General Discussions
One important concept when considering the frame invariance of Maxwell's equations involves the nature of a spherical wave front. Imagine several inertial reference frames (IFRs), traveling in different directions with different velocities. For an instant, we allow the origins of each of these frames to coincide. At that very instant, we cause there to be a flash of light emitted at the instantaneously coincident origins of all frames. Let us pick one very special reference frame, in which the source is stationary. Clearly, in this IFR, light will expand from the origin of the reference frame in a spherical shell. In other words, assume that within this reference frame, we draw a sphere of radius one light second.
We now randomly place light detectors at various points on the sphere. One second after the flash, all detectors on this sphere will simultaneously go off, indicating that light from the flash has reached them. There is no question that, in this frame where source and detectors suffer no relative motion, the light from the source expands in a spherical shell. But what of the other IFRs whose origins only coincided with this special frame at the time of the flash? Will they also experience an expanding spherical shell?
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