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Two comoving frames will have different values of length between masses so the forces will be different in two frames.

Is it enough to prove that the gravity rule has to be modified?

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It's not clear what you are asking. If you are asking whether length contraction by itself is enough to determine that the Newtonian gravitation law must be modified, the answer is no. If you are asking how close a result length contraction can get us to the right answer, the answer is sometimes. But it is not clear how we could tell you what "close enough" is. In summary, the answer to your question is no.

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Two comoving frames will have different values of length between masses so the forces will be different in two frames.

Is it enough to prove that the gravity rule has to be modified?

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No. Here's an interesting homework assignment:Kashmir said:

Two comoving frames will have different values of length between masses so the forces will be different in two frames.

Is it enough to prove that the gravity rule has to be modified?

https://www.physicsforums.com/threa...e-inside-the-suns-gravitational-field.983171/

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Thank you. I'll look into it.PeroK said:No. Here's an interesting homework assignment:

https://www.physicsforums.com/threa...e-inside-the-suns-gravitational-field.983171/

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I'm not sure I see how this thread is helpful. The thread left it hanging whether the answer given was correct (I don't think it is); in fact the thread left hanging a highly pertinent question from @Orodruin, namely, how ##\gamma## is to be defined, or more precisely how the speed ##v## is to be defined; is it the actually measured speed relative to static observers, or just the coordinate speed?PeroK said:Here's an interesting homework assignment

If there is a proof somewhere in the literature that, at least for some special cases, the heuristic "plug the Newtonian gravity formula into SR" happens to work, a reference to that might be helpful. I'm not sure any such reference exists. But certainly the thread referred to is not such a reference.

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There is a related question to this, namely, that Newton's gravity depends on the relative positions of the masses at some instant of time. But "instant of time", i.e., simultaneity, is frame dependent in relativity; if the two masses are moving relative to each other, their notions of simultaneity will be different, and which one should be used for the Newtonian force law? IsKashmir said:

Two comoving frames will have different values of length between masses so the forces will be different in two frames.

Is it enough to prove that the gravity rule has to be modified?

Einstein explicitly considered the latter question in 1907, and his answer was yes. I don't know if he explicitly considered whether the frame dependence of the distance itself would lead to a similar answer, but I think it would.

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Kashmir said:Newton's gravity depends on the euclidean distance between two masses.

Two comoving frames will have different values of length between masses

PeterDonis said:Newton's gravity depends on the relative positions of the masses at some instant of time. But "instant of time", i.e., simultaneity, is frame dependent in relativity

Actually, I think the question Einstein considered in 1907 was more basic than either of the above: Newtonian gravity says that gravity propagates instantaneously, but "instantaneously" is frame-dependent in relativity. A relativistic theory cannot have instantaneous propagation; instead, one would expect that a relativistic interaction would propagate at the speed of light, as electromagnetism does. But just plugging a speed of light interaction speed into Newtonian gravity does not work. Carlip's classic paper on aberration and the speed of gravity discusses this:PeterDonis said:Einstein explicitly considered the latter question in 1907

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

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You think its enough , this length contraction to decide that Newtons gravitation should be modified?PeterDonis said:but I think it would.

I am getting conflicting answers.

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Does it matter? You know the answer - that GR is needed - and in a sense that is the only answer. Asking whether length contraction by itself is enough is somewhat hypothetical.Kashmir said:You think its enough , this length contraction to decide that Newtons gravitation should be modified?

I am getting conflicting answers.

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Focusing on length contraction specifically is not really correct. Length contraction is not the only relevant consequence of SR that affects the Newtonian gravitation law, as I show in posts #6 and #7. So the correct question to ask is simply whether the Newtonian gravitation law can be incorporated as-is into a theory based on SR. And the answer to that question is no.Kashmir said:You think its enough , this length contraction to decide that Newtons gravitation should be modified?

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Will this give you an answer that is close? Sometimes.

Is it close enough? How could we possible tell you what "close enough" is?

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That is not interesting. It is fundamentally flawed … as I pointed out in that thread …PeroK said:No. Here's an interesting homework assignment:

https://www.physicsforums.com/threa...e-inside-the-suns-gravitational-field.983171/

As statedvanhees71 said:That's a very misleading homework. If they had ask for the motion of a particle in the Coulomb field of a fixed (i.e., very massive) particle, neglecting radiation reaction, it'll have been fine

Orodruin said:It is particularly unfortunate as you could actually make a reasonable problem by replacing gravity by the motion of a test charge in a static electric field.

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I know that GR is needed, I was just curious and tried to see how many things went wrong with Newtonian mechanics in SR setting.PeroK said:Does it matter? You know the answer - that GR is needed - and in a sense that is the only answer. Asking whether length contraction by itself is enough is somewhat hypothetical.

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NewtonianKashmir said:I know that GR is needed, I was just curious and tried to see how many things went wrong with Newtonian mechanics in SR setting.

Newtonian

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Just one. You get the wrong answer.Kashmir said:how many things went wrong with Newtonian mechanics in SR setting.

But isn't that enough?

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You don't even get an answer as the two are incompatible.Vanadium 50 said:Just one. You get the wrong answer.

But isn't that enough?

This thread also reminded me of an XKCD classic:

With the alt-text: "Of these four forces, there's one we don't really understand." "Is it the weak force or the strong--" "It's gravity."

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