Assume we have two rigid body spheres of rest radius r in relative motion v along the x-axis. O is the stationary sphere and O' is the moving sphere. The moving sphere has a light source and clock at its origin.

The stationary sphere has a clock at its origin.

Assume when the origins of the two spheres are co-located, the two clocks are synched, and the light is flashed.

The following are the deductions from SR.

Light must proceed spherically from the center of the O sphere and strikes the rigid body sphere simultaneously.
Light must proceed spherically from the center of the O' sphere and strikes the rigid body sphere simultaneously.
O' does not believe O is struck simultaneously.
O does not believe O' is struck simultaneously.


For an observer sitting at O, when r/c elapses on its clock, all rigid body sphere points are struck simultaneously.

For an observer sitting at O', when r/c elapses on its clock, all rigid body sphere points are struck simultaneously.

Now, allow O to elapse a time of rγ/c since the flash of light occurred. This implies light has proceeded a distance rγ in all directions from O. In addition, by time dilation, the clock at O' elapsed r/c.

However, when the clock of O' elapses r/c, all of its sphere points are struck simultaneously. This implies light is a distance r in all directions from the center O'.

Now, only the positive x-axis light beam will be considered.

According to LT, x' = (x- vt)γ.Since t = rγ/c and x = rγ, then x' = (rγ- v(rγ/c))γ = rγ(γ - vγ/c).

But, since the clock of O elapsed rγ/c, then the clock of O' elapsed r/c and hence, x' = r since O' must meet is rigid body sphere simultaneity requirements when the clock at O' clock reads t/c.

Therefore, under the rules of SR, when the clock of O elapses rγ/c, the one light beam is located at both x' = r/c and x' = rγ(γ - vγ/c) which is a contradiction.

Alternatively, when the clock at O elapses rγ/c, light is a distance rγ in all directions as stated above.

In addition, the clock at O' must elapse r/c because of time dilation. Since the time elapsed r/c on the clock of O', then light must be a distance r from O' in all directions and in particular along the positive x-axis.

By LT, x = (x' + vt')γ. Since x' = r and t' = r/c, then x = (r + vr/c)γ = r(γ + vγ/c).

Hence, along the positive x-axis, light is a distance rγ/c from O, while at the same time, light is a distance r(γ + vγ/c) from O which is a contradiction.

Same problem as before, Jack. You're assuming absolute simultaneity.
Boring.

Here's a clue: learn how to apply the lorentz transform to events. That's both t and x coordinates.

This is the system I explained to you over in Pseudo. You're simply starting a new thread to avoid accepting or addressing all the things already said to you by myself and Pete on this system. There is no contradiction in SR, causality is preserved. The only contradiction is between your ears.