Suppose that A\', B\' and C\' are at rest in frame S\', which moves with respect

Question

Suppose that A', B' and C' are at rest in frame S', which moves with respect to S at speed v in the +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 spherical wave. According to an observer in S', do the wave fronts arrive at A' and C' simultaneously? According to an observer in S, do the wavefronts arrive at A' and C' simultaneously? If you answered no to either 1, or 2., what is the difference in their arrival times and at which point did the front arrive first?

Explanation / Answer

a) Yes, as A and C are placed equidistant from B, for an observer is S'.

b) No, for an observer based in S, as the S' is moving with a relative velovity v with respect to S,

c) For an observer in S, the time will vary depending on the direction of wavefront ' movement with respect to the movement of the S'

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