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Popular expositions of general relativity start with a thought experiment showing that it is impossible to distinguish a constantly accelerating frame of reference in a free fall from a free floating frame of reference.

Thought Experiment:
Person A is a small closed box, free-falling towards earth. Person B is in a small closed box floating around in space. If they both do the same experiments, they should see the same results. For example, if they have a small ball and toss it inside their box, they would both see that ball travel in a straight line (not curving) towards the wall. They would also both feel themselves floating around as if there was no gravity.

The same thought experiment could be applied to a frame undergoing a constant jerk. Does that lead to a new theory of relativity?

safesphere
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Mark
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    In what thought experiment is it impossible to distinguish a constantly accelerating frame of reference from a free floating frame of reference? – md2perpe Sep 30 '18 at 16:21
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    I think you have either misspoken or misunderstood. Many popular expositions begin by talking about the path of a light beam in an accelerating frame of reference; showing that it is possible to distinguish accelerating frames from inertial ones. Then they talk about the equivalence between gravity and acceleration. – dmckee --- ex-moderator kitten Sep 30 '18 at 16:37
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    @dmckee If person A is in a closed box, free-falling towards earth, and person B is just floating around in a box in space, can they actually know who is who because light seems to be bending inside person A's box, but it is going straight in person B's box? – Mark Sep 30 '18 at 17:04
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    @md2perpe I edited the question to describe the thought experiment – Mark Sep 30 '18 at 17:09
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    Okay, what Einstein said was that a freely falling frame of reference and a freely floating frame of reference can not be distinguished. And a constantly accelerating frame of reference could not be distinguished from a frame being still in a gravity field with the same acceleration. – md2perpe Sep 30 '18 at 17:10
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    @md2perpe Right, and likewise, a constantly jerking frame of reference cannot be distinguished from a free floating frame of reference. Why is the second derivative special? I think we could just keep going. – Mark Sep 30 '18 at 17:12
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    "free-falling towards earth" OK. That gets to the core issue. The notion of acceleration is defined differently in Newtonian and Einsteinian physics. I've written a little about the difference on the site before. The freely falling frame is inertial and the standing on the ground frame is not inertial. Wrapping your head around this requires starting from the principle of relativity and is a little easier if you have already had a detailed treatment of inertial pseudoforces in classical mechanics. – dmckee --- ex-moderator kitten Sep 30 '18 at 17:13
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    A frame of reference with a jerk will not be distinguishable from a gravity field varying in the same way. – md2perpe Sep 30 '18 at 17:20
  • The key words of the thought experiment are freely falling: a freely falling frame of reference in a gravity field is indistinguishable from a freely falling/floating frame of reference in outer space. – md2perpe Sep 30 '18 at 17:38
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    @md2perpe "A frame of reference with a jerk will not be distinguishable from a gravity field varying in the same way." - According to what? It is not given and not obvious that the next derivative is relative. For example, speed is relative in the classical physics, but acceleration is not. So the fact that acceleration is relative in relativity does not automatically imply that jerk is also relative. – safesphere Sep 30 '18 at 17:53
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    If all acceleration, not only constant acceleration, is relative then how could jerk not be relative? – md2perpe Sep 30 '18 at 19:47
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    @md2perpe Your question is not addressed to anyone, so no notification is sent. Whom are you asking, the OP? In any case, jerk may or may not be relative, but either way it is not obvious and must be rigorously shown before making a claim. This is exactly what the OP is asking. The question is excellent while a lack of understanding of it here is truly puzzling. To answer your question, your logic is that the next derivative must be relative, but this logic fails in the classical physics, as well as in special relativity where speed is relative, but the next derivative (acceleration) is not. – safesphere Sep 30 '18 at 20:11
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    @md2perpe Similarly, acceleration is relative in general relativity, but it does not automativpcally follow from anywhere that the next derivative (jerk) is relative. This may depend on the specific formulation of the equivalence principle and on other things. I am not saying jerk is not relative in GR. I am only saying that it is not self evident whether it not it is relative and must be proven mathematically based on well defined assumptions. – safesphere Sep 30 '18 at 20:19
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    @safesphere. I think that we are mixing two different discussions: relative motion and the equivalence principle. That makes the discussion a bit confusing. And I do not think that the OP asks whether jerk is relative. Read the post again! He asks whether asserting the equivalence of a constant jerk free fall would imply a new theory of relativity. – md2perpe Sep 30 '18 at 21:17
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    @md2perpe Your comment makes no sense to me: "I do not think that the OP asks whether jerk is relative". The question title is, "Relativity of jerk". You say: "He asks whether asserting the equivalence of a constant jerk free fall would imply a new theory of relativity". This is exactly the meaning of my comments above. Sorry, but comments are not for discussions. You are welcome to post a comprehensive answer if you believe you understand the question. – safesphere Sep 30 '18 at 21:34
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    @safesphere. Read the last paragraph of the post. – md2perpe Oct 01 '18 at 06:06

1 Answers1

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Gravity happens to measurably correspond to a constant acceleration, not jerk. So, no, this doesn't lead to a new theory of gravity. At least not immediately. On the other hand, strictly speaking, there is actually a slight jerk involved in free fall if an object falls long enough for the increasing gravitational field to become relevant. Whether a model for our world involving relativity of jerk could be built, is something I'd like to know myself...

MrFrety
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