# Has a real clock corrections, with respect to an ideal clock?

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1. Oct 26, 2014

### ORF

Hello

In Special (and General) Relativity, has a physical (real) clock corrections, with respect to an ideal (mathematical) clock? For example, the physical clock has mass, so it will affect its own measure. This is only an example I thought, I don't know if there are more corrections (depending on how the clock works).

If this question is already answered in this forum, just tell me, and I will delete this thread.

Thank you for your time :)

Greetings
PS: My mother language is not English, so I'll be glad if you correct any mistake.

2. Oct 26, 2014

### ghwellsjr

When discussing thought problems in relativity, we assume that the clocks measure time perfectly. For example, when explaining Special Relativity, we talk about two clocks in relative motion approaching the speed of light and accelerating instantly while totally ignoring the influence of gravity. These experiments cannot actually be done for a multitude of reasons. The accuracy of a physical clock is the least of our problems.

But experiments have been done with physical clocks in which their accuracy is good enough to demonstrate that the Lorentz Transformation is the correct understanding of the way physics works and that the Galilean Transformation is not.

3. Oct 26, 2014

### harrylin

Welcome to Physicsforums :)

If I understand you correctly then the answer is yes - but it depends a bit on how you say it, and some details can make a difference.
Suppose that you have two identical clocks in identical conditions except for one thing: one clock has a massive lead bottom. That clock will tick very slightly slower according to general relativity.

Similarly, suppose that you have two identical clocks in identical conditions, except for the design speed with which the balance wheel turns: with a different gear ratio it is made to turn exactly 10 times faster according to classical mathematics. In reality it should then turn very slightly less than 10 times faster according to special relativity.

However, I think that in practice the effects of these examples are too small to measure with mechanical clocks.

4. Oct 26, 2014

### ORF

Hello

Thank you both, for your quickly answer and for the warm welcome.

I suppose that for some problems, the accuracy is truly important; maybe in geoposition, satellite (and spacial waste) movements.

@harrylin: thank you for your graphical examples; I think they clear the question very well. I also think the order of magnitude of the corrections in mechanical clocks will be very small. However, it's said that some atomic clocks are expected to neither gain nor lose a second in more than several hundreds million years. I don't know how they compute the uncertainty, but I thought that it would be possible measure the own clock's effects with this accuracy*.

In the opposite point in the size scale, would the mass have a measurable contribution in the frequency of pulsars as relativistic correction?

Maybe exist more cases where we can find the same idea, but now I can not imagine more. If another example comes to my mind, I will post here. I'll be glad if anyone else thinks in another example.

Greetings.
*or trueness; I don't know the subtle difference between them.

5. Oct 26, 2014

### Staff: Mentor

No, it isn't. The clocks are very accurate, yes, but they are also very small in terms of their gravitational effect--far too small for that effect to be measurable even with the accuracy of the clocks.

No, because the frequency you are talking about is not frequency of light (or other radiation) emitted by the pulsars (which will indeed be redshifted significantly by the pulsars' gravity). It's the frequency of the pulsars' rotation and orbital motion as we observe them. The only way the mass of the pulsars would affect those observations would be if we were deep inside the pulsars's gravity well (for example, if we were riding on the surface of one of them).

6. Oct 26, 2014

### WannabeNewton

We commonly make the assumption that given an arbitrarily accelerating observer, at any given event on said observer's worldline the observer's rest frame is equivalent to an instantaneously comoving (local) inertial frame which takes for granted that accelerating clocks are equivalent at any given instant to a momentarily comoving inertial clock. In reality of course this is not true since an accelerating clock undergoes stresses of various kinds causing it to deviate operationally from an ideal (inertial) clock. If the characteristic scales of the system are such that these stresses are negligible then this assumption is valid to great accuracy but the point is there will be corrections due to acceleration/tidal stresses on the accelerating clock causing deviation from the momentarily comoving inertial clock.

In principle these deviations can affect standard SR formulas such as time dilation. See e.g. https://www.physicsforums.com/threads/radar-distance-rindler-observer.730009/#post-4619764 and https://www.physicsforums.com/threads/spring-with-2-masses-free-fall.731181/#post-4620023

7. Oct 27, 2014

### harrylin

I fully agree. Moreover atomic clocks don't have a balance wheel, so that my example is not applicable.
I also concur with that answer, but for a different reason. I'm pretty sure that astronomers can't calculate how fast a particular pulsar is expected to rotate according to classical mechanics vs. relativity (or, surely, not with enough accuracy; compare https://en.wikipedia.org/wiki/Pulsar#Formation).

8. Oct 27, 2014

### Staff: Mentor

I think it's even more basic than that: we can't observe directly the parameters that would determine the rotation rate (some of them are aspects of how the pulsar was formed, so they aren't even observable at all today). So when we observe a given rotation rate, we could construct both a classical (Newtonian) model consistent with that rate, and a relativistic model consistent with that rate; the two models would have somewhat different parameter values, but we have no way of checking the parameter values to see which model fits the data.

However, the OP was not asking how pulsars confirm a relativistic (as opposed to Newtonian) model; he was assuming that the relativistic model is correct (which is what virtually all physicists in the field do), and asking about its consequences. My answer was based on the same assumption.

9. Oct 27, 2014

### harrylin

Indeed, my answer was based on that same assumption, that he wants to know the relativistic corrections. :)

10. Oct 27, 2014

### ghwellsjr

What is the difference between the relativistic corrections for a physical (real) clock and an ideal (mathematical) clock?

I got the impression that he is thinking that Time Dilation is the deviation of a physical clock from the "trueness" (as he mentioned in post #4) of an ideal clock and therefore needs a correction. A mass in the vicinity of a real clock (whether part of the clock or not) causes it to tick at a different rate than if the mass were not there, but this would be the same for an ideal clock because time is progressing differently in the vicinity of a mass.

11. Oct 27, 2014

### Staff: Mentor

Relativistic corrections to "rate of time flow" without any consideration of the particular dynamics of a system (such as a pulsar). Not relativistic corrections to a classical model of the internal dynamics of pulsars. At least, that's how I'm interpreting the OP--he's welcome to clarify if I'm wrong.

12. Oct 27, 2014

### harrylin

I understood relativistic corrections to the frequency of clocks, starting from a calculation without those corrections - like the GR correction to the perihelion of Mercury. Indeed, it will be good if he clarifies what he is looking for exactly. :)

13. Oct 27, 2014

### harrylin

"trueness" was there used as synonym for "accuracy"; that's a different issue. also, I don't linger on "ideal" as that's personal as well as topic related. What he asked about concerns "a measurable contribution in the frequency of pulsars as relativistic correction", in the sense of how (in the first post) "it will affect its own measure". For me that's a clear question; let's see if I understood him correctly. :)

Last edited: Oct 27, 2014
14. Oct 28, 2014

### ORF

Hello

Sorry for the delay, I broke my little toe yesterday and I spent the day in the hospital.

*-Thank you for answering; I didn't expect so many people here :)

*-Yes, I assume the GR is tested enough.

*-I used the word [relativistic] "corrections", but maybe it's an error of translation; other expressions, as "mass factors" or "mass contributions" (with respect to SR, or even to classical mechanics), might sound better.

You're right, my fault.

Yes; I thought the question should be about the simplest case.

@ghwellsjr, @PeterDonis: maybe the first question wasn't enough clear (sorry for that). I will try to remake it:

-has a real clock a "rate of time flow" different from a mathematical/ideal clock?*
-If the answer is yes, what is the order of magnitude of this difference? (and, what can be the origin of the difference? I supposed the GR)

I read that some pulsars are more precise than atomic clocks, and because of that, I used the idea in the example. I'm not an astronomer (and I've never met any), so if the next sentence sounds stupid, please just overlook it: I've heard the pulsars lose their kinetic energy by radiation, so, is it possible to compare the rate of radiation and the rate of frequency, and use them as a way to check the theories? (classical mechanics, SR and GR)

@harrylin: mmm... I had not thought about the trueness (accuracy) of the astronomers' measurements, good remark :)

On the other hand, I think GR affects atomic clocks too, although they works at quantum levels (Wu et al made an experiment with quantum interference, testing successfully the GR). My doubt is the order of magnitude of the difference between an ideal clock (the clock which measure the "time" in the mathematical expressions of SR and GR), and the atomic clock of 2 lb which is in a lab :)

Yes, yes, thank you very much :) :)

Sorry for such a long statement; I tried to sum it up. And again, please, forgive my grammar errors, and I'll be glad if you correct any mistake.

Greetings.
*Maybe I should make a clarification: I refer to an ideal clock as a clock which measure the parameter "time" that appears in the equations; and to a real clock as a clock which is used in the real life.
PS: I thought the words accuracy, trueness and precision have the meaning which is explained here:
http://en.wikipedia.org/wiki/Accuracy_and_precision#Terminology_of_ISO_5725

15. Oct 29, 2014

### ghwellsjr

16. Oct 29, 2014

### harrylin

Thanks for your clarification of "ideal"! The mass of a clock is included in those mathematical expressions, and to my knowledge no deviation from theory has been observed. However, real atomic clock frequency can also depend on temperature for example. You may like the discussion by clock experts here: http://www.nist.gov/pml/div688/2013_1_17_newera_atomicclocks.cfm

17. Oct 29, 2014

### ghwellsjr

Let's not confuse the issue. At the atomic level, temperature is motion. If the atoms are moving with respect to the lab frame, then they are experiencing Time Dilation and so they are properly displaying a different time than that the lab rest frame. That is the reason it is important to get their temperature as low as possible which simply means that you want to reduce the relative motions between all the atoms in the cloud.

18. Oct 29, 2014

### ORF

Hello

@ghwellsjr: I insisted because it seemed to me that your answer wasn't complete enough. The question is just out of curiosity. :)

@harrylin: thank you for your interest. Yes, the NIST discussion is a good starting point.

Best regards.
PS: I thought that (in statistical mechanics) temperature is not just "atomic motion" :)

19. Oct 29, 2014

### harrylin

The NIST article that I linked to mentions a number of influences on time keeping, including temperature and magnetic fields. Anyway, you suggest that the main effect of temperature on real cesium clocks is due to time dilation - good thinking!
However, NIST appears to disagree with you: "cooling dramatically lowers the background radiation and thus reduces some of the very small measurement errors" - http://www.nist.gov/pml/div688/nist-f2-atomic-clock-040314.cfm

20. Oct 29, 2014

### ghwellsjr

Is my last answer complete enough?

We're talking about a cloud of many thousand cesium atoms in a "gaseous" state in an otherwise evacuated chamber except that unlike normal gases which would randomly fill the chamber and bounce off the walls and each other due to thermal excitations (which is what their random motions are), these atoms are constrained by laser beams shining on them from different directions to hopefully bring them to a stop within the overlap of the beams which is what forms the cloud.

21. Oct 29, 2014

### ghwellsjr

There's no disagreement. You can't get the atoms in the cloud to stop moving when they are bombarded by random thermal radiation from the walls of the chamber. They don't have to touch the walls to be excited by the radiation emitted by the walls even if it is at a very low temperature.

22. Oct 31, 2014

### harrylin

Maybe yes; in any case, you identified one more possible correction of a real clock due to a relativistic effect "on itself". :)

I imagined that peaks in the microwave background can directly affect the observed apparent resonance frequency. That as well as relativistic frequency reduction could be part of the suggested causes for corrections due to the microwave background radiation.

Out of curiosity I dug a little deeper in the literature about cesium clocks to see what is said about this. To my surprise, several papers mention inaccuracy due to first order Doppler shift! Thus, depending on the configuration, even ordinary Doppler can significantly affect the measured frequency which serves as time reference in a real atomic clock.

And of course NIST mentions still other causes for corrections in the link I gave. Moreover, a real clock has issues with instabilities ("noise") so that regular calibrations remain required.

23. Nov 2, 2014

### ghwellsjr

The specific transition frequency of an individual cesium atom is exact, trying to exploit that frequency in a real atomic clock is a challenge.

There's no resonant frequency in a cesium atom or in an atomic cesium clock. It's based on the transition frequency of the atom. When you have a cloud of cesium atoms, it's the combined effect of all of them being excited at different times and if they are not all at rest with respect to each other, there can be a spread in the observed transition frequency.

What is "relativistic frequency reduction"? If you are thinking that it is only a one-way shift caused by Time Dilation and therefore can be calculated out, keep in mind that there will be a Doppler shift in both directions depending on the relative speeds of each atom and the detector. The thermal noise increases the spread of the observed frequency. You have to reduce the temperature of the whole apparatus to eliminate the problem. That's the whole point of the second-generation of atomic cesium clocks.

After a stable cloud of cesium atoms is formed in an atomic clock on earth, the cloud is launched in an upward direction in an evacuated tube to allow the cloud to be in free fall while it is going up and back down the tube. This is why it is called a fountain clock. It's during this time that the transition frequency is being measured and of course, in the frame of the lab, it is in motion so there will be a first order Doppler shift but this can be calculated out since the speed profile of the cloud is known.

Is the real clock you are referring to here the atomic cesium clock or the other clocks that are calibrated against the atomic cesium clock? Keep in mind, that for purposes of establishing UTC, the second that we get from the atomic cesium clock is not the same duration as the second of UTC.

24. Nov 2, 2014

### Staff: Mentor

It's supposed to be, isn't it? The cesium transition defines the SI second, and the SI second is the UTC second. Are you just referring to the measurement inaccuracies, or something else?

25. Nov 2, 2014

### ghwellsjr

The second is different at different elevations. An atomic clock at Greenwich, England near sea level ticks at a different rate than one at Boulder, Colorado at about a mile elevation and neither one ticks at the UTC rate.