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Oct23-11, 07:02 AM
PF Gold
P: 4,745
Here's the problem. Neither Sam nor Sally have any way of knowing if the distant light bulbs actually come on simultaneously, they can only know if the light propagating through space arrives at their own locations simultaneously, correct? That's because we cannot track the progress of light through space, we just don't know where it is at any given point in time.

So to solve this problem, Einstein creates the concept of a Frame of Reference in which he defines, not measures, the propagation of light to be c. This means that if you see two distant lights that are an equal distance from you come on simultaneously, then those two remote events are simultaneous, by definition in that FoR, not by measurement.

Another FoR, moving with respect to the first one, because it uses its own definition for the propagation of light, will determine that events that are simultaneous in the first FoR are not simultaneous in the second FoR, simply because it has defined the propagation of light to be c in its FoR.

The images for your scenario are all from the point of view of a FoR in which Sam is at rest. So in image (b), when Sam actually sees the light from the two equidistant bulbs arrive simultaneously at his location, then this FoR defines, not measures, the two events of the light bulbs as happening simultaneously as depicted in image (a). Note that in all your images, the two bulbs are depicted as being equidistant and stationary with respect to Sam at all times.

So it's because the problem is stated from the point of view of a FoR in which Sam is at rest and the facts that he sees the two flashes simultaneously and the bulbs are equidistant from him, that we can say the two flashes occurred simultaneously, by definition in that FoR which means that Sally will neither see the flashes simultaneously nor conclude that they occurred simultaneously in a FoR in which she is at rest.