Time dilation derivations - help me out just looking for references

[elegysix]

I'm looking for another derivation of time dilation which does not involve moving clocks or mirrors...

I feel like those aren't very clear - is there any other way time dilation has been derived?

thanks

 

[maverick_starstrider]

How good is your math or physics background?

 

[elfmotat]

The obvious one is the case where Δx=0 between two events in the Lorentz Transformation.

 

[ghwellsjr]

I'm looking for another derivation of time dilation which does not involve moving clocks or mirrors...

I feel like those aren't very clear - is there any other way time dilation has been derived?

thanks

Time dilation was proposed prior to Einstein's relativity at a time when scientists believed in an absolute ether rest state and they believed motion through it would result in a detectable ether wind, as they called it. The Michelson-Morley Experiment (MMX) was designed to detect this ether wind but no matter how fast the apparatus was traveling through the ether (as a result of the Earth's motion), it always appeared as if they were stationary in the ether because they could never detect any ether wind. Not willing to give up on the idea of a fixed ether, the scientists explained it away by proposing that motion through the ether would cause objects to contract along the direction of motion and this would also result in the appearance of clocks running slower (time dilaiton). But although MMX did not have clocks, it did have mirrors.

So let's think of another kind of experiment that we could perform today that would also produce the effects that are independent of our motion through the presumed ether. Let's imagine that we are looking at a laser that is shining at us and that we and the laser are moving with respect to the ether, maybe towards each other, maybe away. We want to cover all the situations. If we didn't know anything about relativity, we would use the normal Doppler Effect to predict what frequency we would see the laser light compared to the frequency that it was emitting.

So here's an assignment for you: look up Doppler Effect in wikipedia and study the equation that shows how the frequency is modified. Convince yourself that it is dependent on both our speed through the ether and the laser's speed through the ether. In other words it is not independent of our relative motions through the ether like MMX showed. In other words, that equation doesn't work for light like it does for sound in air or water.

When you've done that, I need to ask you a couple questions:

Do you believe that equation is wrong?

If so, do you believe that it is not just an optical illusion that makes it wrong?