Okay, I still don't get the solution (which I will lay out) to the following problem:
Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the positive x-direction. Let B' be located exactly midway between A' and C'. At t'= 0, a light flash occurs at B' and expands outward as a spherical wave.
I know that according to an observer in S', the wave fronts arrive simultaneously at A' and C'. I also know that they are not simultaneous in S frame. Now I find the time difference between the events as recorded by an observer in S.
Let distance from B' to C' and B' to A' be L. Then the time difference between the events as seen by frame S is:
$$\delta T = T(B' \to C') - T(B' \to A') = L/(c-v) - L/(c+v).$$
My question is, does this not contradict Einstein's Second Postulate? I thought the speed of light to any observer is always $c$? So why in the deltaT equation can we write $c-v$ and $c+v$? Shouldn't the speed of light be $c$ to any observer?