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If we have two reference frames K and K' which are moving relative to one another, special relativity suggests that there would be time dilation. In K, time appears to pass slower in K', whereas in K' time appears to pass slower in K.

The most common proof of this is by using light clocks and demonstrating that from one perspective, light has to travel a greater distance and therefore the clock would go slower. I have two questions that I'd appreciate help with:

  1. Surely time dilation is a consequence of the peculiar way of measuring time with a light clock. If I used a mechanical clock, or an atomic clock where there are no distances involved, wouldn't the time be the same?

  2. I don't understand why we can assume light travels the same in all reference frames. Is there a proof?

I would appreciate any help

Qmechanic
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ED2468
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3 Answers3

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  1. In any given frame, all accurate clocks moving at a given speed tick at the same rate. So if one (e.g. your light clock) ticks slowly, they all tick slowly.

  2. What does "why" mean? Do you want to deduce the invariance of light speed from other assumptions? The derivation will depend on what assumptions you allow.

WillO
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I'm only an undergrad, but here's my best response

A light clock illustrates how time is passing in each reference frame. Imagine you have a light clock next to your mechanical clock. If the light clock experiences time dilation surely the mechanical clock will as well - time can't pass differently for the two objects in the same reference frame. The only explanation for the fact that light travels a longer distance in someone else's reference frame than in your reference frame AND that the speed of light is constant is that time MUST be different in different reference frames. I hope that helps a little bit.

You can just take this as an axiom. We're making an assumption either way: either we assume it's the same in all reference frames or that it varies :)

We can deduce the fact that the speed of light is constant from the invariance of the Maxwell equations in different reference frames. Give that a google search if you want to understand why we have relativity.

Steve
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There are several misconceptions in your question. Firstly, time does not 'pass slower' in the way you suppose. Time always passes at the rate of a second per second. However, in two frames of reference that are moving relative to each other, time in one frame is out of synch with time in another, and that allows the time interval between two events in one frame to differ from the time interval between the same two events in another. Note that it is the interval that differs- for example, it might be 5 seconds in one frame and 4 in another. A clock in the second frame will record fewer seconds not because it is running slow but because the interval is actually a second shorter. Any good clock will therefore record the interval as 4 seconds. The fact that light clocks are usually mentioned in books about SR is because they illustrate the underlying principles in a clear way.

The Michelson Morley experiment was famously the first to drive home the point that the speed of light seemed to be independent of any reference frame, but the principle has since been proven countless times both by experiments and by practical applications of radar etc. Googling 'proof of relativity', or a similar search string, will throw up all you need to know.

Professor Sushing
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