I'm studying a chapter about Rindler coordinates right now. In this they say that two Rindler observers at $x = 1/a_1$ and $x= 1/a_2$ will both have speed $v =0$ at $\tau = 0$ compared to the inertial system $(X,T)$. This I understand, quite logical. Then they continue saying that a translation in Rindler time ($=a\tau$) is actually equivalent with a Lorentz-boost in the $X$-direction. From this they deduce that on a random Rindlertime two Rindler observers will have equal velocities with respect to "a" (not specified) inertial frame so that they are in rest with respect to each other. I don't really get that last argument. So two observers that accelerate at different accelerations are always at rest with respect to each other?

First of all the boost will be different because they have different acceleration $a_1$ and $a_2$. And to be at rest with respect to each other, do you just need to be at rest in one (random) inertial frame? Can someone explain this in detail to me, I think I'm just missing some basic insights from special relativity here.


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