Consider the usual two inertial frames S and S' in standard configuration. In S' the standard lattice clocks all emit a 'flash' at noon. Prove that in S this flash occurs on a plane orthogonal to the x-axis and traveling in the positive x-direction at (de-Broglie-) speed c^2/v.
Lorentz transforms. The invariant interval (ct^2 - x^2 - y^2 - z^2 = ct'^2 - x'^2 - y'^2 - z'^2). To clarify standard configuration is just an orthogonal x y z for s and then an orthogonal x' y' for s' where x and y are parallel to x' and y' respectively and s' is moving away from s at speed v along the x and x' axis.
The Attempt at a Solution
I'm struggling to begin. I think I'm misunderstanding something... because in thinking about limiting cases. Say we have an S' frame that happens to be the same as S (so v = 0), then the problem makes no sense. I feel like in that case the flash should be moving at a speed of 0. Perhaps this is misunderstanding what it means by a "flash occurring on a plane".
I just really need a hint on how to get started on this : (.