Relative Velocity of Particle ##p##: S vs S

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SUMMARY

The discussion centers on the relative velocity of a particle ##p## moving with velocity ##u\hat i## in reference frame S and its velocity in frame S', which is ##-c \hat i##. It is established that the concept of absolute rest is non-physical, as no inertial frame can move at the speed of light (c) relative to another inertial frame. The conversation highlights the inconsistency that arises when attempting to define the velocity of particle ##p## in both frames, ultimately concluding that such definitions lead to undefined results.

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TL;DR
Considering two frames S(absolute rest) and S' where S' is moving with respect to S with a velocity ##c\hat i##
A particle ##p## is moving with a velocity ##u\hat i## with respect to S ...
The velocity of ##p## with respect to S' is then ##-c \hat i##...

Another part...
Similarly taking the velocity of particle ##p## with respect to S' as ##-c\hat i## the velocity of ##p## with respect to S is then coming to be undefined ,however it should be coming to be ##u\hat i##??isn't it...
 
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Unfortunately there is nothing we can discuss here. The idea of absolute rest is non-physical and even in theory there is no such thing as an inertial frame moving at c with respect to another inertial frame.
 
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