Can we really ever accurately test SR time dilation?

[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.

 

[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$\theta$dt 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$\theta$dt 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.