Can we really ever accurately test SR time dilation?

[PAllen]

—then you've just shown that in this family of synchrony conventions, time dilation is independent of the convention..

Actually, what I show is: for this family of synchronization conventions (it a a commonly used family in SR), used to establish inertial polar coordinates, time dilation for a body with pure tangential motion is unaffected by the convention.

 

[VantagePoint72]

Actually, what I show is: for this family of synchronization conventions (it a a commonly used family in SR), used to establish inertial polar coordinates, time dilation for a body with pure tangential motion is unaffected by the convention.

Well, OK, so it's even a slightly weaker result than I said. The point is that there are other families available, and they can be used to establish inertial frames, and time dilation can for a body with pure tangential motion can be eliminated in them—as is done explicitly in the papers I've cited.

 

[PAllen]

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.

No, it won't because I've read many such explanations and they seem obvious to me. Application to transverse Doppler, analyzed in a single inertial frame, still seems different to me, and not covered in such papers I've seen. Specifically, what I am still not convinced of: Is there a synchronization convention, used to set up a single system of inertial coordinates in which my apparatus is at rest, that explains transverse Doppler as not related to time dilation?

 

[VantagePoint72]

Is there a synchronization convention, used to set up a single system of inertial coordinates in which my apparatus is at rest, that explains transverse Doppler as not related to time dilation?

I'm not entirely sure what you mean by "a single system of inertial coordinates" since, by definition, we need two such systems if we're going be comparing coordinate time from one to proper time from another. However, I did exactly what you are asking in post 32, using Winnie's synchronization convention. It constructs a system of coordinates in which your apparatus is at rest and the interval at which the pulses are emitted by a transversely moving emitter in this frame is the same as the interval at which they are emitted in the emitter's frame. Hence, there is no time dilation. They are received at a different interval by the apparatus ("explaining" the Doppler shift) because of the relativity of simultaneity. I thought you had agreed with this already.

 

[PAllen]

I'm not entirely sure what you mean by "a single system of inertial coordinates" since, by definition, we need two such systems if we're going be comparing coordinate time from one to proper time from another.

I don't see this. I am considering time dilation (definitely a coordinate dependent quantity) as a measure of d\tau/dt for some world line in one set of coordinates. All we need is one set of coordinates and a metric.

However, I did exactly what you are asking in post 32, using Winnie's synchronization convention. It constructs a system of coordinates in which your apparatus is at rest and the interval at which the pulses are emitted by a transversely moving emitter in this frame is the same as the interval at which they are emitted in the emitter's frame. Hence, there is no time dilation. They are received at a different interval by the apparatus ("explaining" the Doppler shift) because of the relativity of simultaneity. I thought you had agreed with this already.

I had to take parts of that on faith due lack of access to the paper. My most recent effort started as an effort to convince myself once and for all of the validity of that (#32) argument, from scratch, in my own terms. Unfortunately, I got a different result. Also, #32 and the accessible parts of the Winnie paper don't discuss the metric at all. I was hoping to come up with: see, if set \epsilon this way, then d\tau/dt could be made 1 where we want to.

 

[VantagePoint72]

I don't see this. I am considering time dilation (definitely a coordinate dependent quantity) as a measure of d\tau/dt for some world line in one set of coordinates. All we need is one set of coordinates and a metric.

No, you need one set of coordinates, a metric, and a worldline for your emitter. The worldline implicitly defines a second reference frame: the rest frame of the emitter. Whether you do the calculation with two frames defined in this manner, or with one frame and the corresponding form of the metric, the calculation is doing the exact same thing.

I had to take parts of that on faith due lack of access to the paper. My most recent effort started as an effort to convince myself once and for all of the validity of that (#32) argument, from scratch, in my own terms. Unfortunately, I got a different result.

You get a different result because you're not using the key fact that Winnie does: you can define different synchrony conventions for frames moving in opposite directions. I think we're at an impasse here, as there's a limit to what I can do. I've quoted several references, provided links to them, offered to make them available privately due to the pay wall, and quoted extensively from them. At this point what you do with all this is up to you.

 

[PAllen]

You get a different result because you're not using the key fact that Winnie does: you can define different synchrony conventions for frames moving in opposite directions. I think we're at an impasse here, as there's a limit to what I can do. I've quoted several references, provided links to them, offered to make them available privately due to the pay wall, and quoted extensively from them. At this point what you do with all this is up to you.

I think we are meaning something different by synchronization convention. I mean: I have collection of mutually at rest, identically constructed, clocks. I want to synchronize them. I don't see two frames involved. I could see a rule that I synchronize clocks to the 'left' of chosen master different from those to the 'right'.

[edit: however, using this as a hint for the approach I want to use, if in my post#49, I allow ε(\theta), then I get d\thetadt term in the metric, and then it is possible satisfy d\tau/dt = 1 for the emitter world line at the appropriate event. So this is the key - you need synchronization that is anisotropic, not just different for 'away versus back'. This allows for anisotropic one way speed of light toward the receiver, accounting for the measured doppler without time dilation. I had to work this out my own way to really get it.]

 

[VantagePoint72]

I think we are meaning something different by synchronization convention. I mean: I have collection of mutually at rest, identically constructed, clocks. I want to synchronize them. I don't see two frames involved. I could see a rule that I synchronize clocks to the 'left' of chosen master different from those to the 'right'.

This is also what I am referring to. Forget the caveat I mentioned about different conventions for frames moving in opposite directions. It's not relevant to what you're describing, and it's just causing confusion. We only have one direction for the emitter's motion so we only need to use one of the conventions Winnie derives. The point was that you need to use a different convention to accomplish the same thing for transverse motion in the other direction. Never mind though.

The derivation of the synchronization convention you are after exists, and is in the paper I've referred to. Short of re-typing the paper in question, I'm sorry, but there's nothing more I can add to this conversation.

 

[PAllen]

This is also what I am referring to. Forget the caveat I mentioned about different conventions for frames moving in opposite directions. It's not relevant to what you're describing, and it's just causing confusion. We only have one direction for the emitter's motion so we only need to use one of the conventions Winnie derives. The point was that you need to use a different convention to accomplish the same thing for transverse motion in the other direction. Never mind though.

The derivation of the synchronization convention you are after exists, and is in the paper I've referred to. Short of re-typing the paper in question, I'm sorry, but there's nothing more I can add to this conversation.

See my edit to #57 - it only takes one generalization of what I did in #49.

 

[VantagePoint72]

[edit: however, using this as a hint for the approach I want to use, if in my post#49, I allow ε(\theta), then I get d\thetadt term in the metric, and then it is possible satisfy d\tau/dt = 1 for the emitter world line at the appropriate event. So this is the key - you need synchronization that is anisotropic, not just different for 'away versus back'. This allows for anisotropic one way speed of light toward the receiver, accounting for the measured doppler without time dilation. I had to work this out my own way to really get it.]

Sorry, this confusion was my fault. Winnie is using an anisotropic one-way speed of light. The synchronization is anisotropic in a particular frame for the same reason it needs to be different for 'away versus back' to eliminate the time dilation effect both times. I wasn't clear on this, and was using the two interchangeably. Glad you were able to work it out despite my muddying the waters.

 

[PAllen]

We only have one direction for the emitter's motion so we only need to use one of the conventions Winnie derives. The point was that you need to use a different convention to accomplish the same thing for transverse motion in the other direction. Never mind though.

And now, of course, this is clear. If some ε(θ) function works for the emitter going one way, you would need -ε(θ) for the emitter moving the opposite way.

[edit: Not quite. Given some ε(θ) works for one way, and assuming θ=0 represents the leg of the T apparatus, then for the reverse one needs ε2(θ) such that ε2'(0) = -ε'(0). ε2(θ) itself must be be > 0, < 2, just like ε(θ).]

 

[VantagePoint72]

And now, of course, this is clear. If some ε(θ) function works for the emitter going one way, you would need -ε(θ) for the emitter moving the opposite way.

Given he comes at the problem from a very different direction, I can't tell at the moment if this is equivalent: but Winnie's result is that if $\epsilon_r$ is the convention used to eliminate time dilation in a right moving frame and $\epsilon_l$ the same for the left, then $\epsilon_r + \epsilon_l = 1$. He's working in Cartesian coordinates though—I'd have to go more slowly through your derivation to try to figure out if this lines up.

Side note—though this should go without saying—all this applies equally well to length contraction. And, as I mentioned earlier, we even have to be careful with relative velocities when we start futzing around with these conventions. Obviously Einstein's convention is preferred for good reason.

 

[PAllen]

Given he comes at the problem from a very different direction, I can't tell at the moment if this is equivalent: but Winnie's result is that if $\epsilon_r$ is the convention used to eliminate time dilation in a right moving frame and $\epsilon_l$ the same for the left, then $\epsilon_r + \epsilon_l = 1$. He's working in Cartesian coordinates though—I'd have to go more slowly through your derivation to try to figure out if this lines up.

Side note—though this should go without saying—all this applies equally well to length contraction. And, as I mentioned earlier, we even have to be careful with relative velocities when we start futzing around with these conventions. Obviously Einstein's convention is preferred for good reason.

See correction above. Note that I am only interested in d \tau/dt at one point on a world line, so the constraints are not as strong.

 

[VantagePoint72]

See correction above. Note that I am only interested in d \tau/dt at one point on a world line, so the constraints are not as strong.

So, as far as I can tell, your derivation agrees with (or at least is compatible with) Winnie's. That's encouraging.

 

[Dale]

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).

No, my whole reason for introducing RMS is that it is a test theory of SR and also includes simultaneity as part of the theory. Winnie is interesting, but not responsive to the OP since it isn't a test theory.

I am trying to work out the relationship between a Winnie/Reichenbach frame and a RMS frame. RMS clearly contains frames that Winnie does not, but you claim that the reverse is also true. I have not been able to confirm it yet.

 

[Dale]

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.

Yes, I recognize that.

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.

Inertiality places a restriction on the allowable set of coordinates. I am not convinced that these restrictions are not testable. Winnie/Reichenbach is not a test theory and already assumes time dilation, so proofs based on that seem flawed to me. I.e. it is illogical to assume time dilation and then try to prove anything about experimental tests of time dilation. You have to start by assuming a theory whereby you can actually test time dilation.

What is needed is a test theory with the most general simultaneity parameters possible. You have claimed that RMS is not such a theory, but I am still working that out. Winnie is not relevant to the question (since it isn't a test theory), but it may be that there exist some Winnie frames that are not representable by RMS, in which case RMS is not relevant either (since the simultaneity convention may not be as general as possible for inertial frames).

 

[VantagePoint72]

What is needed is a test theory with the most general simultaneity parameters possible. You have claimed that RMS is not such a theory, but I am still working that out. Winnie is not relevant to the question (since it isn't a test theory), but it may be that there exist some Winnie frames that are not representable by RMS, in which case RMS is not relevant either (since the simultaneity convention may not be as general as possible for inertial frames).

You can't eliminate time dilation once and for all in any Winnie frame. Once you pick your synchrony convention, it will still exist in frames other than the two you were specifically working to eliminate it in. So, if that, for you, constitutes proof that time dilation is a "real thing" then fine. However, my view is since in any particular experiment you might wish to test the phenomenon, there is a convention (or set of conventions if you are using multiple frames) that will allow you eliminate time dilation from the mathematics, I don't consider it a fundamental explanation or something that can be directly measured. But if your point is that in a test theory in which you've made particular choices for all your conventions, time dilation will inevitably show up somewhere then you are right.

Essentially, I am saying that there is no single experiment you can do in which you can point to the result and say, "That is because of time dilation." It is not something that happens to things, it's not a dynamical thing. It's a bookkeeping device that, once you pick your synchrony conventions, ensures all the theory's invariants come out like they're supposed to. This, I think, was George's point at the very beginning of all this. The Redhead and Debs article I linked on the twin's paradox makes this point well, I think. They demonstrate that, because of the arbitrary nature of time dilation, it doesn't make any sense to ask questions like, "From the traveling twin's frame, at what point does the home twin's clock pick the 'extra time' needed to account for the age difference at the end?" Whether you try to answer the question with the traveling twin's acceleration, lines of simultaneity, light rays being exchanged by the twins, or any of the other usual explanations for the paradox, you cannot give a convention-free answer to the question. You can place the "extra time" pretty well anywhere you want with a suitable synchrony convention.

Hence, if you believe the fact that the bookkeeping device has to be used somewhere (but where is arbitrary) counts as some sort indirect evidence for time dilation, then fine. I just don't believe it's sensible to point to something that only makes sense in a particular choice of coordinates and say it's evidence for something occurring. Time dilation doesn't "happen"—clocks traversing worldlines of different lengths is what happens, and time dilation is how we explain it within an arbitrarily chosen reference frame whose clocks are synchronized by an arbitrary convention.

 

[Mentz114]

... clocks traversing worldlines of different lengths is what happens, and time dilation is how we explain it within an arbitrarily chosen reference frame whose clocks are synchronized by an arbitrary convention.

I agree with everything in your last post except this bit. I don't think time dilation explains different elapsed clock times for different worldlines. As is often pointed out in connection with the twin paradox - two inertial observers will reciprocally see the others clock slow in their own coordinates, but this symmetry is not necessarily present in the clock times.

 

[Dale]

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

this Winnie frame clearly can't be expressed as an RMS frame.

I have worked through the math. As far as I can tell, any Winnie frame can be expressed as a RMS frame by setting: e=(2\epsilon-1)/c.

The transform from the Ʃ frame to a stationary RMS frame with a different synchronization convention simplifies to:
$t=T+eX$
$x=X$

For the Winnie/Reichenbach convention you can convert from an Einstein synchronized frame (T,X) by calculating $t=T_E+\epsilon(T_R-T_E)$ where $T_E$ is the time of emission of a radar pulse at x=X=0 and $T_R$ is the time of reception of the reflection. Since in the Einstein frame we have:
$(T-T_E)c=X$
$(T_R-T)c=X$
We can substitute and simplify to obtain:
$t=T+(2\epsilon-1)X/c$

So I don't see that the Winnie convention is any more general than the RMS convention, it is simply a different way to write e.

 

[VantagePoint72]

I agree with everything in your last post except this bit. I don't think time dilation explains different elapsed clock times for different worldlines. As is often pointed out in connection with the twin paradox - two inertial observers will reciprocally see the others clock slow in their own coordinates, but this symmetry is not necessarily present in the clock times.

This is wrong. If by "see", you are suggesting the exchange of light rays then both twins do not "see" the others clock running slow the entire time. Consult any of the numerous threads in which ghwellsjr does the calculation with the relativistic Doppler effect. If by "see", you mean "computes in their coordinates" then the traveling twin must take into account a discontinuity in the home twin's time coordinate when he (the traveling twin) turns around/synchronizes watches with a passing third person/whatever. And, again, all these things are synchrony dependent. If the traveling twin applies time dilation correctly to the home twin, without mistakenly considering himself to be in an inertial frame the entire trip, then both twins predict the same differential aging. As, of course, they must.

I don't wish to get into a tangent on the twin's paradox for it's own sake. I've provided a reference I invite you to read. If you want to discuss it, please make a new thread.

 

[TrickyDicky]

So there's been mention at the beginning of the thread (I believe around posts #17 and#20) of the relation of the simultaneity convention with geometry, specifically the statements:
"The geometry of an apparatus at rest is not a function of the choice of simultaneity convention."
by Dalespam and "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." by PAllen.
At this point of the discussion has this "too perverse" simultaneity convention been taken seriously?
Can we link simultaneity convention to geometry and under what circumstances?

 

[VantagePoint72]

I have worked through the math. As far as I can tell, any Winnie frame can be expressed as a RMS frame by setting: e=(2\epsilon-1)/c.

Assuming your calculation is right and it is true that every Winnie frame can be converted to an RMS frame, there would have to also be a dependence of RMS's $a$ on Winnie's $\epsilon$. In Winnie's paper, $\epsilon = \frac{\sqrt{c^2 - v^2} + (v - c)}{2v}$ eliminates time dilation between the frame whose clocks are being synchronized and a frame moving to the right at $v$. By your calculation, this corresponds only to a particular value of $e$—but as you've noted, $a$ is independent of $e$ and so time dilation can't be eliminated in RMS frame by this transformation.

I don't know where your mistake is—maybe missing the dependence of $v$ on the synchrony convention, or something like that—but there has to be one. There is a contradiction otherwise: if every Winnie frame could be written as an RMS frame, then it would be possible to eliminate time dilation in an RMS frame by using the Winnie frame that has no relative time dilation. Eliminating relative time dilation is impossible in RMS if $a$ and $e$ are independent. Therefore, either it is impossible to write this Winnie frame as an RMS frame, or $a$ depends on $\epsilon$ and is equal to 1 for $\epsilon = \frac{\sqrt{c^2 - v^2} + (v - c)}{2v}$.

Edit: have you looked over the recent posts from PAllen? As he noticed, the important bit is that you can synchronize clocks differently in either direction from your reference clock. Winnie uses this to eliminate time dilation from the Lorentz transformations, and PAllen worked out how to use it to eliminate time dilation directly from the metric. It doesn't look like this anisotropy is possible with RMS frames. It's not something you would be interested in for a test theory, since for a test theory the idea is to pick a convention and establish it once and for all.

 

[VantagePoint72]

So there's been mention at the beginning of the thread (I believe around posts #17 and#20) of the relation of the simultaneity convention with geometry, specifically the statements:
"The geometry of an apparatus at rest is not a function of the choice of simultaneity convention."
by Dalespam and "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." by PAllen.
At this point of the discussion has this "too perverse" simultaneity convention been taken seriously?
Can we link simultaneity convention to geometry and under what circumstances?

No, we've all agreed that for an object at rest, geometrical notions like angles do not depend on clock synchronization. PAllen worked out himself how to use a simultaneity convention to eliminate time dilation from his transverse Doppler effect thought experiment without compromising this. We're not going to drag the discussion back to something that we moved on from a long time ago, so please read the rest of the discussion yourself to see how we got here.

 

[Dale]

I don't know where your mistake is—maybe missing the dependence of $v$ on the synchrony convention, or something like that—but there has to be one. There is a contradiction otherwise: if every Winnie frame could be written as an RMS frame, then it would be possible to eliminate time dilation in an RMS frame by using the Winnie frame that has no relative time dilation.

I am not sure that this is actually a contradiction. Considering just the time coordinate, RMS essentially has two degrees of freedom (a,e) and Winnie has one (ε). Every time convention in Winnie can be replicated in RMS by some e(ε), as shown above. If you set t=t' in Winnie you can solve for ε and claim that you have eliminated time dilation. You can also do the same in RMS, but you wind up with one equation in two unknowns. You can solve that for e, and you should get e(ε), but that equation still does not fix a. So you can use that synchronization convention and still perform experiments to measure a.

Maybe I am just tying myself in mental knots. I understand the idea of the non-standard synchronization conventions, but I have not used them enough to have an intuitive understanding of how they work. There may be a mistake, but I cannot see it. I don't think that Winnie's result is wrong, just that it isn't relevant to the question of whether or not time dilation can be tested. There are additional degrees of freedom involved in a test that Winnie has removed.

 

[PAllen]

Maybe I am just tying myself in mental knots. I understand the idea of the non-standard synchronization conventions, but I have not used them enough to have an intuitive understanding of how they work. There may be a mistake, but I cannot see it. I don't think that Winnie's result is wrong, just that it isn't relevant to the question of whether or not time dilation can be tested. There are additional degrees of freedom involved in a test that Winnie has removed.

What I showed, in a very explicit way in #49 generalized as described in #57, is simply that within SR alone (no need to allow empirically distinguishable theory), the interpretation of transverse doppler is really affected by simultaneity convention. Specifically, for any given apparatus at rest in an inertial frame, a suitably perverse simultaneity convention will cause you to interpret the transverse doppler measurement as being due to anisotropy of one way light speed (varying as a function of θ from the base of the apparatus), rather than being due to time dilation (dτ/dt), which you will think is unity for the emitter world line at the event of its transverse emission.

What is perverse about this interpretation is that to achieve this as you move and reorient your apparatus, you must assume that the simultaneity convention follows your apparatus. In the terms I used, you must assume that θ=0 is the direction of the leg of the T, however you place it, with angles measured e.g. clockwise from there. That is, that the anisotropy of one way light speed follows your apparatus around. And if you have multiple apparatus with different orientations, you assume that variation of one way lightspeed with direction in the vicinity of each is determined by the orientation of each apparatus.

Less perverse is to adopt a single ε(θ) relative to some 'special direction', and interpret that for some orientations transverse doppler is due purely to one way light speed variation; in some orientations due purely to time dilation; and for other orientations, a mixture.

 

[VantagePoint72]

I am not sure that this is actually a contradiction. Considering just the time coordinate, RMS essentially has two degrees of freedom (a,e) and Winnie has one (ε). Every time convention in Winnie can be replicated in RMS by some e(ε), as shown above. If you set t=t' in Winnie you can solve for ε and claim that you have eliminated time dilation. You can also do the same in RMS, but you wind up with one equation in two unknowns. You can solve that for e, and you should get e(ε), but that equation still does not fix a. So you can use that synchronization convention and still perform experiments to measure a.

Ahhhhh I finally understand your objection. Yes, of course, Winnie's formula for time dilation assumes the validity of the standard Lorentz transformations for standard synchrony, so it does not do what you are asking. Fortunately, he does do what you are asking elsewhere: his second 1970 paper, where he formulates what he calls the $\epsilon$-Lorentz transformations in section 8.

These explicitly have two degrees of freedom, the synchronization conventions for both frames you are transforming between, which Winnie calls $\epsilon$ and $\epsilon'$. What you are calling the time dilation factor in the Lorentz transformations actually depends on both of these. However, when you then use the $\epsilon$-Lorentz transformations to derive the time dilation formula (i.e. the ratio of coordinate time to proper time, $d\tau/dt$) one of these drops out and you only need to worry about synchronization in one frame. Conversely, if you compute this ratio using the RMS transformations, it depends on both $a$ and $e$.

In the general $\epsilon$-Lorentz transformations of Winnie, it looks to me that what you are considering the time dilation term in the transformations can be eliminated with a suitable choice of both $\epsilon$ and $\epsilon'$. However, I need to take a closer look to be sure of this. The key difference between Winnie and RMS is what Histspec said: "ε was meant by [RMS] to describe the conventionality of synchrony only in moving frames", whereas Winnie's general transformations allow you to fiddle with the synchronization in both frames.

Winnie's second paper is http://www.jstor.org/stable/186671, but I expect we'll have the pay wall issue again. [edit: see end of this post for a link]

In any case, we've been referring to two different things as "time dilation". I've been calling $d\tau/dt$ time dilation and you've been calling the coefficient of $t$ in the (generalized) Lorentz transformations time dilation. As I said, I think both can be set to unity (though probably not at the same time) in Winnie's scheme, but at the very least the former definitely can.

Edit: here are Winnie's $\epsilon$-Lorentz transformations: http://imgur.com/qs3WN5I. I have it to work it through, but it looks like a suitable choice of $\epsilon$ and $\epsilon'$ will set the coefficient of $t$ to unity.

 

[VantagePoint72]

Follow up: according to a quick calculation, if we synchronize clocks in S using the standard ($\epsilon = 1/2$) convention and S' has (dimensionless) velocity $\beta$ in S, then we can synchronize the clocks in S' with $\epsilon' = \frac{(1+\beta) - \sqrt{1 - \beta^2}}{2\beta}$. With this synchronization, the coefficient of $t$ in the expression for $t'$ in terms of $t$ and $x$ is exactly 1. A quick plot on WolframAlpha confirms that the above relationship gives $0 < \epsilon' < 1$ for $0 \leq \beta < 1$.

 

[VantagePoint72]

Less perverse is to adopt a single ε(θ) relative to some 'special direction', and interpret that for some orientations transverse doppler is due purely to one way light speed variation; in some orientations due purely to time dilation; and for other orientations, a mixture.

Yes, and I'm fine with this. This was my point in an earlier post: once you've established your conventions, time dilation (in either sense that we've been using the word) will necessarily show up somewhere (in fact, it will show up with most orientations and velocities other than precisely the ones you were working around) in order to "balance the books". It is purely the fact that where you make it show up is arbitrary that it can't be considered something directly measurable. There is, strictly speaking, the "ultra perverse" view that the speed of light adapts itself to all of your experiments—being sensitive both to the orientation of your equipment and the relative velocity of your frames)—in just such as a way as to always eliminate time dilation. This, I agree, is crazy and probably pushing the idea to far. I think I would sum all of this up as follows:

"Experiments can confirm that time dilation is necessary in our transformation laws, but it can't tell us when. That is, they can't distinguish between time dilation and other relativistic effects like relativity of simultaneity at any given time, so we can't point to a particular experiment and say, 'This is time dilation'. However, while we can't directly detect time dilation, we can do multiple experiments and conclude that unless nature adapts itself to experiments physicists do (sort of like the defense made by those who argue against confirmation of Bell's inequality because not all the loopholes have been closed simultaneously), time dilation is necessary to explain what is observed in at least one of them. That said, though, nature could just be that perverse..."

After all this, that, I believe, is the ultra-pedantic way of describing the relation between time dilation and experiment in special relativity.

 

[TrickyDicky]

No, we've all agreed that for an object at rest, geometrical notions like angles do not depend on clock synchronization. PAllen worked out himself how to use a simultaneity convention to eliminate time dilation from his transverse Doppler effect thought experiment without compromising this.

PAllen gave references to the posts where he deals with this in a recent post replying to Dalespam. I disagree that everyone agreed with what you are saying in general terms. The specific procedure used by PAllen introduces some specific conditions. See below.

What I showed, in a very explicit way in #49 generalized as described in #57, is simply that within SR alone (no need to allow empirically distinguishable theory), the interpretation of transverse doppler is really affected by simultaneity convention. Specifically, for any given apparatus at rest in an inertial frame, a suitably perverse simultaneity convention will cause you to interpret the transverse doppler measurement as being due to anisotropy of one way light speed (varying as a function of θ from the base of the apparatus), rather than being due to time dilation (dτ/dt), which you will think is unity for the emitter world line at the event of its transverse emission.

What is perverse about this interpretation is that to achieve this as you move and reorient your apparatus, you must assume that the simultaneity convention follows your apparatus. In the terms I used, you must assume that θ=0 is the direction of the leg of the T, however you place it, with angles measured e.g. clockwise from there. That is, that the anisotropy of one way light speed follows your apparatus around. And if you have multiple apparatus with different orientations, you assume that variation of one way lightspeed with direction in the vicinity of each is determined by the orientation of each apparatus.

I have a question about this, it would seem as this convention is not only perverse but contrary to the spirit of SR, I mean: can we introduce anisotropy just like that?

 

[VantagePoint72]

I have a question about this, it would seem as this convention is not only perverse but contrary to the spirit of SR, I mean: can we introduce anisotropy just like that?

Yes, that is the entire reason for this discussion. Look up "conventionality of simultaneity in special relativity". The predictions of SR are invariant with respect to an anisotropic one-way speed of light (which is not measurable), so long as it's anisotropic in just such a way that the two-way speed of light is isotropic (which is measurable). Since clocks are synchronized in SR with one-way light pulses, or an equivalent scheme like slow-clock transport, calling two space-like separated events in SR "simultaneous" is a convention; not a fact. Moreover, you don't even have to use the same synchronization procedure for different frames (those that are rotated or boosted from your original frame). It is strange not to do so—which is PAllen's point—but nothing in relativity prevents you from it.

 

[Dale]

within SR alone (no need to allow empirically distinguishable theory).

Yes, but if you don't allow an empirically distinguishable theory then you cannot test time dilation anyway.

What is needed is a test theory with a truly general synchronization convention. RMS is the only one I know of with any synchronization convention at all and I think that it covers the Winnie convention, but my confidence on that point is low.

 

[Dale]

In any case, we've been referring to two different things as "time dilation". I've been calling $d\tau/dt$ time dilation and you've been calling the coefficient of $t$ in the (generalized) Lorentz transformations time dilation. As I said, I think both can be set to unity (though probably not at the same time) in Winnie's scheme, but at the very least the former definitely can.

Yes, I certainly agree that the former can be set to 1 through some arbitrary coordinate transform. I think that the OP was probably asking about the latter.

I wonder if this whole discussion could be framed in terms of invariants rather than all of these messy coordinates. E.g. could we make a test theory of SR by finding some quantity which is unchanged under RMS or similar transformations where the different parameters would have some clear physical meaning independent of ANY coordinates.

 

[PAllen]

Yes, but if you don't allow an empirically distinguishable theory then you cannot test time dilation anyway.

What is needed is a test theory with a truly general synchronization convention. RMS is the only one I know of with any synchronization convention at all and I think that it covers the Winnie convention, but my confidence on that point is low.

I'm looking at a slightly different question. We measure transverse doppler. This is a clear cut measurement, and it was not predicted by any of the historically earlier theories (Newtonian corpuscular light; naive aether theory - as opposed to LET). So what phenomenon is this measuring (beyond the tautological transverse doppler)? If you choose Einstein synchronization, it measures time dilation. If you allow general, anisotropic synchronization procedure (but still in one inertial frame, and still within the bounds that separated synchronized clocks reading the same time describe events with spacelike separation), then it is no longer true that transverse doppler is necessarily a measure of time dilation - though it remains a prediction of the theory.

[edit: Perhaps it's worth noting that even without such complexity, what is measured in one frame as transverse doppler, will have a completely different explanation (but same prediction) in the frame of the emitter. The emitter (using just Einstein synch), will claim the receiver's clock is slow, but the point of reception is past the transverse point, and the redshift from moving partly away dominates over the receiver time dilation, explaining why the receiver is still predicted to measure redshift.]

 

[VantagePoint72]

RMS is the only one I know of with any synchronization convention at all and I think that it covers the Winnie convention, but my confidence on that point is low.

It may cover the Winnie convention we were discussing earlier, but it definitely doesn't cover the Winnie convention in the generalized $\epsilon$-Lorentz transformations I posted above. The latter depends on synchrony conventions in both the frame you're transforming from and the frame you're transforming to. RMS only covers one of those, so it can't encapsulate every possible form of the Winnie's generalized transformations. In particular—having now gotten on board with the fact that it's the coefficient of $t$ in the transformation to $t'$ that you're worried about, not the value of $d\tau/dt$—RMS can't accommodate the demonstration I gave above that a judicious (OK, fine, perverse) choice of $\epsilon$ and $\epsilon'$ sets that coefficient to one.

I agree that this doesn't constitute a test theory since it is just a generalization of the Lorentz transformations. It would be interesting to see a test theory that, like Winnie, allows you to set the synchrony conventions in both frames. However, my feeling is this wouldn't change anything: in Winnie's $\epsilon$-Lorentz transformations (I've also seen this referred to as the "Winnie-Edwards transformations"), I've shown above that the so-called "time dilation" term can be eliminated for a particular velocity. I can't imagine this wouldn't be possible in a model that makes weaker assumptions by not assuming the validity of the Lorentz transformations.

I wonder if this whole discussion could be framed in terms of invariants rather than all of these messy coordinates.

A framing in terms of invariants would be about testable predictions like differential aging or relativistic Doppler shifts—which, as we've seen, require a somewhat arbitrary combination of time dilation and relativity of simultaneity. Since time dilation—whether you mean $d\tau/dt$ or a particular coefficient in the Lorentz transformations by the term—is inherently tied up with coordinates, I don't see how you could possibly separate the coordinates out. What you get if you try to do that are precisely the quantities we've already seen can be explained in particular instances without time dilation.

 

[VantagePoint72]

Just to emphasize my earlier point: I'm fine with saying that "time dilation can be empirically tested" in the sense you can measure a bunch of invariants and confirm that if your synchrony conventions are fixed in all your frames (even if they're arbitrary in the first place), then time dilation is needed in your formulas. However, I don't think this is meaningful since we are, after all, talking about an effect that is defined in terms of non-physical coordinates. As I've said, my feeling is that time dilation is just a bit of mathematical machinery used to "balance the books". The physical effects are differential aging, frequency shifts, and things of that nature. They are the values at the bottom of your ledger. Time dilation, length contraction, and relativity of simultaneity are just what make the numbers come out right—and exactly where you need to use each of them is essentially up to you.

 

[Dale]

A framing in terms of invariants would be about testable predictions like differential aging or relativistic Doppler shifts—which, as we've seen, require a somewhat arbitrary combination of time dilation and relativity of simultaneity. Since time dilation—whether you mean $d\tau/dt$ or a particular coefficient in the Lorentz transformations by the term—is inherently tied up with coordinates, I don't see how you could possibly separate the coordinates out. What you get if you try to do that are precisely the quantities we've already seen can be explained in particular instances without time dilation.

Well, with that comment I wasn't specifically thinking about time dilation any more, I was thinking about SR in general. It seems to me that you should be able to express any physical theory entirely in terms of coordinate independent mathematical objects (I.e. If you cannot do that then it is not a physical theory). That should include test theories. Then you would have coordinate independent parameters which you could test and for which you would have unambiguous physical meaning.

I don't know what such a theory would look like, nor what parameters might arise, but I am sure it would be highly informative.

 

[VantagePoint72]

I don't know what such a theory would look like, nor what parameters might arise, but I am sure it would be highly informative.

Agreed, it would be interesting to see a fully generalized test theory like that.

You know, the irony of all this is that I only know about Winnie because of you, PAllen, and ghwellsjr. There was a thread a few months ago in which conventionality of simultaneity was raised (I used it in a resolution to the twins paradox) and I attempted to argue against conventionality—and, for what's worth, I'm still not completely sold on it due mostly to Malament's theorem. However, the three of you gave me some proper hell for it and so I wound up digging into some research on the issues and wrote a rather lengthy paper on it and some related questions. It was in doing this that I learned from Winnie that relativity of simultaneity as a fundamental explanation for things isn't the only thing that comes under the axe if you accept the conventionality thesis. And, half a year later, here we are again!

 

[PAllen]

Agreed, it would be interesting to see a fully generalized test theory like that.

You know, the irony of all this is that I only know about Winnie because of you, PAllen, and ghwellsjr. There was a thread a few months ago in which conventionality of simultaneity was raised (I used it in a resolution to the twins paradox) and I attempted to argue against conventionality—and, for what's worth, I'm still not completely sold on it due mostly to Malament's theorem. However, the three of you gave me some proper hell for it and so I wound up digging into some research on the issues and wrote a rather lengthy paper on it and some related questions. It was in doing this that I learned from Winnie that relativity of simultaneity as a fundamental explanation for things isn't the only thing that comes under the axe if you accept the conventionality thesis. And, half a year later, here we are again!

Well, gwellsjr was consistent. I got caught up thinking transverse doppler allowed an escape clause to measure, in that there was no plausible way to treat it as not caused by time dilation. I should have caught on much faster that this couldn't be true. No regrets - working through a specific case in detail is rarely a bad idea.

 

[VantagePoint72]

No regrets - working through a specific case in detail is rarely a bad idea.

Agreed. Appreciate that you soldiered on even when I started getting ornery It was a good illustration.

 

[TrickyDicky]

Yes, that is the entire reason for this discussion. Look up "conventionality of simultaneity in special relativity". The predictions of SR are invariant with respect to an anisotropic one-way speed of light (which is not measurable), so long as it's anisotropic in just such a way that the two-way speed of light is isotropic (which is measurable). Since clocks are synchronized in SR with one-way light pulses, or an equivalent scheme like slow-clock transport, calling two space-like separated events in SR "simultaneous" is a convention; not a fact. Moreover, you don't even have to use the same synchronization procedure for different frames (those that are rotated or boosted from your original frame). It is strange not to do so—which is PAllen's point—but nothing in relativity prevents you from it.

It is not so clear cut what SR prevents you or doesn't prevent you from doing.
One accepted view is that SR postulates only admit Einstein synchronization as the unique simultaneity convention(wich would make it no more a convention) as soon as one introduces a physical observer. Even if the relativity of simultaneity assures that simultaneity is not absolute for an abstract omniscient observer that looks at the Minkowski spacetime in a kind of block-ish way.
In any case fiddling with the one-way speed of light in such perverse and IMO contrary to SR postulates spirit way is ok I guess if it is promoted in this thread by our knowledgeable members , but I find it a bit arbitrary that one can speculate about an unmeasurable one way speed of light while not allowing to talk about a photon's frame that so frequently comes up in this forum(wich I think is rightly done). Talking about the one way speed of light amounts to the same thing IMO.

 

[VantagePoint72]

I find it a bit arbitrary that one can speculate about an unmeasurable one way speed of light while not allowing to talk about a photon's frame that so frequently comes up in this forum(wich I think is rightly done). Talking about the one way speed of light amounts to the same thing IMO.

You're missing the point. It is precisely because the one-way speed of light is immeasurable that the consequences of conventional simultaneity have to be considered. Speculation about it would be arguing for a particular synchrony convention—i.e. exactly what you're doing—when the fact is that the physical predictions of SR are invariant under changes of synchronization conventions. While I'm not a mentor, I would assume the reason people aren't allowed to discuss a photon's frame is because, as a photon is never at rest in any frame, it doesn't exist and hence any discussion about it is meaningless.

 

[TrickyDicky]

You're missing the point. It is precisely because the one-way speed of light is immeasurable that the consequences of conventional simultaneity have to be considered. Speculation about it would be arguing for a particular synchrony convention—i.e. exactly what you're doing—when the fact is that the physical predictions of SR are invariant under changes of synchronization conventions. While I'm not a mentor, I would assume the reason people aren't allowed to discuss a photon's frame is because, as a photon is never at rest in any frame, it doesn't exist and hence any discussion about it is meaningless.

Oh, I didn't know the second postulate of SR is now considered speculation since it assumes isotropy. I'd rather say introducing anisotropy of one way speed of light in convoluted and "perverse" (your words) ways looks like speculating, regardless of the invariance of final results in computations. At least for me the same way I favor SR over LET, I favor the interpretation that respects SR postulates when the predictions are the same.

 

[PAllen]

Oh, I didn't know the second postulate of SR is now considered speculation since it assumes isotropy. I'd rather say introducing anisotropy of one way speed of light in convoluted and "perverse" (your words) ways looks like speculating, regardless of the invariance of final results in computations. At least for me the same way I favor SR over LET, I favor the interpretation that respects SR postulates when the predictions are the same.

It's a definition, not a postulate. Choosing different clock synch simply means you will than measure non-isotropic c, and you end up with a metric more complex than Minkowski.

 

[TrickyDicky]

It's a definition, not a postulate.

Apologies. All my references call them postulates, I'll make sure they get this corrected.

Choosing different clock synch simply means you will than measure non-isotropic c, and you end up with a metric more complex than Minkowski.

I'm fine with Minkowski, thanks.

 

[bobc2]

I would assume the reason people aren't allowed to discuss a photon's frame is because, as a photon is never at rest in any frame, it doesn't exist and hence any discussion about it is meaningless.

I personally think that one must be careful in speaking about the existence of photons. From the vantage point of the 4-dimensional universe populated by 4-dimensional objects (represented by either world lines or world tubes) a photon would exist as a 4-dimensional object, perhaps represented by a world line (in the absence of knowledge about any photon structure). From this vantage point Lorentz frames are not necessary for the existence of a particle (worldline or world tube), notwithstanding how natural the convention is for describing many physical phenomena. If you are taking a hyperspace “birds eye view” of the 4-dimensional universe you don’t see coordinates, although you could notice symmetries among the patterns exhibited within the population of 4-D objects (which would be related to our laws of physics). In the 4-D universe view all objects are “all there at once” and exist at rest in a sense (possibly in a hypertime sense).

These comments are not intended to force on the PF a particular view of spacetime but merely to bring up the kinds of things you should perhaps consider if you are going to bring up the existence of a photon.

 

[DrGreg]

I would assume the reason people aren't allowed to discuss a photon's frame is because, as a photon is never at rest in any frame, it doesn't exist and hence any discussion about it is meaningless.

I personally think that one must be careful in speaking about the existence of photons.

I think when LastOneStanding said "it doesn't exist", he/she meant "a photon's frame", not "a photon".

 

[VantagePoint72]

I think when LastOneStanding said "it doesn't exist", he/she meant "a photon's frame", not "a photon".

Indeed—ambiguous pronouns take another victim.

 

[TrickyDicky]

I would assume the reason people aren't allowed to discuss a photon's frame is because, as a photon is never at rest in any frame, it doesn't exist and hence any discussion about it is meaningless.

Precisely that a photon is never at rest in any frame leads to the one-way speed of light not being measurable, it has to be postulated and that requires a (unique) convention, the one given by Einstein in his second postulate-definition.

 

[VantagePoint72]

Precisely that a photon is never at rest in any frame leads to the one-way speed of light not being measurable, it has to be postulated and that requires a (unique) convention, the one given by Einstein in his second postulate-definition.

No, it does not. One-way velocities of everything change when you change your synchrony convention, and these $\epsilon$-dependent one-way frame velocities in all directions are still required to be less than the one-way speed of light in those directions. There are no physical consequences of changing your synchronization. The existence of a time-like frame with light at rest would be very much a physical consequence. Einstein was well aware himself that it was a convention for the one-way speed of light when he laid out the postulates. As PAllen said, the simultaneity convention Einstein used is a definition, not one of the postulates.

I don't know what poor references you are referring to that call the Einstein clock synchronization a postulate, but in the 1905 paper Einstein certainly doesn't do so: "We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A. [Emphasis Einstein's]"

 

[bobc2]

Frames Don't Exist

Indeed—ambiguous pronouns take another victim.

The reason I assumed you were referring to the photon as not existing is that I wouldn't think anyone would refer to Frames as "existing." Frames are defined mathematically, but they don't exist. Of course some would consider photons to physically exist and others would say the existence of photons is not a subject of physics (nor would some consider the existence of any object a subject of physics).

But never mind my comments here since it is clear now that you were not referring to the existence of photons.