# Ehrenfest thought experiment

1. Sep 13, 2009

### bcjochim07

1. The problem statement, all variables and given/known data
Paul Ehrenfest suggested the following thought experiment to illustrate the dramatically different observations that might be expected, dependent on whether light moved relative to a stationary ether or according to Einstein's second postulate:

Suppose that you are seated at the center of a huge dark sphere with a radius of 3e8 and with its inner surface higly reflective. A source at the center emits a very brief flash of light that moves outward through the darkness with uniform intensity as a 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?

2. Relevant equations

3. The attempt at a solution

a) Against the ether to the edge it would take:

(3.0e8 m)/(3.0e8-30000 m/s) = 1.00010001 sec

with the ether back to the center: (3.0e8m)/(3.0e8+30000 m/s) = 0.999 sec
My book says the answer to this part is at 2 sec. a bright circle reflected from the great circle perpendicular to the motion. And I think this makes sense to me because the light should be reflected back to the center at 1.9991 sec.

b) For this part, my book says the entire interior lights up at 2sec.

I don't understand the difference between these two answers or I can't quite picture it (the difference between seeing a bright circle and the entire interior lighting up) and why you would see something different in each case. Could somebody give me a good explanation of what is going on here? Thanks.