I understand time dilation with light clocks, but

[KarlRixon]

Imagine I were to make a light clock by placing two mirrors facing each other, with a photon bouncing between them vertically, such that one complete round trip for the photon takes exactly one second. I understand that if this contraption were moving horizontally at significant speed, an observer with a stationary frame of reference would perceive my clock 'ticking' slower than once per second. This seems to make perfect sense to me because the photon (according to the 'stationary' observer) must travel diagonally in order to hit the opposite mirror. Since this leads to a path which is longer than the straight-line distance that the photon travels according to an observer moving with the clock, I can see that time must change given that speed is constant and distance is increased.

So far so good. However where it all falls down for me is when you attach a 'regular' mechanical wristwatch (for example) to the light clock. Special relativity requires that according to an inertial observer, the light clock and the mechanical clock cannot fall out of sync. So it follows that to the 'stationary' observer, both clocks run slower. What I can't get my head around is *why* the mechanical clock slows. With the light clock the distance traveled by the photon appears to change, but there is no traveling photon in the mechanical clock.

I'm sorry if this is a stupid question, but it really has me stumped. I will be extremely grateful if someone can explain this to me!

 

[DaveC426913]

With the light clock the distance traveled by the photon appears to change, but there is no traveling photon in the mechanical clock.

Why are you limiting this dilation to only photons? Everything is affected in the same way. The photon is just an example of one thing that's easy to conceptualize.

 

[KarlRixon]

Dave,

Thanks for the reply.

I understand that the principle applies equally to everything, but with a photon clock I can understand *why* the principle applies - distance has changed while speed has remained constant, and since time results from dividing distance by speed, time must change. This is easy for me to visualise and it seems to make perfect sense.

I don't mean that I think this only applies to photons, and that the mechanical clock has no photons so this doesn't apply - my post was perhaps worded badly. I understand and accept that the mechanical clock is equally subject to this effect. It's just that in the example of the photon clock, I can "see" the diagonal path the photon moves. What I don't understand is, what is the equivalent factor for a mechanical clock which makes the principle apply? There is no diagonal movement resulting in a longer distance, in turn resulting in a dilation of time (or is there?).

 

[DaveC426913]

Dave,

Thanks for the reply.

I understand that the principle applies equally to everything, but with a photon clock I can understand *why* the principle applies - distance has changed while speed has remained constant, and since time results from dividing distance by speed, time must change. This is easy for me to visualise and it seems to make perfect sense.

I don't mean that I think this only applies to photons, and that the mechanical clock has no photons so this doesn't apply - my post was perhaps worded badly. I understand and accept that the mechanical clock is equally subject to this effect. It's just that in the example of the photon clock, I can "see" the diagonal path the photon moves. What I don't understand is, what is the equivalent factor for a mechanical clock which makes the principle apply? There is no diagonal movement resulting in a longer distance, in turn resulting in a dilation of time (or is there?).

Agreed. I've always sort of the glossed over that same point, like it's a blind spot.

 

[JesseM]

I don't mean that I think this only applies to photons, and that the mechanical clock has no photons so this doesn't apply - my post was perhaps worded badly. I understand and accept that the mechanical clock is equally subject to this effect. It's just that in the example of the photon clock, I can "see" the diagonal path the photon moves. What I don't understand is, what is the equivalent factor for a mechanical clock which makes the principle apply? There is no diagonal movement resulting in a longer distance, in turn resulting in a dilation of time (or is there?).

You derive all conclusions about clocks from the two basic postulates of SR:

1. All laws of physics work the same way in different inertial frames
2. Something moving at c in one inertial frame also moves at c in other inertial frames

You use postulate 2 to show that a light clock must run slower in a frame where it's moving. Then you use postulate 1 to show that any arbitrary clock must run slower by the same factor, since if that type of clock keeps pace with a light clock in a frame where both are at rest, then 1 requires that it's true in all frames that a non-light-clock keeps pace with a light clock if both are at rest in that frame (and any two clocks moving alongside each other will have some rest frame).

 

[Al68]

I understand that the principle applies equally to everything, but with a photon clock I can understand *why* the principle applies - distance has changed while speed has remained constant, and since time results from dividing distance by speed, time must change.

I think you have the cause and effect backward here. The distance traveled is the result, not the cause, of the combination of speed and elapsed time. The choice of distance between the mirrors was to anticipate the result, not cause it. And both the light clock result and the "regular" clock result is the result of time "passing slower".

 

[Janus]

Dave,

Thanks for the reply.

I understand that the principle applies equally to everything, but with a photon clock I can understand *why* the principle applies - distance has changed while speed has remained constant, and since time results from dividing distance by speed, time must change. This is easy for me to visualise and it seems to make perfect sense.

I don't mean that I think this only applies to photons, and that the mechanical clock has no photons so this doesn't apply - my post was perhaps worded badly. I understand and accept that the mechanical clock is equally subject to this effect. It's just that in the example of the photon clock, I can "see" the diagonal path the photon moves. What I don't understand is, what is the equivalent factor for a mechanical clock which makes the principle apply? There is no diagonal movement resulting in a longer distance, in turn resulting in a dilation of time (or is there?).

Let's say that in addition to the bouncing light, you have a bouncing ball, which bounces x times for every one bounce of the light. So the question is, Why does this ball bounce up and down the same number of times with respect to the light when the clock is moving with respect to you, and thus show the same time dilation as the light?

The reason is that the ball, while it doesn't travel at c, itis subject to the rules of Relativistic velocity addition. It travels at a diagonal, and its speed as measured along that diagonal is such that, due to the rules of velocity addition, that it will take longer to complete a round trip by the same factor that the light does.

It can also be shown that the time it takes for the ball to make the round trip is the same no matter which direction it bounces with respect to the motion of the clock.

Since a mechanical clock is made of moving parts, all of which are subject to the same rules of velocity addition, each of these parts will show a slowing of their cyclic motion in the same way that the bouncing ball did, and the clock ticks in sync with the light pulse.

 

[DaveC426913]

I think you have the cause and effect backward here. The distance traveled is the result of multiplying the speed by the elapsed time. And "time passing slower" is the cause, not the effect, of both the light clock result and the regular clock's result.

If time dilation were the cause, then this experiment is flawed in trying to show that. This experiment is designed to show that time dilation comes about through no other means than geometry of fast-moving objects. There is no trime dilation invoked in the experiment, yet its results show it.

 

[JesseM]

I think you have the cause and effect backward here. The distance traveled is the result of multiplying the speed by the elapsed time. And "time passing slower" is the cause, not the effect, of both the light clock result and the regular clock's result.

It seems confusing to use the language of "cause and effect" when talking about the logical relations between abstract concepts like time dilation and the invariant speed of light, as opposed to reserving that language for causal relationships between specific physical events. I mean, if we're going to use "cause and effect" for logical relations, couldn't you also say the two basic postulates of relativity (particularly the one about the invariant speed of light) are the "cause" of time dilation?

 

[Al68]

It seems confusing to use the language of "cause and effect" when talking about the logical relations between abstract concepts like time dilation and the invariant speed of light, as opposed to reserving that language for causal relationships between specific physical events. I mean, if we're going to use "cause and effect" for logical relations, couldn't you also say the two basic postulates of relativity (particularly the one about the invariant speed of light) are the "cause" of time dilation?

Yeah, I worded that poorly. I meant that the clock readings are the result, not the cause, of the elapsed time.

 

[KarlRixon]

Thank you all for your replies.

Janus your point about the velocity of the moving parts of the mechanical clock makes perfect sense, thank you.

I think the real issue I'm having here (but am slowly getting my head around) is accepting that SR is explaining something that "just is", but which I'm struggling to conceptualize because it is so foreign. By that I mean that the two postulates of SR have been proven to be correct time and again, but rather than accept it I automatically want to know "why" it is the way it is because it seems so hard to accept. I suppose it's like asking "why does light move at c" - it just does.

 

[Saw]

KarlRixon, yours is a good and well posed question. When trying to answer, there are two possible approaches:

One approach is the one that JesseM has taken and clearly explained. As you have yourself noted, you need postulate 2 to conclude that the light clock suffers time dilation. And you need postulate 1 to conclude that the mechanical clock suffers time dilation, too.

Another approach is looking for a reason related to the nature of the interactions that govern the light or the mechanical clock. In this line, Lorentz would have said that the reason for everything is the ether; in the case of the light clock, because light is a perturbation in that medium; in the case, of the mechanical clock, because its “moving thing” (think of the ball cllock that Janus mentioned) is accelerated in every collisison with the wall clocks through an electromagnetic interaction; and in the case of other devices based on other sorts of interactions (eg: a moun that “beta decays”), because all forces in nature are alike and governed by similar rules… Looking at historic records, Einstein himself was not far from this second approach.

In my view, both approaches are complementary, not contradictory, they are simply placed at different levels. The first follows the abstract route: it is like a rule of thumb, a quick and dirty way to formulate what happens and it has been confirmed by experiments so far. The second makes a try at going one step further in the task of explanation but it has been little elaborated, apparently it cannot be confirmed (that ether would be undetectable) and it is true that it does not seem to add much light to the issue…

PS: What Janus said about the relativistic law of addition of velocities is true, but it must be mentioned that such law is derived by precisely assuming time dilation. In general, all reasoning in approach one is circular. For example, postulate 2 relies on time dilation: the speed of light would not be measured to be c by all observers if there were no time dilation (and other phenomena like length contraction and relativity of simultaneity). That is not bad, it is normal, but it does show that approach one is not an explanation at the level you are asking for.

 

[pervect]

A general comment. If you aren't a professional physicist, and if you want to understand modern physics, I would advise you to read more and "do your own thinking" less if you want to understand modern theories. There's a place for doing your own thinking of course, but if you do that exclusively, you'll get out of touch with the mainstream theories that everyone else has.

As for example, in this thread, several people have run into similar issues. Enough so that we even have a name for it - the issue is the relativity of simultaneity. Unfortunately, if you don't know what we mean when we say "relativity of simultaneity", and you're not motivated to find out when we mention it, instead going back to your own thoughts, I'm not sure how much help we can be. Going back to your own thinking isn't going to teach you how modern physics is going to work. It actually would make the most sense if you WERE a professional physicist - but in that case, you'd still be expected to understand the modern theories that everyone else had. You'd also be expected to be familiar with the wide range of testing that had been done on the theories. The core of science is really in the testing part, not the thinking up part - the theories have to be well thought out enough to make predictions of actual experiments that can be carried out - and consistent with known experimental results.

 

[timetravel_0]

I think the real issue I'm having here (but am slowly getting my head around) is accepting that SR is explaining something that "just is", but which I'm struggling to conceptualize because it is so foreign. By that I mean that the two postulates of SR have been proven to be correct time and again, but rather than accept it I automatically want to know "why" it is the way it is because it seems so hard to accept. I suppose it's like asking "why does light move at c" - it just does.

I think its silly to stop asking why and just give into just cause. If we gave into just cause then we would still be mistified by the rabbit in a hat magic trick. Light moves at a specific speed for a reason - I too have thought the same question and am not a physicist so I don't have an answer. But discovering answers to these questions sometimes undercovers great discoveries that change the course of modern physics.

 

[KarlRixon]

If you aren't a professional physicist...

What gave me away?!

I take your point, though this question was actually bugging me as a result of my struggling to understand something I was reading a physics book, certainly not as a result of any intellectual effort on my part! I really have no intention of "doing my own thinking" as such, I'm just trying to learn about a subject which fascinates me, but I know very little about having only been educated in it to secondary (high) school level. However I'm finding learning physics a double-edged sword as the fact that it can be so mind-boggling is both what makes it so interesting but also hard to comprehend for a non-scientist such as myself.

I'll keep reading, hopefully it will all 'click' at some point, and if not, I'm having fun trying to understand it!

 

[KarlRixon]

I think its silly to stop asking why and just give into just cause. If we gave into just cause then we would still be mistified by the rabbit in a hat magic trick. Light moves at a specific speed for a reason - I too have thought the same question and am not a physicist so I don't have an answer. But discovering answers to these questions sometimes undercovers great discoveries that change the course of modern physics.

You're quite right of course, but my point is really that I will have to just accept some things for now without getting hung up in questioning "why?" too deeply, because I don't have the breadth of knowledge necessary to understand the answers yet. That's not to say that everybody should just accept that things are the way they are - after all if everybody did that, as you point out, we'd still be living in caves.