Question

Lorentz Transformation Derived?

Answer 1

argh, I have a good one to show you but I have to leave right now...
If nobody else answers I'll give you mine in a couple hours
see ya!

Answer 2

google it :P its easy derivation. . .

Answer 3

imagine a time be a time clock where light is reflected across two mirrors separated by distance d on a spacecraft moving at velocity v

the time for light to pass between these two is \(ct_r\) where \(t_r\) is the time for observed from someone on the ship (the "rest" time)

the distance the ship travels is \(vt_o\) where \(t_o\) is the time as seen from an outside observer, and \(v\) is the velocity of the ship

the distance the light moves as seen from an outside observer is \(ct_o\)

by the Pythagorean theorem we have\[(ct_r)^2+(vt_o)^2=(ct_o)^2\]\[(c^2-v^2)t_o^2=c^2t_r^2\]\[t_o=\frac{ct_r}{\sqrt{c^2-v^2}}\]divide top and bottom by c\[t_o={t_r\over\sqrt{1-({v^2\over c^2})}}\]