Can we really ever accurately test SR time dilation?

1. May 29, 2013

DiracPool

The two most famous "tests" for the accuracy of time dilation in SR are 1) the plane that flew around the globe with the atomic clock, and 2) the muon experiments on the mountain. I'm assuming, of course, that all the experimental controls are correct and so are the results. My question is how do we rule out the effects of acceleration in testing a pure SR Lorentz contraction model? The plane flying around the globe obviously experiences centripetal acceleration among others, and the muons decelerate when they travel through the atmosphere (don't they?)

This problem also relates to the twin paradox, where many explanations use the "turn around" acceleration to control for the anomalies of "who is receding from whom," etc.

Obviously, the best thing to do would be to test the twins' age differences when the traveling twin reached the distant planet and before it made any accelerating turn around. But can that be done, even in principle, through some sort of clock synchronization? How can time dilation be tested reliably in truly SR non-accelerating frames?

2. May 29, 2013

VantagePoint72

Special relativity is perfectly capable of handling accelerated motion, and this was taken into account with experimental tests of time dilation such as Hafele-Keating. The popular notion that SR is somehow unable to handle accelerated reference frames is wrong.

3. May 29, 2013

DiracPool

Thanks, but my question wasn't whether or not SR could handle accelerations, it was could we test time dilation without the consideration of acceleration. The Lorentz contractions model that time dilation occurs in systems of non-accelerated reference frames. Is there a reliable way we can test that?

4. May 29, 2013

VantagePoint72

Then I don't understand your question. Why should we need to test it without acceleration? The overall prediction for time dilation that will occur during an accelerated trip is obtained by breaking the motion up into infinitesimal inertial segments and using the inertial time dilation formula. It's the exact same formula being tested, just applied to curved worldlines.

5. May 29, 2013

pervect

Staff Emeritus
MTW mentions that neutrons in a nucleus are accelerating at about 10^29 m/s^2, that even greater accelerations occur in scattering experiments, and that no effects due to these accelerations have been noticed - that SR seems to handle such situations just fine.

The text didn't give more details, i.e. what might one measure exactly to compare between a neutron/proton in a nucleus and a free one to look for acceleration effects. I'd expect that proton spin (nuclear magnetic resonance) would be affected if there was some sort of "acceleration effect".

One obvious difficulty is that you need some theory that predicts acceleratio to have an effect in the first place to compare to SR which predicts no effect. Offhand, I don't know of any such test theory (but I can't say I've looked for one, either).

6. May 29, 2013

Staff: Mentor

When I was a graduate student, one of my friends worked on an experiment that studied beams of short-lived hyperons (sigmas and xis, I think), produced at Fermilab using collisions of protons in a "production target". The design of the beamline and apparatus depended critically on the time-dilated lifetimes of the particles. If there were no time dilation, the particles would not even have reached the detector! As far as I recall, the beams were straight-line between the production target and the detector: no centripetal acceleration.

7. May 29, 2013

ghwellsjr

Contraction applies to length, not to time. Did you really mean this?
SR Time Dilation is not observable or measurable and cannot be tested, just like the one way speed of light cannot be tested. All we can do, or rather all we need to do is show that it is consistent with other things that can be measured and observed.

So when you ask about the "best thing to do", you seem to realize that it will require a different kind of clock synchronization than what is available to us now and you are correct. Einstein made it clear that we cannot determine synchronization of remotely located clocks without defining (not measuring or observing) their synchronization and he does that by defining the one way speed of light. The rest is just mathematics.

If you understand that SR Time Dilation is a mathematical calculation of the ratio of the progress of Coordinate Time to the progress of Proper Time on a moving clock in a particular Inertial Reference Frame (IRF) and that it is mathematically different in another IRF as determined by the Lorentz Transformation process, then I think you will come to grips with the fact that it is non-observable and non-testable but consistent with anything that can be observable and measurable.

8. May 29, 2013

Staff: Mentor

There are many acceleration-free tests of SR time dilation. See here: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Tests_of_time_dilation

The seminal test was the Ives and Stillwell test where they measured the relativistic Doppler (classical Doppler w/ time dilation) on particles moving inertially in the lab. There are other tests which measure only the transverse Doppler so it is purely time dilation.

However, for me a more convincing experiment is to go the other way and subject the particles to incredibly high accelerations and detect if there is any additional effect due to the acceleration beyond the speed. That has also been done, e.g. by Bailey et al. for accelerations up to ~10^18 g. Since they detected no additional acceleration effects at such high accelerations you would not expect the acceleration to affect the results on any of the other experiments either.

9. May 29, 2013

Staff: Mentor

I disagree with this. The one way speed of light depends on your synchronization convention, but the transverse Doppler effect (which is entirely time dilation) does not.

10. May 29, 2013

VantagePoint72

No, I think George is right. I'm not entirely sure where the simultaneity convention sneaks its way into this example, but it must be do somewhere: you can completely eliminate time dilation between any two particular frames with an especially perverse choice of simultaneity convention. Winnie does this in one of his famous 1970 papers ("Special Relativity Without One-Way Velocity Assumptions").

11. May 29, 2013

Staff: Mentor

In transverse Doppler there is only a single clock (no synchronization) and it is a direct measurement of time dilation. Furthermore, even the non-transverse Doppler shows time dilation and requires only a single clock.

Time dilation and relativity of simultaneity are independent features of the Lorentz transform. You can have one without the other, so I wouldn't assume that the measurements are inextricably linked. I just don't see how they would be linked.

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12. May 29, 2013

VantagePoint72

There is only one clock at the receiver itself; however, interpreting the transverse relativistic Doppler effect as purely a time dilation effect is equivalent to assuming standard synchrony between the different points along the emitter's worldline.

Again, I refer you to the Winnie papers. It's possible to choose a simultaneity convention such that there is no time dilation between the emitter and receiver frames. With such a choice, the relativistic Doppler effect (which, like differential aging, is an invariant) would be attributed entirely to the relativity of simultaneity. Conversely, with the standard synchrony convention one would (as you are) attribute the transverse relativistic Doppler effect entirely to time dilation. Since which it is ultimately depends on your choice of convention, it is not meaningful to say that the transverse Doppler effect is a direct test of time dilation.

13. May 29, 2013

ghwellsjr

Simultaneity sneaks its way in when you define "at the point of closest approach" which is frame dependent.

Keep in mind, I've stated the definition of Time Dilation being the ratio of Coordinate Time to Proper Time. If some other definition is used, it needs to be stated.

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14. May 29, 2013

Staff: Mentor

Hmm, I have to think about this. I am not at all convinced, but it is worth looking into deeper.

15. May 29, 2013

PAllen

This is interesting. One way of observing transverse Doppler has no clock and no synchronization and one reference frame:

Have an emitter of known type (e.g. an LED laser) move along a barrier with an opening, and a detector placed on a line perpendicular to the barrier from the opening. It detects redshift. It seems it would take a very perverse interpretation to call this other than time dilation: LED running slow moving past the opening.

16. May 29, 2013

VantagePoint72

This, again, requires standard synchrony between the various points along the laser's path. There is no avoiding that fact. Perhaps it will help if I give a more specific citation: Winnie's first paper is here; see the section "4. Time dilation and the choice of $\epsilon$". Indeed, I referred to the required simultaneity convention as "perverse" in post #10. Nonetheless, it is a permissible convention in SR.

Relativity of simultaneity and time dilation are not independent effects in the Lorentz transformations. By fiddling around with your choice of the one-way speed of light, you can change the magnitude of one effect at the expense of the other (between two particular frames). If it were possible to measure time dilation (a coordinate effect) with no further assumptions, it would be equivalent to a direct measurement of the one-way speed of light due to Winnie's equation 4-7.

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17. May 29, 2013

PAllen

I am well aware of the conventionality of simultaneity (I've read other papers with similar parametrization of simultaneity)[edit: and I definitely agree with the conventionality of simultaneity]. But I don't understand how it applies to this scenario. We have nothing but an apparatus at rest and a moving emitter. The fixed geometry of the apparatus defines 'transverse'. As a measurement, the result is invariant. What I am looking for, be comfortable with the point of view you espouse, is any plausible way to interpret this experiment as other than detecting time dilation in the frame of the apparatus. Would you have to say that simultaneity convention determines what is perpendicular in a rigid apparatus at rest?? If that is the resolution, I find that too perverse to take seriously. Maybe there is another way ...?

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18. May 29, 2013

VantagePoint72

And hence the apparatus at rest must establish a synchrony convention for the different points along the emitter's path. Consider a derivation of the relativistic Doppler effect where individual pulses of light are being emitted at regular intervals. Since the clock is in motion, successive pulses are emitted at different places according to the receiver's frame. You can make the separation between the two places arbitrarily small—and even take a limit if you wish—but they are still at different places, even if infinitesimally so. Hence, in the receiver's frame the period by which the emitter sends out its pulses requires a comparison of two different clocks along emitter's path.

Of course, there is no ambiguity about the period at which the receiver receives the pulses. Maybe this is the confusion. That is the relativistic Doppler effect and is convention-free. However, for you to equate the period at which the pulses are received with the period at which they are emitted (in the receiver's frame) requires standard synchrony along the emitter's path—at least, in the neighbourhood of the point which you are considering.

In Winnie's equation 4-8, you can see that a judicious choice of $\epsilon$ eliminates the time dilation factor altogether between two particularly chosen frames. So, how can it not be relevant here? We only have two frames (the receiver and the emitter) and you can see that you can choose a simultaneity convention such that the receiver's frame does not contain a time dilation term for the emitter's frame. So, how could time dilation be measured directly if it's been eliminated by a coordinate transformation??

I agree it's very intuitive to make the assignment that the "period measured by receiver" and the "period of the emitter in the receiver's frame"—and the isotropy of the one-way speed of light is intuitive too!—but it is not a required assignment in SR, for the exact same reason as the one-way speed of light.

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19. May 29, 2013

VantagePoint72

Yes, that is precisely what you have to say, and there is no other way. Consider how you determine what is perpendicular: if I draw a straight line $L$ and some point $P$off the line, the line $M$ that is through $P$ and perpendicular to $L$ is the one such that given two points, $A$ and $B$, equidistant along $L$ on either side of the intersection of $L$ and $M$, the distances $AP$ and $BP$ are the same. But for the moving emitter, "distance" requires a simultaneity convention to pick the spatial slice you are measuring in! It is precisely the usual Einstein convention for synchrony that allows you to do this in the way you are thinking. If you find the conclusion "too perverse to take seriously", then you are forced to reject the conventionality of simultaneity too. It is the same assumption.

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20. May 29, 2013

Staff: Mentor

I am with PAllen on this one. A simultaneity convention does not change the geometry of an object at rest. A simultaneity convention merely determines which events along a given pair of worldlines are considered simultaneous. If all of the events on a worldline occur at the same spatial location then re-mapping the simultaneity convention does nothing to the geometry.

The geometry of an apparatus at rest is not a function of the choice of simultaneity convention. A Doppler measurement can be constrained to be transverse through an apparatus at rest in the lab. The resulting measurement measures time dilation regardless of the simultaneity convention.