Relevant/irrelevant clocks for experimental tests of relativity

[DanMP]

TL;DR

What clocks can be considered relevant for [i]experimental tests[/i] of relativity?

[Mentors' note: Both this summary and the thread title have been edited to clarify that the question is about the physical clocks used in actual experiments - see post #28]

Recently, in this forum, highly respected members referred to clocks like pendulum and hourglass as if they are relevant for relativity. Are they really? Besides the lack of accuracy, they depend on acceleration/gravity, so they would not work at all in inertial frames and they could not indicate properly gravitational time dilation neither. So why even bother mentioning them when asked about clocks in discussions about relativity?

[Mentors’ note: this post has been edited to remove some off-topic provocation]

 

[Nugatory]

“Usable for experimental tests of relativity” and “relevant for relativity” are different things. There are practical reasons why we don’t use hourglasses or pendulum clocks in our labs, but an analysis of their limitations is quite relevant to understand the distinction between proper time and pre-relativity notions of time.

 

[Ibix]

they could not indicate properly gravitational time dilation neither.

Of course they can. They may need to be recalibrated at different gravitational field strengths, but that's fine. The one higher up, correctly calibrated, will tick faster than the one lower down. And even in free fall you can always put one in a centrifuge, although you'd have to recalibrate again.

More fundamentally, there isn't really any problem in principle with making a more precise pendulum clock (use magnetic bearings in a vacuum, control temperature, etc) - it's just much easier to do with atomic clocks and the forthcoming nuclear clocks. So any type of clock is relevant to relativity, assuming you have conditions under which it will work and you've taken sufficient care around design. Otherwise, either (a) your device is not a clock (that is, relativity is right and your understanding of how your device operates is flawed and you are wrong to call it a clock) or (b) relativity (and science in general) is wrong to claim that there is a meaningful concept of time.

 

[anuttarasammyak]

Clocks have progressed recently to measure tiny time. Atomic clocks, for an example, can show SR and GR effects.

 

[Ibix]

Just to add: the Twin Paradox thought experiment routinely uses the visible signs of human aging as a clock. That's incredibly crude technologically and wildly imprecise for many purposes (far more so than a pendulum clock), but definitely relevant.

 

[DanMP]

Of course they can. They may need to be recalibrated at different gravitational field strengths, but that's fine. The one higher up, correctly calibrated, will tick faster than the one lower down. And even in free fall you can always put one in a centrifuge, although you'd have to recalibrate again.

How is this recalibration performed? It can be done without using a non gravitational clock? If you use one, why bother mentioning these gravitational clocks in discussions about relativity?

So, we have atomic clocks, human ageing, etc., highly dependent on electromagnetism. Are there relevant clocks for relativity which are not depending on electromagnetism in order to work?

 

[russ_watters]

How is this recalibration performed? It can be done without using a non gravitational clock? If you use one, why bother mentioning these gravitational clocks in discussions about relativity?

So, we have atomic clocks, human ageing, etc., highly dependent on electromagnetism. Are there relevant clocks for relativity which are not depending on electromagnetism in order to work?

You asked for examples and were given examples and now you're complaining about the examples. Maybe your starship has a science museum and the curator thought it would be cool to have a relativistic pendulum clock, and they never calibrate it. Who cares? What's the point of this? Mod note: it needs to get a point rapidly.

 

[Ibix]

How is this recalibration performed?

Fire a bullet horizontally from a standard gun a standard height above the floor. The distance it travels before hitting the floor gives you $g$ and the pendulum clock's period is $2\pi\sqrt{l/g}$.

why bother mention these gravitational clocks in discussions about relativity?

Because relativity claims that time is a measurable thing. If a device cannot even in principle measure it then it is not a clock; conversely, claims made about "clocks" must be true of all types of clock including crude ones, or else they are only claims about some types of clock.

Are there relevant clocks for relativity which are not depending on electromagnetism in order to work?

The thorium clocks currently in development. Radioactive decay is also usable, the physics of which depend on the strong and weak forces. Planetary motion depends on gravity.

 

[vanhees71]

Well, the thorium "nuclear clock" is also based on an electromagnetic transition, but one of the nucleus rather than the atom, which makes it just more robust against external influences than atomic clocks.

One should also be aware that time is not an observable in contemporary physics but just a parameter, and it's always somehow indirectly measured through some observables. In the case of atomic (or perhaps soon nuclear) clocks the frequency of the em. waves emitted due to transitions between quantum states of the atom (or nucleus) is used.

You can of course use any other device for more or less measuring time. A purely mechanical one is a pendulum, moving in the gravitational field of the Earth (or for the purist geometrodynamics afficionados the space-time curvature due to the presence of the Earth) or the motion of the Earth around the Sun and/or its rotation around its axis etc.

 

[DrClaude]

So, we have atomic clocks, human ageing, etc., highly dependent on electromagnetism. Are there relevant clocks for relativity which are not depending on electromagnetism in order to work?

How about a wind-up watch?

 

[Ibix]

Well, the thorium "nuclear clock" is also based on an electromagnetic transition, but one of the nucleus rather than the atom,

But the available energy levels and hence the frequency depend on the strong force, right? If so, I guess whether it should be on my list depends on what OP means by "not depending on electromagnetism in order to work".

 

[russ_watters]

Note that there are several direct applications of radioactive decay for timekeeping in archeology/geology.

 

[Nugatory]

How about a wind-up watch?

Beat me to it - these rely on the natural frequency of a balance wheel driven by a spring.

Another example would be dating by radioactive decay, and indeed we sometimes see the twin paradox described by comparing the amount of decay in two identical samples of radioactive material, one on the spaceship and one staying at home.

 

[FactChecker]

TL;DR Summary: What clocks can be considered relevant for relativity?

Recently, in this forum, highly respected members referred to clocks like pendulum and hourglass as if they are relevant for relativity. Are they really? Besides the lack of accuracy, they depend on acceleration/gravity, so they would not work at all in inertial frames and they could not indicate properly gravitational time dilation neither. So why even bother mentioning them when asked about clocks in discussions about relativity?

[Mentors’ note: this post has been edited to remove some off-topic provocation]

Everything that you mention reflects the relativistic effects on time and distance. It might be tough to use them as simple clocks, but any physical process that is affected by time and distance is "relevant".
In most discussions of relativity, a "clock" is just a conceptual, theoretical, physical measurement of elapsed time. The details of real clocks are of interest to experimenters, but they use far more sophisticated clocks than pendulums and hourglasses.

 

[Vanadium 50]

This seems a lot like the recently closed thread.

The problem with a pendulum clock was explained in the closed thread. It doesn't measure time at a point, but it measured it over the sweep of the pendulum. If this matters, well, then it matters.

When you sweep this away (get it? sweep?) it is not clear what the point or this thread is.

As a PS, the "nuclear clock" is essentially electromagnetic - it gives you a very narrow linewidth in the VUV. It's also a long ways away. Lots to do before you can pick one up at Wal-mart. A clock based on radioactive decay, as mentioned above, is not electromagnetic.

 

[Dale]

TL;DR Summary: What clocks can be considered relevant for relativity?

clocks like pendulum and hourglass as if they are relevant for relativity. Are they really?

Do you think relativity cannot explain or handle hourglasses or pendulum clocks?

Besides, as @russ_watters mentioned, you specifically asked for those examples.

 

[PeterDonis]

they would not work at all in inertial frames

More precisely, in free fall, yes.

they could not indicate properly gravitational time dilation neither.

Wrong. Gravitational time dilation involves accelerated clocks, not freely falling clocks.

 

[ersmith]

More precisely, in free fall, yes.Wrong. Gravitational time dilation involves accelerated clocks, not freely falling clocks.

A small nit: I believe gravitational time dilation applies to free falling clocks both in theory (in the time coordinate in the Schwarzschild metric) and in practice (e.g. the GPS clocks are in orbit, hence in free fall, and the GR correction for them is based on their altitude).

 

[PeterDonis]

I believe gravitational time dilation applies to free falling clocks

It is possible to attribute part of the "rate of time flow" of freely falling clocks to gravitational time dilation, but the way that is done involves calculating what the "rate of time flow" would be for an accelerated clock that was hovering at rest at the same altitude. So if we want to measure gravitational time dilation by itself, without other extraneous factors, we need to use accelerated clocks.

 

[PeterDonis]

the GPS clocks are in orbit, hence in free fall, and the GR correction for them is based on their altitude

The GPS correction for the orbiting clocks includes both a gravitational correction for altitude and a speed correction for their orbital velocity. (Also, the correction is to the "rate of time flow" of a clock at rest on the rotating Earth's geoid, which involves additional complexities.)

 

[PeterDonis]

the time coordinate in the Schwarzschild metric

The Schwarzschild time coordinate (in standard Schwarzschild coordinates) reflects the "rate of time flow" of a clock at rest at infinity. From the time coordinate alone you cannot tell anything about gravitational time dilation.

 

[Ibix]

A small nit: I believe gravitational time dilation applies to free falling clocks both in theory (in the time coordinate in the Schwarzschild metric) and in practice (e.g. the GPS clocks are in orbit, hence in free fall, and the GR correction for them is based on their altitude).

As Peter says, this is not quite correct. Consider that I'm at the base of a mountain on the Moon. There is a clock on the top of the mountain, another in a rocket flying in circles around the peak and a third in orbit at the peak's height (the atmosphere would interfere with that last on Earth, which is why I'm setting this on the Moon). All three clocks are at the same height above me, but all three will show different clock rates. If there's a meaningful concept called "gravitational time dilation" then it can't lead to three clocks at the same height having different rates. So which (if any) is gravitationally time dilated?

The only sensible answer to this turns out to be the one sitting on the mountaintop, hovering st constant altitude. There's formal maths backing this up, but loosely speaking such clocks see their natural definition of time such that "space" doesn't change with "time". Other observers see the gravitational field changing over time in one sense or another - so gravitational time dilation is the effect on hovering observers (which is why pendulum clocks work for this).

The effect on other clocks, the ones in orbit and flying around, doesn't really have a name (unless it's just time dilation). It can be broken down into an effect due to gravitational time dilation and a separate one due to speed relative to hovering observers at the same altitude, though, which is probably what you've heard of.

 

[ersmith]

@Ibix and @PeterDonis thank you for the clarifications. I still maintain that it would be more accurate to say that gravitational time dilation is proportional to the gravitational potential ($\frac{GM}{r}$) rather than gravitational acceleration ($\frac{GM}{r^2}$ in the weak field limit) and that it's somewhat misleading to say that a clock in free fall is subject to no gravitational time dilation. But I suppose ultimately that's a matter of nomenclature and pedagogy rather than physics. Perhaps we should continue this discussion in a new thread rather than derailing this one any further.

 

[PeterDonis]

I still maintain that it would be more accurate to say that gravitational time dilation is proportional to the gravitational potential ($\frac{GM}{r}$) rather than gravitational acceleration ($\frac{GM}{r^2}$ in the weak field limit)

Who said otherwise?

it's somewhat misleading to say that a clock in free fall is subject to no gravitational time dilation.

Nobody here has claimed that, so you are attacking a straw man.

I think you need to read the responses from myself and @Ibix more carefully.

 

[PeterDonis]

Perhaps we should continue this discussion in a new thread

If you want to go into more detail, yes, let me know and I can move your posts and their responses to a new thread.

 

[Ibix]

I still maintain that it would be more accurate to say that gravitational time dilation is proportional to the gravitational potential ($\frac{GM}{r}$) rather than gravitational acceleration ($\frac{GM}{r^2}$ in the weak field limit)

I don't think I did say that - I certainly did not intend to do so and I agree that would be an error. The need for acceleration is entirely to do with the OP's desire to use a pendulum clock, whose calibration depends on $g$.

somewhat misleading to say that a clock in free fall is subject to no gravitational time dilation.

I don't think we said that either: again the OP is talking about clocks that do depend on a non-zero acceleration, and seems to think this stops them from being used to measure gravitational time dilation. I think you are reading counterarguments to the OP's claims in a more general context than we are writing them.

 

[ersmith]

If you want to go into more detail, yes, let me know and I can move your posts and their responses to a new thread.

There's no need -- it's clear that we're in violent agreement on the math, and have at most a minor quibble about the exact words used to describe the math.

Bringing this back to the OP, I think anyone who knows general relativity would agree that the math is crystal clear: it doesn't matter what kind of clock you use, GR predicts that they will all tick at the same rate when in the same environment (so long as they're able to function properly in that environment, of course). I suppose the OP is concerned that this needs a specific experiment to verify it, but given the tremendous weight of experimental evidence in favor of general relativity, the default assumption has to be that GR is correct in this prediction as it has been in every other prediction that we've been able to test.

 

[DanMP]

Hi everyone, and thank you for answering here. Unfortunately I am very busy, so I cannot write much today. Maybe later in the week, or next week. Until then I need to clarify something:

When, in the OP, I wrote:

TL;DR Summary: What clocks can be considered relevant for relativity?

I meant clocks as manmade devices, not some abstractions. (Such a clock, in my opinion, must have at least the following parts: one for generating events, one for counting the events and one for displaying the results.)

And the clocks relevant for relativity I'm asking for are the clocks actually and successfully used in experiments of interest for relativity, like the Hafele-Keating experiment or the determination of the speed of light, clocks suitable for GPS satellites, for instance. This means that the clocks must be accurate enough and also able to work without alterations in various conditions (you cannot continuously recalibrate the pendulum in the H-K experiment).

Having that in mind I wrote that a pendulum is not relevant for relativity.

I'll be back with more clarifications and answers.

 

[russ_watters]

And the clocks relevant for relativity I'm asking for are the clocks actually and successfully used in experiments of interest for relativity, like the Hafele-Keating experiment or the determination of the speed of light, clocks suitable for GPS satellites, for instance. This means that the clocks must be accurate enough and also able to work without alterations in various conditions (you cannot continuously recalibrate the pendulum in the H-K experiment).

Having that in mind I wrote that a pendulum is not relevant for relativity.

I think you already know the answer here. Pendulum clocks have not been used in a relativity experiment, only much more precise clocks have(various atomic clocks)*. So what? What is your point?

*I'd argue that radioactive muons count, but you'd probably say they don't. Either way, my question stands.

 

[Vanadium 50]

So I can use a muon beam I make myself but not one from cosmic rays? A gear of aluminum or brass is OK because I have to refine or allow it, but not iron because one can just find it in the ground?