What Would You See in Ehrenfest's Thought Experiment?

[bcjochim07]

Homework Statement

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?

Homework Equations

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.

 

[Jhero]

it is important to keep an open mind and explore all possibilities in order to understand the world around us. In this thought experiment, Paul Ehrenfest is showing us the stark contrast between the observations that would be made if light moved through a stationary ether versus if Einstein's second postulate is correct.

In the first scenario, where the sphere is moving through the ether at a constant speed, the light emitted from the source would take slightly longer to reach the edge of the sphere due to the motion of the ether. This would result in a bright circle of light being reflected back to the center at 2 seconds, as you correctly calculated. This is because the light would be traveling against the ether, which would cause a slight delay in its journey.

On the other hand, in the second scenario where Einstein's second postulate is correct, the speed of light is constant and does not depend on the motion of the observer or the source. This means that the light would reach the edge of the sphere at the same time, regardless of the sphere's motion. Therefore, the entire interior of the sphere would light up at the same time, at 2 seconds. This is because the light would be traveling at the same speed in all directions, creating a uniform intensity of light throughout the sphere.

The difference between these two scenarios is due to the different assumptions about the nature of light and its behavior. In the first scenario, the ether is assumed to exist and have an effect on the speed of light, while in the second scenario, the speed of light is constant and independent of any external factors.

Overall, this thought experiment emphasizes the importance of understanding the fundamental principles of physics and how they can drastically impact our observations and understanding of the world around us.