Freethought & Rationalism Archive

Answerer · 10-02-2002, 04:18 AM

It is funny to note that even after so many experimental confirmations and applications on relativity. Many people are still skeptic of GR and its founder.

Ted Hoffman · 10-02-2002, 04:48 AM

Jesse,
Thanks for your serious response. I really appreciate the way you are handling this seriously. I must apologise for my incorrect interpretation of Van Flanderns objection concerning the rubber sheet analogy. His main objection is that it violates the causality principle (that crap about the sheet bending downwards and self-referencing argument was mine, not his).

I have noted your comments and written to Steve Carlip (I understand he is an expert in the mathematics of gravitation physics) I await his response. Your haughty and disdainful attitude about my ability to understand the answers for the questions I have asked aside, I just hope to get some concrete response concerning all allegations against Tom V.F. all I have seen so far is "you are incompetent because you dont agree with us" or "the fact that you even question the formulas is in itself evidence that you don't understand them". Even if I can't understand the math, at least it will be a specific valid response to whatever arguments TVF is advancing and I can read further or ask an expert to explain to me what the heck the formulas mean and so on.

Save me the superciliousness please; you don't know me that well.

[ October 02, 2002: Message edited by: Intensity ]

Steven S · 10-02-2002, 07:30 AM

How can you tell Van Flandern counters the criticism of his debunkers? Do you know GR?
In anycase, I suggest this archived collection of posts from sci.physics.* dealing with Van Flandern's
claims:
<a href="http://math.ucr.edu/home/baez/PUB/debate" target="_blank">http://math.ucr.edu/home/baez/PUB/debate</a>

Steven S

Jesse · 10-02-2002, 09:18 AM

Intensity:
Thanks for your serious response. I really appreciate the way you are handling this seriously. I must apologise for my incorrect interpretation of Van Flanderns objection concerning the rubber sheet analogy. His main objection is that it violates the causality principle (that crap about the sheet bending downwards and self-referencing argument was mine, not his).

Not true, Van Flandern said this in the <a href="http://groups.google.com/groups?q=the+speed+of+gravity+repeal+speed+limit&h l=en&lr=&ie=UTF-8&selm=8oafnc%248gr%241%40nntp9.atl.mindspring.net &rnum=1" target="_blank">post</a> you referred to earlier:

Quote:

Just think about the rubber sheet analogy, even as an analogy. If the
target body sits on the side of a dent in the rubber sheet, why wouldn't it
stay in place forever? What gives the target body a sense of which direction
is "down" unless a tangible force (such as gravity under the sheet) comes
along and gives it a push or pull in some preferred direction? Those are the
kinds of issues that equations alone cannot begin to answer. But enabling
possible physics answers to such questions is what my paper is all about.

Looks like he is making just the same mistake in his understanding of the rubber sheet analogy.

Intensity:
I have noted your comments and written to Steve Carlip (I understand he is an expert in the mathematics of gravitation physics) I await his response. Your haughty and disdainful attitude about my ability to understand the answers for the questions I have asked aside

There is nothing "haughty and disdainful" about noting that someone who is not extremely well-versed in general relativity would not be able to follow a mathematical derivation of the speed of gravity in GR--I know I certainly couldn't, having taken only a single introductory class in the subject. I guessed that you were probably not any more familiar with the detailed mathematics of GR than I, am I wrong on this?

Intensity:
I just hope to get some concrete response concerning all allegations against Tom V.F. all I have seen so far is "you are incompetent because you dont agree with us" or "the fact that you even question the formulas is in itself evidence that you don't understand them".

Again, remember that we are not debating empirical questions about how gravity works in real life, but simply mathematical questions about GR itself. And much more specific allegations have been offered so far, specifically the allegation he is wrong about there being a free parameter other than G in the spacetime metric, and also that he is wrong that general relativity predicts that gravity should be instantaneous (regardless of the empirical issue of whether it is instantaneous in real life). Also, of course, I felt that he was incompetent for his misunderstanding of the rubber sheet analogy, which I don't think any expert in relativity would make.

Intensity:
Even if I can't understand the math, at least it will be a specific valid response to whatever arguments TVF is advancing and I can read further or ask an expert to explain to me what the heck the formulas mean and so on.

How? If he agrees that general relativity says gravity moves at c or that there is no free parameter in the space-time metric, how could he make a case for this except by going into the details of the math?

Intensity:
Save me the superciliousness please; you don't know me that well.

You are either very well-versed in the math of GR or you're not. I hardly think there is anything "supercilious" about pointing out that if you're not (and I'm not either, as I've said), then you won't be able to follow the details on this issue. Anyway, as far as haughtiness goes, your constant insinuations that my point of view is based only on dogma and close-mindedness come across as pretty haughty in themselves.

[ October 02, 2002: Message edited by: Jesse ]

atrahasis · 10-03-2002, 12:05 AM

sorry, wrong login

[ October 03, 2002: Message edited by: Black Moses ]

Ted Hoffman · 10-03-2002, 12:29 AM

Steven S: Do you know GR?

Intensity: Do you?

Jesse: Not true, Van Flandern said this in the post you referred to earlier:

Intensity: Causality principle please. Lets not misrepresent what he is arguing. If you want to insist, fine. I have withdrawn what I said earlier.

Jesse: There is nothing "haughty and disdainful" about noting that someone who is not extremely well-versed in general relativity would not be able to follow a mathematical derivation of the speed of gravity in GR--I know I certainly couldn't, having taken only a single introductory class in the subject. I guessed that you were probably not any more familiar with the detailed mathematics of GR than I, am I wrong on this?

Intensity: Its quite simple my friend: DONT doesnt mean CANT ok? You don't know how much I am ready to put on this. Besides, I am not you, so projecting your inability to grasp GR equations on me is incorrect.

Jesse: Again, remember that we are not debating empirical questions about how gravity works in real life, but simply mathematical questions about GR itself.

Intensity This is where y'all go very wrong. He has no problem with the math at all.
His problem is not that the maths is wrong.
Let me repost what he said earlier:

Quote:

I'm pointing out that this mathematical approach pays a terrible price in physics by violating the causality principle. Those equations may work, but call for instantaneous updating of distant fields to infinity, or the absence of regeneration in static fields, either of which makes the acceleration of bodies magical (i.e., without physical cause)....

To use a loose analogy, you cite equations that describe the acceleration of bodies, but not the cause of that acceleration. But equations, however elegant, do not have the means to make physical bodies accelerate. Only interaction with a tangible entity can do that. If a "field" or "curved space-time" is the cause of the acceleration of a target body, then the field or curvature must consist of tangible entities that can act on matter.

Are we clear? Its not the math, its the practical applicability.

Though I must admit, its incorrect to direct his criticism to an analogy. He should be addressing potential wells vis a vis some photon travelling in space, not some silly analogy of a rubber sheet and some two balls.

Jesse : How? If he agrees that general relativity says gravity moves at c or that there is no free parameter in the space-time metric, how could he make a case for this except by going into the details of the math?

Intensity : And that is what I am looking forward to.

Jesse You are either very well-versed in the math of GR or you're not.

Intensity This is simplistic and fallacious. I can follow an argument, I have done maths and physics to a respectable level and where I do not follow I can read more or ask experts.

Spare me this loser talk.

Jesse : I hardly think there is anything "supercilious" about pointing out that if you're not (and I'm not either, as I've said), then you won't be able to follow the details on this issue.

Intensity: I don't need you to tell me what I can or cannot understand. Let me be the judge of that Jesse. Please.

If you can't understand, shut the hell up and let me try. Ok?

Jesse Anyway, as far as haughtiness goes, your constant insinuations that my point of view is based only on dogma and close-mindedness come across as pretty haughty in themselves.

Intensity For someone who claims to know nothing about GR to turn around and claim an expert does not understand the GR field equations is pretentious, childish.

As far as other experts stance concerning TVFs ideas, I am well aware of them, thanks to you. But what I have seen so far is that TVF was wrong in thinking GPS programmers have not incorporated GR in their software (And I dont give a rats ass about whether he is wrong or right about GPS), that he does not understand the GR field equations (and I have seen no evidence for that), that he said Einstein "jiggered" with the multipliers and that TVF is therefore wrong in assuming there are "free" parameters where there are none (I have yet to get his side of the story on this - and I dont think its that important anyway), that he is a crank (an ad hominem - anyone who questions GR is a crank [some psychological crap about the need to feel significant and attract attention to oneslef]) and that other experts disagree with him (on the grounds that he questions standard theories, which they accept and do not question).
All that I have seen has not shown me the following (which are what I am interested in):

1. That TVF is wrong when he argues that FTL speeds are possible and his demonstrations and calculations are consistent with LR, GR but falsifies SR which forbids propagation speeds faster than lightspeed in forward time.

2. That he is wrong to argue that "General relativity has a geometric and a field interpretation. [but] If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated"

3. Evidence that TVF does not understand GR field equations or any (other) GR maths.

That is all. Let's see what Steve Carlip has to say. There is no hurry. If you have evidence for the three, point me to them

Steven S · 10-03-2002, 05:42 AM

Quote:

Originally posted by Intensity:
Steven S: Do you know GR?

Intensity: Do you?

Yes, but I'm not an expert. I've had two courses on GR, lots of differential geometry, plus my first advisor was a relativist before I switched to particle theory. I've also written a pedagogical article describing three ways to go about the canonical quantization of gravity.
My point is I don't understand why people spend time arguing over the merits of scientific theory X vs Y when they really do not understand eithor X or Y. How can you say Y is better than X when you don't even know what X says? I certainly don't try to counter criticism Behe levels at evolution because I know next to nothing about molecular biology.

Steven S

[ October 03, 2002: Message edited by: Steven S ]

Jesse · 10-03-2002, 08:07 AM

Jesse: Not true, Van Flandern said this in the post you referred to earlier

Intensity:
Causality principle please. Lets not misrepresent what he is arguing. If you want to insist, fine. I have withdrawn what I said earlier.

But explain to me how the following direct quote of Van Flandern has anything to do with the causality principle:

Quote:

If the target body sits on the side of a dent in the rubber sheet, why wouldn't it stay in place forever? What gives the target body a sense of which direction is "down" unless a tangible force (such as gravity under the sheet) comes along and gives it a push or pull in some preferred direction?

To me it looks for all the world like he is worrying about the force pulling objects "down" into dents in the rubber sheet, which would be a total misunderstanding of the rubber sheet analogy. But if you can explain to me how he is actually talking about the "causality principle" here (ie the question of whether gravitational effects travel at FTL speeds) then I'm willing to listen.

Jesse: There is nothing "haughty and disdainful" about noting that someone who is not extremely well-versed in general relativity would not be able to follow a mathematical derivation of the speed of gravity in GR--I know I certainly couldn't, having taken only a single introductory class in the subject. I guessed that you were probably not any more familiar with the detailed mathematics of GR than I, am I wrong on this?

Intensity:
Its quite simple my friend: DONT doesnt mean CANT ok? You don't know how much I am ready to put on this. Besides, I am not you, so projecting your inability to grasp GR equations on me is incorrect.

No need to be rude, dude. I didn't say that I had an inability to grasp GR, and I didn't say you did either. I just said that I don't think either you or I currently know enough about GR to be able to follow the mathematics involved in the speed-of-gravity debate. Do you have a detailed understanding of differential geometry and tensor mathematics? These are not things that could be explained fully in an email or on a web page, you'd need to hit the books to pick them up. If you're willing to do that, I applaud the effort. I'd suggest finding a copy of <a href="http://www.amazon.com/exec/obidos/ASIN/0716703440/internetinfidelsA/" target="_blank">Gravitation</a> by Misner, Wheeler, and Thorne, which is pretty much the gold standard in GR textbooks.

Jesse: Again, remember that we are not debating empirical questions about how gravity works in real life, but simply mathematical questions about GR itself.

Intensity
This is where y'all go very wrong. He has no problem with the math at all.
His problem is not that the maths is wrong.

Look, the question of whether there are free parameters in the space-time tensor is a mathematical question, not an empirical one. Likewise, the question of whether the Einstein field equations imply gravitational effects travel at c or at infinite velocity is also a mathematical question, independent of the question of how fast they travel in real life.

All the relativists who are asked about this question say one thing, Van Flandern says another. Maybe you are confident that Van Flandern is right and they are wrong, but either way, these are mathematical questions and not empirical ones, I don't see how you can disagree with that.

Intensity:
Let me repost what he said earlier:

Quote:

I'm pointing out that this mathematical approach pays a terrible price in physics by violating the causality principle. Those equations may work, but call for instantaneous updating of distant fields to infinity, or the absence of regeneration in static fields, either of which makes the acceleration of bodies magical (i.e., without physical cause)....

But again Intensity, this is an issue where all the relativists say Van Flandern has gotten the math wrong, that when you actually study the equations of GR they do not involve "instantaneous updating of distant fields", but only local changes that propogate at the speed of light. Van Flandern is saying one thing about what the equations imply, all the relativists are saying something different; one side must be getting the math wrong, period.

Intensity:
Are we clear? Its not the math, its the practical applicability.

The point is that his statements about what the equations of GR do or do not imply are disputed by all the relativists who are asked about this issue. And deciding who is right and who is wrong is just a mathematical issue. I realize that Van Flandern is also questioning the practical applicability of the equations of GR, but that's not what I'm interested in here, OK?

Jesse You are either very well-versed in the math of GR or you're not.

Intensity
This is simplistic and fallacious. I can follow an argument, I have done maths and physics to a respectable level and where I do not follow I can read more or ask experts.

I didn't say you couldn't read more. I just said that until you do, you will not be capable of following the arguments--it would be like trying to understand Maxwell's equations when you had never taken calculus.

Jesse : I hardly think there is anything "supercilious" about pointing out that if you're not (and I'm not either, as I've said), then you won't be able to follow the details on this issue.

Intensity:
I don't need you to tell me what I can or cannot understand. Let me be the judge of that Jesse. Please.

Again, I think you are misunderstanding me. I do not mean to imply that you are incapable of understanding arguments about GR, just that you don't currently have the background knowledge to follow them. And I don't think you'll find sufficiently detailed explanations online, you (or anyone else) would need to hit the books to pick it up.

Jesse Anyway, as far as haughtiness goes, your constant insinuations that my point of view is based only on dogma and close-mindedness come across as pretty haughty in themselves.

Intensity
For someone who claims to know nothing about GR to turn around and claim an expert does not understand the GR field equations is pretentious, childish.

But in agreeing with Van Flandern you are making the same claim about all the relativists who disagree with him! Both sides cannot be right here. I am not dogmatically claiming Van Flandern must be wrong here, I'm just saying that when you have a large number of experts in the subject saying one thing about the math and a maverick who did not get his Ph.D. in the subject saying something else, I would put my money on the experts. Again, I am only talking about the mathematical issue of what the Einstein field equations say about the speed of gravity and the number of free parameters in the metric, not any empirical issues relating to how gravity works in the real world! Van Flandern and the relativists are saying fundamentally different things about these purely mathematical issues, and one side must be in error.

Intensity:
As far as other experts stance concerning TVFs ideas, I am well aware of them, thanks to you. But what I have seen so far is that TVF was wrong in thinking GPS programmers have not incorporated GR in their software (And I dont give a rats ass about whether he is wrong or right about GPS), that he does not understand the GR field equations (and I have seen no evidence for that), that he said Einstein "jiggered" with the multipliers and that TVF is therefore wrong in assuming there are "free" parameters where there are none (I have yet to get his side of the story on this - and I dont think its that important anyway), that he is a crank (an ad hominem - anyone who questions GR is a crank [some psychological crap about the need to feel significant and attract attention to oneslef])

Did anyone on this thread actually say "Van Flandern is a crank"? If not, why bring it up?

Intensity:
and that other experts disagree with him (on the grounds that he questions standard theories, which they accept and do not question).

Once again, I am only talking about disagreement on straightforward mathematical issues, like whether the equations of GR do or do not imply that gravitational effects are instantaneous.

Intensity:
All that I have seen has not shown me the following (which are what I am interested in):

1. That TVF is wrong when he argues that FTL speeds are possible and his demonstrations and calculations are consistent with LR, GR but falsifies SR which forbids propagation speeds faster than lightspeed in forward time.

2. That he is wrong to argue that "General relativity has a geometric and a field interpretation. [but] If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated"

3. Evidence that TVF does not understand GR field equations or any (other) GR maths.

That is all. Let's see what Steve Carlip has to say. There is no hurry. If you have evidence for the three, point me to

Again, until you acquire the necessary background in GR you will not be in a position to understand the details of this debate. If you just want qualitative descriptions of why Van Flandern�s calculations are wrong, I suggest looking at the collection of posts which both I and Steven S posted earlier:

<a href="http://math.ucr.edu/home/baez/PUB/debate" target="_blank">http://math.ucr.edu/home/baez/PUB/debate</a>

For example, here�s a summary of the claim that gravitational effects travel at light speed, not instantaneously, in GR:

Quote:

According to general relativity,
changes in the gravitational field propagate at the speed of light.
To be specific, it is impossible to send a signal from one place to
another at superluminal speed by manipulating a gravitational field.
One common source of confusion on the subject arises from the fact
that the gravitational field of a massive body that is in free fall
generally points in a direction that is quite close to the *present*
position of the body, not to the place where it was one
light-travel-time ago. This is perhaps an odd and surprising fact
(although if you consider analogies in electromagnetism it becomes
a little bit less surprising), but it cannot be used to send a
signal faster than light, and so, at least according to the way
most physicists like to talk, it does not count as "gravity
traveling faster than light."

People generally ask the following question: what would happen to the
Earth's orbit if the Sun suddenly disappeared? General relativity
gives a particularly annoying answer to this question: it says, "The
Sun can't disappear, since that would violate mass-energy
conservation. So I'm not able to tell you what would happen if it
did." However, general relativity can tell you what would happen to
the Earth's orbit if you suddenly shook the Sun violently. There
would be no change in the orbit until at least 8 minutes (the
light-travel time from Sun to Earth) had elapsed.

Here are two posts which describe the only postulates needed to uniquely derive the Einstein field equations (in contrast with Van Flandern�s claim that there are free parameters which Einstein could have jiggled to get a correct prediction of the perihelion of Mercury) and also a description of how Van Flandern goes wrong by using approximations instead of solving the equations directly:

Quote:

Tom Van Flandern (metares@well.sf.ca.us) wrote:

> If one allows gravity to have a propagation delay
> in a computer calculation, the resulting orbit is a spiral instead
> of a closed ellipse.

Indeed, *if* one is foolish enough to run a program that describes
gravity simply by Newton's force law with a propagation delay
stuck in.

> General relativity was faced with this dilemma during its formulation,
> and special relativity demanded that nothing propagate faster than
> light. So the problem was solved elegantly - by decree! It was decided
> that gravity is not a traditional force with traditional propagation.
> Instead, whatever aspect of it changes over time must do so at speed c.
> Then, to restore the unphysical torque such a delay would apply to
> orbits, the postulate was added that gravity does not emanate from
> the present direction of the Sun, nor from its lighttime-retarded
> position, but rather from its *future* position one lighttime ahead.
> In that way, when the force propagates from the future position and
> is retarded by traveling at the speed of light, it ends up acting from
> its true, instantaneous position, as observations require. This is a
> fairly ingenious solution to an apparently unsolvable problem; but
> then, Einstein was no slouch in these matters.

As a "historical" comment, this is pure garbage. As a comment on
the intellectual and conceptual foundations of general relativity,
it's not much better. Sorry for the strong language, Tom, but the
fact is that rather than going out and learning general relativity,
you seem to have just made this story up.

The real "postulates" of general relativity have virtually nothing
in common with this description. They are (in one version) that

1) spacetime is a four-dimensional Lorentzian manifold (that is,
a four-manifold with a pseudo-Riemannian metric of signature 2);
2) there is no "prior geometry," i.e., no background geometric
structures apart from those determined by the metric;
3) the gravitational Lagrangian is built from the metric and its
curvature, and is a density (so the gravitational action is
coordinate-independent);
4) the action contains no more than two derivatives of the metric.

That's it. This (plus a bit of differential geometry as a tool)
is enough to derive Einstein's field equations, from which the
characteristics Tom describes above are *deduced*. To say that these
properties are put in "by decree" or "postulated" is just silly; it's
like saying that Newton's law of gravity is F=GMm/r^2 with the added
decree that planetary orbits are ellipses and the additional postulate
that these ellipses obey Kepler's laws. Tom, you surely know better
than to confuse a postulate with a conclusion!

I wrote

>> a calculation shows that the force on A points not towards
>> B's retarded position, but towards B's "linearly
>> extrapolated" retarded position.

to which Tom replied,

> It's a rare day indeed when I catch Steve in a misstatement. [...]
> However, a calculation with the binary pulsar shows that the
> linearly extrapolated retarded position is not good enough to prevent
> spiraling at an unacceptable rate. The acceleration of each pulsar
> during a single lighttime interval must also be considered.

This is true. But my statement above was taken out of context; it
referred to electromagnetism, not gravity. (I thought I had made this
clear, but perhaps not; if not, I apologize.) For electromagnetism,
which is a spin one interaction, the effective "electrostatic" force
can be determined from a linear extrapolation; for gravity, which is
a spin two interaction, something more like a quadratic extrapolation
comes out of the field equations.

Note, by the way, that in formulating the laws of electromagnetism,
Maxwell did not "postulate" or "decree" this behavior; as in general
relativity, it comes from a computation, not an assumption.

> As accurately as modern observations and computations can tell,
> the force on A points toward the true, instantaneous position of B.

Well, no, not quite. If this were true, angular momentum would be
exactly conserved in binary pulsar systems, and orbits would be
stable. Instead, the orbits decay (albeit very slowly); translated
back into Newtonian language, this means that the force on A *doesn't*
quite point towards the instantaneous position of B, though it's
very close.

Steve Carlip
carlip@dirac.ucdavis.edu

and

Quote:

Oz (Oz@upthorpe.demon.co.uk) wrote:
: carlip@dirac.ucdavis.edu (Steve Carlip) wrote:

: >The real "postulates" of general relativity have virtually nothing
: >in common with this description. They are (in one version) that
>
: >1) spacetime is a four-dimensional Lorentzian manifold (that is,
: > a four-manifold with a pseudo-Riemannian metric of signature 2);
: >2) there is no "prior geometry," i.e., no background geometric
: > structures apart from those determined by the metric;
: >3) the gravitational Lagrangian is built from the metric and its
: > curvature, and is a density (so the gravitational action is
: > coordinate-independent);
: >4) the action contains no more than two derivatives of the metric.

: Sad, but does this effectively mean that a basic
: understanding of the key points of GR, and in particular
: it's main differences to SR (at least as examples) are not
: easily followed without being able to manipulate and follow
: the above mathematical tools.

Well, I think it depends on what you count as a "basic
understanding." A comparable question would be whether
it's possible to understand Maxwell's electrodynamics
without calculus. Certainly qualitative descriptions
are possible, but it's not clear whether they really get
to the "guts" of the theory.

For example, it's not hard to give non-calculus descriptions
of Gauss's law, Faraday's law, etc.; but it's quite a bit
harder to show that these laws combine to predict that
electromagnetic radiation travels at the speed of light.
I expect that such an explanation is possible, but in
some sense it would be post hoc---once you've figured
out the solution, you can go back and try to explain why
it comes out that way. There's nothing wrong with that,
provided you don't take it too seriously; the danger is
that you can confuse understanding such a post hoc description
of an example with understanding the whole theory, which
can lead to new "predictions" that can be radically wrong.

In electrodynamics, for instance, it would be fairly easy
to make the same mistake that Tom has made about general
relativity by trying to apply post hoc explanations to make
new predictions. Say, for example, that you have learned
that electromagnetic disturbances propagate at the speed
of light, and that opposite charges attract each other
with an inverse-square-law force. Using these two facts,
you could try to work out the orbits of two oppositely
charged bodies, by using Coulomb's law with a propagation
delay added in. You would find, just as in Tom's example,
that the orbits were highly unstable. If you then went
back and did the real computation, though, you'd find a
much smaller instability. You could then, if you wanted,
add a new layer of post hoc explanations, and use the
results to try to make new predictions, which would require
still more post hoc explanations, ... Obviously, if you
do this long enough you will end up with a ridiculously
complicated version of what was initially a fairly simple
theory. This doesn't mean that Maxwell's theory itself
requires these layers upon layers of assumptions; it merely
means that your approach to understanding the theory is one
that misses the real underlying structure.

Steve Carlip
carlip@dirac.ucdavis.edu

If Carlip claims that Van Flandern is using approximations when making his claim about orbital decay, rather than solving the equations exactly, I see no reason to think he is simply lying.

(incidentally, all of the threads that these posts come from can be found using a google groups �Advanced group search��for example, the two posts above come from <a href="http://tinyurl.com/1rof" target="_blank">this</a> thread).

[ October 03, 2002: Message edited by: Jesse ]

Jesse · 10-03-2002, 08:38 AM

Another interesting post on why Van Flandern's claim that gravitational effects travel instantaneously in GR is incorrect:

Quote:

------------------------------------------------------------------------
Re: speed of gravity
Author: Steve Carlip <carlip@dirac.ucdavis.edu>
Date: 1995/11/07
Forum: sci.physics
------------------------------------------------------------------------

Jeff Wilson (jdwilson@bnr.ca) wrote:

: Anyone who responds to the above, how about Eddington's paradox? Does
: anyone have a solution for this?

: Here is a quote from Eddington's book Space, Time, and Gravitation, page 94.

: "If the Sun attracts Jupiter towards its present position S, and Jupiter
: attracts the Sun towards its present position J, the two forces are in the
: same line and in balance. But if the Sun attracts Jupiter towards its
: previous position S1, and Jupiter attracts the Sun towards its previous
: position J1, when the two forces started out to cross the gulf, then the
: two forces give a couple. This couple will tend to increase the angular
: momentum of the system, and, acting cumulatively, will soon cause an
: appreciable change of period (duration of orbit-- S.M.), disagreeing with
: observations if the speed is at all comparable with that of light."

You might really call this "Laplace's paradox"---the idea of
using this phenomenon to investigate the speed of gravity was
first (I think) published by Laplace in 1805. The answer,
somewhat oversimplified, is this:

Note first that Eddington is implicitly assuming that gravity
is a central, velocity-independent force---that is, that the
force exerted by the Sun has components only in the direction
of S (or S1), and that this force is simply that of Newtonian
gravity, independent of the velocity of the Sun or Jupiter.
If one starts with these assumptions and puts in a propagation
delay---that is, if one tries to describe gravity simply as
Newtonian gravity with a finite propagation speed stuck in---
one definitely gets a contradiction with observation unless
this speed is much greater than c. But this "Newtonian gravity
with propagation delay" is not the way modern physics describes
gravity---it is not general relativity.

Strictly speaking, gravity is not a "force" in general relativity,
and a description in terms of speed and direction can be tricky.
For weak fields, however, one can describe the theory in a sort
of Newtonian language. In that case, though, one finds that the
"force" in GR is not quite central---it does not point directly
towards the source of the gravitational field---and that it depends
on velocities as well as positions. The net result is that the
effect of propagation delay is almost exactly cancelled; general
relativity very nearly reproduces the infinite-propagation-speed
Newtonian predictions.

This cancellation may seem less strange if one notes that a similar
effect occurs in electromagnetism. If a charged particle is moving at
a constant velocity, it exerts a force that points toward its present
position, not its retarded position, even though electromagnetic
interactions certainly move at the speed of light. Here, as in
general relativity, subtleties in the nature of the interaction
"conspire" to disguise the effect of propagation delay. It should
be emphasized that in both electromagnetism and general relativity,
this effect is not put in by hand, but comes out of the equations;
in fact, it is required by conservation laws that are built into the
foundations of the theory.

This cancellation is not quite exact, although the effect is not
observable in the Solar System. The slow change in the periods of
binary pulsar systems can, in fact, be described as the result of
the failure of propagation-delay effects and noncentrality and
velocity-dependence of the gravitational "force" to exactly cancel.
This argument (and a much more detailed and technical description
of the phenomenon I'm describing) is given by Damour in his article
in _300 Years of Gravitation_ (Hawking and Israel, editors, 1987).

Steve Carlip
carlip@dirac.ucdavis.edu

Original post is <a href="http://tinyurl.com/1ros" target="_blank">here</a>.

I remember that in electromagnetism if you have a charge moving at constant velocity, things work out so that other charges will be attracted to its current position, despite the light speed delay. But if the charge suddenly accelerates, other charges will continue to be attracted to what its current position would have been if it had maintained a constant speed, until the "news" of the change propogates to them at light speed. Apparently something similar happens in GR, but it sounds like the effect works out even more nicely, so that even for objects moving in orbits (which are not straight lines, obviously) other objects will still be attracted to something close to the object's current position. This was made more explicit in a post by Steve Carlip which I quoted in my last post:

Quote:

For electromagnetism,
which is a spin one interaction, the effective "electrostatic" force
can be determined from a linear extrapolation; for gravity, which is
a spin two interaction, something more like a quadratic extrapolation
comes out of the field equations.

However, as pointed out in another post I quoted earlier, if you suddenly jiggled an object (or caused it to diverge from its orbit, perhaps) then according to GR distant objects would not react to this change until the effects of the change propogated out at light speed.

[ October 03, 2002: Message edited by: Jesse ]

Ted Hoffman · 10-04-2002, 02:16 AM

Jesse,
Thanks for your thoughtful post. I apologise for coming across as rude. I was a bit ticked off by the attempts to dissuade me from digging further based on my layman status as far as GR is concerned.

Perharps I can address the rest of your post later (I am a bit too excited now because bot Steve Carlip and Van Flandern have replied to the emails I sent them

). Thanks for providing insightful links to this "controversy".

And oh, for the record, the "crank" thing, I got it from salon.com and Vorkosigan earlier (in "When the Gods Came Down" thread), also provided me with a link that labelled him as such.

Steven S Yes, but I'm not an expert. I've had two courses on GR, lots of differential geometry, plus my first advisor was a relativist before I switched to particle theory. I've also written a pedagogical article describing three ways to go about the canonical quantization of gravity.
Intensity Thanks, with your knowledge, can't you follow on the calculations TVF has used in the link I provided above in arguing that FTL speeds are possible? Or is Tom making post hoc explanations to make new predictions in GR?
You could at least provide us with a Laymans opinion?

Ok, now for the emails from the experts <wrings his hands excitedly, heart thumping audibly>

Where do I start? Lets see, lets start with Steve Carlip:

Intensity You have stated that Maxwells equations, which are used in Electrodynamics are much simpler mathematically "one can actually
write down the exact solution of Maxwell's equations for a moving charge, and read off from that solution the fact that in Maxwell's theory, all electromagnetic effects propagate at the speed of light." but I am not sure about the applicability of Maxwells equations as far as GR equations are concerned.

Steve CarlipThey'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">

Intensity So my request here is for you to provide links (if you have already addressed these before) where I can find your (counter) arguments concerning:
1. TVFs objections to the rubber-sheet analogy for its inconsistency with the casuality principle.

Steve Carlip The rubber sheet analogy is an analogy, and so by definition is ``flawed'' if one tries to overinterpret it. I have never understood Van Flandern's definition of ``causality''---it seems to me to be, roughly, ``If I can't picture it in terms of little billiard balls bouncing around or ripples
of water on a pond, then it's not causal.''

The real problem with the rubber sheet analogy is that it concentrates on spatial curvature, while what's really important is spacetime curvature;
for the analogy to work, you have to think of one of the dimensions of the sheet as time. But the fact that TVF has spent so much time on this
analogy is itself a sign of his poor nderstanding of GR. The analogy is occasionally made in popularizations, but never that I know of in real
GR textbooks, since it's problems are well known.

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

>

Intensity 3. His claim that "We [can] show that aberration has been suppressed in the GR equations of motion through setting gravity’s propagation speed to infinity; and that the absence of aberration cannot be explained through some mathematical “cancellation” because that would cancel tidal forces too"

Steve Carlip That's categorically false. What more can I say? He starts with a set
of approximate equations of motion in which the ``mathematical cancellation'' he's talking about has already taken place, put *back* a finite speed of gravity, and then shows that that gives the wrong result. It has nothing whatsover to do with GR.

If you want to see the cancellation in detail, see my paper Phys. Lett. A267
(2000) 81, available on line from <a href="http://arXiv.org/abs/gr-qc/9909087" target="_blank">http://arXiv.org/abs/gr-qc/9909087</a> .
Note that the speed of gravity is explicitly there, and that it cancels from terms involving aberration at low orders. Note also that for all his posturng about responding to that paper, Van Flandern never once refers to a single equation in it.

Intensity 4. His claim that "General relativity has a geometric and a field interpretation. If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated. Meanwhile, the field interpretation avoids this problem by allowing faster-than-light propagation in forward time.
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.

Intensity 5. Most importantly, evidence that he has a poor grasp of the field equations in question.

Steve Carlip It's hard to even know where to start. He consistently confuses an approximation to a particular set of solutions to GR (the Einstein-Infeld-Hoffmann approximation) with the full theory, without trying to understand where the approximation came from. He claims that a multipole expansion (which he apparently had never seen before) involved time-averaging. In E&M, he believes that the electric and magnetic fields obtained from the Lienard-Wiechert potentials propagate infinitely fast, something that can be checked (and refuted) by a straightforward calculation. He has stated that the equations of motion used to analyze binary pulsars are ``are simply assumed to come from one-body Schwarzschild solutions of the field equations summed over all bodies (i.e., using superposition),'' a claim that is patently wrong.

Here's one quote from TVF, from a 1995 Usenet post:

In article <4aoah9$4jn@nkosi.well.com>,
Tom Van Flandern <metares@well.sf.ca.us> wrote:
Think about this simple concept in the context of this discussion about the speed of gravity. Yes, in GR, the curvature at a point is given by the
stress-energy tensor. But what is the direction* of the radius of curvature? Is it toward where the source mass is now, or where it was one
lighttime ago when the source mass presumably emitted the stress-energy?
Einstein's simple equation is ambiguous on this critical point.
Steve CarlipThis is so obviously not true that I can't even imagine where he got it from. He's claimed that:
Tom Van Flandern It is off-topic to mention gravitational waves here because they are not a component of gravitational force. But their inferred (not observed) propagation speed is also c. For both those reasons, and because they are disturbances of the "light-carrying medium" (= "spacetime" in traditional parlance), it is my opinion that "gravitational waves" are actually very-long-wavelength light-waves.

Steve Carlipwhich is completely silly. I could go on, but perhaps your best bet is to look at some of his Usenet posts and the responses.

Steve Carlip
__________________________________________________
Intensity Well, ladies, lets look at what Tom has to say:
__________________________________________________
Intensity I have been researching on push gravity...

Tom Van Flandern The latest word on that subject, of course, is in a new book that answers all objections previously raised. [Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. Edwards, ed., Apeiron Press, Montreal.] I wrote one chapter therein.

Intensity Some of the points are unrelated but I was provided with links (like this one: <a href="http://dir.salon.com/people/feature/2000/07/06/einstein/index.html?pn=3" target="_blank">http://dir.salon.com/people/feature/2000/07/06/einstein/index.html?pn=3</a> ) concerning "relativity deniers" and related stuff.

Tom Van Flandern It is a strong indicator of what is really going on that some people are still citing that one-sided, inaccurate article, but failing to cite the rebuttal subsequently published in the same source: <a href="http://salon.com/people/letters/2001/07/23/hughes/index.html." target="_blank">http://salon.com/people/letters/2001/07/23/hughes/index.html.</a> Incidentally, I don’t know the person who wrote the rebuttal, and had nothing to do with it. I declined to send anything to Salon myself because I didn’t feel they deserved to increase their circulation by doing hatchet articles about personalities instead of informative articles about both sides of an interesting scientific controversy.

Intensity There is this assertion (I think Steve Carlip is behind it) that you do not understand GR field equations (since I have seen no evidence for that, I see no need to pursue it further),...

Tom Van Flandern Steve was a worthy advocate for his position for the first eight years of our debates. But in the last two, he has suddenly turned ad hominem and started talking about me instead of the issues. My response is that I understand GR and the issues well enough to continue to get my papers published in mainstream, peer-reviewed journals. And in the latest of these***, I have been joined by a co-author who has an impeccable reputation in physics and is himself on the editorial board of a major physics journal – J.P. Vigier at the Univ. of Paris. I read Steve’s change of attitude as a response to seeing that he is starting to lose ground and momentum in this debate. But perhaps he is being excessively peer-pressured or has some other reason for this unfortunate change of tactics.
**“Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions”, T. Van Flandern and J.P. Vigier, Found.Phys. 32(#7), 1031-1068 (2002).

One thing that Carlip and other relativists do not like is that I prefer the general mathematical language of celestial mechanics (my professional specialty) and the central role of equations of motion (as required to compare GR to experiments or observations) over the now-common tensor formulations of potential fields as used in MTW and other current works dealing exclusively with GR. It appears to me that Carlip’s understanding of GR equations of motion is deficient. But I do not go around castigating him for that. I try to explain the bits he is unfamiliar with, or provide citations. We all have knowledge gaps, some we are aware of and some we are not. He used to do the same for me, but no longer. <Intensity:

>

Intensity but there is this story about you claiming that Einstein "jiggered" with some multipliers which Alley denied having said. You later explained that: "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." Carlip countered this by saying that "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." .

Tom Van Flandern 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. Having made its choice, there are no further adjustable parameters in the GR field equations. But when Einstein was originally trying to pick the right form for the field equations, he did have many choices. 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.” 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. 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. <Intensity: emphasis mine>

Intensity So, what exactly are these "choices of coefficients of potential phi" which he made? because Carlip says "Van Flandern seems to have invented a free parameter where none exists. There is [only] one free parameter, but it's just Newton's gravitational constant, G, and is fixed completely by the requirement that the theory reduce to Newtonian gravity in the weak-field, low-velocity limit". (emphasis mine).

Tom Van Flandern For a good discussion of metric coefficients, see the attached article by Brunstein from the Meta Research Bulletin in MS Word format. If you can read Word documents, you should be able to see the equations, which are difficult to deal with in plain text formats. 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.

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.

Now consider my editorial note in the Brunstein paper:

Quote:

Because the time component c^2 dt^2 dominates the spatial components [in the metric] in most applications, it is conceptually easier, and helps avoid relativistic paradoxes, to think of ds/c as a duration of “proper time” interval (time interval on a local clock affected by speed and/or gravity) rather than as some sort of “distance”.

In the context of that paper or any discussion of “metrics”, this makes more physical sense. 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&#8221

is a minimum.)

When I try (like the above) to suggest alternate interpretations of the physics behind the math of GR that make more physical sense, the response is “I just don’t understand relativity”. In a way, the complaint is valid. I truly don’t understand the physics of the interpretations that the relativists place on these concepts. That doesn’t mean I haven’t learned them as well as the next fellow. I just think some of the interpretations violate one or more physical principles, so I try to find ways to explain the same math that don’t have that problem.

From the discussion site whose link you provided:

Intensity as quoted from this discussion: But what I have seen so far is that TVF was wrong in thinking GPS programmers have not incorporated GR in their software...

Tom Van Flandern Well, I sure would have been wrong if I had said that, but I am not that uninformed, having worked as a consultant on improving the accuracy of the system. This sounds like nonsense from the Chris Hillman page, which I debunked in a recent posting to sci.physics. I guess I’ll add that post to this message as a second attachment. See also my published article, which mentions the details of the GR contribution to the GPS clock rates: “What the Global Positioning System tells us about relativity”, in “Open Questions in Relativistic Physics”, F. Selleri, ed., Apeiron, Montreal, pp. 81-90 (1998). Also available at <http://metaresearch.org>, “cosmology” tab, “gravity” sub-tab.

Hillman is the poster of the “debate” site that contains only one side of a debate, but omits my responses except as quoted in messages from others. That means that thread-ending messages from me to which there was no response are not present, leaving an incorrect impression of the conclusions reached. It speaks for itself when a record of a “debate” quotes only one side of it.

I’ll be on travel again all next week, but this message and enclosures should give you material to hold up your end of the discussion for a while. BTW, I thought your messages were on target and showed considerable insight. You are doing great, and I appreciate it very much. Don’t let anybody convince you these matters are beyond your understanding, even though the “experts” like to think they are among the elite few who really understand them. That’s usually just a smokescreen for “I can’t answer your questions!” Best wishes. -|Tom|-
<intensity: His intense face cracks up in a radiant smile huh, huh,

>

THE ATTACHMENTS

This first one is about relativity working in the GPS:

"[b]Sam Wormley[b]" <swormley1@mchsi.com> quotes from a web site with this acknowledgement and disclaimer: “I [Chris Hillman] am grateful for helpful comments from several people. All opinions expressed on this page and any errors or scientific inaccuracy are of course the sole responsibility of Chris Hillman.”

Tom Van F. It is refreshing to see people take responsibility for their errors.

c.h.: “Relativity Theory Isn't Working in the GPS.”

Tom Van F. This is the title of Hillman’s article about my interpretation of the GPS. But I never said or implied any such thing.

c.h.: In a paper remarkable chiefly for the extraordinary number of obvious errors it contained (see above), Tom Van Flandern, (``The speed of gravity-- what the experiments say'' Phys.Lett.A 250 (1998) 1-11,), stated:...

Tom Van F. That is a false and unjustifiable claim. Two papers appeared attempting to rebut the arguments in the cited work:

G.E. Marsch & C. Nissim-Sabat, “Comments on ‘The speed of gravity’”, Phys.Lett.A, v. 262, pp. 103-106 (1999/11/01).

S. Carlip, “Aberration and the speed of gravity”, Phys.Lett.A, v. 267, pp. 81-87 (2000/03/15).

and both were subsequently rebutted themselves:

T. Van Flandern, “Reply to comments on ‘The speed of gravity’”, Phys.Lett.A, v. 262, pp. 261-263 (1999/11/01).

T. Van Flandern & J.P. Vigier, “Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions”, Found.Phys. 32(#7), 1031-1068 (2002).

This last, in fact, gives answers satisfactory to neutral parties to every objection yet raised to the conclusion that the speed of gravity vastly exceeds the speed of light.

Tom Van F. the Global Positioning System (GPS) showed the remarkable fact that all atomic clocks on board orbiting satellites moving at high speeds in different directions could be simultaneously and continuously synchronized with each other and with all ground clocks.

Note that Hillman does not actually rebut this or anything else I said. He just makes a variety of unsupported claims and sets up several strawmen arguments which he then has fun beating the stuffing out of. The essential points in my paper, such as the above, remain untouched.

c.h.: in postings to sci.physics.relativity, Van Flandern has clearly stated that he believes that changes in electrostatic and gravititostatic potentials are transmitted instantly (literally!), just as if electromagnetism and gravity were truly governed by the Poisson equation, a viewpoint which is mathematically utterly inconsistent with both str and gtr, contrary to his claims in an earlier (and also wildly erroneous) paper, ``Possible new properties of gravity'', Astrophysics and Space Science 244 (1996).

Tom Van F. Just about every specific claim made here is wrong or very confused. First, I have never maintained or claimed in any paper, forum, or newsgroup, publicly or privately, that changes in electrostatic and gravitostatic potentials, or generally in electrodynamic or gravitational potentials, are transmitted faster than light, let alone instantly. One can find the opposite statement in most of my papers: Potentials and changes in potentials propagate at lightspeed, period.

Second, even for gravitational and electrodynamic forces, I have always been careful to qualify that the propagation speeds, however fast, cannot be infinite. That would be a violation of the causality principle.

Third, I’d like to think I have never confused electrostatics or electrodynamics with electromagnetism, as Hillman does in his above statement.

Finally, it is undisputed in the literature that Lorentzian relativity (LR) satisfies all experimental constraints and is fully consistent with the math of general relativity (GR), yet permits faster-than-light propagation in forward time. So Hillman’s convoluted last few lines, whatever they mean, can have no import to the issues here.

c.h.: Since Van Flandern also claims special expertise in the GPS system, by virtue of having worked as a ``consultant'' in its design

Tom Van F. Again, this is a pure fiction. My interest in GPS and work as a university researcher and contractor for the military on improving the accuracy of the system began long after the system went operational.

c.h.: (On the other hand, Neil Ashby (Physics, University of Colorado) has written extensively in journals such as GPS World, IEEE Spectrum, and has written some of the official documentation for the GPS system; at this point, some readers may want to skip directly to <“General relativity in the global positioning system”>, a short paper by Ashby which quickly debunks Van Flandern's claims.)

Tom Van F. This is an irrelevant appeal to authority together with a false claim at the end, complete with a broken link so no one can check. It the real world, Neil Ashby and I have discussed these matters on a few occasions, in person and by email. He has received my response to his GPS position paper published in the May issue of Physics Today, over which we have only very minor differences, mostly of interpretation. If he has any objections to my interpretations, he has yet to say so.

Hillman, who has no background or experience with the GPS, then launches into an explanation of how he thinks it works. He uses the way civilian receivers process satellite information to determine ground coordinates as an example. But this is completely irrelevant to the pseudorange and range rate data continually collected and processed by the Air Force Monitor Stations that are the basis for keeping the system operational. The latter is not only a completely different data type, but also is 2-3 orders of magnitude more accurate. Civilian receivers do not even have their own clocks, but instead rely on the orbiting clocks. Monitor stations do have ground clocks for direct comparison with signals from orbiting clocks. Hillman, a mathematical relativist who rarely dabbles in practical physics anyway, is way out of his depth here.

The rest of the long, rambling article defends relativity against mythical accusations never actually made (at least by me), and ignores the real issue of whether LR or special relativity (SR) better represents reality. The statement I did make. “the Global Positioning System (GPS) showed the remarkable fact that all atomic clocks on board orbiting satellites moving at high speeds in different directions could be simultaneously and continuously synchronized with each other and with all ground clocks”, strongly suggests that LR has the better predictive power of the two models. -|Tom|-

Tom Van Flandern - Washington, DC – see our web site on replacement astronomy research at <http://metaresearch.org>

THE SECOND ATTACHMENT

<sorry about the formulas - I will provide a link to those interested - after I have put it on the web>

Not-So-Cosmic Censorship and Black Holes
Karl Brunstein
<wethinks@netidea.com>
Meadow Creek, British Columbia, Canada V0G 1N0

Abstract. Equivalents of the Schwarzschild metric that are static and that do not exhibit black holes are presented for the first time and discussed. Though they do not imply the actual, physical realization of a naked singularity, they nevertheless present one with a serious dilemma: How does one reconcile the simultaneous prediction and lack of prediction of a phenomenon by the same theory?

An Overview
General Relativity is Einstein’s theory of gravity. In it, the four-dimensional spacetime of Special Relativity is distorted by a massive object, say, a star. It is through this distortion that the star manifests its gravitational field. Einstein’s field equations, as they are called, describe the distortion and gravitational field.
The most important fundamental situation to be treated by the field equations is that of spherical objects of any mass. An exact solution for this class of problems was found years ago by Schwarzschild. The classical tests of General Relativity are based on his solution.
The solution has a troublesome feature: an additional singularity, or “infinity”, at a point outside the one it shares with Newton’s gravitational law at . For years, no one thought of giving real, physical meaning to it, probably because singularities generally indicate a theory is inadequate in the region in question. A familiar example is the historically important singularity known as the “ultraviolet catastrophe,” predicted by classical blackbody radiation theory. Simple laboratory measurement made its absurdity clear. As one knows, it led in 1900 to Planck’s quantum hypothesis, an expedient solution that led to quantum theory.
Interest in the Schwarzschild singularity lay, with one notable exception, nearly dormant for decades. In the 1960s, several individuals seriously began to ascribe physical reality to it. The school grew, their ideas finally blossoming with the “black hole”. In spite of claims to the contrary, no black holes have been discovered. Objects have been found that appear so massive that, according to this school, they must be the black holes expected by the theory.
The discussion that follows demonstrates that the Schwarzschild singularity is in fact a flaw in General Relativity. The black hole concept leads one directly and inescapably into a gross internal inconsistency.
To follow the discussion, one needs to understand the concept of metric. A spacetime is completely described by its metric, its four-dimensional analytic measure of “distance”. With the metric, one knows all about gravity and the properties of spacetime in a region. The metric is analogous to an expression for the hypotenuse of a right triangle, generalized to four dimensions, in that it expresses the “distance” between two neighboring event points in terms of four coordinate components. In the absence of gravity, Special Relativity holds. The Pythagorean theorem (extended to four dimensions) defines the metric, with either the time component an imaginary number, or the three spatial components imaginary, arbitrarily. Namely: in two dimensions, ; in four dimensions, either , or .
Without changing the “distance”, , gravity modifies its distribution among the four components. [Because the time component dominates the spatial components in most applications, it is conceptually easier, and helps avoid relativistic paradoxes, to think of as a duration of “proper time” interval (time interval on a local clock affected by speed and/or gravity) rather than as some sort of “distance”. -- Ed.] The spacetime is distorted by the gravitating mass, or star. One is then in the domain of General Relativity. In all cases considered here, the effects enter into the metric as two to four variable coefficients, metric coefficients, in which the gravitating mass appears as a parameter. That is, two, three, or all four terms on the right side of the previous two expressions for are multiplied by a function, a metric coefficient, in which the star’s mass appears.
To determine the metric coefficients, one solves Einstein’s field equations. The 10 partial differential equations are cumbersome, so a utilitarian notation and conventions, a shorthand, is used. It employs both subscripts and superscripts, but to avoid ambiguity does not generally use exponents. To square one writes , for example. The notation is not required in our discussion and is not used after Equation 1.

Introduction
There is an ever-present danger in theoretical physics that appears to have reached palpable proportions in the field of classical General Relativity. It is the threat that the rising mountain of literature in the field will bury any essential elements that have been earlier overlooked, should they fail to support the dominant schools of thought at the top. Presented here are static solutions to Einstein’s field equations for an uncharged, non-rotating, spherically symmetric mass – the problem treated by Schwarzschild many years ago – that exemplify this present-day counter-productive development. The metrics expressing these solutions do not exhibit black holes. They are fundamental to the understanding of General Relativity. Yet up until now, they are nowhere in print. [1]
Because of this, many continue to entertain the misconception that General Relativity unavoidably predicts black holes. This is particularly so for the Schwarzschild problem. A few quotations will illustrate the pervasiveness of this belief and the importance attached to it because of its bearing on the issue of naked singularities.
The general situation with regard to a spherically symmetrical body is well known … the body passes within its Schwarzschild radius . [2] No one who accepts general relativity has found any way to escape the prediction that black holes must exist. [3]
One such question (to be addressed, finally, by numerical methods) is the Cosmic Censorship conjecture and the appearance of naked singularities. This question is probably the most important open question in classical general relativity. [4] Whenever simple configurations of matter collapse according to the rules of general relativity, the collapsed region always seems to be enveloped in a black hole before a singularity forms. [5] [A singularity surrounded by an “event horizon” – defined later in this article – is called a “black hole”, and is responsible for “cosmic censorship” because information cannot get out. Its opposite, a singularity with no event horizon, is called “naked”. – Ed.] How a situation like this has been fostered is a curious and interesting topic, but not properly physical science. The intent here is to present a remedy to the widespread misconception that has resulted.
Essential Background
To appreciate the discussion, one needs to have certain fundamentals freshly in mind: In General Relativity one assumes that a Riemannian metric may be assigned to spacetime, i.e.,
, (1)
and that the are determined by Einstein’s field equations plus the boundary conditions of the problem. For an uncharged, non-rotating, gravitating mass with spherical symmetry in otherwise-empty space, one has as one possible solution the Schwarzschild metric,
, (2)
given here in standard form for spherical polar coordinates with the gravitating mass centered at the origin. The mass distribution need not be time independent. For example, the object might pulsate in a spherically symmetric manner with the total mass-energy held constant. To lend simplicity to our subsequent discussion, we rewrite (2) as
, (3) where
(4)
(5)
(6)
One can use (3) to deduce readily that the velocity of light in the radial direction, and perpendicular to it, as inferred by an observer in flat spacetime, are
(7)
(8)
Plausibly there could exist an object with radius less than , its “Schwarzschild radius”. The surface of a sphere defined by the radius is labeled an “event horizon” in that . Clearly, no event inside the object’s Schwarzschild radius, or the event horizon, could be communicated to the outside. [6] One should have a Schwarzschild black hole.
Solutions to the Schwarzschild problem are infinite in number. One might surmise this immediately by noting that yet another solution can be obtained from one previously known by an arbitrary transformation of the four coordinates. Birkhoff has indeed demonstrated that all solutions to the Schwarzschild problem, static or otherwise, are related in this way. [7] Moreover, there is nothing within General Relativity theory to specify which of the infinite solutions is uniquely “physically correct.” This feature of the theory has been universally understood, after Einstein, to reiterate the fact that the choice of coordinates is of no physical consequence. Pauli has stated, for example, “the many possible solutions of the field equations are only formally different. Physically they are completely equivalent.” [8]
The conclusion proceeds directly from the general principle of relativity: If “all Gaussian coordinate systems are essentially equivalent for the formulation of the general laws of nature” [Einstein’s emphasis], [9] it follows that descriptions of physical events according to these laws must conform to the extent that there be no contradictions between systems with respect to the fundamental nature of the events. It is in this sense that the systems are equivalent. It can be further argued, “the great power possessed by the general principle of relativity lies in the comprehensive limitation which is imposed on the laws of nature in consequence.” [9]

"Probable-Possible, my black hen, She lays eggs in the Relative When. She doesn't lay eggs in the Positive Now Because she's unable to Postulate How.”
-- From: “The Space Child’s Mother Goose”, Frederick Winsor, Simon & Schuster, NY (1958, 1966)

Solutions Without Black Holes
A one-parameter family of solutions to Einstein’s field equations for the Schwarzschild problem is given below. One substitutes expressions (9) (10) and (11) into Equation (3) to obtain the solutions in the form of the associated metrics. We have set :
(9)
(10)
(11)
In the metrics of (9), (10) and (11), one has equivalently defined a new radial coordinate with the relationship
. (12)
Substituting for in (3), (4), (5) and (6) brings the metric form to that characterized by (9), (10) and (11), but in the coordinate with , and unchanged. The prime notation has been dropped. Boundary conditions continue to be satisfied if the exponential terms approach unity as approaches infinity or approaches zero, so that the metrics go over into that of flat spacetime for these limits. One can easily verify that this condition is met for . Therefore, one has an infinite number of solutions of this form.
A particularly simple solution is obtained by setting . Relationships (9), (10) and (11) become:
(13)
(14)
(15)
The notable feature of the family of solutions characterized by (9), (10) and (11) is that they exhibit no black holes whatsoever for the infinite subset . [10] One sees this immediately in the particular solution associated with (13), (14) and (15). [I.e., there are no infinities other than at . – Ed.]
All of these solutions exhibit a singularity at the origin. This is not surprising because, in like manner with the standard and isotropic forms, they make use of coordinate systems in which the Newtonian approximation follows in that is asymptotic to as approaches infinity. It should be recognized that the uncertainty principle by itself casts serious doubt on the possibility of a physical singularity developing at the site of this mathematical one. [11] The singularity has merely pointed up the limitations of the theory. It inescapably brings down on one the fact that, if one could indeed momentarily wink at the uncertainty principle and localize the mass at , there would remain the problem of the gross violation of local flatness at that point, a problem these solutions share with both the isotropic and standard metric forms. As with them, one is stuck with the singularity at with its completely arbitrary properties. To argue that there is a black hole there is untenable. To further argue that the singularity is somehow “within” or “enveloped” by the black hole compounds the blunder. If one wishes nevertheless, in face of this, to suppose a combined black hole and singularity, one is conjuring a physical phenomenon that for all observers is to be realized only after infinite time has elapsed – a concept wholly without meaning.
As a spherical polar coordinate, naturally takes on only positive values. It cannot be maintained that the range of physically accessible 3-space should somehow exceed this, that can take on negative values, and that solutions restricted to positive values are “geodesically incomplete”, as has been suggested to me. To argue this is to give special status to coordinate systems such as those represented by the standard and isotropic metric forms, and thus to throw away the general principle of relativity. One could on this same basis as easily argue that the standard metric form summons up “geodesically fictitious” 3-space. (Nonetheless, we shall take up the opposite supposition, that can in fact take on negative values, in the Appendix. We shall see, not surprisingly, that it leads to a gross physical inconsistency.) Again in Einstein’s words, “We shall introduce in the general theory of relativity arbitrary coordinates, , , , , which shall number uniquely the space-time points, so that neighboring events are associated with neighboring values of the coordinates; otherwise, the choice of coordinates is arbitrary.” [12] The only primacy that black-hole-exhibiting metrics can have is purely accidental – historical precedence, a logical defense that has not been valid in science since the demise of Scholasticism.
Discussion
Existence and nonexistence cannot possibly be construed as equivalent formulations of the same event or phenomenon.
General Relativity’s failure to ensure the existence of black holes does indeed remove much of the significance attached to the latter topic: “If it [cosmic censorship] does not hold, then the formation of a naked singularity during collapse would be a disaster for general relativity theory. In this situation, one cannot say anything precise about the future evolution of any region of space containing the singularity since new information could emerge from it in a completely arbitrary way.” [13] Clearly, in the coordinate systems under consideration, no black hole is formed--nor is any naked singularity likely to be physically realized. There is a disaster here, nevertheless. It is the simultaneous prediction and lack of prediction of a phenomenon by the same theory. At the same time, another door is apparently more widely opened, since there is still much that is germane that is likely to be forthcoming from the study of particle physics under the extreme conditions in the interior of a neutron star. [14]
Bergmann, in discussing in very general terms issues that would seem to encompass this one, has suggested we take a hard, pragmatic approach to winnowing statements that follow from General Relativity by adopting the following criterion: “There exists a subset of physical variables, the ‘observables’, whose values are independent of the choice of coordinate system employed. Thus, any relationship between observables is ‘meaningful’, and conversely, these are the only relationships that are legitimate.” [15] Perhaps this stern waving away of General Relativity’s encompassing of the tentative phenomenon of black holes is premature; perhaps not. Brushing aside modesty for the moment, I propose instead a more “moderate” approach, a new physical principle, to be placed alongside the cosmic-censor hypothesis. Does General Relativity predict black holes? Yes and no. Voila, the “principle of indecision.”
Appendix
Let us, for the sake of argument, momentarily accept the possibility that the solutions characterized by (9), (10) and (11) merely ignore the space “inside the black hole.” That is, let us suppose for the moment that negative values of are physically meaningful in those solutions. One could argue that the area of the surface is not zero for these solutions, so there is no reason to restrict r to positive values.
This reasoning immediately produces a paradox. By allowing negative values of in the metrics of (9), (10) and (11), one has that the mass-independent “Newtonian” singularity is naturally at , while the mass-dependent singularity is at , inside the Newtonian singularity. This is of course just opposite the arrangement that follows from the standard or isotropic form. The mass-dependent or mass-independent qualities are clearly distinguishing physical characteristics, and to have them reverse order like this depending on one’s choice of coordinate system is a blatant absurdity. The hand is inside the glove in the one instance, and the glove is inside the hand in the other, arbitrarily.
The widely used isotropic metric form reflects much these same considerations. For it, the area of the surface also is not zero. The inference that as a consequence takes on negative values breaks rather puzzling new ground. One has for the speed of light

Setting (leading to a zero surface area) gives one an infinite value for . So one has, what, a white hole(?) at , which is inside a Newtonian singularity at , which is again inside a black hole at ?
References
[1] These solutions were included as an aside in an unpublished work by D.H. Menzel in 1975. I am indebted to Earle Whipple for making that work available to me.
[2] Penrose, R., “Gravitational Collapse and Space-Time Singularities”, Phys.Rev.Lett. 14, 57-59 (1965).
[3] Misner, C.W., Thorne, K.S. and Wheeler, J.A., Gravitation, Freeman, San Francisco, 620 (1973).
[4] Goldwirth, D.S., Ori, A. and Piran, T., “Cosmic Censorship and Numerical Relativity”, in Frontiers in Numerical Relativity, eds. C.R. Evans, L.S. Finn, and D.W. Hobill, Cambridge Univ. Press, Cambridge, 415 (1989).
[5] Shapiro, S.L. and Teukolsky, S.A., “Black Holes, Naked Singularities and Cosmic Censorship”, Amer.Scientist 79, 330-343 (1991).
[6] Oppenheimer, J.R. and Snyder, H., “On Continued Gravitational Contraction”, Phys.Rev. 56, 455-459 (1939).
[7] Birkhoff, G.D., Relativity and Modern Physics, 2nd ed., Harvard Univ. Press, Cambridge, 253-256 (1927).
[8] Pauli, W., Theory of Relativity, reprinted 1981 by Dover Press, New York, 160 (1921).
[9] Einstein, A., Relativity, reprinted 1961 by Crown Publishers, New York, 97, 99 (1916).
[10] Non-static solutions that do not display singularities other than at the origin have been known for many years. Rightfully or wrongfully, they appear to have been discounted as physically unimportant because of their complicated time dependence. See Moller, C., The theory of Relativity, Oxford Univ. Press, London, 327-328 (1960).
[11] Harrison, B.K., Thorne, K.S., Wakano, M. and Wheeler, J.A., Gravitation Theory and Gravitational Collapse, Univ. of Chicago Press, Chicago, 141-142 (1965).
[12] Einstein, A., The Meaning of Relativity, reprinted 1974 by Princeton Univ. Press, Princeton, 61 (1922).
[13] Shapiro, S.L. and Teukolsky, S.A., “Formation of Naked Singularities: The Violation of Cosmic Censorship”, Phys.Rev.Lett. 66, 994-997 (1991).
[14] Olive, K.A., “The Quark-Hadron Transition in Cosmology and Astrophysics”, Science 251, 1194-1199 (1991).
[15] Bergmann, P.G., “Physics and Geometry”, in Proceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science, ed. Y. Bar Hillel, North Holland, Amsterdam, 346 (1965).

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

10-02-2002, 04:48 AM	#12
Ted Hoffman Veteran Member Join Date: Feb 2001 Location: "" Posts: 3,863	Jesse, Thanks for your serious response. I really appreciate the way you are handling this seriously. I must apologise for my incorrect interpretation of Van Flanderns objection concerning the rubber sheet analogy. His main objection is that it violates the causality principle (that crap about the sheet bending downwards and self-referencing argument was mine, not his). I have noted your comments and written to Steve Carlip (I understand he is an expert in the mathematics of gravitation physics) I await his response. Your haughty and disdainful attitude about my ability to understand the answers for the questions I have asked aside, I just hope to get some concrete response concerning all allegations against Tom V.F. all I have seen so far is "you are incompetent because you dont agree with us" or "the fact that you even question the formulas is in itself evidence that you don't understand them". Even if I can't understand the math, at least it will be a specific valid response to whatever arguments TVF is advancing and I can read further or ask an expert to explain to me what the heck the formulas mean and so on. Save me the superciliousness please; you don't know me that well. [ October 02, 2002: Message edited by: Intensity ]</p>

10-03-2002, 12:05 AM	#15
atrahasis Regular Member Join Date: Mar 2002 Location: South of Sahara Posts: 216	sorry, wrong login [ October 03, 2002: Message edited by: Black Moses ]</p>

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10-02-2002, 04:18 AM	#11
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	It is funny to note that even after so many experimental confirmations and applications on relativity. Many people are still skeptic of GR and its founder.

10-02-2002, 07:30 AM	#13
Steven S Regular Member Join Date: Jun 2000 Location: Raleigh, NC Posts: 167	How can you tell Van Flandern counters the criticism of his debunkers? Do you know GR? In anycase, I suggest this archived collection of posts from sci.physics.* dealing with Van Flandern's claims: <a href="http://math.ucr.edu/home/baez/PUB/debate" target="_blank">http://math.ucr.edu/home/baez/PUB/debate</a> Steven S

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