Where does the Lorentz factor arise from? I couldn't find the derivation in my textbook.

Question

roadjester · Answer

The lorentz factor $\gamma$ is derived from the switching between refernce frames.

roadjester · Answer

Let's say I have a beam of light that is propagating so the distance it travels in the S frame is x=ct. In the S' frame it is x'=ct'.

Let's say gamma is some unknown constant. So from the Galileo transformation you know that x'=x-vt which is incorrect so for the lorentz transformation you stick a gamma there.

So:
$\large x'=\gamma(x-vt)$
$\large x=\gamma(x'+vt')$

roadjester · Answer

so from the top you substitute to get rid of x and x'.
Therefore:
$\large ct'=\gamma (ct-vt)$
$\large ct=\gamma (ct'+vt')$

Multiply the two together and both t and t' cancel.

Now just solve for $\gamma$. Simple.

=)

anonymous · Answer

OMG, I feel really stupid not to have realised it earlier. Thank you for the help!

roadjester · Answer

no prob