ant

2014-Sep-27, 04:34 PM

Traditionally the famous Einstein's light clock is served as an example, which leads to the time dilation phenomena.

I propose to consider a little modified version of the clock: with a refractive medium: n <> 1.

The light impulse propagate with a speed c/n, thus the right triangle relation gives:

(c/n)^2 = c_y^2 + v^2\to c_y = c/n \sqrt{1 - n^2 v^2/c^2}

So, the moving clock slows down

\sqrt{1 - n^2 v^2/c^2} times,

what is different than the desired result:

1/\gamma = \sqrt{1 - v^2/c^2}

Only for a refractive index n = 1, means for the vacuum, the clock slows down correctly!

Impossible! What's that, where is a mistake?

I propose to consider a little modified version of the clock: with a refractive medium: n <> 1.

The light impulse propagate with a speed c/n, thus the right triangle relation gives:

(c/n)^2 = c_y^2 + v^2\to c_y = c/n \sqrt{1 - n^2 v^2/c^2}

So, the moving clock slows down

\sqrt{1 - n^2 v^2/c^2} times,

what is different than the desired result:

1/\gamma = \sqrt{1 - v^2/c^2}

Only for a refractive index n = 1, means for the vacuum, the clock slows down correctly!

Impossible! What's that, where is a mistake?