Time dilation questions

Question

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:

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?
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

Too short for a proper answer, but: 1) Surely time dilation would not be the topic of hundreds of posts here on physics SE if it were just an artefact of using a weird clock? And 2) The constancy of the speed of light is a postulate of relativity, motivated by, among other things, the Michelson-Morley experimen and Maxwell's equations being Lorentz-invariant. — Marius Ladegård Meyer, Oct 05 '23 at 21:00
Surely time dilation is a consequence of the peculiar way of measuring time with a light clock. Because… why? — Ghoster, Oct 05 '23 at 21:17
Is there a proof? Physics isn’t a branch of mathematics. The relevant question is “Is there experimental evidence?” and the answer is Yes. — Ghoster, Oct 05 '23 at 21:21
@Marius Ladegård Meyer Calm down bud obviously I am aware of how successful SR is, I clearly don't understand how time dilation isn't anything but a consequence of light clocks which is why I asked the question. — ED2468, Oct 05 '23 at 21:22
@Ghoster Every time I see time dilation, it's always with moving light clocks and the distance between them, can it be demonstrated without this notion? — ED2468, Oct 05 '23 at 21:23
Demonstrated in the laboratory? Demonstrated by mathematical reasoning? Starting from what postulates? — Ghoster, Oct 05 '23 at 21:25
@Ghoster I don't know that's my question. I am not satisfied with how time dilation is almost universally demonstrated with this idea of light clocks, shouldn't such a widely accepted phenomena be able to be approached from different angles? — ED2468, Oct 05 '23 at 21:29
"shouldn't such a widely accepted phenomena be able to be approached from different angles? " Yes, there are many different ways to derive time dilation. If your question is why you happened to consult a few sources that derive it this way and not some other sources that derive it another way, the answer probably contains the word "coincidence". — WillO, Oct 05 '23 at 22:57

score 1 · Answer 1 · answered Oct 05 '23 at 21:02

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.
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.

answered Oct 05 '23 at 21:02

WillO

15,072

How can a light clock be equated to a mechanical clock do they not measure time differently? It is not obvious how a mechanical clock would be affected by time dilation. For the record I am in no way questioning SR which most of these people think I am doing. Obviously I am wrong, but why? – ED2468 Oct 05 '23 at 21:32
What is the definition of a clock? Answer: something that tells time. So by definition of "clock", any two clocks placed next to each other must measure time the same way, otherwise one of the clocks are faulty. – Marius Ladegård Meyer Oct 05 '23 at 22:34
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@ED2468: What you are missing is relativity. Nothing in the laws of physics can distinguish a "non-moving" observer from an observer in uniform motion. If all your light clocks ran at a different speed from all your mechanical clocks, you'd know you were in motion. Relativity forbids that. – WillO Oct 05 '23 at 22:47

score 1 · Answer 2 · answered Oct 05 '23 at 21:07

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.

That does help. But what confuses me as that light clocks and (e.g.) mechanical clocks measure time very differently. Light clocks use the time it takes for light to pass between mirrors, whereas mechanical clocks use the energy stored in springs for instance. How would the principle of time dilation apply to a mechanical clock? — ED2468, Oct 05 '23 at 21:26
@ED2468 The simplicity of light clock means it is relatively simple to analyze, unlike a mechanical clock whose analysis will depend on the details of its construction… and will likely be much harder to analyze. In spite of this difficulty with analyzing mechanical clocks, the principle of relativity and its implications have much more experimental support than any alternative. As ghoster suggested, visit https://physics.stackexchange.com/questions/570966/why-is-the-photon-clock-equivalent-to-all-clocks — robphy, Oct 06 '23 at 00:07

Marco Ocram · Answer 3 · 2023-10-06T05:55:04.877

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.

I think near the end of your first paragraph, you meant to say light clocks, not time clocks — RC_23, Oct 05 '23 at 22:45
@rc_23 I did indeed. Many thanks. That's what happens when I post sleepy answers just before going to bed! — Marco Ocram, Oct 06 '23 at 05:56

Time dilation questions

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