Are All Particle-Rest Inertial Frames the Same?

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Discussion Overview

The discussion centers on the nature of particle-rest inertial frames in the context of special relativity. Participants explore whether all particle-rest frames are equivalent or if they differ due to spatial rotations, considering the implications of the postulates of special relativity.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that all inertial frames are equivalent in special relativity, suggesting that the motion of a free particle can be described in any inertial frame.
  • Another participant clarifies that while all inertial frames are equivalent, there can be infinitely many frames in which a particle is at rest, differing by spatial axes but sharing a timelike axis.
  • A participant questions whether all particle-rest frames are the same inertial frame, emphasizing the absence of space rotations between these frames.
  • Another participant introduces the idea that different inertial frames are not equivalent if two particles are moving with respect to each other, implying that their rest frames cannot be the same.

Areas of Agreement / Disagreement

Participants express differing views on the equivalence of particle-rest frames, with some asserting that they are equivalent while others argue that they differ due to spatial rotations and the relative motion of particles.

Contextual Notes

The discussion includes assumptions about the nature of inertial frames and the implications of the postulates of special relativity, which remain unresolved.

PFfan01
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According to special relativity, all inertial frames of reference are equivalent for descriptions of physical phenomena. Suppose that there is a free particle in free space. Observed in any of the frames, the motion of particle can be described by a velocity, and by Lorentz boost, one can get a particle-rest frame where the particle is at rest. My question is: Are all the particle-rest frames the same?
 
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All inertial frames are the same in special relativity, by hypothesis. It's one of the postulates of relativity.
 
Sorry, I did not make it clear. What I mean is: Are all the particle-rest frame the same inertial frame? There are no space rotations (corresponding to space orthogonal transformation) between these particle-rest frames?
 
You are free to rotate axes, so if I understand your question, there are infinitely many frames in which the particle is at rest. They use different spatial axes but share a timelike axis.
 
PFfan01 said:
Sorry, I did not make it clear. What I mean is: Are all the particle-rest frame the same inertial frame? There are no space rotations (corresponding to space orthogonal transformation) between these particle-rest frames?

I suspect you might be misunderstanding "equivalent" in this context. Different inertial frames are not equivalent. The posulates of SR are 1) that the speed of light is the same in all inertial reference frames; and, 2) the laws of physics are the same in all inertial frames.

But, if two particles are moving with respect to each other then their rest frames cannot be the same.
 

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