Can we really ever accurately test SR time dilation?

[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?

 

[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.

 

[DiracPool]

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.

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?

 

[VantagePoint72]

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?

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.

 

[pervect]

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).

 

[jtbell]

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.

 

[ghwellsjr]

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?

Contraction applies to length, not to time. Did you really mean this?

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?

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.

 

[Dale]

My question is how do we rule out the effects of acceleration in testing a pure SR Lorentz contraction model?

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.

 

[Dale]

SR Time Dilation is not observable or measurable and cannot be tested, just like the one way speed of light cannot be tested.

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.

 

[VantagePoint72]

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.

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").

 

[Dale]

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").

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.

 

[VantagePoint72]

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.

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.

 

[ghwellsjr]

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").

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.

 

[Dale]

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

 

[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.

 

[VantagePoint72]

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.

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 http://www.jstor.org/stable/186029; 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.

 

[PAllen]

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 http://www.jstor.org/stable/186029; 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.

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 ...?

 

[VantagePoint72]

I am well aware of the conventionality of simultaneity (I've read other papers with similar parametrization 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.

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.

 

[VantagePoint72]

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 ...?

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.

 

[Dale]

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.

 

[Dale]

Basically, regardless of coordinates or simultaneity convention, there is a predicted Doppler shift. If time dilation does not occur then that Doppler shift has one value (given by the conventional Doppler formula). If time dilation does occur then that Doppler shift has a different value (given by the relativistic Doppler formula). The difference is measurable regardless of synchronization convention and is equal to time dilation.

 

[VantagePoint72]

The resulting measurement measures time dilation regardless of the simultaneity convention.

This is a fundamentally meaningless statement. Again, see equation 4-8 in the paper I've linked. The time dilation factor explicitly depends on your choice of simultaneity convention. Imprecise statements about geometry—using words that imply particular conventions, even if you aren't aware of them because the implication is very subtle—do not refute explicit calculation. The explicit calculation is there: time dilation depends on simultaneity convention, and so it is meaningless to say you can "measure" it independently of such a convention.

The difference is measurable regardless of synchronization convention and is equal to time dilation

The difference is indeed measurable, regardless of synchronization convention. However, it is only equal to time dilation in the standard convention. You are confusing "the frequency of the emitted light as detected by the receiver" and "the frequency of the emitted light as produced by the emitter, according to the receiver's frame". These are not a priori the same thing: equating them is imposing Einstein's synchrony convention.

I don't think I have anything further to add, since I believe Winnie's calculation settles the matter pretty definitively. If George would like to weigh in again, I would like to hear it, as I believe we are in agreement on this. Perhaps he can make a more compelling case where, apparently, I'm failing.

 

[Dale]

Again, see equation 4-8 in the paper I've linked.

I can only see the first page without paying, which I won't do. However I am well familiar with the idea of setting a factor, usually denoted with an ε, which makes it so that the one-way speed of light differs from the two-way speed of light. It amounts to a different simultaneity convention, but does not change any of the experimentally measurable results. It is therefore completely equivalent to SR, experimentally, as it needs to be.

Experimentally, SR, even with non-standard simultaneity conventions, predicts a transverse Doppler shift which is not predicted classically. Regardless of ε. Otherwise the different simultaneity conventions would lead to testable consequences which would dismiss them experimentally.

I suspect that you are overstating or overgeneralizing whatever result you are pointing to in that paper.

 

[Dale]

The difference is indeed measurable, regardless of synchronization convention. However, it is only equal to time dilation in the standard convention. You are confusing "the frequency of the emitted light as detected by the receiver" and "the frequency of the emitted light as produced by the emitter, according to the receiver's frame".

This is a valid point. I suppose that in the non-standard synchronization case the metric has some pseudo-gravitational components in it as well. So there is Doppler as well as "gravitational" redshift. The total shift being equal to the measured shift, but not attributed the same way.

 

[VantagePoint72]

Experimentally, SR, even with non-standard simultaneity conventions, predicts a transverse Doppler shift which is not predicted classically. Regardless of ε. Otherwise the different simultaneity conventions would lead to testable consequences which would dismiss them experimentally.

I suspect that you are overstating or overgeneralizing whatever result you are pointing to in that paper.

I have been very explicit that, regardless of your convention, you get the same prediction for what the detector measures. What am I denying is that you get to call this "time dilation" without having established a synchrony convention. I sketched the derivation of the transverse Doppler effect to demonstrate how this is the case, which no one apparently has a response to.

I find it rather presumptuous that are willing to believe I'm "overstating or overgeneralizing" something you haven't even seen. However, I will copy the equation in question here. You say you are familiar with Reichenbach's $\epsilon$, so I won't go into details on that. In the following, $t'$ refers to time in the primed frame moving to right at $v_\epsilon$ in the unprimed frame (the $\epsilon$ emphasizing that this is a convention-dependent quantity since it is a one-way speed), and $t_\epsilon$ is the time that passes in the unprimed frame according to this convention (as read off by comparing different clocks since the primed frame is moving—hence the $\epsilon$). I drop Winnie's convention of putting a vector-like right arrow over certain quantities to indicate that the primed frame is moving to the right. He does this to compare with the corresponding formula for when the primed frame moves to the left—which must be different to ensure isotropy of the two-way speed of light. The result is the synchrony dependent time dilation equation between two particular frames:

$t' = t_\epsilon \sqrt{\frac{(c - v_\epsilon(2\epsilon - 1))^2 - v_\epsilon^2}{c^2}}$

Einstein's synchrony convention is $\epsilon = 1/2$, which clearly reproduces the usual formula. Much more interesting for the discussion at hand is the choice $\epsilon = \frac{c}{2v_\epsilon}$. As I said, $v_\epsilon$ is also dependent on the convention and, using its formula in terms of $v$, the velocity according the usual synchrony convention, Winnie shows that for the choice:

$\epsilon = \frac{\sqrt{c^2 - v^2} + (v-c)}{2v}$

there is no time dilation between the two frames we are examining. You cannot measure something that is a coordinate dependent effect. For this choice of $\epsilon$, there is no time dilation between the receiver and emitter: the measured Doppler shift is due entirely to the relativity of simultaneity between the two frames.

I appreciate that pay walls can be an issue, however I would have preferred you just asked me to quote the relevant parts. Waving your hand and dismissing everything I've said without even having seen the relevant derivation is not really conducive to a good discussion.

 

[VantagePoint72]

This is a valid point. I suppose that in the non-standard synchronization case the metric has some pseudo-gravitational components in it as well. So there is Doppler as well as "gravitational" redshift. The total shift being equal to the measured shift, but not attributed the same way.

I don't know if "pseudo-gravitational" is the right word; however you get the same prediction due to the different equations for relativity of simultaneity. In any case, the result is (exactly as you say) that the measured effect is attributed differently (i.e. not necessarily to time dilation) in the different synchrony convention.

 

[PAllen]

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.

I am not talking about the difference in interpretation in the emitter frame versus the apparatus frame. I'm talking about interpreting the apparatus, in its own rest frame, using a different simultaneity convention. What I am not getting, and would really appreciate a more detailed discussion of, is the mechanics of how: all in one inertial frame, changing the simultaneity convention changes the angles measured on a given apparatus. I cannot access more than one page of that Winnie paper, and it is not obvious they discuss this (though I obviously can't tell).

It would thus be very helpful if you demonstrate:

We have some object that is validly described as a T-square using Einstein simultaneity. Then we choose a different simultaneity and measure the angle between the T-square legs as something different than 90°. I do not claim it won't happen, I just don't see the mechanics, and your discussion above doesn't help because it refers to emitter frame.

 

[VantagePoint72]

We have some object that is validly described as a T-square using Einstein simultaneity. Then we choose a different simultaneity and measure the angle between the T-square legs as something different than 90°. I do not claim it won't happen, I just don't see the mechanics, and your discussion above doesn't help because it refers to emitter frame.

Ah, I think I see what you meant. I was only referring to determining the moment at which the emitter passes "overhead". It is only with moving objects that this is synchrony-dependent; with a static object, then certainly I agree nothing should change.

In any case, I don't think this is relevant to my point, which is that the clock synchronization along the emitter's path determines to what extent the transverse Doppler shift must be attributed to time dilation and to what extent it must be attributed to relativity of simultaneity. I've quoted the relevant parts of the paper in #25.

 

[PAllen]

Ah, I think I see what you meant. I was only referring to determining the moment at which the emitter passes "overhead". It is only with moving objects that this is synchrony-dependent; with a static object, then certainly I agree nothing should change.

In any case, I don't think this is relevant to my point, which is that the clock synchronization along the emitter's path determines to what extent the transverse Doppler shift must be attributed to time dilation and to what extent it must be attributed to relativity of simultaneity. I've quoted the relevant parts of the paper in #25.

That still doesn't quite convince me. Say I have an LED at rest near my apparatus. I measure it's frequency. Now I put it in a gun and shoot it along the top of my apparatus and measure the frequency at the bottom of my apparatus; I find it red shifted. I do assume that the LED in its own rest frame 'considers' its frequency to be the same as I measured when it was in the lab rest frame. I'm not trying to be obstinate, I just don't see how call this a simultaneity effect rather than a time dilation effect, no matter what synchronization I use - unless synchronization really does effect angle measurements for objects at rest (because then synchronization is changing transverse motion into motion at some other angle, thus changing the interpretation of the measured shift).

[One key point is that light based distance measurements need only the two way speed of light and one clock; these are not affected by simultaneity convention in an inertial frame.]

 

[Dale]

What am I denying is that you get to call this "time dilation" without having established a synchrony convention.

That becomes a semantics issue, which I think is not what the OP was asking about. The OP is asking about experimental tests of relativity. In other words, what experimental predictions differ between SR and Newtonian physics and how can those predictions be tested?

$t' = t_\epsilon \sqrt{\frac{(c - v_\epsilon(2\epsilon - 1))^2 - v_\epsilon^2}{c^2}}$

Einstein's synchrony convention is $\epsilon = 1/2$, which clearly reproduces the usual formula.

Here the formula ASSUMES all of the physical content of SR, by design. You could use the ε synchronization convention in Newtonian mechanics as well, but then for ε=1/2 you would get 1. It is tests of this that the OP is interested in, i.e. do the results for a given synchronization convention follow the Newtonian or the relativistic prediction. This is an additional physical degree of freedom that is not removed by synchronization convention.

A more clear derivation would be to start with one of the test theories of SR, rather than the Lorentz transform. Then, apply the coordinate transform for the synchronization. Then, regardless of the choice of ε you are still left with a physical degree of freedom representing time dilation. This is what is done when testing a theory and this is why time dilation is experimentally testable, not merely a consequence of the simultaneity convention.

I appreciate that pay walls can be an issue, however I would have preferred you just asked me to quote the relevant parts. Waving your hand and dismissing everything I've said without even having seen the relevant derivation is not really conducive to a good discussion.

Fair enough, my comments were out of line and I apologize for that.

 

[PAllen]

That still doesn't quite convince me. Say I have an LED at rest near my apparatus. I measure it's frequency. Now I put it in a gun and shoot it along the top of my apparatus and measure the frequency at the bottom of my apparatus; I find it red shifted. I do assume that the LED in its own rest frame 'considers' its frequency to be the same as I measured when it was in the lab rest frame. I'm not trying to be obstinate, I just don't see how call this a simultaneity effect rather than a time dilation effect, no matter what synchronization I use - unless synchronization really does effect angle measurements for objects at rest (because then synchronization is changing transverse motion into motion at some other angle, thus changing the interpretation of the measured shift).

[One key point is that light based distance measurements need only the two way speed of light and one clock; these are not affected by simultaneity convention in an inertial frame.]

I think I see the way out of my conundrum. There is obviously no disputing transverse doppler - that is an actual measurement. There is also no dispute that my proposed apparatus (in principle) measured transverse Doppler without clocks or synchronization. HOWEVER, what Winnie's analysis shows that using an arguably perverse simultaneity convention between inertial frames, the explanation of transverse Doppler is that it is due to relativity of simultaneity. Then my apparatus is interpreted as measuring this predicted simultaneity effect.

 

[VantagePoint72]

Say I have an LED at rest near my apparatus. I measure it's frequency. Now I put it in a gun and shoot it along the top of my apparatus and measure the frequency at the bottom of my apparatus; I find it red shifted. I do assume that the LED in its own rest frame 'considers' its frequency to be the same as I measured when it was in the lab rest frame. I'm not trying to be obstinate, I just don't see how call this a simultaneity effect rather than a time dilation effect, no matter what synchronization I use - unless synchronization really does effect angle measurements for objects at rest (because then synchronization is changing transverse motion into motion at some other angle, thus changing the interpretation of the measured shift).

Pick out the point, M, at which the emitter passes overhead. I agree with you that the spatial coordinates of this point are invariant under changes of synchrony convention. The emitter has velocity $v$. Now imagine the emitter is producing very short pulses of light with proper period $T'$. In order to make any frequency judgments, the emitter has to receive at least two of these pulses (so how small the slit can be depends on the emitter's proper frequency). Suppose two pulses are emitted very near to M at points A and B.

The receiver measures the two pulses to arrive some time apart which I'll call, $\tilde{T}$. This time is related to $T'$ by the transverse Doppler shift. But now you ask: what is the reason for this difference? Well, in the receiver's frame there is a clock at A and a clock at B which have somehow been synchronized. We simply read off the times at which the two pulses are emitted, according to the local clock, and take the difference ($T$). If the one-way speed of light is isotropic and we've used the standard synchronization scheme, we find this difference is equal to the interval measured by the detector. The conclusion is that the time dilation of the emitter accounts for the difference between when we measured the frequency of the emitter while at rest.

However, suppose we've chosen a different synchronization convention (i.e. using the same scheme but with the one-way speed of light not assumed to be isotropic). In particular, we could use the convention Winnie discusses in which we will find that $T = T'$. That is, the unprimed observer concludes that the pulses were emitted the same time apart as the primed observer says: no time dilation. So why did we receive the pulses at a different interval? The one way speed of light is no longer isotropic! Light is being received from A and B in slightly different directions and hence the pulses arrive at the detector at a different interval than they were emitted (for simplicity we can imagine A and B are equidistant from M in the detector frame). Or, put another way, the events when the two pulses were emitted are simultaneous with different events at the receiver's location in this convention than the were in the other convention. Now it is relativity of simultaneity that accounts for $\tilde{T}$ being difference from $T'$.

In either case, there is no disagreement about what the receiver measures. However, time dilation refers to difference between emission interval between the two reference frames. The emission interval in the receiver frame only equals the reception interval if the clocks at the locations of the two emissions are synchronized in the standard way.

 

[VantagePoint72]

HOWEVER, what Winnie's analysis shows that using an arguably perverse simultaneity convention between inertial frames, the explanation of transverse Doppler is that it is due to relativity of simultaneity. Then my apparatus is interpreted as measuring this predicted simultaneity effect.

Yep, that's it. I agree it's perverse—I said that from the beginning—but it's allowed.

 

[VantagePoint72]

That becomes a semantics issue, which I think is not what the OP was asking about. The OP is asking about experimental tests of relativity. In other words, what experimental predictions differ between SR and Newtonian physics and how can those predictions be tested?

Yes, I agree it's not what the OP was after, but bear in mind how we got here. George pointed out that you can't measure time dilation directly, but you can measure it's consequences. I think this was a very good point to make (and not at all just semantics). It is always emphasized in threads here on the twin's paradox that time dilation and differential aging are not the same thing. The former is a coordinate effect and the latter is a coordinate-invariant effect. Not keeping track of what is coordinate-dependent and what it is invariant is one of the main reasons people get confused in SR. So, George was right to clarify this point and, since you and PAllen both said he was wrong, I think I was right to explain why he wasn't.

 

[DiracPool]

Contraction applies to length, not to time. Did you really mean this?

Ooops, I meant Lorentz transformations. I wrote that at about 4am pacific time (USA)

 

[Dale]

So, George was right to clarify this point and, since you and PAllen both said he was wrong, I think I was right to explain why he wasn't.

I still think that this is wrong. When you are talking about experimental tests of SR you are necessarily talking about a test theory, the most common of which is the Mansouri Sexl test theory. In that theory the transform from the preferred inertial frame to any other inertial frame is given by:

t=aT+ex
x=b(X-vT)
y=d \, Y
z=d \, Z

Perhaps the OP should have asked if there were any experimental tests of the Mansouri Sexl parameter a rather than asking if there are any experimental tests of time dilation, but the synchronization convention adopted has absolutely no bearing whatsoever on the value of a. The synchronization convention is contained in e which is the only parameter which is not experimentally testable.

The value of the Mansouri Sexl parameter a is experimentally testable, it is not an artifact of the synchronization convention, and it is usually interpreted as time dilation. Therefore I think that it is incorrect to say "SR Time Dilation is not observable or measurable and cannot be tested, just like the one way speed of light cannot be tested." It is certainly not just like the one way speed of light in this respect.

 

[PAllen]

I"m not sure how it relates to Mansouri Sexl test theory framework, but it is worth noting that choosing ε not 1/2 for simultaneity constructs a non-orthonormal frame with different metric from Minkowski. Dalespam suggested this in passing. Using ε=1/2 is what assures orthonormality globally for inertial frames and locally for non-inertial frames (in SR). It is still certainly valid to say simultaneity is conventional, and it is not required to use orthonormal coordinates, but you do have to bring in general metric and connection. The metric must become more complex in any frame in which you chose ε ≠ 1/2.

 

[Histspec]

The value of the Mansouri Sexl parameter a is experimentally testable, it is not an artifact of the synchronization convention, and it is usually interpreted as time dilation. Therefore I think that it is incorrect to say "SR Time Dilation is not observable or measurable and cannot be tested, just like the one way speed of light cannot be tested." It is certainly not just like the one way speed of light in this respect.

The Mansouri-Sexl (RMS) model only partially includes conventionality of simultaneity, because it is assumed that the one-way speed of light is isotropic in Σ (Einstein convention), while ε was meant by them to describe the conventionality of synchrony only in moving frames. Therefore, the independence of a, b, and d on synchronization in RMS is only apparent, because it depends on the (implicit) synchronization convention that is used in the "preferred" aether frame.

However, authors such as Edwards, Winnie, or Anderson/Stedman applied different synchronization conventions in all reference frames. See Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998), "Conventionality of synchronisation, gauge dependence and test theories of relativity", Physics Reports 295 (3-4): 93–180

p. 141:The assumption of isotropy in Σ is responsible for the lack of generality of the Mansouri-Sexl formalism and underlies this common deficiency of interpretation. If this is borne in mind, there is no problem with the Mansouri-Sexl theory; the isotropy assumption in Σ is economical in helping to reduce the parameters of the theory. A simple resolution of the matter is to accept the Mansouri-Sexl formalism with this caution.

p. 143: Mansouri and Sexl ... acknowledged the conventionality of synchronization in a laboratory frame S through the introduction of their parameter ε. The (logically distinct) conventionality of synchronization in the preferred frame Σ is of equal significance. Mansouri and Sexl simply chose Einstein synchronization in Σ. While such gauge fixing is perfectly acceptable in analysing experiment, it obscures the conventional content of the formalism, in particular that of the claim to test the isotropy of the one-way speed of light. ... The function of the Mansouri-Sexl type of test theory is not so much as a test for a preferred frame as a test of Lorentz invariance.

p. 148: Since the analyses of the results of the experiments mentioned above do not take into account synchrony considerations in the hypothesised preferred frame, it is not explicitly obvious that the dilation and contraction factors (the parameters a and b in the Mansouri and Sexl test theory) are dependent on the synchrony choice in the aether frame and thus definitely not measurable...

So RMS is still a useful test theory of SR, because it can describe Lorentz violations (for instance, deviations in the two-way speed of light, or differences between Einstein synchronization and slow-clock-transport synchronization). However, the specific values of a, b, and d are themselves based on conventions in the assumed "preferred" frame which are reasonable and useful, but they can obtain different values in accordance with the more general synchronization frameworks of Edwards, Winnie, or Stedman/Anderson.

 

[VantagePoint72]

I"m not sure how it relates to Mansouri Sexl test theory framework, but it is worth noting that choosing ε not 1/2 for simultaneity constructs a non-orthonormal frame with different metric from Minkowski. Dalespam suggested this in passing. Using ε=1/2 is what assures orthonormality globally for inertial frames and locally for non-inertial frames (in SR). It is still certainly valid to say simultaneity is conventional, and it is not required to use orthonormal coordinates, but you do have to bring in general metric and connection. The metric must become more complex in any frame in which you chose ε ≠ 1/2.

Fine, but the question was never about the conventionality of simultaneity itself and what that means for the metric. I've been clear from the beginning that the question I was addressing was whether conventionality of simultaneity necessarily entails the immeasurability of time dilation. The answer to that is yes.

I was going to address DaleSpam's mistaken reading of the RMS test theory, but Histspec has taken care of that. I'm a bit disappointed that the inevitable conclusion from the fact that time dilation is defined in terms of a coordinate is still not being accepted, after all this back and forth—including a specific, concrete demonstration that shows how the time dilation explanation is not inherently fundamental. You cannot define time dilation without a simultaneity convention, full stop. The general construction provided by Winnie (and by many other since) constitutes a formal mathematical proof of this, and so any attempted counterexamples will necessarily have a flaw in them. If you guys want to see the whole paper, you're welcome to PM me an address I can send it to. But in the meantime, we're not going to get anywhere by having ever more elaborate schemes proposed that you then want someone to dig through to find exactly where the simultaneity convention is subtly being used. When you've proven that there are infinitely many primes, you don't continue proposing candidates for the largest prime.

 

[PAllen]

Fine, but the question was never about the conventionality of simultaneity itself and what that means for the metric. I've been clear from the beginning that the question I was addressing was whether conventionality of simultaneity necessarily entails the immeasurability of time dilation. The answer to that is yes.

I was going to address DaleSpam's mistaken reading of the RMS test theory, but Histspec has taken care of that. I'm a bit disappointed that the inevitable conclusion from the fact that time dilation is defined in terms of a coordinate is still not being accepted, after all this back and forth—including a specific, concrete demonstration that shows how the time dilation explanation is not inherently fundamental. You cannot define time dilation without a simultaneity convention, full stop. The general construction provided by Winnie (and by many other since) constitutes a formal mathematical proof of this, and so any attempted counterexamples will necessarily have a flaw in them. If you guys want to see the whole paper, you're welcome to PM me an address I can send it to. But in the meantime, we're not going to get anywhere by having ever more elaborate schemes proposed that you then want someone to dig through to find exactly where the simultaneity convention is subtly being used. When you've proven that there are infinitely many primes, you don't continue proposing candidates for the largest prime.

No need to get huffy about this. I thought it was an interesting discussion. I'd been familiar with conventionality of simultaneity used to show you cannot objectively say where along different world lines aging difference originates for differential aging scenarios. (And in GR, to argue against over interpreting SC coordinates). I had never given thought to what it implies about interpreting transverse Doppler (which is described often - and now I see, misleadingly - as test of pure time dilation).

 

[VantagePoint72]

No need to get huffy about this.

Sorry, didn't mean to come off that way.

 

[Dale]

The Mansouri-Sexl (RMS) model only partially includes conventionality of simultaneity, because it is assumed that the one-way speed of light is isotropic in Σ (Einstein convention), while ε was meant by them to describe the conventionality of synchrony only in moving frames.
...
However, the specific values of a, b, and d are themselves based on conventions in the assumed "preferred" frame which are reasonable and useful, but they can obtain different values in accordance with the more general synchronization frameworks of Edwards, Winnie, or Stedman/Anderson.

I have to read the Anderson article (it is rather large), but RMS is definitely more general than the Winnie convention. Regardless of the intention of RMS the mathematics doesn't constrain their formalism this way. You can always set v=0 and e≠0 to get a stationary frame with an anisotropic one way speed of light. The Winnie convention assumes that the two-way speed of light is c and only allows the one way speed to vary. RMS is more general because it allows both. Essentially, with Winnie's convention every frame becomes Σ for ε=1/2.

Any Winnie frame can be expressed as a RMS frame, but not vice versa.

I may have something different to say once I finish the Anderson paper, but Winnie doesn't make the case.

 

[Dale]

I'm a bit disappointed that the inevitable conclusion from the fact that time dilation is defined in terms of a coordinate is still not being accepted, after all this back and forth—including a specific, concrete demonstration that shows how the time dilation explanation is not inherently fundamental.

This is a good point. Since time dilation is a ratio of proper time to coordinate time it clearly depends on the coordinates and judicious choices of coordinates allows any value to be selected, with no physical content whatsoever.

In that context it is important to mention that the reason the the RMS parameters a, b, and d are testable is that they are parameters describing the transform between different INERTIAL frames. Obviously you can adopt arbitrary parameters in the transformation between an inertial and a non-inertial frame but once you have constrained both Ʃ and S to be inertial then you have something you can test.

So properly, the OP should have asked not about "SR time dilation" but about "SR time dilation in inertial frames". The former is purely a matter of convention, but the latter is physics. You are correct to point out the distinction.

 

[PAllen]

Just want to emphasize that Mansouri-Sexl is a test theory framework for testing SR; as such it encompasses theories empirically distinguishable from SR. Conventionality of simultaneity is normally used to ferret out which features of SR are fundamental versus convention; it is a given that all experimental predictions remain the same. I'm not sure the scope of the Winnie paper, but the one's I've read on conventionality of simultaneity all assume SR and are unconcerned with distinguishing it from related theories - thus, obviously, two way speed of light is c and is isotropic.

 

[Histspec]

I have to read the Anderson article (it is rather large), but RMS is definitely more general than the Winnie convention. Regardless of the intention of RMS the mathematics doesn't constrain their formalism this way. You can always set v=0 and e≠0 to get a stationary frame with an anisotropic one way speed of light. The Winnie convention assumes that the two-way speed of light is c and only allows the one way speed to vary. RMS is more general because it allows both. Essentially, with Winnie's convention every frame becomes Σ for ε=1/2.

Any Winnie frame can be expressed as a RMS frame, but not vice versa.

I may have something different to say once I finish the Anderson paper, but Winnie doesn't make the case.

RMS appears only more general because it allows for Lorentz symmetry violations in the form of anisotropic two-way speed and non-equivalence between Einstein synchronization and slow-clock transport synchronization.

But our discussion was about transformations that are empirically indistinguishable from the Lorentz transformation, making the one-way speed of light conventional in all frames of reference. Now, Mansouri and Sexl discussed internal synchronization only in terms of Einstein synchronization and slow-clock transport synchronization; and conventionality only in terms of external or absolute synchronization, by which they tried to emulate an "aether theory" equivalent (or not in the presence of Lorentz violations) to relativity.
So all of their definitions explicitly relied on the assumption of Einstein synchronization in the aether frame, with the Mansouri-Sexl transformation:

dt=ad\tau+\epsilon\cdot dx/c
dx=b\cdot(d\xi-vd\tau)

Anderson et al. reformulated this under consideration of the synchronization dependence in Σ. The Tildes denote that terms are now explicitly synchrony-dependent through the choice of the synchrony vectors \kappa_{0},\kappa in Σ and S, respectively (p. 144):

d\tilde{t}=\tilde{a}d\tilde{\tau}+\tilde{\epsilon}\cdot dx/c
dx=\tilde{b}\cdot(d\xi-\tilde{v}d\tilde{\tau})

with

\xi,\tilde{\tau}=\tau-\kappa_{0}\cdot\xi, for Σ;
x,\tilde{t}=t-\kappa\cdot x, for S;
\tilde{v}=v/(1-\kappa_{0}\cdot v/c);
\tilde{a}=a/(1-\kappa\cdot v/c)

 

[VantagePoint72]

Any Winnie frame can be expressed as a RMS frame, but not vice versa.

In addition to the more thorough comment above mine, I'd add that this statement cannot be true in light of the earlier discussion. Your entire reason for introducing RMS into the discussion was that the time dilation effect cannot be made to vanish in its frames with a particular choice of synchrony (at least, any choice allowable by the system's construction). However, I have shown above a particular situation where two frames and a simultaneity convention may be chosen for Winnie's system such that time dilation vanishes. Since time dilation can't vanish in the RMS system with a particular synchrony convention, this Winnie frame clearly can't be expressed as an RMS frame.

 

[Dale]

the one's I've read on conventionality of simultaneity all assume SR and are unconcerned with distinguishing it from related theories - thus, obviously, two way speed of light is c and is isotropic.

And they assume the physical content of time dilation and length contraction.

 

[VantagePoint72]

And they assume the physical content of time dilation and length contraction.

This may run up against the pay wall issue again, but you might like to check out this paper. It treats the twin's paradox as generally as possible and makes no assumptions about the physical content of time dilation and length contraction. It follows Reichenbach, Winnie, etc., and demonstrates how you can reproduce the prediction of differential aging without ever committing to any particular stance on the physicality of these other coordinate-based effects.

In any case, this:

So properly, the OP should have asked not about "SR time dilation" but about "SR time dilation in inertial frames". The former is purely a matter of convention, but the latter is physics. You are correct to point out the distinction.

still isn't right. Winnie's frames are both inertial. Even when we are restricting our attention to inertial frames, coordinates are still arbitrary, and (as you agreed above) time dilation is tied to how you define your coordinates. That is ultimately the reason we are forced to accept the simultaneity of conventionality in the first place. It's the GR lesson: coordinates aren't physical. Ever.

 

[PAllen]

Bear with me, but I can't let go of this discussion. In particular, I
decided to calculate the metric in coordinates based on a
synchronization parameter, and I seem to be able to show transverse
doppler cannot be reduced to a simultaneity effect. Specifically,
d \tau/dt cannot be made 1 for the measurement configuration I have
proposed.

First, let's clarify the coordinates with parametric
synchronization. I assume there is some inertial world line defining
an origin. For my transverse Doppler apparatus, I would make this the
base of the T. Spatial coordinate positions are measured two way speed of
light + clock at origin, thus not affected by synchronization. Angles
are not affected. Clock rates for rest clocks are not affected. Only
clock synchronization is affected. To make the factors slightly nicer,
I use a synchronization paremeter \epsilon that is twice the usual, so \epsilon=1
defines Einstein synchronization; and 0<\epsilon<2 is required for it to be a
valid synchronization (t=k slices are spacelike). I will use capital
letters for alternate coordinates rather than primes. I will use polar
style coordinates around the T base. Then the coordinate transform
from standard is:

R=r
\Theta = \theta
T = t + (\epsilon-1)r

the metric in these coordinates is (assuming c=1, of course, and
timelike line element):

d \tau^2 = dT^2 + 2(1-\epsilon)dRdT - \epsilon(2-\epsilon)dR^2 - R^2 d\Theta^2

As expected, it is orhogonal only if \epsilon=1. So now I ask, in these
coordinates, what condition must be satisfied for d\tau/dt=1 on some
world line? It is an immediate consequence of the metric that the
following is required:

0 = 2(1-\epsilon)dR/dT - \epsilon(2-\epsilon)(dR/dT)^2 - R^2 (d \Theta/dT)^2

Now, for the path of an emitter moving along the top of the T, at the
point of emitting throught the slot, dR/dT=0 (pure tangential motion
here). From this it is obvious that the condition cannot be met. More,
it follows that when dR/dT=0, the synchronization parameter has no
effect on d\tau/dT, and you have the same value as for standard
coordinates.

Thus, transverse doppler seems inherently a measure of d\tau/dt = time
dilation as a function of speed (R d\Theta/DT).

 

[VantagePoint72]

Bear with me, but I can't let go of this discussion. In particular, I
decided to calculate the metric in coordinates based on a
synchronization parameter, and I seem to be able to show transverse
doppler cannot be reduced to a simultaneity effect...

I don't think you are using $\epsilon$ the same way Winnie does. His result requires different synchrony conventions for right-going and left-going frames (again, I said it was perverse). I mentioned that briefly in an earlier post but didn't focus on the point. So, you've restricted yourself to a particular set of synchrony conventions which do not exhaust all the options. This is the same issue Histspec pointed out with RMS: it is not fully general. Without checking your calculations in detail—I'll assume they're right—then you've just shown that in this family of synchrony conventions, time dilation is independent of the convention. We already know that such families exist. The claim isn't "for all families of synchrony conventions, there is one that can eliminate time dilation between two particular frames"; it's "there exists a family of conventions such that one can eliminate time dilation between two particular frames". That's all that's sufficient to establish that time dilation is not fundamental.

If you have access, I suggest looking at the Redhead and Debs paper I mentioned in #48 (or PM me for a copy). The way in which they demonstrate how to account for the twin's paradox using essentially any combination of time dilation and relativity of simultaneity that you like might help assuage your remaining doubts.