How did Einstein know speed of gravity?

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I just watched the first part of Brian Greene's television program on PBS The Elegant Universe. In The Elegant Universe, the narrator shows a model of the solar system, and the narrator says that according to Newtonian theory, if the sun disappeared, the Earth's trajectory around the sun would change instantly. The narrator says that Einstein realized that nothing can travel faster than the speed of light. Therefore, the force of gravity cannot travel faster than the speed of light. It showed the model of the solar system again. It said that Einstein realized that if the sun disappeared, the sun's gravitational pull would keep acting upon the Earth until the sun's rays of light no longer reached earth. According to the narrator, Einstein realized that the sun's gravitational pull would keep acting upon the Earth until the sun's rays no longer reached Earth because gravity does not travel faster than the speed of light. To me, this is circular reasoning. Why did Einstein know that if the Sun disappeared, the Sun's gravitational pull would keep the Earth in orbit until the rays of light no longer reached Earth? Because gravity does not travel faster than the speed of light. How did Einstein know that gravity does not travel faster than the speed of light? Because Einstein knew that if the Sun disappeared, the Earth would stay in orbit around the sun until the Sun's rays of light no longer reached Earth.

Is there any explanation for how Einstein knew the speed of gravity that is not circular? If so, what is the explanation?
 

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Dale
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How did Einstein know that gravity does not travel faster than the speed of light? Because Einstein knew that if the Sun disappeared, the Earth would stay in orbit around the sun until the Sun's rays of light no longer reached Earth.
No, he "knew" gravity does not travel faster than light because if it did then it would violate either relativity or causality.
 
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Dale, I believe that the whole point of the models of the solar system and all the background info in The Elegant Universe that I just told you about in my original post was info that was told to show how General Relativity was proved to be true. So I think that what you just said is begging the question.

Maybe i'm missing something. i'll admit that you might be right on this.
 
  • #4
Dale
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Theories are "proved to be true" by experiments. The theoretical considerations outlined above are what motivated Einstein to look for a new theory of gravity. But no amount of theoretical justification can ever prove a theory.
 
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How was Relativity proved to be true if it wasn't by the speed of gravity?
 
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Ibix
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I don't think Greene is reasoning here. He's simply stating the implications of Newtonian gravity (simultaneous causality), then that Einstein knew that this was inconsistent with special relativity, then what an Einsteinian model must say.

A consequence of special relativity is that anything travelling faster than light allows effects to precede causes. And simultaneous causation, which is what Newtonian gravity implies, is particularly troublesome because special relativity does not include a general notion of simultaneity. That means that at least one of Newtonian gravity and special relativity is wrong.

Einstein had many reasons to believe special relativity was correct - notably that that noone could explain the Michelson-Morley experiment without it. He was also aware that the precession of Mercury's orbit did not quite match what Newtonian gravity predicted. His reasoning isn't circular, and is grounded in experimental results. Greene may or may not be presenting it in a helpful way.
 
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Mister T
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How did Einstein know that gravity does not travel faster than the speed of light? Because Einstein knew that if the Sun disappeared, the Earth would stay in orbit around the sun until the Sun's rays of light no longer reached Earth.

I don't recall that argument having been put forth in that show.

The premise is that gravity can't travel faster than light, something attributed to Einstein. The conclusion is that if the sun disappeared Earth would remain in orbit for however long it takes sunlight to reach Earth. That's what I recall.

And since the conclusion follows from the premise, it's something Einstein would also have been aware of.
 
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If you think of 'c' as not as being the 'speed of light', but as a limit to the speed at which information of any kind can propagate...
(as seen from any given frame)...
That makes a bit more sense, (to me).
 
  • #10
I just watched the first part of Brian Greene's television program on PBS The Elegant Universe. In The Elegant Universe, the narrator shows a model of the solar system, and the narrator says that according to Newtonian theory, if the sun disappeared, the Earth's trajectory around the sun would change instantly. The narrator says that Einstein realized that nothing can travel faster than the speed of light. Therefore, the force of gravity cannot travel faster than the speed of light. It showed the model of the solar system again. It said that Einstein realized that if the sun disappeared, the sun's gravitational pull would keep acting upon the Earth until the sun's rays of light no longer reached earth. According to the narrator, Einstein realized that the sun's gravitational pull would keep acting upon the Earth until the sun's rays no longer reached Earth because gravity does not travel faster than the speed of light. To me, this is circular reasoning. Why did Einstein know that if the Sun disappeared, the Sun's gravitational pull would keep the Earth in orbit until the rays of light no longer reached Earth? Because gravity does not travel faster than the speed of light. How did Einstein know that gravity does not travel faster than the speed of light? Because Einstein knew that if the Sun disappeared, the Earth would stay in orbit around the sun until the Sun's rays of light no longer reached Earth.

Is there any explanation for how Einstein knew the speed of gravity that is not circular? If so, what is the explanation?

It is not the sun's gravitational pull that would keep acting upon us, because the Sun does not act upon us. That's Newtonian mechanics. The presence of the Sun distorts spacetime, which is what causes gravity. If the Sun were to disappear all of a sudden, spacetime would still be distorted, but would "return to normal" at the speed of light, since no changes can propagate any faster. There is no circular reasoning there. Inversely, if you were to summon a star to existence, changes in spacetime would propagate at the speed of light, not instantly.
 
  • #11
PeterDonis
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If the Sun were to disappear all of a sudden

Then the laws of physics would be violated--specifically, the law that says the covariant divergence of the stress-energy tensor is zero. This is the GR version of local conservation of mass/energy, and it means that an object containing mass/energy, like the Sun, can't just "disappear"; the mass/energy in it has to go somewhere. See below.

if you were to summon a star to existence

Same problem here. It turns out to be non-trivial to formulate a scenario in which the "speed of gravity" can be directly tested, that doesn't violate local conservation of energy. However, there are plenty of ways to test it indirectly. The general idea is to look for ways in which "gravity is changing" that don't require mass/energy to appear or disappear. One way is to look at the orbits of objects in the spacetime surrounding a large mass like the Sun, and see if they are different from what Newtonian theory would predict. One of the classic tests of GR, the precession of the perihelion of Mercury, is this kind of test--the extra precession is due to the finite "speed of gravity".

The classic paper on this topic is Carlip:

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

It is worth reading for anyone interested in this topic. As Carlip notes in the paper, another indirect effect of the finite speed of gravity is the orbital decay of binary pulsars, which has been measured.
 

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