Consider an object which responds to two different signals A and B: it responds to signal A with blue color and signal B with red color. Also, it responds only to the signal that reached first. In case they both reach together, there is no observation.

Now consider three observers $x,y,\,z$. If event that both signals reaches at the same time for $x$, then for $y$ and $z$ there must exist velocity $v_1$ and $v_2$ such that these signals aren't simultaneous to them. Let for $y$ A reached first and for $z$ B reached first. Then what will be the actual color the object emits?

  • $\begingroup$ An event is always simultaneous with itself, regardless of who does the measuring. $\endgroup$ – WillO Mar 2 '15 at 17:46

Events that happen at the same time and the same position in one inertial frame happen simultaneously in all inertial frames, you can easily verify this just by looking at how the Lorentz transformation creates a one-to-one relation between spacetime coordinates in one frame and spacetime coordinates in any other frame. It's only if events occur at different positions in space that you can have a situation where one frame says the two events were simultaneous and other frames say they weren't. So if your "object" is at a single point in space when two signals reach it simultaneously in one frame, then all frames agree the signals reached it simultaneously.

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