I Are All Particle-Rest Inertial Frames the Same?

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In special relativity, all inertial frames are equivalent for describing physical phenomena, but this does not mean that all particle-rest frames are identical. Each particle-rest frame can be considered a different inertial frame, as they may involve different spatial axes while sharing a common timelike axis. The discussion highlights that while the laws of physics and the speed of light remain consistent across inertial frames, the rest frames of different particles are not the same if they are in motion relative to each other. Thus, the concept of equivalence in inertial frames does not imply uniformity among all particle-rest frames. The nuances of spatial rotations and their implications on particle motion are key to understanding this distinction.
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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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