The Speed of Gravity: Debated Answers

[McKy]

I have been looking for a defined speed of gravity. Unfortunately I have gotten various answers from various sources. The two answers I have received are that the speed of gravity is instantaneous due to the affect it would have on the orbit of planets if it where not. And the other that says that it should travel at the speed of light due to relativity.

 

[starthaus]

I have been looking for a defined speed of gravity. Unfortunately I have gotten various answers from various sources. The two answers I have received are that the speed of gravity is instantaneous due to the affect it would have on the orbit of planets if it where not. And the other that says that it should travel at the speed of light due to relativity.

Second one is correct.

 

[talk2glenn]

I have been looking for a defined speed of gravity. Unfortunately I have gotten various answers from various sources. The two answers I have received are that the speed of gravity is instantaneous due to the affect it would have on the orbit of planets if it where not. And the other that says that it should travel at the speed of light due to relativity.

Gravity does not have a "speed", any more than length or width do. Gravity is a function of the shape of spacetime (a depression or well, if you will). It is the masses which move through space that have velocity relative to one another, but space itself does not (note that it is not at rest either; it cannot move or not move, period - what would it move relative to?).

The acceleration of objects in space due to gravity, on the other hand, is a function of the mass of the two objects and their distance from one another.

We treat gravity as a force in elementary Newtonian physics for conceptual ease. It does not actually work this way. You are imagining that gravity does in fact work this way, and of course it follows logically that if the Earth is to exert a force on the moon, it must reach out and pull with some "thing", and that "thing" must have a speed. But your preconception is wrong.

 

[George Jones]

As starthaus has said, the speed of gravity is the speed of light.

the speed of gravity is instantaneous due to the affect it would have on the orbit of planets if it where not.

This is actually quite interesting. I don't know if you want a technical or a non-technical explanation. If you want a technical explanation, skip to link at the bottom of this post. What follows is my attempt at a non-technical explanation. I probably have introduced some inaccuracies.

Newtonian gravity predicts closed circular and elliptical orbits. This prediction depends on the fact that Newtonian gravitational force is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. If Newtonian gravitational force weren't directed along this line, orbits wouldn't be closed.

As the Earth orbits the Sun., the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse?

To answer these questions, I am going to talk briefly about the main equation of Einstein's theory of gravity, general relativity, G = T. Here, G is a geometrical quantity that depends on the curvature of spacetime, and T is a physical quantity that depends on the distribution and flows of mass and energy in the universve.

In Einstein's theory, gravity is a manifestation of spacetime curvature. If T depends not only on position, but also on flow of matter, then (by the equals sign) G, spacetime curvature, and (thus) gravity are affected by the velocities of objects. This feature is not present in Newtonian gravity.

As an example, consider a uniformly dense planet. According to Newton, the gravitational field of the planet is independent of the spin of the planet. According to Einstein, however, a planet's gravitational field is not independent of its spin. Spin puts the matter of the planet in motion, so different spins give different gravitational fields. To test this for the Earth, a satellite carrying gyroscopes has been put into orbit.

Back to the Earth and Sun. Form the point of view of the Earth, the mass of the Sun moves, and so, according to Einstein, this motion contributes to the gravitational field of the Sun. The field of the Sun depends on where the Sun is, and on how the Sun moves.

These two contribution's to the Sun's gravitational field, position and velocity, add to produce an "effective force" that *appears* to point towards where the Sun is now, not where it was eight minutes ago.

What happens if the Sun magically disappears? The Earth will continue on in its orbit for another eight minute under the influence of an "apparent force" directed towards where the Sun would have been. After eight minutes, the Earth realizes that the Sun isn't there, and stops orbiting the missing Sun.

This was the subject of a technical paper published in 2000 by Steve Carlip (pdf file up and right of abstract),

http://arxiv.org/abs/gr-qc/9909087.

 

[bcrowell]

FAQ: How fast do changes in the gravitational field propagate?

General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational waves travel at the speed of light. Gravitational waves have never been detected directly, but the loss of energy from the Hulse-Taylor binary pulsar has been checked to high precision against GR's predictions of the power emitted in the form of gravitational waves. Therefore it is extremely unlikely that there is anything seriously wrong with general relativity's description of gravitational waves.

It is difficult to design empirical tests that specifically check propagation at c, independently of the other features of general relativity. The trouble is that although there are other theories of gravity (e.g., Brans-Dicke gravity) that are consistent with all the currently available experimental data, none of them predict that gravitational disturbances propagate at any other speed than c. Without a test theory that predicts a different speed, it becomes essentially impossible to interpret observations so as to extract the speed. In 2003, Fomalont published the results of an exquisitely sensitive test of general relativity using radar astronomy, and these results were consistent with general relativity. Fomalont's co-author, the theorist Kopeikin, interpreted the results as verifying general relativity's prediction of propagation of gravitational disturbances at c. Samuel and Will published refutations showing that Kopeikin's interpretation was mistaken, and that what the experiment really verified was the speed of light, not the speed of gravity.

A kook paper by Van Flandern claiming propagation of gravitational effects at >c has been debunked by Carlip. Van Flandern's analysis also applies to propagation of electromagnetic disturbances, leading to the result that light propagates at >c --- a conclusion that Van Flandern apparently sincerely believes.

Fomalont and Kopeikin - http://arxiv.org/abs/astro-ph/0302294

Samuel - http://arxiv.org/abs/astro-ph/0304006

Will - http://arxiv.org/abs/astro-ph/0301145

Van Flandern - http://www.metaresearch.org/cosmology/speed_of_gravity.asp

Carlip - http://xxx.lanl.gov/abs/gr-qc/9909087v2

 

[stevmg]

I always was under the impression that the motion in spacetime was due to the ever present march of time in all frames of reference (no absolute time, of course), and time dilation makes the relative "expansions" different for different FRs. So, imagine 3D space (can be more than that) and an invisible 4th dimension, time. The worldlines keep expanding. If spacetime is curved in the 4th Dimension (time0 the world lines will be curved which means acceleration or gravity.

The parable of the two travelers (p. 184, Taylor/Wheeler Spacetime Physics, 1st Edition, 1963, 1965) who live in a 2D world but which is the surface of a sphere. The sphere is in 3D but the travelers only know 2D. Time marches on to the travelers so even though they may think they are sitting still, as time marches "North", the travelers are brought together involuntarily and appear to accelerate towards each other.

Einstein did think that the effects of gravity traveled at the speed of light. This makes sense from the point of view of the worldline in time as light travels at the speed of light.

 

[Passionflower]

As the Earth orbits the Sun., the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse?

Actually it is not but the effect is very small since the curvature here is very small. Orbits (not including orbits with massless test particles) are generally not closed in GR exactly due to the finite speed of curvature propagation which is equal to c.

 

[stevmg]

If we are feeling the pull of gravity from the Sun eight minutes late then in each nanosecond prior to that we were feeling the Sun's pull from eight minutes before then, and thus, we were still and always under the Sun's pull. From a strictly Newtonian concept, "machs nichts" as were always under a perpendicular pull which creates the near circular motion of the Earth's orbit.

The one question I do not understand using Newtonian logic is why would the planets degenerate into an elliptical orbit with one foci being the "main man?," i.e., with the Sun located at one if the foci? Then only planet that screws this up is mercury with some perihelion (I don't even know what that means) because it is moving faster and sime relativisic effects do take place as opposed to the slower moving outer planets which seem to obey Newton quite well.

A little help, please...

stevmg

Just think of rainfall from a large cloud on a perfectly windless day, i.e., perpendicular to you as you attempt to run through it. Even though the rain left the clouds some 10 or 15 minutes before, you still get drenched if it is in you path as you run. The same with the Earth as it attemts to run through the Sun's gravitational field which started eight minutes before.

 

[McKy]

Alright, so there are two schools of thought. Speed of c and speed far greater the c.

Theoretically could this be tested?

Maybe Take three objects. Two gyroscopes and a heavy mass. Two Super sensitive gyroscopes similar to those that where employed on 'Gravity Probe B' (really interesting test by the way), to measure the third object at rest. Then move the object observing the resulting affects on the gyroscopes. If gravitational forces move at c then the gyroscopes should be be affected at a time lag. *Would this experiment fail because of non-instantaneous acceleration?*

 

[Naty1]

nobody said faster than c.

 

[Jonathan Scott]

Alright, so there are two schools of thought. Speed of c and speed far greater the c.

No, there's one school of thought - speed of c - and one or two crackpots.

 

[spikenigma]

I've seen this topic on the site so many times and is always interesting. As I far as I've seen the only experiment (Sergei Kopeikin and Edward Fomalont - 2002) was heavily criticised as only measuring the speed of light.

Gravity is just too weak to measure without a theoretical GUT moon particle acelerator.

 

[bcrowell]

Theoretically could this be tested?

Nobody has a good, unambiguous method for testing it, for the reasons described in #5.

If gravitational disturbances didn't propagate at c, then GR would be in serious trouble. It would be very surprising if GR was so deeply flawed, since, e.g., energy loss to gravitational radiation by the Hulse-Taylor system matches up perfectly with GR's predictions.

 

[George Jones]

Alright, so there are two schools of thought. Speed of c and speed far greater the c.

I hope you don't think that bmy previous post gives evidence for this, because this isn't true.

 

[stevmg]

It is possible to cast a shadow that moves >c but not an electromagnetic wave or particle.

I don't if there is any experiment that tested gravitational pull, then stopped it, and measured the time it took for the effect of "no-g" to take (or lose) hold.

Again, as far as the Earth orbiting the Sun, the "gravitational waves" that attract the Earth towards the Sun are already out there, even if they eminated 8 minutes prior and they have been there a long long time so one cannot escape them just because they started eight minutes ago. One would have to sit triangulated between the Earth and Sun, blow up the Sun and see if the Earth took eight minutes before it traveled "straight".

Can anyone tell me why Keppler's law is right? Why do planets orbit in ellipses rather than circles?

 

[bcrowell]

Can anyone tell me why Keppler's law is right? Why do planets orbit in ellipses rather than circles?

Kepler's first law is not right. It's a nonrelativistic approximation. Planets move in orbits that are only approximately ellipses. Kepler's first law is approximately right because Newtonian mechanics is approximately right, and Newton's proof of Kepler's first law is valid for Newtonian mechanics.

I don't understand what you have in mind when you refer to circles as an alternative to ellipses.

 

[stevmg]

Kepler's first law is not right. It's a nonrelativistic approximation. Planets move in orbits that are only approximately ellipses. Kepler's first law is approximately right because Newtonian mechanics is approximately right, and Newton's proof of Kepler's first law is valid for Newtonian mechanics.

I don't understand what you have in mind when you refer to circles as an alternative to ellipses.

In other words, why don't the planets have the Sun as the literal center of a circle around which they orbit. Of course a circle is an ellipse but I mean what stopped it from being "completely round?"

I am not hung up on Kepler's laws per se, just the circle-ellipse question.

 

[Ken Natton]

You’ll understand, I hope stevmg that I do not suppose to tell you anything. I have no idea if this is really the answer you’re looking for. The YouTube clip I’ve posted below is an unfortunately very short clip of Feynman lecturing – to an audience I feel rather than to a genuine academic group – in which he addresses this question. The point about the ellipse is that although the speed of the planet changes at different points in its orbit, depending on its proximity to the sun, the area enclosed by a triangle defined by the sun, and the planet’s start and end point of its orbit over a specified fixed period is always constant. Anyway, Feynman explains it better than me. Watch the clip.

http://www.youtube.com/watch?v=NAzpc2RToOw&feature=related

 

[DrGreg]

The one question I do not understand using Newtonian logic is why would the planets degenerate into an elliptical orbit with one foci being the "main man?," i.e., with the Sun located at one if the foci?

A planet goes in whatever direction you throw it in (so to speak). If you throw it perpendicular to the radius at the correct speed, it goes in a circle, but if you throw it at a different angle from the same place, or even in the same direction but at a different speed, it goes in an ellipse.

When the solar system first started to form, it's likely everything started off moving in circles, but the lumps of matter that later merged to form planets would have collided and interacted gravitationally, deviating from circles to ellipses.

Then only planet that screws this up is mercury with some perihelion (I don't even know what that means) because it is moving faster and sime relativisic effects do take place as opposed to the slower moving outer planets which seem to obey Newton quite well.

"Perihelion" is the point of closest approach to the Sun. According to Newton's theory it should be at the same place every orbit, but in relativity it moves slightly from one orbit to the next. The effect is tiny and affects Mercury the most (where the spacetime curvature due to the Sun is highest).

 

[dcwarrior]

Isn't a possible test for the "speed of gravity" to take Newtonian calculations with respect to some large and quick orbiting objects (close-orbiting binary stars?), and then re-do the same calculations using the more complicated equations using relativity and see how different results they give over various periods? Then if they do show a difference in a relevant time scale, observe the model atronomical objects at the relevant interval and see which better predicts the location of the objects at the end of the period?

 

[George Jones]

Isn't a possible test for the "speed of gravity" to take Newtonian calculations with respect to some large and quick orbiting objects (close-orbiting binary stars?), and then re-do the same calculations using the more complicated equations using relativity and see how different results they give over various periods? Then if they do show a difference in a relevant time scale, observe the model atronomical objects at the relevant interval and see which better predicts the location of the objects at the end of the period?

Yes, this has been done:

Kepler's first law is not right. It's a nonrelativistic approximation. Planets move in orbits that are only approximately ellipses. Kepler's first law is approximately right because Newtonian mechanics is approximately right, and Newton's proof of Kepler's first law is valid for Newtonian mechanics.

Mercury's observed orbit is better predicted by GR, as are the orbits of pulsars.

 

[bcrowell]

Isn't a possible test for the "speed of gravity" to take Newtonian calculations with respect to some large and quick orbiting objects (close-orbiting binary stars?), and then re-do the same calculations using the more complicated equations using relativity and see how different results they give over various periods? Then if they do show a difference in a relevant time scale, observe the model atronomical objects at the relevant interval and see which better predicts the location of the objects at the end of the period?

This has been done in the case of the Hulse-Taylor system. Newtonian gravity predicts that the two stars follow Kepler's laws forever. GR predicts that they dissipate energy as gravitational waves. Observations verify this prediction of GR to high precision. The problem is that this doesn't prove that every aspect of GR (including propagation of gravitational disturbances at c) is correct. This is what I was referring to in #5. You can't test propagation at c unless you have a viable test theory that predicts something other than propagation at c. But there is no such viable theory. (Newtonian gravity hasn't been viable since about 1919.)

 

[dcwarrior]

This has been done in the case of the Hulse-Taylor system. Newtonian gravity predicts that the two stars follow Kepler's laws forever. GR predicts that they dissipate energy as gravitational waves. Observations verify this prediction of GR to high precision. The problem is that this doesn't prove that every aspect of GR (including propagation of gravitational disturbances at c) is correct. This is what I was referring to in #5. You can't test propagation at c unless you have a viable test theory that predicts something other than propagation at c. But there is no such viable theory. (Newtonian gravity hasn't been viable since about 1919.)

Thanks, when I saw someone cited the Hulse-Taylor system I was able to see that people have been working on "relativistic celestial mechanics" for some time.

However, given that the relativistic equations (which assume gravity goes at c) seems to explain the observed motions quite well, is there any way to test what happens if you relax that assumption? (Maybe not, I understand.)

The reason the binary star example was so great to explain to lay people like me is that it's intuitively easy to understand, If two objects are circling, and gravity "moves" at a "finite speed" (say, c) then if the two objects are moving quite fast compared to c, you'd expect as a layperson that the pull object A feels from object B is based on where object B was some time ago versus where it is now, and therefore you might expect the equations to come out differently. If anyone is familiar with those equations, I assume that concept is taken into account?

Also, I seem to recall at least one interview where I thought an astronomer said he assumes that gravity is instantaneous. I wish I could remember what he actually said.

I looked at the question on some other forums and there were a lot of huffy answers about "nothing can go faster than c" and over-reliance on the circular reasoning of that one direct attempt to prove gravity propagates at c. It seems to me that those in the know could be a lot more authoritative to those who seem to think the astronomy/physics community has missed the boat on this by going straight to the work people have done on celestial mechanics, with the binary star work as a big example.

 

[bcrowell]

However, given that the relativistic equations (which assume gravity goes at c) seems to explain the observed motions quite well, is there any way to test what happens if you relax that assumption?

GR doesn't assume that gravity travels at c. Propagation of gravitational disturbances at c can be proved from GR, not the other way around. (Actually, propagation at c isn't even strictly true in GR. It's only true in the limit where the amplitude of the gravitational waves is small.) So you can't just make a version of GR where gravity@c is relaxed as an assumption, because it's not an assumption. To get a theory without g@c, you would have to figure out some other theory that was different from GR in some way, such that this change in the theory had the side-effect of changing GR's prediction of g@c. There certainly are other known viable theories of gravity, such as Brans-Dicke gravity, but none of them predict anything other than g@c.

The reason the binary star example was so great to explain to lay people like me is that it's intuitively easy to understand, If two objects are circling, and gravity "moves" at a "finite speed" (say, c) then if the two objects are moving quite fast compared to c, you'd expect as a layperson that the pull object A feels from object B is based on where object B was some time ago versus where it is now, and therefore you might expect the equations to come out differently. If anyone is familiar with those equations, I assume that concept is taken into account?

http://en.wikipedia.org/wiki/Gravitational_radiation#Orbital_decay_from_gravitational_radiation

Also, I seem to recall at least one interview where I thought an astronomer said he assumes that gravity is instantaneous. I wish I could remember what he actually said.

Either your memory is wrong or the person being quoted is incompetent, a crank, being misquoted, having his/her statement oversimplified, ...

 

[dcwarrior]

now we are talking about two different things, then. Perhaps they come out to the same thing in the end:

A static gravity FIELD (say, between two objects not moving with respect to one another) is, correct me if I'm wrong, not necessarily particles or waves flowing from one to another but just a function of space-time? Therefore, that's why you say gravity doesn't travel at c? Because "speed" is not relevant? (Query - how does the one object "know" the other is there?)

So what you are saying is, when you move the one object relative to the other, the outward propagation of the distance at which each object senses from the other the change in gravity is limited to the speed of c, correct?

GR doesn't assume that gravity travels at c. Propagation of gravitational disturbances at c can be proved from GR, not the other way around. (Actually, propagation at c isn't even strictly true in GR. It's only true in the limit where the amplitude of the gravitational waves is small.) So you can't just make a version of GR where gravity@c is relaxed as an assumption, because it's not an assumption. To get a theory without g@c, you would have to figure out some other theory that was different from GR in some way, such that this change in the theory had the side-effect of changing GR's prediction of g@c. There certainly are other known viable theories of gravity, such as Brans-Dicke gravity, but none of them predict anything other than g@c.

 

[bcrowell]

A static gravity FIELD (say, between two objects not moving with respect to one another) is, correct me if I'm wrong, not necessarily particles or waves flowing from one to another but just a function of space-time? Therefore, that's why you say gravity doesn't travel at c? Because "speed" is not relevant?

Gravity *does* travel at c (in the low-amplitude limit). Yes, there is no meaningful way to talk about speed in the case of a static field.

 

[stevmg]

Thanks, when I saw someone cited the Hulse-Taylor system I was able to see that people have been working on "relativistic celestial mechanics" for some time.

However, given that the relativistic equations (which assume gravity goes at c) seems to explain the observed motions quite well, is there any way to test what happens if you relax that assumption? (Maybe not, I understand.)

The reason the binary star example was so great to explain to lay people like me is that it's intuitively easy to understand, If two objects are circling, and gravity "moves" at a "finite speed" (say, c) then if the two objects are moving quite fast compared to c, you'd expect as a layperson that the pull object A feels from object B is based on where object B was some time ago versus where it is now, and therefore you might expect the equations to come out differently. If anyone is familiar with those equations, I assume that concept is taken into account?

Also, I seem to recall at least one interview where I thought an astronomer said he assumes that gravity is instantaneous. I wish I could remember what he actually said.

I looked at the question on some other forums and there were a lot of huffy answers about "nothing can go faster than c" and over-reliance on the circular reasoning of that one direct attempt to prove gravity propagates at c. It seems to me that those in the know could be a lot more authoritative to those who seem to think the astronomy/physics community has missed the boat on this by going straight to the work people have done on celestial mechanics, with the binary star work as a big example.

Even if the "pull" came earlier the pull was always there even though you are feeling the pull from some time ago, it is still a "pull." It would only make a difference at the very beginning, not after equilibrium was established.

Make sense?

Just think of running under a rain cloud. You get hit with water from eight or nine minutes before but you still get wet.

 

[stevmg]

You are also correct about tautological (circular) reasoning. However, there has been no evidence so far that gravity is instaneous or or whatever.

If gravity is caused by a bend in spacetime of the ct axes which bends the worldlines and produces acceleration (which is gravity), then it would probably be such that light speed is the limiting speed.

Again, relativity may be a small microcosm of a much greater reality, so the jury will never be totally in.

 

[dcwarrior]

Even if the "pull" came earlier the pull was always there even though you are feeling the pull from some time ago, it is still a "pull." It would only make a difference at the very beginning, not after equilibrium was established.

Make sense?

Just think of running under a rain cloud. You get hit with water from eight or nine minutes before but you still get wet.

yes, but you could definitely tell the difference. If stand still your head and shoulders are wet but if you run, your whole front gets wet. The point about moving is, (and I think we'd need to consult one of the celestial mechanics folks) is that if 2 objects are orbiting quickly compared to the speed of light, at equilibrium, the pull comes from a different direction from its then-current position. Which of course may already be taken into account by the equations, but I don't know that.

 

[stevmg]

yes, but you could definitely tell the difference. If stand still your head and shoulders are wet but if you run, your whole front gets wet. The point about moving is, (and I think we'd need to consult one of the celestial mechanics folks) is that if 2 objects are orbiting quickly compared to the speed of light, at equilibrium, the pull comes from a different direction from its then-current position. Which of course may already be taken into account by the equations, but I don't know that.

I don't think so. The pull is always perpendicular to the tangent of the orbit (let's assume it is a circle) even though the origin of the pull was from some time prior.

We just had a downpour here in Melbourne FL and I ran through it and yet everything got wet...

aaa-choo!

At least it ain't oil!

 

[stevmg]

A planet goes in whatever direction you throw it in (so to speak). If you throw it perpendicular to the radius at the correct speed, it goes in a circle, but if you throw it at a different angle from the same place, or even in the same direction but at a different speed, it goes in an ellipse.

When the solar system first started to form, it's likely everything started off moving in circles, but the lumps of matter that later merged to form planets would have collided and interacted gravitationally, deviating from circles to ellipses.

"Perihelion" is the point of closest approach to the Sun. According to Newton's theory it should be at the same place every orbit, but in relativity it moves slightly from one orbit to the next. The effect is tiny and affects Mercury the most (where the spacetime curvature due to the Sun is highest).

Missed seeing that reply before. Thanks a million, DrGreg. So apparently the perihelion of Mercury precesses a little...

Sort of like a gyroscope - but that's all Newtonian and I still haven't got that one down and probably never will.

 

[stevmg]

Hey, dcwarrior

You are probably correct, because the perpendicular pull on a binary star is perpendicular to where the other star used to be, so it always "lags" behind where it should be. Wouldn't that just be another larger circle? Try and figure that one out just based on a time delay, much less relativity.

stevmg

PS - I'm dry now.

 

[bcrowell]

[...]the perpendicular pull on a binary star is perpendicular to where the other star used to be, so it always "lags" behind where it should be. Wouldn't that just be another larger circle? Try and figure that one out just based on a time delay, much less relativity.

There is a straightforward argument that the time lag should lead to the loss of energy to gravitational radiation. See http://www.lightandmatter.com/html_books/genrel/ch09/ch09.html#Section9.2 , subsection 9.2.1, second paragraph. Taylor and Wheeler make a similar argument in Spacetime Physics, but they phrase it in terms of Atlas doing mechanical work on two planets.

I don't think the existence of a time delay by itself is enough to imply the perihelion shift. The perihelion shift exists even for a test particle orbiting in a Schwarzschild spacetime. Since the Schwarzschild metric is static, the speed of propagation of gravitational effects is irrelevant.

For a nonmathematical explanation of the perihelion shift, see http://www.lightandmatter.com/html_books/genrel/ch06/ch06.html#Section6.2 , subsection 6.2.6, second paragraph.

 

[stevmg]

There is a straightforward argument that the time lag should lead to the loss of energy to gravitational radiation. See http://www.lightandmatter.com/html_books/genrel/ch09/ch09.html#Section9.2 , subsection 9.2.1, second paragraph. Taylor and Wheeler make a similar argument in Spacetime Physics, but they phrase it in terms of Atlas doing mechanical work on two planets.

I don't think the existence of a time delay by itself is enough to imply the perihelion shift. The perihelion shift exists even for a test particle orbiting in a Schwarzschild spacetime. Since the Schwarzschild metric is static, the speed of propagation of gravitational effects is irrelevant.

For a nonmathematical explanation of the perihelion shift, see http://www.lightandmatter.com/html_books/genrel/ch06/ch06.html#Section6.2 , subsection 6.2.6, second paragraph.

I wasn't suggesting that the perihelion shift was due to time delay. I downloaded those two references you gave in .pdf format (you web .pdf converter on IE8) and let me tell you it will take me thirteen forevers to get through them - but I will.

 

[bcrowell]

I downloaded those two references you gave in .pdf format (you web .pdf converter on IE8)

You can download the whole book in pdf format here: http://www.lightandmatter.com/genrel/