1 Stephen Speicher |
Speed of Gravity | maandag 22 oktober 2001 6:57 | |
2 Tom Van Flandern |
Re: Speed of Gravity | maandag 22 oktober 2001 18:08 | |
3 Martin Hogbin |
Re: Speed of Gravity | maandag 3 september 2001 10:27 | |
4 novastar |
Re: Speed of Gravity | dinsdag 23 oktober 2001 18:36 | |
5 Tom Roberts |
Re: Speed of Gravity | woensdag 24 oktober 2001 5:54 | |
6 Tom Van Flandern |
Re: Speed of Gravity | donderdag 25 oktober 2001 19:06 | |
7 Nicolaas Vroom |
Re: Speed of Gravity | donderdag 25 oktober 2001 21:17 | |
8 Tom Roberts |
Re: Speed of Gravity | zondag 28 oktober 2001 5:08 | |
9 Joe Fischer |
Re: Speed of Gravity | zondag 28 oktober 2001 15:57 | |
10 Nicolaas Vroom |
Re: Speed of Gravity | dinsdag 30 oktober 2001 17:22 | |
11 Steve Carlip |
Re: Speed of Gravity | dinsdag 30 oktober 2001 20:45 | |
12 Tom Van Flandern |
Re: Speed of Gravity | donderdag 1 november 2001 8:26 | |
13 Steve Carlip |
Re: Speed of Gravity | vrijdag 2 november 2001 2:26 | |
14 Tom Van Flandern |
Re: Speed of Gravity | woensdag 7 november 2001 10:16 | |
15 Nicolaas Vroom |
Re: Speed of Gravity | woensdag 7 november 2001 14:46 |
On Sun, 21 Oct 2001, Tom Van Flandern wrote:
> | [about Steve Carlip] The following are examples of ad hominem remarks targeted at me personally, rather than at the issues on the table, from Steve's last post: |
Tom, these remarks are not examples of ad hominem. The fallacy of ad hominem is attacking the person _in lieu of actual arguments_. Steve Carlip has, as far as I can see, addressed all of the relevant issues, several times. You may disagree with his counterarguments, but he has made them.
The remarks you cite are insults, not ad hominem. And, to be fair, from the time I started reading this incarnatation of the thread (just a short while ago) I noted several insults which you oferred to Steve. For instance (not verbatim), you accused him of putting out a smokescreen of technical discussion which people cannot understand, for the purpose of creating an illusion of having addressed the issue. That is quite insulting, indeed.
> |
The Einstein-Infeld-Hoffman (EIH) approximation (GR equations of motion) is representative of general relativity because they are the form in which GR is tested against observations, and because the only potentially significant omission from those equations is the gravitational radiation term. However, that term is negligible in all solar system examples, represents only a small effect even in binary pulsars, and produces primarily orbital acceleration of the stars but no detectible effect elsewhere. In particular, gravitational radiation has no significant effect on the observer in my binary star example. Steve's point here is therefore a red herring argument. |
Frankly, Tom, I can understand Steve's frustration when you deny his point by essentially repeating what you asserted before. Steve gave you his argument against this before, and included two separate quotes from MTW as well one from Damour, all in support of his argument.
Tom, to attempt to represent EIH _as if_ it were general relativity is to ignore the very basis upon which EIH was built. In addition to the restrictions which Steve documented, there are others which have an historical context. For instance, the EIH assume its results are meaningful to extended objects, the limited validity of which Einstein (and others) were well-aware of at the time. The motion of our solar system needs to consider tidal forces in a high enough approximation, and failure to do so will conflict with the celestial mechanics laws which follow from GR. This, and other issues, are discussed by Peter Havas in his article "The Early History of the 'Problem of Motion' in General Relativity," appearing in _Einstein and the History of General Relativity_, Einstein Studies Volume 1, edited by Don Howard and John Stachel.
> |
Steve, I'm sympathetic. You may be getting way out of your depth here. |
Tom, don't be too surprised by other's insults when you make comments such as these to a man who is a recognized expert in this field.
Stephen sjs@compbio.caltech.edu
Welcome to California. Bring your own batteries.
Printed using 100% recycled electrons. --------------------------------------------------------t we read that it is speed of light, then not...
"Stephen Speicher" sjs@compbio.caltech.edu writes:
> | [ss]: I noted several insults which you offered to Steve. For instance (not verbatim), you accused him of putting out a smokescreen of technical discussion which people cannot understand, for the purpose of creating an illusion of having addressed the issue. That is quite insulting, indeed. |
I take your point, and apologize to Steve for that. The frustration of having telling arguments ignored must have clouded my judgment. But then, if I take Steve literally, he sees me as doing the same thing. It is amazing how difficult communication can be at times.
>> | [tvf]: The Einstein-Infeld-Hoffman (EIH) approximation (GR equations of motion) is representative of general relativity because they are the form in which GR is tested against observations, and because the only potentially significant omission from those equations is the gravitational radiation term. However, that term is negligible in all solar system examples, represents only a small effect even in binary pulsars, and produces primarily orbital acceleration of the stars but no detectible effect elsewhere. In particular, gravitational radiation has no significant effect on the observer in my binary star example. Steve's point here is therefore a red herring argument. |
> | [ss]: Frankly, Tom, I can understand Steve's frustration when you deny his point by essentially repeating what you asserted before. Steve gave you his argument against this before, and included two separate quotes from MTW as well one from Damour, all in support of his argument. |
I specifically addressed the quotes from MTW, and hope the points I made were clear. Steve and I discussed Damour in depth much earlier in this debate. Damour has done more than anyone I know to deal with the speed of gravity issue in GR, and it is simply amazing to see that he basically gave up on treating this rigorously and adopted the position of simply assuming that a speed of gravity equal to c is possible.
But as Damour's work pertains to Steve's point, Damour's equations of motion support my argument, not Steve's. Damour has no magical time-lag-transition term that allows the direction of gravitational force to pass from instantaneous-source-directed to retarded-source-directed as distance from the source increases. And a quick numerical evaluation shows just how negligible the largest contributions from gravitational radiation (using the Damour formulas) really are.
> | [ss]: Tom, to attempt to represent EIH _as if_ it were general relativity is to ignore the very basis upon which EIH was built. |
I hope we're not playing with words here. The EIH equations of motion represent GR, and are used for testing the predictions of GR. I did not say they *were* GR. I do say they represent the gravitational acceleration predicted by GR fully and fairly for testing purposes, including for purposes of the general binary star example we were discussing. With the addition of the tiny gravitational radiation effect, one has everything needed to deal with all known dynamical applications of GR to astrophysics.
There are no truncated or missing terms from this approximation at an observationally significant level of precision, contrary to what Steve maintains. The EIH expansion is complete to the order shown, and any higher order terms would be truly negligible. Because I can't prove a negative (that no additional significant terms from some other cause potentially exist), the burden is on Steve, who is making the claim, to produce a citation or an argument to show that such terms do exist. I have shown that Steve's argument based on chapter 36 is in error because Steve did not notice that chapter 36 derives *only* the gravitational radiation effect, and makes important approximations regarding the gravitational acceleration effect while doing so. Specifically, it averages the separate fields of the two stars into a single, non-revolving field when considering gravitational waves in the radiation zone.
> | [ss]: In addition to the restrictions which Steve documented, there are others which have an historical context. For instance, the EIH assume its results are meaningful to extended objects, the limited validity of which Einstein (and others) were well-aware of at the time. The motion of our solar system needs to consider tidal forces in a high enough approximation, and failure to do so will conflict with the celestial mechanics laws which follow from GR. |
Why do you raise these valid but insignificant points here, seemingly implying they are relevant to the point on the table when they are not? The EIH equations are correct and complete for the purposes of this discussion, and specifically for my binary star example. Are you trying to make some sort of aesthetic argument?
>> | [tvf]: Steve, I'm sympathetic. You may be getting way out of your depth here. |
> | [ss]: Tom, don't be too surprised by other's insults when you make comments such as these to a man who is a recognized expert in this field. |
To the extent that the intent of my remark may be misunderstood, I apologize for this also. My actual intent, however, was not to insult but to help Steve save face for having made an understandable blunder in the celestial mechanics arena by not realizing that the gravitational force field oscillations had been averaged out of the potential expression he thought was complete. Steve may be the world's leading expert on the GR field equations for all I know, but when he crosses over into other areas, he sometimes makes mistakes, as he has found me doing in his specialty area many times. My intent was to make it easier for Steve to concede the mistake, as opposed to forcing him to defend it. -|Tom|-
Tom Van Flandern - Washington, DC - see our web site on replacement astronomy research at http://metaresearch.org>
On Mon, 22 Oct 2001, Tom Van Flandern wrote:
> | "Stephen Speicher" sjs@compbio.caltech.edu writes: |
> > |
[ss]: I noted several insults which you offered to Steve. For instance |
> |
(not verbatim), you accused him of putting out a smokescreen of
technical discussion which people cannot understand, for the
purpose of creating an illusion of having addressed the issue.
That is quite insulting, indeed.
I take your point, and apologize to Steve for that. The frustration of having telling arguments ignored must have clouded my judgment. But then, if I take Steve literally, he sees me as doing the same thing. It is amazing how difficult communication can be at times. |
Your penultimate sentence explains your last one, and this was the main reason I spoke up in the first place. Communication is a two-way street, but as the challenger to the accepted theory it is encumbent upon you to be even more precise than your opponents. You need to set a higher standard, since you first must demonstrate that you grasp the standard theory before you can validly be critical of it.
You may believe it or not, Tom, I am more open to your criticism than most, yet I must say, again, that I understand the source of frustration expressed by others over your idiosyncratic explanations, not of your own approach, but of your characterization of standard theory.
If, as you say above, you now have a glimmer that others feel the same frustration towards you as you do towards them, then I submit the next step is for you to become better acquainted with the terminology of modern relativity. You should be free to define and use your own terminology in regard to your theory, but you should not intermingle such concepts with the standard theory when you are attempting to be critical of what it is.
Perhaps you are so deeply involved in your own perspective that it is difficult to appreciate the perspective of others. Were your theory the prevalent one, you could afford such a position. However, being the challenger, I think you need to better understand the actual perspective of your opponents _if_ you want to communicate with them. If all you want to do is present your view, then that is a different matter. However, as I'm sure you are aware, these newsgroups are not the best place to do so.
I'll get off my soapbox now and leave this thread to all the original participants. I hope you understand, Tom, that whatever I have said was offered in good will, hoping that more value can be brought to this never-ending thread, by both sides.
Stephen sjs@compbio.caltech.edu
Welcome to California. Bring your own batteries.
Printed using 100% recycled electrons. --------------------------------------------------------
So ... what is the conclusion ? Where are these eight lost minutes between gravity and light affect from sun ?
> | So ... what is the conclusion ? |
That Tom Van Flandern uses a _PUN_ on the word "speed", and applies the word to a phenomenon to which the standard meaning does not apply. In particular, he _NEVER_ addresses any usual sort of measurement of speed: the ratio of a distance to the time-of-flight over it.
Remove this pun from his argument, and there is no argument. Yes indeed, SPEAKING LOOSELY: GR predicts that the "gravitational force vector" from the sun points to where it is "now" (not 8 minutes ago), to within incredible accuracy. But this can in no way be interpreted as "speed of propagation" of the "gravitational force", unless one redefines the word "speed" in Tom Van Flandern's outrageously-unusual way.
> | Where are these eight lost minutes between gravity and light affect from sun? |
Your question does not make sense. The "eight minutes" are not "lost", and are not "anywhere". There is indeed an angular difference between "gravitational direction to the sun" and "light direction to the sun"; it is determined by various orbital parameters of the earth.
Tom Roberts tjroberts@lucent.com
> | [ns]: So ... what is the conclusion? Where are these eight lost minutes between gravity and light affect from sun? |
The Sun's light and gravity appear to propagate from the same source to the same target along the same linear path, yet the forces they produce on the target (radiation pressure and gravitational acceleration) operate in directions that are not parallel. Light pressure operates from the retarded position of the Sun, and gravitational acceleration is closely toward the true, instantaneous position of the Sun.
In classical physics, the explanation is simple, because the angle of operation of a force depends on its propagation speed. So the above fact simply means that light propagates at speed c and gravity at a speed very much greater than c.
Alternative explanations of the same fact raise more questions than they answer. E.g.: ** "Nothing propagates from the source to the target." This removes the cause from the physics, thereby violating the causality principle; and removes the source of the new momentum transferred to the target, thereby creating momentum from nothing. ** "The target anticipates the motion and acceleration of the source relative to the target during the gravity transit time." This is equivalent to "Trust the equations and don't worry about their implications." But the physics behind such an assertion seems to require the operation of magic. The only known physical mechanism that can make the direction of propagation of gravity the same in the source frame and in the transversely moving target frame is near-infinite propagation speed.
This simple solution, gravity propagating much faster than light, violates no known physics, but is in conflict with the proof in SR that nothing can propagate faster than light in forward time. However, the mathematically equivalent Lorentzian relativity (LR) makes the same predictions as SR in the sub-light-speed domain, but has no speed limit. So anything shown to propagate faster than light in forward time simply favors LR over SR and leaves the rest of physics intact.
and "Tom Roberts"
> | [tr]: Tom Van Flandern uses a _PUN_ on the word "speed", and applies the word to a phenomenon to which the standard meaning does not apply. In particular, he _NEVER_ addresses any usual sort of measurement of speed: the ratio of a distance to the time-of-flight over it. |
There are two ways in common use to measure speed. One is to divide the measured distance traveled by the time interval required. The other is to divide the measured speed of the source relative to the target by the angle (in radians) traversed by the source during the transit time. These two methods are physically equivalent. For example, if a bird observes the angle between where it sees an archer fire an arrow and where it sees the archer when that arrow arrives, it just divides its own speed by that angle and has the speed of the arrow. From the archer's perspective, the angle is the "Kentucky windage" -- the angle by which the archer must lead the bird so that the arrow and bird will arrive at the same place at the same time -- which depends simply on the ratio of the bird's speed to the arrow's speed.
In short, there is no "trick" or "pun" here. This is simple, uncontroversial, classical physics.
That said, Tom Roberts has failed to notice that the new general binary star example I have focused on over the past two months uses "speed of gravity" in the sense he prefers: distance divided by time interval. And it applies directly to the GR equations of motion. In short, in those equations (MTW p. 1095), oscillations in the acceleration of a distant observer are in-phase with the true, instantaneous positions of the binary stars, and not with their retarded positions, *at any distance*. That can only be possible if the gravitational signals propagate from the revolving stars to the distant observer with infinite speed. The GR equations of motion, like the Newtonian equations they reduce to for such simple cases, have infinite gravity propagation speed built in. "Infinite speed" here means that a gravitational signal generated by revolving binary stars reaches an indefinitely large distance in an immeasurably small time. That's no "pun" on the meaning of the word "speed".
> | [tr]: Remove this pun from his argument, and there is no argument. Yes indeed, SPEAKING LOOSELY: GR predicts that the "gravitational force vector" from the sun points to where it is "now" (not 8 minutes ago), to within incredible accuracy. But this can in no way be interpreted as "speed of propagation" of the "gravitational force", unless one redefines the word "speed" in Tom Van Flandern's outrageously-unusual way. |
I read "outrageously-unusual" to mean "different than TR was taught". The sense in which I use "speed" is ordinary and classical. Relativists (like most people) resist changes in the way they were taught to think about things. But in any cost-benefit analysis, this simple change of interpretation has a great deal to recommend itself. One of the nicest benefits is lifting the speed limit for the universe without need to mess with the rest of physics.
> | [tr]: There is indeed an angular difference between "gravitational direction to the sun" and "light direction to the sun"; it is determined by various orbital parameters of the earth. |
The angle between the directions of forces applied by light and gravity is determined solely by the transverse speed of the Earth relative to the Sun. The ratio of that speed to the speed of light gives the angle by which solar photons arriving at Earth are retarded, or equivalently the angle by which photons leaving the Sun must lead the Earth to hit it.
If we replace "photons" in this example with arrows, the angle between the Sun's position at arrow-launch and its position at arrow-arrival is always the speed of the Earth divided by the speed of the arrow. This holds for all arrow speeds up to and including the speed of light. The simplest interpretation of observations is that it continues to hold for "arrows" (such as gravity) traveling faster than light. Alternate explanations violate the causality and "no creation ex nihilo" principles, and do not explain the GR equations of motion.
Consider what relevant physical difference exists between a bird/Earth flying over an archer/Sun at a known speed that causes the physics describing the latter to differ from the physics describing the former. And can any relativist explain why there is no propagation time delay for oscillations of gravitational force in the GR equations of motion for a binary star? -|Tom|-
Tom Van Flandern - Washington, DC - see our web site on replacement astronomy research at http://metaresearch.org>
Tom Roberts
> |
novastar wrote:
Remove this pun from his argument, and there is no argument. Yes indeed, SPEAKING LOOSELY: GR predicts that the "gravitational force vector" from the sun points to where it is "now" (not 8 minutes ago), to within incredible accuracy. But this can in no way be interpreted as "speed of propagation" of the "gravitational force", unless one redefines the word "speed" in Tom Van Flandern's outrageously-unusual way. |
Do't you mean the "gravitational force vector" from the earth points to where the sun is "now" (not 8 minutes ago) exactly
If that is true do you agree with: The "gravitational force vector" from the sun points to where the earth is "now" (not 8 minutes ago) exactly.
If that is true do you agree with: The "gravitational force vector" from the earth points to where the star "alpha one" is "now" exactly ie not in the direction where we see "alpha one" now.
If you agree the question boils down to: What is the definition of "gravitational force vector" I think you and Tom disagree
Secondly how do you demonstrate that the two directions are different
> > | Where are these eight lost minutes between gravity and light affect from sun? |
> |
Your question does not make sense. The "eight minutes" are not "lost", and are not "anywhere". There is indeed an angular difference between "gravitational direction to the sun" and "light direction to the sun"; it is determined by various orbital parameters of the earth. Tom Roberts tjroberts@lucent.com |
> |
Tom Roberts |
> > | SPEAKING LOOSELY: GR predicts that the "gravitational force vector" from the sun points to where it is "now" (not 8 minutes ago), to within incredible accuracy. But this can in no way be interpreted as "speed of propagation" of the "gravitational force", unless one redefines the word "speed" in Tom Van Flandern's outrageously-unusual way. |
> | Do't you mean the "gravitational force vector" from the earth points to where the sun is "now" (not 8 minutes ago) exactly |
No, I mean approximately, as I said.
> | If that is true do you agree with: The "gravitational force vector" from the sun points to where the earth is "now" (not 8 minutes ago) exactly. |
No. This too is only approximate.
> | If that is true do you agree with: The "gravitational force vector" from the earth points to where the star "alpha one" is "now" exactly ie not in the direction where we see "alpha one" now. |
The approximation is not so good....
> | If you agree the question boils down to: What is the definition of "gravitational force vector" I think you and Tom disagree |
Yes, we disagree. I consider "gravitational force vector" to be merely an _APPROXIMATION_. GR itself has no such concept, but in some approximations to GR it can be a useful concept.
> | Secondly how do you demonstrate that the two directions are different |
By measuring them, of course. I don't know if such measurements can be performed to the requisite accuracy.
Tom Roberts tjroberts@lucent.com
In sci.physics.relativity Tom Roberts wrote:
> | Nicolaas Vroom wrote: |
>> | Tom Roberts wrote: |
>> > | SPEAKING LOOSELY: GR predicts that the "gravitational force vector" from the sun points to where it is "now" (not 8 minutes ago), to within incredible accuracy. But this can in no way be interpreted as "speed of propagation" of the "gravitational force", unless one redefines the word "speed" in Tom Van Flandern's outrageously-unusual way. |
>> |
Do't you mean the "gravitational force vector" from the earth points to where the sun is "now" (not 8 minutes ago) exactly |
> |
No, I mean approximately, as I said. |
Tom Roberts, please don't let the qwasi-Newtonians lead you into a discussion of a "force vector" for orbital motion or free motion in free space. I think you have a very good feel for General Relativity and the mathematics it is based on, which uses as it's basic thrust, an attempt to resolve all free motion as inertial motion.
>> | If that is true do you agree with: The "gravitational force vector" from the sun points to where the earth is "now" (not 8 minutes ago) exactly. |
> |
No. This too is only approximate. |
Is this a good example of how a third-degree
interrogation can lead to a confession by an innocent?
I really don't see what TvF has to gain by the
(eight year, he claims) perpetuation of this thread.
"Speed of Gravity" is not a measured phenomena,
and is pure speculation, based on the incorrect Newtonian
concept of "attraction".
This thread doesn't even make sense as a topic
for a Newtonian newsgroup such as sci.physics let alone
making sense, or being topical in sci.physics.relativity.
>> | If that is true do you agree with: The "gravitational force vector" from the earth points to where the star "alpha one" is "now" exactly ie not in the direction where we see "alpha one" now. |
> |
The approximation is not so good.... |
If the approximation uses Newtonian concepts it is contrary and almost diametrically opposite to General Relativity. "not so good" should mean "wrong as ....".
>> | If you agree the question boils down to: What is the definition of "gravitational force vector" I think you and Tom disagree |
> |
Yes, we disagree. I consider "gravitational force vector" to be merely an _APPROXIMATION_. GR itself has no such concept, but in some approximations to GR it can be a useful concept. |
Perhaps this is getting to the heart of the issue,
popular accounts of the study, observations, and experiments
put forth by physicists almost invariably use a Newtonian
type approximation, which may be somewhat correct quantitatively,
but which destroys the very objective of resolving free motion
as inertial motion.
Please note that I do not claim any measure of
proficiency in mathematics at all, and my statements are
based on my opinions and what I have read about General
Relativity (mostly as written by Einstein) in a casual
sitting, leaving me with envy of anyone having a formal
understanding of the mathematics.
But this does not diminish my convictions that
General Relativity must treat free, non-interaction motion
as inertial motion, and only in this way can gravitational
mass naturally equal inertial mass.
>> | Secondly how do you demonstrate that the two directions are different |
> |
By measuring them, of course. I don't know if such measurements can be performed to the requisite accuracy. Tom Roberts tjroberts@lucent.com |
A very good thing for TvF to consider, because, even
though no delay is used in celestial mechanics calculations,
there is no "gravity ray or beam" to produce an image as
there is in the case of a "light ray or beam".
I don't think students of General Relativity should
be led into thinking that a "force" needs to be exerted on
orbiting bodies, as that concept then leads the student to
thinking that some hypothetical particle or medium capable
of such great "strength" might have to exist, it does NOT.
If, at some time, such a particle or entity is
found, then a "speed of propagation" may be appropriate,
but as of now, in relation to General Relativity, this
topic is so skewed by incorrect assumptions toward the
incorrect concepts of "gravitational force" as taught
in Newtonian gravitation, it should be dropped.
Each model has it's place in science, but Newtonian
gravitation is specifically constructed to work with and
complement Newtonain mechanics, and that ain't bad.
But General Relativity should be studied as the
resolution of free motion as inertial motion, and this
can only be done _geometrically_ and NOT by "forces"
acting.
Joe Fischer
--
Tom Roberts
> | Nicolaas Vroom wrote: |
> > |
Tom Roberts |
> > > |
SPEAKING LOOSELY: GR predicts that the
"gravitational force vector" from the sun points to where it is
"now" (not 8 minutes ago), to within incredible accuracy. But this can in no way be interpreted as "speed of propagation" of the "gravitational force", unless one redefines the word "speed" in Tom Van Flandern's outrageously-unusual way. |
> > | Do't you mean the "gravitational force vector" from the earth points to where the sun is "now" (not 8 minutes ago) exactly |
> |
No, I mean approximately, as I said. |
> > |
If that is true do you agree with: The "gravitational force vector" from the earth points to where the star "alpha one" is "now" exactly ie not in the direction where we see "alpha one" now. |
> |
The approximation is not so good.... |
> > |
If you agree the question boils down to: What is the definition of "gravitational force vector" I think you and Tom disagree |
> |
Yes, we disagree. I consider "gravitational force vector" to be merely an _APPROXIMATION_. GR itself has no such concept, but in some approximations to GR it can be a useful concept. |
> |
> > |
Secondly how do you demonstrate that the two directions are different |
> |
By measuring them, of course. I don't know if such measurements can be performed to the requisite accuracy. |
At page 195: Laplace calculated that the sun had not lost a 2-millionth
part of its substance in recorded history and that the effect of the
impact on the secular equation of the moon is undetectable.
... except that now gravity is given a velocity of 1 *10**9 times
the speed of light, which is to say, infinite.
IMO what Laplace tried to do is to calculate the speed of the
corpuscules (ie gravitons ?) based on the influence they have
on the motion of the moon when they collide with the moon.
IMO this influence is almost zero
The same is true if you consider light ie the photons that strike
the moon. Also that influence is almost zero.
At page 34 Laplace shows the equations of motions (r, phi)
of a body p describing any orbit around S.
The gravitational forces are (I expect) in the direction of S
What Laplace should have done is to give the equations
(I definitely do not blame him for that)
when the gravitational forces are not in the direction of S
ie of a moving Earth, Moon system.
First I expect that for the Earth Moon system the
difference is small compared with an Earth at rest
Secondly I expect that Laplace could not measure this difference.
> |
Tom Roberts tjroberts@lucent.com |
In sci.physics Tom Van Flandern
> | MTW equations (36.48) and (36.49) average out the particular time variation in the potential for my double star example by expanding the combined gravity fields in powers of 1/r, where r is the distance from the center of mass. They adopt a potential field that is, at great distances, much like that of a highly-flattened oblate spheroid (because the binary stars are confined to a plane, and their field oscillations are averaged out). |
For the benefit of anyone who is following this and doesn't have a copy of MTW on hand, the equations in question are just a standard multipole expansion, of the sort you learn in a good undergraduate course in E&M. There is no time averaging -- in particular, the time variation Tom is concerned with is most certainly not averaged out -- and there is nothing there even remotely related to oblate spheroids. I have no idea where Tom got this description from (except perhaps that oblate spheroids are the only examples he knows of mass distributions with quadrupole moments?).
Steve Carlip
>> | [tvf]: MTW equations (36.48) and (36.49) average out the particular time variation in the potential for my double star example by expanding the combined gravity fields in powers of 1/r, where r is the distance from the center of mass. They adopt a potential field that is, at great distances, much like that of a highly-flattened oblate spheroid (because the binary stars are confined to a plane, and their field oscillations are averaged out). |
> | [sc]: For the benefit of anyone who is following this and doesn't have a copy of MTW on hand, the equations in question are just a standard multipole expansion, of the sort you learn in a good undergraduate course in E&M. There is no time averaging -- in particular, the time variation Tom is concerned with is most certainly not averaged out ... |
Let's retain just the first (Newtonian) term in the expansion, phi
= -M/r, for a binary star where both components have equal mass m (combined
mass 2m = M) and circular orbits around an origin O. Let the observer be a
distance r away from O, and the stars be a distance R for O. Then we can
write an expression for the combined potential of the two stars at the
observer. The general expression uses vectors and is messy in ASCII, so let
me write it for two particular cases:
a) Stars in-line with observer: phi_a = -m/(r-R) -m/(r+R)
b) Stars in plane of sky for observer: phi_b
= -m/sqrt(r^2+R^2) -m/sqrt(r^2+R^2) = -M/sqrt(r^2+R^2)
By inspection, we can see that the sum of the two potentials at the observer is not the same for these two cases. [That should be obvious just from the fact that case (a) has a potential singularity away from the origin and case (b) does not.] Do you see that this effect is the source of the principle variation in the gravitational acceleration experienced by the observer? [That follows from force being the gradient of the potential.] Do you further see that the formulas you are looking at on MTW p. 1000 do not include this variation? [Neither the factor R that separates the individual stars from the origin nor their angular motion about that origin is considered by MTW. They are averaged out, which is an okay approximation for MTW's stated purpose (gravitational radiation), but not for ours (gravitational acceleration).]
As I've been saying for several messages now, one of us is dead wrong
here. I thought this example was fairly straightforward. If I haven't made
the point clear yet, I suggest we take it to a neutral expert who may
succeed where we have failed in communicating with one another. Can the
precise point where we disagree be phrased fairly in the following language?
"Does MTW p. 1000, eqn. (36.49a), contain the Newtonian potential
contributed by both components of a binary star, or have the separate
contributions of the two components been averaged for purposes of describing
the potential in the (far) radiation field?"
> | [sc]: ... and there is nothing there even remotely related to oblate spheroids. I have no idea where Tom got this description from (except perhaps that oblate spheroids are the only examples he knows of mass distributions with quadrupole moments?). |
I was using an analogy ("like an oblate spheroid") hopefully familiar to you because you seemed not to understand how the equation in question works for binary stars.
In my previous message to Steve, at least two points should have been responded to, but were not:
>> | [tvf]: "Steve agrees that gravitational acceleration is roughly toward the instantaneous position of source bodies in the near zone, but claims that it changes to being toward the retarded source body positions in the radiation zone. However, clearly such a phenomenon, if it were reality, would represent a failure of Newtonian gravitation for a weak-field, low-velocity case (the radiation zone). This is contrary to the claim that GR reduces to Newtonian gravity in the weak-field, low-velocity limit." |
This seems a serious problem for Steve's claims. Any comment?
>> | [tvf]: "Where is this hypothetical transition formula claimed to exist by Steve in which the acceleration of a target body develops a time lag from instantaneous source positions to retarded source positions?" |
This also seems problematic for Steve's position. Any comment? -|Tom|-
Tom Van Flandern - Washington, DC - see our web site on replacement astronomy research at http://metaresearch.org>
In sci.physics Tom Van Flandern
> |
Let's retain just the first (Newtonian) term in the expansion, phi
= -M/r, for a binary star where both components have equal mass m
(combined mass 2m = M) and circular orbits around an origin O.
Let the observer be a distance r away from O, and the stars be a
distance R for O. Then we can write an expression for the combined
potential of the two stars at the observer. The general expression
uses vectors and is messy in ASCII, so let me write it for two
particular cases: a) Stars in-line with observer: phi_a = -m/(r-R) -m/(r+R) b) Stars in plane of sky for observer: phi_b = -m/sqrt(r^2+R^2) -m/sqrt(r^2+R^2) = -M/sqrt(r^2+R^2) |
Good. Now take the difference of phi_a and phi_b, using the fact that r>>R. Taylor expanding, you get
phi_a - phi_b = (M/r) [ (3/2)(R/r)^2 + (5/8)(R/r)^4 + ... ]
where the dots refer to terms of order (R/r)^6 or higher. Note that the leading term in the difference goes as MR/r^3. It's a quadrupole term.
> | Do you further see that the formulas you are looking at on MTW p. 1000 do not include this variation? |
Of course they do. It's in quadrupole term in eqn. (36.49a), the term (3 I_{jk}x^j x^k)/(2r^5). The factor of 3/2 is the 3/2 in the difference between phi_a and phi_b, and the x^j x^k/r^5 gives the 1/r^3 in the difference (along with the complete angular dependence ---remember that in spherical coordinates, x^i = r times some angular terms). The time dependence is not averaged out; it is there in the time dependence of I_{jk} -- see eqn. (36.46). Note that from the unnumbered equation on the bottom of page 999, from which eqn. (36.49a) was derived, that this time dependence is dependence on the *retarded* time. (That's also what the square brackets in eqn. (36.48) around T^{00} mean.)
> | In my previous message to Steve, at least two points should have been responded to, but were not: |
>>> | [tvf]: "Steve agrees that gravitational acceleration is roughly toward the instantaneous position of source bodies in the near zone, but claims that it changes to being toward the retarded source body positions in the radiation zone. However, clearly such a phenomenon, if it were reality, would represent a failure of Newtonian gravitation for a weak-field, low-velocity case (the radiation zone). This is contrary to the claim that GR reduces to Newtonian gravity in the weak-field, low-velocity limit." |
That's roughly true. The claim that ``GR reduces to Newtonian gravity in the weak-field, low-velocity limit'' is sometimes stated a bit too blithely. It's really valid only in the near zone (which, of course, is the only place it's ever been tested). This is what Damour meant in the quote I gave in an earlier post: ``the post-Newtonian expansion is basically a near-zone expansion of the exact h^{\mu\nu}, i.e., an expansion only valid up to a radius, r, around the system which is much smaller than the characteristic wavelength, lambda, of the gravitational radiation emitted by the system...''
>>> | [tvf]: "Where is this hypothetical transition formula claimed to exist by Steve in which the acceleration of a target body develops a time lag from instantaneous source positions to retarded source positions?" |
It's complicated. See, for example, Pati and Will, Phys. Rev. D62 (2000) 124015, which is specifically about this issue.
Steve Carlip
> | [sc]: Note that the leading term in the difference goes as MR/r^3. It's a |
Okay.
>> | [tvf]: Do you further see that the formulas you are looking at on MTW p. 1000 do not include this variation? |
> | [sc]: Of course they do. It's in quadrupole term in eqn. (36.49a), the term (3 I_{jk}x^j x^k)/(2r^5). The factor of 3/2 is the 3/2 in the difference between phi_a and phi_b, and the x^j x^k/r^5 gives the 1/r^3 in the difference |
Point taken.
> | [sc]: The time dependence is not averaged out; it is there in the time dependence of I_{jk} -- see eqn. (36.46). |
True in a sense. But later, we have this related exchange:
>> | [tvf]: Where is this hypothetical transition formula claimed to exist by Steve in which the acceleration of a target body develops a time lag from instantaneous source positions to retarded source positions? |
> | [sc]: It's complicated. See, for example, Pati and Will, Phys. Rev. D62 (2000) 124015, which is specifically about this issue. |
I am days away from departing on a two-week expedition to Guam for the Leonid meteor storm, and won't be able to follow up this reference until I return. You suggest that all the answers are there, but I have a very difficult time seeing my way through the following dilemma.
An observer at any distance in the near zone accelerates in oscillating fashion nearly in phase with the instantaneous positions of the components of a binary star. One possible interpretation is that the speed of gravity is nearly instantaneous. The explanation you prefer is that the retarded positions of the stars get extrapolated forward by their retarded velocities and retarded accelerations during the light-time to the observer, so that their near field is everywhere similar to what the instantaneous stars would have generated.
However, as the distance of the observer gets greater, the above extrapolation gets to be a poorer and poorer approximation of the true position of the stars, and even of any position the stars could ever actually occupy. Extrapolations with a constant acceleration soon depart radically from the actual star paths. You suggest that, just as the observer approaches distances at which these extrapolations are starting to deteriorate hopelessly far from reality, nature changes in such a way that no extrapolation at all applies anymore. Really distant (far field) observers respond to fully retarded positions of the source stars without any forward projection.
Now I admit this "solves" the problem mathematically, but how does this not qualify as a "deus ex machina"? I am able to see it only as an implausible physical description of what must happen in the math to avoid contradicting observational data. But it completely lacks physical motivation. Can you provide any context for me to regard this solution as other than a miracle of physics?
It does not help me to take this great suspension of credulity that the competing interpretation of the same facts (gravity propagating much faster than light) is *so* simple. And the only amendments to GR it would require are in these far-field parts that you agree (below) have never been observationally confirmed.
> | [sc]: The claim that GR reduces to Newtonian gravity in the weak-field, low-velocity limit" is sometimes stated a bit too blithely. It's really valid only in the near zone (which, of course, is the only place it's ever been tested). |
So according to you, the statement should be corrected to read "GR reduces to Newtonian gravity in the weak-field, low-velocity, near-zone limit." Interesting. This discussion is rewriting the textbooks. :-) Why don 't MTW mention this new restriction on p. 989 in their derivation of "rigorous formulas", where they detail the weak-field and low-velocity restrictions, but no "near-zone" restriction. There is no hint that the Newtonian potential in the far field begins to deteriorate into something non-Newtonian.
Indeed, I know that would be shocking news to most of my colleagues in celestial mechanics, and probably to most physicists as well. I assume that, if gravity has this light-time delay in the far field that you claim, then objects orbiting out there (such as Oort cloud comets) should experience transverse acceleration due to the aberration of the Sun at that distance. Certainly, galactic astronomers have never taken into account the transverse acceleration of star motions implied by a light-time-delayed source of gravity in the galactic far field. This is a show-stopper for other applications too.
But then, I suspect physically implausible ideas such as this "near-zone limit" for the applicability of Newtonian gravity (observationally untested, as you say) only survive if not-too-much attention is drawn to them. -|Tom|-
Tom Van Flandern - Washington, DC - see our web site on replacement astronomy research at http://metaresearch.org>
Tom Van Flandern
> | However, as the distance of the observer gets greater, the above extrapolation gets to be a poorer and poorer approximation of the true position of the stars, and even of any position the stars could ever actually occupy. Extrapolations with a constant acceleration soon depart radically from the actual star paths. You suggest that, just as the observer approaches distances at which these extrapolations are starting to deteriorate hopelessly far from reality, nature changes in such a way that no extrapolation at all applies anymore. Really distant (far field) observers respond to fully retarded positions of the source stars without any forward projection. |
To try a slightly different example: Consider two stars A and B and two observers A (on star A) and B (on star B) Observer A sends out a very narrow light beam A which just strikes (or hits) the place where B stands. Observer B sends out a very narrow light beam B which just strikes (or hits) the place where A stands.
Both stars are not rotating. Distance between stars is constant.
Question 1: From the view point of Observer A is the angle of the transmitted signal A and the angle of the received signal B identical ?
Question 2: From the view point of Observer B is the angle of the transmitted signal B and the angle of the received signal A identical ?
Question 3: Is the path that beam A follows identical as the path that beam B follows ? (ie any point in space that is hit by signal A is also hit by signal B simultaneous, assuming both signals are transmitted continuous)
I expect most probably not
Question 4: Is it possible that the path that beam A follows
identical is as the path that beam B follows ?
When ? Under which conditions ?
Assume that the outcome of question 1 is not identical.
Consider that both stars are the only stars in the Universe
and are attracted towards each other.
Question 5: For star A will the direction of movement
be identical as signal A? or signal B ? or different ?
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