Are All Particle-Rest Inertial Frames the Same?

[PFfan01]

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?

 

[Ibix]

All inertial frames are the same in special relativity, by hypothesis. It's one of the postulates of relativity.

 

[PFfan01]

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?

 

[Ibix]

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.

 

[PeroK]

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.