Assume O and O' are clocks are in relative motion in the standard configuration.

 

Assume the stationary frame is O.

 

According to SR, when the clock O elapses t, the clock in O' elapses t/γ, thus, when the clock in O elapses tγ, the clock in O elapses t.

That is simple time dilation.

 

By the measure at c logic of SR, if light is emitted when O and O' are co-located, light proceeds spherically from the origin of each.

This website shows this.

http://casa.colorado.edu/~ajsh/sr/paradox.html

 

Now, considering O', when its clock elapses r/c, light proceeds a distance r in all directions. This is the SR measure at c logic.

 

OK, now for the experiment, when the clocks O and O' are co-located, light is emitted at the co-location point by O'.

 

Only the positive x-axis will be considered.

Let r be a chosen distance.

 

1) Allow the time γr/c to elapse in O.

2) By SR, light proceeds a distance γr in O.

3) Since γr/c elapses in O, then r/c elapses on the clock of O'.

4) By SR logic, when r/c elapses in O', light proceeds r in all directions. Hence, the light is a distance r from O' along the positive x-axis.

5) When γr/c elapses in O, O' is located at a position vt or v(γr/c) in the coordinates of O.

6) But, since r/c elapsed in O', then light is a distance r from O'. Therefore, in O light is a distance vt + r/γ from O or v(γr/c) + r/γ = γr( v/c + 1/γ²)

 

 

Hence, gathering all the SR logic, when the clock of O elapses γr/c, light is located at

γr( v/c + 1/γ²) and γr which is a contradiction.

We've gone over this already