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MathematicalPhysicist

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here are a few questions about these frames:

1. if two events occur at the same point in some inertial frame S, prove that their temporal order is the same in all inertial frames, and that the least time seperation is assigned to them in S.

2. if two events occur at the same time in some inertial frame S,prove that there is no limit on the time seperations assigned to these events in other frames, but that their space seperation varies from infinity to a minimum which is measured in S.

3. in the inertial frame S' the standard lattice clocks all emit a 'flash' at noon. prove that in S this flash occurs on plane orthogonal to the x-axis and travlling in the positive x direction at speed c^2/v.

well im not sure what to do in 2 or 1.

but in three, the beam of light from S' obviously travels at speed c, and according to einstein's postulate the speed of light is constant to all observers, so shouldnt the flash travel at c?

anyway, i know that the flash should travel a distance of vt, where v is the speed of S', where t is the time in S, so we should have ct'=vt where t' is the time measured in S', but is this correct?

i would like to advise me how to solve 1 and 2.

thanks in advance.