suppose that you are seated at the center of a huge dark sphere with a radius of

Question

suppose that you are seated at the center of a huge dark sphere with a radius of 3x10e8 m (300,000,000m) and with its inner surface highly reflective. A source at the center emits a very brief flash of light that moves outward through the darkness with uniform intensity as an expanding spherical wave. What would you see during the first 3 seconds after the emission of the flash if (a) the sphere moved through the ether at a constant 30 km/s and (b) if Einstein's second postulate is correct?

Modern physics 5th edition tipler and llewellyn: Chapt. 1(Relativity 1), problem 5,

Explanation / Answer

(a) In this case, the situation is analogous to Example 1-3 with L = 3*10^8 m v = 3*10^4 m/s and c = 3*10^8 m/s If the flash occurs at t = 0, the interior is dark until t = 2 s at which time a bright circle of light reflected from the circumference of the great circle plane perpendicular to the direction of motion reaches the center, the circle splits in two, one moving toward the front and the other toward the rear, their radii decreasing to just a point when they reach the axis 10^(-8)s after arrival of the first reflected light ring. Then the interior is again dark. (b) In the frame of the seated observer, the spherical wave expands outward at c in all directions. The interior is dark until t = 2s, at which time the spherical wave (that reflected from the inner surface at t = 1s) returns to the center showing the entire inner surface of the sphere in reflected light, following which the interior is again dark.

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