Can you explain how you got that formula? Or why that is the case in relativity? I would like to know []

As sophiecentaur implicitly wrote, it's not so immediate, if you don't know relativity very much. From the two postulates of relativity (1. light' speed doesn't depend on the light source's speed; 2. the laws of physics are the same in all inertial frames of reference) you can get the lorentz equations for a boost (= rectilinear movement) along the x direction:

x' = γ(x-v*t)

y' = y

z' = z

t' = γ(t-x*v/c

^{2})

then you derive x' with respect to t' and find the velocity of the object in the prime frame of reference and then you relate dx/dt to that velocity.

If you are interested in the detailed computations...when I come back home, after my holidays [

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