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arnau

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- How to transform between the two moving frames, the properties of a third frame?

A particle is moving in the lab frame ##S'## at ##\beta'_z##. I want to transform coordinates and momenta of the particle to a frame ##S## moving at ##\beta_0##.

At time ##t = t' = 0##:

$$z = \frac{z'} { \gamma_0 (1 - \beta'_z \beta_0) },\,

\gamma\beta_z = \gamma_0 ( \gamma'\beta'_z - \beta_0 \gamma' )$$

But what about at time ##t \ne 0## ?

I don't think it would be correct to do a normal lorentz transformation ## z = \gamma_0 ( z' - \beta_0 c t' )##

Sources would be appreciated. Thanks in advance

At time ##t = t' = 0##:

$$z = \frac{z'} { \gamma_0 (1 - \beta'_z \beta_0) },\,

\gamma\beta_z = \gamma_0 ( \gamma'\beta'_z - \beta_0 \gamma' )$$

But what about at time ##t \ne 0## ?

I don't think it would be correct to do a normal lorentz transformation ## z = \gamma_0 ( z' - \beta_0 c t' )##

Sources would be appreciated. Thanks in advance

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