Note that the horizontal moving light Theory Of Relativity For Musicians clock has to be shortened in length to make it tick at the same rate as its vertical companion – we know that this shortening happens in nature because experiments have confirmed that it happens. You should take that on trust for now, but if you want to check the facts, start by reading up on the Michelson-Morley experiment, but be wary of any assertions that it disproved the aether because it did no such thing, and indeed it actually led to the creation of Lorentz Ether Theory, the most serious rival to Einstein’s theories.
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Next, you need to understand the Theory Of Relativity For Musicians phenomenon of relativity without caring about which theory of relativity might explain it. Still using the page I linked to, I want you to imagine that you are standing with the stationary light clocks on the left of the screen while looking at the moving light clocks. Imagine that a radio signal is sent out every time the moving clocks tick. Those ticks will reach you at a low frequency L when the clocks are moving away from you and a high frequency H when they’re moving towards you. You can do a bit of maths with those values and determine that the moving clocks are ticking half as often as the stationary clocks that you are standing next to. (That particular amount of slowing happens when the moving clocks are moving at 86.6% the speed of light.