here deserve some form of "closure" or redress - in light of the facts the emails have revealed?
Or do we just plod on as if they never arose?

Ted Hoffman · 10-04-2002, 05:53 AM

Here is Carl Brunsteins article <a href="http://www.angelfire.com/empire/intensity/brunstein.htm" target="_blank">Not-So-Cosmic Censorship and Black Holes</a> which TVF has made some comments in.

He provided it in response to a question I asked him about his "allegations" that Einstein had "jiggered" with some multipliers until the field equations came out "right" (based on what Einstein already knew - that Mercury's observed perihelion was 43 arc seconds per century more than predicted by Newton's theory) about which he (TVF) had said:

Quote:

"...the choice of coefficients of potential phi in the space-time metric is arbitrary. Einstein knew the unmodeled perihelion motion of Mercury, and therefore confined his attention to metrics that predicted this quantity correctly."

And Carlip had asserted:

Quote:

Van Flandern seems to be under the impression that there are a bunch of adjustable parameters in general relativity that can be fiddled with. This is certainly not true

I have provided the link with the equations. The document is supposed to demonstrate that as TVF said: "Although Brunstein’s solutions are all “mathematically equivalent” to the Schwarzschild solution, anyone can see that other choices that are not equivalent are also possible".

Oh, incidentally, it seems TVF is not the only expert who thinks GR equations were drawn from many other possible sets.

<a href="http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Pauli.html" target="_blank">Wolfgang Ernst Pauli</a>, who founded the Pauli principle or the exclusion principle and won Nobel Prize in 1945 for it said concerning Einstein's field equations in his (Wolfgang's) book Theory of Relativity: "...the many possible solutions of the field equations are only formally different. Physically they are completely equivalent."

"In other words, there is nothing in any of them which specifies that any one of them is the unique "right answer". Each solution is a system for describing physical events, and therefore may not contradict another solution with respect to the fundamental nature of those physical events." says <a href="http://www.anomalist.com/gonzoscience/blackholes.html" target="_blank">This site</a>

You be the judge.

[ October 04, 2002: Message edited by: Intensity ]

Answerer · 10-04-2002, 07:55 AM

Well, I feel that the site only mentions about the possibility of the non-existence of black hole rather than disproving the total credibility of GR and Einstein.

Jesse · 10-04-2002, 08:14 AM

Intensity:
Jesse,
Nice response, only problem was, you launched into a criticism before reading the whole post - you retreated gracefully though after realizing your error. Overzealous, are you? Or is it just raw impatience?

Not at all, my criticism still stands after reading past that paragraph (I often respond to things that catch my attention as I read them, especially in long posts like that)--the original comment still does not make sense. Notice that even before I read the comment about proper time I did not accuse Van Flandern of not knowing the difference between spatial distance and spacetime distance, I just said that he seems to ignore it in that paragraph, a fact which is made even more confusing by the fact that he mentions it in the next paragraph. It seems like sloppy argumentation, just like his comments about what is pulling objects "down" in the rubber sheet model.

Intensity:
Being one who has denigrated this guy so egregiously, dont you think you its only proper that you say something concerning what you think regarding the disparaging links you provided? The GPS thingy, Einstein "jiggering" the equations, that he doesn't understand GR maths etc? Or are we still too ignorant to voice an opinion even after getting TVF's side of the story?

As I said before, unless one already has a detailed understanding of the math it's just going to remain a he said/she said situation. Van Flandern says one thing when presenting his side, Carlip says something different when presenting his. How can we know who is correct?

Intensity:
And Steve Carlip's affirmative comments concerning FTL speeds being possible?

What the heck are you talking about? Carlip made it quite clear that he believes the equations of GR imply that gravitational influences travel no faster than c. For example, this comment by Carlip affirms my earlier post about electromagnetism and how it creates the appearance of instantaneous effects when a charge is moving at constant velocity, even though all effects actually travel at light speed:

Quote:

They're not the same as GR, but they give an example of the same type of phenomenon, where a force seems to point toward the ``instantaneous'' location of the source despite propagating at the speed of light. You'll find a nice discussion of this in Vol. II,
section 21-1 of the Feynman Lectures.

Note that Van Flandern's response to this is to claim that electromagnetic forces also propagate much faster than light! You'll find this in, for
example, a current thread entitled ``Spacetime Physics review'' in the Usenet newsgroup sci.physics.relativity. You say you're a layman,
and I don't know how much you know about Maxwell's equations, but this is a grotesque violation of the equations. Van Flandern is,
of course, welcome to propose a *different* theory that has the features he claims, but here, as in GR, he claims that he's merely "reinterpreting" Maxwell's equations, which is patent nonsense. < Intensity: I think Steve has made an error here, I think he meant to write "he's merely 'reinterpreting' GR field equations, which is patent nonsense">

Your clarification of Carlip's comment is wrong, BTW. Carlip meant that Van Flandern was "reinterpreting" Maxwell's equations just as he reinterprets GR--see his comment at the beginning of that paragraph, where he points out that Van Flandern claims electromagnetic effects are also instantaneous!

Here is another comment by Carlip showing he does not think GR allows FTL speeds:

Quote:

Intensity ...Lightspeed is not a universal speed limit. "

Steve Carlip It's nonsense. There is a rigorous proof that in GR, no gravitational
influence propagates faster than c: see Robert Low, Class. Quant. Grav.
16 (1999) 543. Van Flandern knows this paper. When first informed of it, he made up an answer (that it only dealt with ``gravitational
radiation''), apparently without reading it. He was told by the author that he was wrong, and that it referred to all gravitational effects.
Since then, when it is brought up he simply ignores it.

Here is the quote by Carlip which I think led you to the belief that he was saying GR does allow FTL propogation of gravity:

Quote:

Intensity 2. His arguments that FTL speeds are possible.

Steve Carlip In some theories, they are. In some, they aren't. There's not much
more to say. <Intensity

>

But since this directly contradicts the Carlip quote I posted above, I suspect that he is contrasting theories of gravity based on GR with theories of gravity that are not, otherwise his comment that "There is a rigorous proof that in GR, no gravitational influence propagates faster than c" would not make sense.

Intensity:
Dont you think all these issues that arose here deserve some form of "closure" or redress - in light of the facts the emails have revealed?
Or do we just plod on as if they never arose?

The situation remains the same--Carlip claims that GR forbids gravity traveling faster than the speed of light, while Van Flandern claims to "reinterpret" it to show that it can (and also, if Carlip is believed, to show that the same is true of electromagnetic influences!) As for the issue of "free parameters" that Einstein could have manipulated to fine-tune his precession-of-Mercury calculation, I did not see Carlip retracting his assertion from the article:

Quote:

Van Flandern seems to be under the impression that there are a bunch of adjustable parameters in general relativity that can be fiddled with. This is certainly not true

The quotes by Brunstein and Pauli do not really shed any light on these matters, since they refer to situations where there are different solutions of the field equations, they do not refer to free parameters in the equations. The fact that a single equation can have multiple solutions should not be surprising--think of x^2 = 9, for example, which can be solved by either x=3 or x=-3. In GR, multiple solutions would presumably involve different possible shapes of spacetime that satisfy the Einstein field equations as well as whatever other constraints are being considered in the problem at hand. When considering whatever constraints apply to the perihelion-of-Mercury problem, would multiple solutions occur here as well? Judging by his earlier comment I think Carlip would say no, and I am not even sure if Van Flandern would disagree, since his comment seemed to deal with free parameters rather than multiple solutions to the same equation.

edit: I just realized that Pauli's quote helps you even less than I thought:

Quote:

...the many possible solutions of the field equations are only formally different. Physically they are completely equivalent.

When a physics equation has multiple solutions that are "formally different" but are physically equivalent, that means each solution yields precisely the same physical predictions. So if there were multiple solutions to the field equations in the perihelion-of-Mercury problem, Pauli is saying they would all yield the same prediction for the actual amount of the perihelion we observe, which means that Einstein could not change his prediction by picking a different solution.

[ October 04, 2002: Message edited by: Jesse ]

Steven S · 10-04-2002, 09:32 AM

Quote:

Originally posted by Intensity:
[QB]Here is Carl Brunsteins article <a href="http://www.angelfire.com/empire/intensity/brunstein.htm" target="_blank">Not-So-Cosmic Censorship and Black Holes</a> which TVF has made some comments in.

I will gladly comment upon some articles you post,
however time constraints put a limit upon how much
I can contribute to the discussion. On the paper you link to...Since it seems there ws an error in how the text was encoded the equations are not loading up. Nevertheless, it seems the author is arguing that if you are clever enough you can pick a coordinate system for the Schwartzchild solution such that there is no singularity. If this is his argument then it is almost definetely false. I don't have my copy of Wald on hand but one of the singularity theorems states that for a body too massive to be supported by neutron degeneracy pressure gravitational collapse is unavoidable. Furthermore, this theorem is proved independent of any coordinate system.

Also Pauli might be saying that in GR depending upon your choice of coordinate patches you get seemingly different solutions. For example, in the Schwartzchild geometry you might see two singularities, one additional one at the event horizon which is unphysical. By changing coordinate charts you eliminate this unphysical singularity. But despite the nastyness of the first solution you still have the same physical situation. Physics is independent of any coordinate chart.

Steven S

[ October 04, 2002: Message edited by: Steven S ]

Ted Hoffman · 10-05-2002, 06:12 AM

Answerer Well, I feel that the site only mentions about the possibility of the non-existence of black hole rather than disproving the total credibility of GR and Einstein.

Intensity Well, it was not meant to disprove the total credibility of GR and Einstein.

Jesse Van Flandern says one thing when presenting his side, Carlip says something different when presenting his. How can we know who is correct?

Intensity It gives me great pleasure to read that beautiful and elegant question. Getting you to this indecisive, somewhat neutral position as concerns this controversy was an uphill task.
Phew! (A while ago, you would have gladly placed your bet on the side with the majority without posing that question)

Jesse the original comment still does not make sense.

Intensity Are you accusing him of being incoherent? I think his point was that physicists use analogies that rely on eucledian space and when pressed to explain why a straight spatial distance is not the shortest path, they get confounded and resort to obfuscation instead of underlining the fact that space in GR terms is manifold with a metric" and that there is already a well-defined means of defining paths between points and measuring their distance - not just in terms of lines. Incidentally he is not the only one.
Read the quote below:

Quote:

Do physicists misunderstand GR? Emphatically yes. Many, perhaps most, learned physicists do not understand GR. The most common interpretation in physicists' minds is that GR predicts that space gets curved by presense of mass. In curved space, straight lines get bent, therefore object fall to earth rather than flying away in a straight line. This is a completely incorrect understanding of GR ... GR does indeed have a spatial curvature component, but it is so miniscule that it couldn't make a speck of dirt fall to the earth. The falling in the GR actually comes from spacetime-curvature, not from space-curvature [Intensity: as the rubber sheet analogy misleads us to think]. And yet there have been interpretations of GR such as "matter tells space how to curve, space tells matter how to move." By claiming that space curvature is the fundamental agent for gravitational movement, this phrase clearly illuminates the fundamental lack of understanding of GR that physicists suffer from.

<a href="http://www.mukesh.ws/" target="_blank"> Says this page</a>

Jesse It seems like sloppy argumentation, just like his comments about what is pulling objects "down" in the rubber sheet model.

Intensity You obviously did not understand his argument. Let me first post the salient parts:

Quote:

A gradient, a slope, or a curvature cannot induce a body at rest in a field to begin moving unless a force acts on that body. This is because, without a force to initiate motion, the body has no reason to choose any one direction over any other direction...In the rubber sheet analogy, if the small target body is at rest on the side of a dent caused by a source mass, it will remain at rest forever until some force acts. The rubber sheet analogy works in our imaginations only because we instinctively imagine gravity under the rubber sheet, with its pull providing a meaning to the concept of “downhill”. But without pre-existing gravity, the small body has no cause to accelerate, either on the rubber sheet or in the geometrical interpretation of GR. The causality principle is violated.

This causality principle is violated because if the rubber sheet and balls were to be placed in an inertial frame (as it should be), the ball would not move at all (no force to propagate it) so the analogy violates the causality principle (which requires an absolute cause-consequence order of events). I would also add its misleading because one can think that space curvature is what makes the ball go down (which is true but misleading).

Jesse But since this directly contradicts the Carlip quote I posted above, I suspect that he is contrasting theories of gravity based on GR with theories of gravity that are not, otherwise his comment that "There is a rigorous proof that in GR, no gravitational influence propagates faster than c" would not make sense.

Intensity It makes total sense. It means he revised his earlier position. His position has changed, while you are here struggling to understand (or is it "accept"?) that.
He said FTL speeds are possible. End of Story . (His vague allusion to "being possible in some theories" obviously meant FTL speeds are possible with GR and LR but not with SR - his "theres not much more to say" is evocative of a man who has resigned himself to the state of affairs).

Jesse The situation remains the same...

Intensity It has changed very dramatically for me however, thanks to the beautiful question you asked above.

Jesse The fact that a single equation can have multiple solutions should not be surprising--think of x^2 = 9, for example, which can be solved by either x=3 or x=-3. In GR, multiple solutions would presumably involve different possible shapes of spacetime that satisfy the Einstein field equations as well as whatever other constraints are being considered in the problem at hand

Intensity It quite disapointing that you can use a simplistic linear equation of x^2 to state the incorrect proposition that "a single equation can have multiple solutions". This is not what the argument is about. Its not about having multiple solutions. Please, and these equations are non-linear. Note that please.

Lets review what Flandern said:

Quote:

Of course, GR has selected one particular form for the field equations, whose solution leads to the Schwarzschild metric or other equivalent metrics, out of a potentially infinite number of possibilities. [Intensity: its about multiple approaches to the solution NOT multiple solutions] Having made its choice, there are no further adjustable parameters in the GR field equations [Intensity: which is the platform from which Carlip was arguing] . But when Einstein was originally trying to pick the right form for the field equations, he did have many choices [Intensity: but his choices were dictated by what parameters brought the correct precession of the perihelion of mercury (5600 seconds per century?) - which Einstein knew beforehand]. In fact, Alley often quotes Einstein with words to the effect that “The left-hand side of the field equations is like a fine marble; but the right-hand side consists of perishable wood.” [Intesity: these are non-linear equations, thats why your x^2 is terribly off the mark] The Yilmaz variant is an example of another choice, in which field stress energy is added to matter stress energy on the right-hand side. [Intensity: this is evidence, if you question it, please find out about the factuality of this claim] So as you see, Carlip here is using a disingenuous play on words when he says there are no adjustable parameters in GR. There are no adjustable parameters in any theory once specific values are set.

Jesse When considering whatever constraints apply to the perihelion-of-Mercury problem, would multiple solutions occur here as well?

Intensity Come on Jesse, we dont need Carlip to figure out this one for us. The only thing that I keep asking myself are: did he really know thre precession of the perihelion of mercury? And if he did, how did he know it?
But if we agree that he did know it beforehand, then its clear that whatever metrics, parameters and equations ane mathematical structures he used, he chose those that conformed to what he already knew. I know he used Riemannian geometry, he tried Eucledian Geometry and Gaussian geometry and with the help of Grossman (his friend and a great mathematician), he developed a general theory of relativity (based on the "Einstein field equations") on what was now called "Gaussian Geometry" .
The precession of the perihelion of mercury is one of the three tests of GR, besudes the deflection of light and the gravitational red shift of light. So with 1/3 of the battle won, the rest was a joyride for GR. Gravitational radiation has not been practically tested as the detection centers were shut down for repairs in 1987 when they should have detected gravitational radiation from a supernova. Other esoteric predictions like the existence of black holes are still on shaky ground.

Jesse Pauli is saying they would all yield the same prediction for the actual amount of the perihelion we observe, which means that Einstein could not change his prediction by picking a different solution.

Intensity NOTE THAT he is talking of the Einstein field equations (a discrete set) not any other equations (of course they have to give "equivalent" predictions - thats why Einsten chose and modeled them!)
I hope you now have a better understanding of the thrust of this argument concerning the equations and parameters.

Steve S I will gladly comment upon some articles you post, however time constraints put a limit upon how much I can contribute to the discussion..

Intensity I understand, I appreciate your effort.

Steve S On the paper you link to...Since it seems there ws an error in how the text was encoded the equations are not loading up.

Intensity I am sorry about this, I have uploaded all related images - it doesn't seem to be working.

Steve S Furthermore, this theorem is proved independent of any coordinate system.

Intensity If its a GR theorem, I would be interested in knowing about this GR theorem that is not based on any coordinate mathematical calculations .

Steve S Also Pauli might be saying that in GR depending upon your choice of coordinate patches you get seemingly different solutions.

Intensity I think you misunderstood - its the equations that are "formally" different. The solutions however are equivalent.

[ October 05, 2002: Message edited by: Intensity ]

Steven S · 10-05-2002, 09:12 AM

Quote:

Originally posted by Intensity:

Intensity If its a GR theorem, I would be interested in knowing about this GR theorem that is not based on any coordinate mathematical calculations.

See chapter 9 of Robert Wald's book General Relativity. To make any sense of this you will need to know a good deal of modern differential geometry.

Quote:

Intensity I think you misunderstood - its the equations that are "formally" different. The solutions however are equivalent.

So are saying that EFE's as a set of partial differential equations have a problem with uniqueness? If this is the case, AFAIK, you are wrong at least for the physically interesting solutions to the EFE. Again see Wald's book.

Steven S

10-04-2002, 02:26 AM	#21
Ted Hoffman Veteran Member Join Date: Feb 2001 Location: "" Posts: 3,863	[ October 04, 2002: Message edited by: Intensity ]</p>

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10-04-2002, 02:40 AM	#22
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	So whats the conclusion?

10-04-2002, 05:09 AM	#24
Ted Hoffman Veteran Member Join Date: Feb 2001 Location: "" Posts: 3,863	Jesse, Nice response, only problem was, you launched into a criticism before reading the whole post - you retreated gracefully though after realizing your error. Overzealous, are you? Or is it just raw impatience? Being one who has denigrated this guy so egregiously, dont you think you its only proper that you say something concerning what you think regarding the disparaging links you provided? The GPS thingy, Einstein "jiggering" the equations, that he doesn't understand GR maths etc? Or are we still too ignorant to voice an opinion even after getting TVF's side of the story? And Steve Carlip's affirmative comments concerning FTL speeds being possible? TVF's thesis (in the link I provided) DOES falsify SR doesnt it? (I expected Steve Carlip to repeat the argument about TVF using post hoc conclusions to make predictions or something to that effect) Dont you think all these issues that arose here deserve some form of "closure" or redress - in light of the facts the emails have revealed? Or do we just plod on as if they never arose?

10-04-2002, 07:55 AM	#26
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	Well, I feel that the site only mentions about the possibility of the non-existence of black hole rather than disproving the total credibility of GR and Einstein.

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