Time Dilation and different clock types

[DAC]

Hello PF.
A moving clock is seen by the platform observer to run slow. This applies to all clock constructions. A light clock runs slow because the light path lengthens and the clock takes longer to tick over.

Other types of clocks don't have a light path to lengthen. By what mechanism do they run slow?

If the answer is, there is no mechanism, time just slows and the clocks record that, then why does the light clock not only slow but also shows the mechanism by which it slows i.e. longer path?
Regards.

 

[Dale]

By what mechanism do they run slow?

By what mechanism is the hypotenuse of a right triangle longer than the side?

 

[russ_watters]

Hello PF.
A moving clock is seen by the platform observer to run slow. This applies to all clock constructions. A light clock runs slow because the light path lengthens and the clock takes longer to tick over.

Other types of clocks don't have a light path to lengthen. By what mechanism do they run slow?

If the answer is, there is no mechanism, time just slows and the clocks record that, then why does the light clock not only slow but also shows the mechanism by which it slows i.e. longer path?

That's not really a "mechanism", that's a skewed observation due to the relativistic effect (it has no effect locally). Any other clock will show similar effects on whatever its particular mechanism of operation is: A pendulum will be observed swing back and forth "slower". A quartz crystal will be observed to vibrate "slower", etc. Point being, there really is no single, direct "mechanism" that you can pinpoint that you can say that speed slows clocks because___________... unless in that blank is that time is relative.

 

[DAC]

By what mechanism is the hypotenuse of a right triangle longer than the side?

" The way it is ". Bruce Hornsby & the Range?

 

[SlowThinker]

" The way it is ".

This also answers you original question.
If you come up with a better answer, it will still answer the original question as well.
Funny answer Dale!

 

[facenian]

I think the problem is with the concept of time itself and not the clock mechanism.What is a good clock?¿What is an ideal clock? if two clocks show different times how do you know which one show the correct one?Wheeler et al said "time is defined so that motion is simple" and that's a good clue. However I think that time is defined when the constancy of light velocity is postulated and this very definition unites space and time.

 

[Dale]

" The way it is ". Bruce Hornsby & the Range?

If you are willing to accept that as a mechanism for Euclidean geometry then it should also be acceptable as a mechanism for Minkowski geometry.

 

[russ_watters]

I think the problem is with the concept of time itself and not the clock mechanism.What is a good clock?¿What is an ideal clock? if two clocks show different times how do you know which one show the correct one?

An ideal clock is one who's tick rate is not affected by physical conditions in its environment, such as temperature, pressure, humidity, gravity, etc, as well as having a high precision and repeatability. The way you determine if a clock is better or worse than another is by identifying and quantifying the sources of error.

That description should sound a lot like how you evaluate pretty much any scientific instrument(s).

 

[russ_watters]

If you are willing to accept that as a mechanism for Euclidean geometry then it should also be acceptable as a mechanism for Minkowski geometry.

It's a bit of an irony to me: Time dilation in some ways seems harder for some people to accept than length contraction because the differences accumulate, are regularly used in real life with GPS, and thus are difficult to ignore...plus, people deal with perspective illusions (of trig) and accept them because they are illusions. But that doesn't mean people accept length contraction, it just means they tend to ignore it.

 

[facenian]

An ideal clock is one who's tick rate is not affected by physical conditions in its environment, such as temperature, pressure, humidity, gravity, etc, as well as having a high precision and repeatability. The way you determine if a clock is better or worse than another is by identifying and quantifying the sources of error.

That description should sound a lot like how you evaluate pretty much any scientific instrument(s).

The problem I see is that this entails a circular reasoning because, how do you evaluate the precision or error of the instrument(in this case clock)? I think we can do this with an atomic clock but then again you must suppose arbitrarily that the atomic clock is more precise, in fact the atomic(cesium) clock is really exact by definition!
However all this does not really answer why we take(arbitrarily) the atomic clock to be better than, for instance, the motion of the Earth except for Wheeler's observation.

 

[russ_watters]

The problem I see is that this entails a circular reasoning because, how do you evaluate the precision or error of the instrument(in this case clock)? I think we can do this with an atomic clock but then again you must suppose arbitrarily that the atomic clock is more precise, in fact the atomic(cesium) clock is really exact by definition!
However all this does not really answer why we take(arbitrarily) the atomic clock to be better than, for instance, the motion of the Earth except for Wheeler's observation.

I don't think that's true - it doesn't really take into consideration what I said at all. Let's take a couple of specific examples:
A pendulum clock is highly impacted by gravity. In a stronger gravitational field it ticks faster as Newton's Laws of gravity and motion predict it must. In orbit, it wouldn't tick at all. This effect is well understood and predictable to a pretty high degree of precision. A quartz oscillator clock is not affected by gravity. It is therefore much more accurate in situations where varying g-acceoerat89hs are present and can be used to measure the inaccuracy of the pendulum clock and match the source of the inaccuracy to the known mechanism that causes it.

I see nothing at all circular about that. Perhaps what you are believing is that the "error" is first detected by comparison to a real clock and then later explained when a more "accurate" real clock is invented, thus the "error" is always referenced to the more accurate clock. That isn't true. The "error" is pre-calculated based on the physical limitations of the clock as an error vs the "ideal" clock, not vs any other real clock.

In short, all real clocks have known mechanisms that cause error. An ideal clock would not. The known mechanisms can't always be easily experimentally verified for the most accurate real clocks and in practice you use known more accurate real clocks to help evaluate less accurate real clocks, but that doesn't make the logic circular.

 

[Mister T]

The problem I see is that this entails a circular reasoning because, how do you evaluate the precision or error of the instrument(in this case clock)?

You build two of them and run them side-by-side to see if they stay in sync.

I think we can do this with an atomic clock but then again you must suppose arbitrarily that the atomic clock is more precise, in fact the atomic(cesium) clock is really exact by definition!

That's not at all true. Atomic clocks had to be shown to be more precise than rotations of planet Earth before metrologists accepted them as a better standard.

However all this does not really answer why we take (arbitrarily) the atomic clock to be better than, for instance, the motion of the Earth except for Wheeler's observation.

Atomic clocks are more precise than Earth rotations. That's the reason and no other. It's not arbitrary. If you used several atomic clocks to repeatedly measure the time for Earth rotations you would find there's a variation in your measurements. But the variations between the readings on the various atomic clocks would be less than the variations between the atomic clocks and the rotations of Earth.

 

[facenian]

I don't think that's true... -

I think you've got a point here and I have to agree with you. You postulated the existence of an ideal time against which you can compare, by calculation, your measurements. I think this way of putting it can break the circularity I was referring to.
Maybe this discussion belongs more to the philosophy of science than to real physics.
By the way could you define easily what is that ideal time?

 

[Mister T]

Maybe this discussion belongs more to the philosophy of science than to real physics.

Maybe. But metrology is not philosophy. Read Post #12.

 

[facenian]

That's not at all true. Atomic clocks had to be shown to be more precise than rotations of planet Earth before metrologists accepted them as a better standard.

Atomic clocks are more precise than Earth rotations. That's the reason and no other. It's not arbitrary. If you used several atomic clocks to repeatedly measure the time for Earth rotations you would find there's a variation in your measurements. But the variations between the readings on the various atomic clocks would be less than the variations between the atomic clocks and the rotations of Earth.

I agree that in a practical sense it is not arbitrary to proclaim that atomic clocks are better that Earth rotation.
However this discussion somehow is similar to the old argument about absolute motion against relative motion.
When you compare two clocks(atomic and earth) and find they do not coincide the only rigorous conclusion is just that, you can not tell which one is correct and which one is right, however we all "know" that atomic clocks are better and that's because we unconsciously apply Wheeler's argument(post #6)

 

[phinds]

Hello PF.
A moving clock is seen by the platform observer to run slow. This applies to all clock constructions. A light clock runs slow because the light path lengthens and the clock takes longer to tick over.

No, the clock APPEARS to run slow. Locally the clock ticks at exactly the same one second per second as does any other clock.

 

[PeterDonis]

I think that time is defined when the constancy of light velocity is postulated

Our current standards use the constancy of the speed of light to define distance, not time. We define time, the second, based on a certain number of cycles of the radiation emitted in a certain atomic transition; then we define distance, the meter, such that the speed of light is exactly 299,792,458 meters per second.

When you compare two clocks(atomic and earth) and find they do not coincide the only rigorous conclusion is just that, you can not tell which one is correct and which one is right, however we all "know" that atomic clocks are better and that's because we unconsciously apply Wheeler's argument(post #6)

Not really. The Earth's rotation looks simplest if we define time based on the Earth's rotation; it looks more complicated if we define time as we currently do, by an atomic standard--just look at how we have to deal with leap seconds and other such corrections.

The reason we say atomic clocks are better is that the clocks themselves are simpler, so it's easier to understand the time they keep as a simple consequence of fundamental physical constants. The Earth is a huge conglomeration of atoms of many different kinds with a complicated structure; obviously the rotation of this thing is going to be a complicated process. Trying to relate that complicated process to something simple like the fundamental constants of the universe is not going to be straightforward at all.

A single energy level transition in a single atom is much, much simpler, and much easier to relate to fundamental dimensionless constants. We want to relate our standards to fundamental dimensionless constants because they are the only physical constants that don't depend on the units we choose; in other words, they don't depend on how we choose to define the second or the meter or any other unit of time or distance (or anything else). For example, the key dimensionless constant that governs atomic energy level transitions is $\alpha$, the fine structure constant. By defining the second using an atomic energy level transition, we are basically using $\alpha$ to define our unit of time.

 

[russ_watters]

But metrology is not philosophy. Read Post #12.

Yes. This issue is most certainly not philosophy.

 

[russ_watters]

By the way could you define easily what is that ideal time?

I already did. It's the first thing you quoted me as saying!

When you compare two clocks(atomic and earth) and find they do not coincide the only rigorous conclusion is just that, you can not tell which one is correct and which one is right...

Again: no. You know the atomic clock is better because you can calculate the error of the other clock (in this case, the Earth) and use the atomic clock to measure it. You cannot do the opposite: you cannot calculate the error of the atomic clock and then use the Earth to measure it.

however we all "know" that atomic clocks are better and that's because we unconsciously apply Wheeler's argument(post #6)

There is nothing unconscious about it: one way, the laws of physics work and the other way, they don't.

 

[Mister T]

When you compare two clocks(atomic and earth) and find they do not coincide the only rigorous conclusion is just that, you can not tell which one is correct and which one is right, however we all "know" that atomic clocks are better and that's because we unconsciously apply Wheeler's argument(post #6)

It's not a simple comparison of one to the other in that way. You must take repeated measurements with each and compare them to each other.

Either you missed my point entirely or you chose to ignore it. It's an issue of precision. A synonym for precision is reproducibility. The results of measurements of time using atomic clocks are more reproducible than the measurements of time using Earth rotations. It has nothing whatever to do with any argument about motion. If pendulum clocks were more precise that's what the metrologists would use to define the standard.

 

[Mister T]

If the answer is, there is no mechanism, time just slows and the clocks record that, then why does the light clock not only slow but also shows the mechanism by which it slows i.e. longer path?

Perhaps this alternative way of stating your question is fair.

Why is it that we can use a light clock mechanism to demonstrate time dilation, but we cannot use a pendulum clock mechanism to do so? Or any other clock mechanism to do so?

I think we could do it with a pendulum clock. One can imagine an arrangement where a mirror is attached to the pendulum bob and a beam of light is reflected off that mirror. It should be possible to show that the light beam has to travel a greater distance when observed from a moving frame of reference and that that would lead to the bob taking more time to complete a swing.

And one can imagine doing a similar thing with a mirror attached to the minute hand of clock.

What's used in all of these examples is a beam of light. And the reason is because its speed is the same when observed from a moving frame of reference.

But it should be possible to do all this with a beam of electrons that moves at some speed that's a good fraction of c. That speed would of course not be the same in all frames of reference, but when calculating the lengths of beam travel one would have to take into account that the velocity of the beam cannot be simply added to the velocity of the observer. One would have to use the relativistic "addition of velocities" formula. It would be a convoluted way of doing it but it would be possible to demonstrate time dilation in this way.

So, you don't need a light clock, you don't even need light.

You see it done with a light clock for two reasons. First, you are likely deriving the time dilation formula, and so you need to do that before deriving other things like the formula for transforming velocities. You could use the pendulum light clock described above to do this. But also the light clock is the most direct and easy-to-understand way. The value is in its pedagogy.

 

[A.T.]

No, the clock APPEARS to run slow. Locally the clock ticks at exactly the same one second per second as does any other clock.

It has nothing to do with appearance and locallity. A moving clock runs slower even locally.

 

[Nugatory]

When you compare two clocks(atomic and earth) and find they do not coincide the only rigorous conclusion is just that, you can not tell which one is correct and which one is right,

That problem is inherent in comparing two clocks. (There's a saying from the old days when dinosaurs roamed the earth, engineers used slide rules, there was no GPS, and sailors navigated by observing the position of heaven bodies at various times: "set to sea with one chronometer or three, but never two").

We can take a half dozen atomic clocks, some of identical construction and others of interestingly different construction. We find that they all remain in sync with one another, they agree about the interval between many different pairs of events, they give repeatable results when used to measure the time evolution of identically prepared systems, and they pass various other sanity tests... Then we are justified in saying that they're measuring something. And Einstein has told us what that something is: "Time is what a clock measures".

We cannot do any of these things with the rotation of the earth. We cannot run multiple rotations in parallel to see if they remain in sync, and the Earth's rotation fails to give repeatable results when used to measure the time evolution of identically prepared systems (for example, the fraction of a sample of radioactive material that decays is not the same from one rotation to another).

 

[russ_watters]

That problem is inherent in comparing two clocks. (There's a saying from the old days when dinosaurs roamed the earth, engineers used slide rules, there was no GPS, and sailors navigated by observing the position of heaven bodies at various times: "set to sea with one chronometer or three, but never two").

I'm sure Navy ships still carry chronometers and require navigators to occasionally use celestial navigation. The ship I was on 15 years ago did indeed carry three quartz chronometers and we recorded their time sync daily against GPS. If I remember correctly, the spread between them was something on the order of 4 minutes. They were never re-set or calibrated, so I assume that deviation developed over the 3 decades that the ship was in service (though I don't recall how they were powered...).
[edit] Now that I think about it, I think they had two batteries in parallel that could be changed individually.

 

[Nugatory]

No, the clock APPEARS to run slow. Locally the clock ticks at exactly the same one second per second as does any other clock.

It has nothing to do with appearance and locality. A moving clock runs slower even locally.

Guys... You're both right, and you've both chosen unfortunate wording that makes you both sound wrong. Phinds, when you used the word "locally" you lost the "at rest relative to the clock" part - and that is kinda important. A.T., you know better than to ever talk about a "moving" anything without saying what the motion is relative to.

How about: both clocks measure proper time along their worldlines. This is also the coordinate time in a frame in which the clocks are at rest, which is why we can say they tick at a rate of one second per second in that frame. In that sense, neither is running slow. However, both are running slow if we compare the amount of proper time between ticks with the amount of coordinate time between ticks in any frame in which the clock is not at rest.

 

[phinds]

Phinds, when you used the word "locally" you lost the "at rest relative to the clock" part - and that is kinda important.

Oh. I just assumed "locally" MEANS at rest relative to the clock, or "in the frame in which the clock is stationary". It didn't occur to me that that needed to be added. Thanks. I'll be more careful about that in the future.

 

[harrylin]

Hello PF.
A moving clock is seen by the platform observer to run slow. This applies to all clock constructions. A light clock runs slow because the light path lengthens and the clock takes longer to tick over.

Other types of clocks don't have a light path to lengthen. By what mechanism do they run slow?[...]

Other types of clocks can be understood as fundamentally having the same mechanism related to the wave nature of matter, but we analyze them differently and so we take into account such things as length contraction and increase of inertia ("relativistic mass"). A nice but rather general discussion of such analyses from the "mechanistic point of view" based on wave mechanics can be found in a very recent paper by Nelson in the AJP: http://arxiv.org/abs/1405.3979
( http://scitation.aip.org/content/aapt/journal/ajp/83/7/10.1119/1.4916360 )

 

[facenian]

Our current standards use the constancy of the speed of light to define distance, not time. We define time, the second, based on a certain number of cycles of the radiation emitted in a certain atomic transition; then we define distance, the meter, such that the speed of light is exactly 299,792,458 meters per second.

I'm not sure if the "concept" itself is the same as the way we choose to define it in a certain system of units.

Not really. The Earth's rotation looks simplest if we define time based on the Earth's rotation; it looks more complicated if we define time as we currently do, by an atomic standard--just look at how we have to deal with leap seconds and other such corrections.

I don't agree with this part. The Earth's rotation will look simple however the laws of physics won't, I do agree however with rest of your following argument and I think that is the spirit of Wheeler's argument

 

[SlowThinker]

I'm not sure if the "concept" itself is the same as the way we choose to define it in a certain system of units.

The constancy of speed of light only defines a conversion factor between space and time, it does not define space and time.
We can measure time in various ways that all agree, and that's the best definition we have so far: time is the thing that clock are measuring.

I don't agree with this part. The Earth's rotation will look simple however the laws of physics won't, I do agree however with rest of your following argument and I think that is the spirit of Wheeler's argument

I don't think you are getting the Wheeler's idea.
If time was defined through Earth rotation, the Newton's gravitational constant would be different every day. Everyone in the world would have to adjust their clock every day, based on the Earth's rotation during the previous day. The satellites in orbit would move with a different speed every day, just because our units of speed and distance would change. The conservation of momentum and energy would not exist, instead there would be a correction factor, different each day.
By choosing a time such that the conservation of energy holds, all this is made much simpler. We just need to adjust the clock if we want to measure the Earth's rotation - because it is irregular indeed.

 

[jartsa]

Let's consider photons in an optical fiber. If the fiber is accelerated transverse to its length, photons and fiber wall will collide in such way that the photons' lengthwise speed decreases.

And now let's consider marbles moving in a tube. If the tube is accelerated transverse to its length, marbles and tube wall will collide in such way that the marbles' lengthwise speed decreases.

In both cases lengthwise motion is slowed down by relativistic collisions.

In some types of clocks time dilation can be understood by understanding collisions.

 

[facenian]

I don't think you are getting the Wheeler's idea.
If time was defined through Earth rotation, the Newton's gravitational constant would be different every day. Everyone in the world would have to adjust their clock every day, based on the Earth's rotation during the previous day. The satellites in orbit would move with a different speed every day, just because our units of speed and distance would change. The conservation of momentum and energy would not exist, instead there would be a correction factor, different each day.
By choosing a time such that the conservation of energy holds, all this is made much simpler. We just need to adjust the clock if we want to measure the Earth's rotation - because it is irregular indeed.

well, I think that's precisely Wheeler's idea!

 

[russ_watters]

well, I think that's precisely Wheeler's idea!

What I, and I think others, objected to mainly was your saying that the choice is arbitrary when in reality it isn't. Wheeler's idea isn't easily/arbitrarily interchangeable with the other side of the coin (that we could easily have chosen Earth's rotation over the atomic clock). You said "you must suppose arbitrarily that the atomic clock is the better choice" and that just isn't correct. The choice is objective (it is objectively true that the atomic clock is better), not arbitrary. I'm not sure if you are still clinging to that wrong understanding or not.

 

[facenian]

I'm not sure if you are still clinging to that wrong understanding or not.

I believe that it is not so much a matter of wrong understanding as a matter of philosophical position that we believe there is a certain arbitrariness in our election of physical laws. I think what Wheeler meant by "time is defined so that motion looks simple" is objective for all the reasons you(and the other guys explained).
It is my belief that the real(objective) definition of time stems from principle of the constancy of light velocity independently of how we measure it operationally.
I found this discussion very enlightening and I learned much from it and I thank you all for that.

 

[Mister T]

We just need to adjust the clock if we want to measure the Earth's rotation - because it is irregular indeed.

Have there been any adjustments recently? I don't recall, and neither do I pretend to understand, all the reasons behind it. But there is a strong argument among many metrologists that these adjustments should not be made.

 

[Mister T]

I believe that it is not so much a matter of wrong understanding as a matter of philosophical position that we believe there is a certain arbitrariness in our election of physical laws.

That's not the same thing as believing that the choice of a time standard is arbitrary. Believing that is a wrong understanding of the very basis of metrology.

It is my belief that the real(objective) definition of time stems from principle of the constancy of light velocity independently of how we measure it operationally.

I think this thread has illuminated the notion that that belief cannot be correct.