# Lorentz Contraction For Non-Simultaneous Events

Suppose in the rest frame $$S$$, event $$A$$ occurs at $$x = 0, t =0$$ and event $$B$$ occurs at $$x = 100, t = 80$$.

Now suppose that frame $$S’$$ is moving with velocity $$V$$ with respect to $$V$$.

Now the question is what is the distance between the events in frame $$S’$$. Since the events occur at different times in the rest frame I was wondering if it is applicable to use the formula $$L = L_0/\gamma$$.

On the other hand if i transform the $$x$$ cords for both events using Lorentz transforms and subtract them i get $$x_B’ - x_A’ = \gamma ( x_B - \beta ct_B - x_1 + \beta ct_A)$$. In this instance since $$t_B \neq t_A$$ you will get a different answer than if you use Lorentz contradiction formula.

So since both approaches yield different answers, I was wondering which one is correct and what the fallacy with the other one is.

• note that $(c\Delta t)^2 - (\Delta x)^2$ is the same for all frames of reference
– JEB
Jan 23 '20 at 4:44