Measuring Time: Identifying Slower Clock w/ Two Identical Clocks

[crastinus]

TL;DR Summary

If two clocks run at slower rates due to relative motion of one to the other, then one should run slower. How do we tell which one?

If we have two clocks, A and B, that are identical, and if one is moving with respect to the other one, we know that they must run at different speeds. (Right?) One must run slower than the other. But we cannot tell which of the two clocks is the "moving" clock.

So, how do we determine which clock works more slowly?

 

[phinds]

Summary:: If two clocks run at slower rates due to relative motion of one to the other, then one should run slower. How do we tell which one?

If we have two clocks, A and B, that are identical, and if one is moving with respect to the other one, we know that they must run at different speeds. (Right?) One must run slower than the other. But we cannot tell which of the two clocks is the "moving" clock.

So, how do we determine which clock works more slowly?

All of this is completely wrong and based on a common misunderstanding.

Clocks all run at the same speed (assuming they are working properly). When viewed by someone you are moving relative to it APPEARS to them that your clock is slow AND it appears to you that their clock is slow. Locally both clocks are just ticking away at one second per second.

 

[PeroK]

Summary:: If two clocks run at slower rates due to relative motion of one to the other, then one should run slower. How do we tell which one?

If we have two clocks, A and B, that are identical, and if one is moving with respect to the other one, we know that they must run at different speeds. (Right?) One must run slower than the other. But we cannot tell which of the two clocks is the "moving" clock.

So, how do we determine which clock works more slowly?

Velocity-based time dilation is symmetric: clock A runs slow, as measured in a frame of reference in which clock B is at rest. And, clock B runs slow, as measured in a frame of reference in which clock A is at rest.

Neither is actually or absolutely running slow.

 

[Dale]

Summary:: If two clocks run at slower rates due to relative motion of one to the other, then one should run slower. How do we tell which one?

If we have two clocks, A and B, that are identical, and if one is moving with respect to the other one, we know that they must run at different speeds. (Right?) One must run slower than the other. But we cannot tell which of the two clocks is the "moving" clock.

So, how do we determine which clock works more slowly?

There is no absolute truth to which clock is slower. In the first clock's frame the second clock is slow, in the second clock's frame the first clock is slow.

As @phinds mentioned, from its own perspective each clock is correct and it is always the other clock that is slow. I wouldn't use the word "appears" because it is not an optical illusion, but he is using "appears" in the sense that a sofa that appears unable to fit through a door may suddenly appear to be able to fit through a door if you turn it 90 degrees. The sofa hasn't changed, but the apparent width depends on how you are looking at it. But the sofa's width is not an optical illusion.

 

[Mister T]

Summary:: If two clocks run at slower rates due to relative motion of one to the other, then one should run slower. How do we tell which one?

So, how do we determine which clock works more slowly?

The clock that's in motion relative to you will run slow, but that way of stating the issue can be confusing. If you want to determine if that moving clock is running slow you will need two clocks. The moving clock passes first one of your clocks then the other. Both of your clocks are at rest relative to you, and you have synchronized them. You compare the readings on the clocks at each passing and come to the conclusion that the moving clock must be running slow.

But how to understand the symmetry? Someone at rest relative to the moving clock can set up two clocks just as you did and conclude that your clock is running slow.

The resolution lies in the fact that when you synchronize your clocks, the person who's at rest relative to the moving clock will not agree that you synchronized your clocks properly and will attribute your claim about his clock running slow to your mistake.

This effect is called the relativity of simultaneity.

 

[crastinus]

Thanks!

Summary:: If two clocks run at slower rates due to relative motion of one to the other, then one should run slower. How do we tell which one?

If we have two clocks, A and B, that are identical, and if one is moving with respect to the other one, we know that they must run at different speeds. (Right?) One must run slower than the other. But we cannot tell which of the two clocks is the "moving" clock.

So, how do we determine which clock works more slowly?

So, the problem here is that, by saying "they must run at different speeds" and "one must run slower than the other", I am making a tacit assumption that time is absolute in some reference frame. Is that right?

(I'm trying to put it in my own words so I can actually understand it.)

 

[Dale]

Thanks!

So, the problem here is that, by saying "they must run at different speeds" and "one must run slower than the other", I am making a tacit assumption that time is absolute in some reference frame. Is that right?

(I'm trying to put it in my own words so I can actually understand it.)

Yes, that is the concern. It is a pretty common mistake when people are first introduced to this concept.

 

[Mister T]

I am making a tacit assumption that time is absolute in some reference frame. Is that right?

Yes. It's like assuming there's a giant clock in the sky somewhere keeping track of absolute time. It was essentially the assumption Newton made.

 

[crastinus]

Thanks.

But, wait: I'm little confused.

If there is a tacit assumption of absolute time in what I said (and I see that there is!), then isn't there also an assumption of relative time in what you all said?

Presumably so. But, of course, what you are saying is derived from the larger and more correct theory.

I think you would point out in reply that the assumption of relative time is based on all the other evidence for the theory. Is that right?

But that leads me to a question: Is there a way to prove the relativity of simultaneity with just a reference to two clocks and their relative motions and the observers?

I think @Mister T is saying, "Yes, because of what happens when you compare the clocks and discrepancies arise." Is that right? So, that comparison is the physical experiment that we could actually run to show the relativity of simultaneity? (I know there is other evidence for it; but I am just trying to see whether relativity of simultaneity can be proved just with two clocks and relative motion.)

 

[crastinus]

Side question: Is it ever possible for one clock to read that some time has passed (a vanishingly small moment, presumably) and the other clock to read that no time has passed? Assuming both are functioning well. Just curious.

 

[PeroK]

But that leads me to a question: Is there a way to prove the relativity of simultaneity with just a reference to two clocks and their relative motions and the observers?

There's a nice fundamental derivation using nothing but the assumption that space and time are homogeneous and isotropic (i.e. there are no preferred directions) that there are essentially only two options:

a) Newtonian space and time.

b) Special Relativity and the Lorentz Transformation.

What you must do is an experiment to determine what is the case for our universe. One of the differences is that in a) there is no maximum speed to which a particle may be accelerated and in b) no particle may be accelerated to the speed of light in a vacuum or beyond. So, you build a particle accelerator and accelerate the particles and find you cannot make them reach $c$. The particles have energies which if Newtonian physics were true would correspond to hundreds or thousands of times the speed of light.

Not only this, but SR leads to a different theory of energy and momentum that is clearly the one at work in particle collisions. I.e. Newtonian physics cannot explain high-energy particle collisions; whereas, the experiments fit SR perfectly.

 

[PeroK]

Side question: Is it ever possible for one clock to read that some time has passed (a vanishingly small moment, presumably) and the other clock to read that no time has passed? Assuming both are functioning well. Just curious.

A clock can't stop in the sense that it always records its own proper time, which no matter how dilated is never zero in any reference frame.

 

[Dale]

then isn't there also an assumption of relative time in what you all said?

Definitely, yes.

I think you would point out in reply that the assumption of relative time is based on all the other evidence for the theory. Is that right?

Also, yes. I like this page for an overview of the large and varied body of evidence for special relativity: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

But that leads me to a question: Is there a way to prove the relativity of simultaneity with just a reference to two clocks and their relative motions and the observers?

Not that I know of. Usually you need to add some events like flashes of light and so forth, and you need to include the second postulate also. Is there any reason to exclude those?

 

[jbriggs444]

Side question: Is it ever possible for one clock to read that some time has passed (a vanishingly small moment, presumably) and the other clock to read that no time has passed? Assuming both are functioning well. Just curious.

No.

If you are working within Special Relativity and you adopt any inertial frame you please and look at the progress of some hypothetical physical clock moving at less then the speed of light, you will find that clock always ticks forward. It never stops. It never ticks backward.

We discard the possibility of physical clocks moving at the speed of light. Such a clock would have no rest frame. Physical clocks moving faster than the speed of light are interesting and lead to problems with causality, so that possibility is normally discarded as well. Google the "tachyonic anti-telephone".