Suppose B is moving with speed v away from A

[unscientific]

Homework Statement

Hi guys, i have a very simple question here about K-calculus.

Suppose B is moving with speed v away from A.

At time = t, an explosion (event) occurs in A, sending light in all directions.

According to the K-Calculus,

The time the explosion occurred in B would be:

t' = kt


But, using lorentz transformations:

t' = γ(t - vx/c²)

Since x = 0,

t' = γt


But it is quite clear that k≠γ..



Nevermind, I have solved it:

Time light from event received by B ≠ Time of event

Bu rather, the observer takes into account and B compensates for the time needed for light from the event to travel to him:

t' = kt - (v/c)t'

t' = kt/(1 + β) = γt (Shown)

 

[unscientific]

Also on a side note, is it possible to prove the K-calculus using geometry? Which basically says that 'u' length along the ct axis would translate into 'k*u' length along the ct' axis..