Can we really ever accurately test SR time dilation?

[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.

 

[DiracPool]

Hey, OP here, just wanted to check in and thank all of you for the now 100 REPLIES! I've learned a lot. Keep em coming!

 

[TrickyDicky]

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]"

Let me quote the mathpages site so you can clarify your confusion:
"Einstein tried to make the meaning of this definition more clear by saying

That light requires the same time to traverse the path A to M (the midpoint of AB) as for the path B to M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.

Of course, this concept of simultaneity is also embodied in Einstein's second "principle", which asserts the invariance of light speed. Throughout the writings of Poincare, Einstein, and others, we see the invariance of the speed of light referred to as a convention, a definition, a stipulation, a free choice, an assumption, a postulate, and a principle... as well as an empirical fact. There is no conflict between these characterizations, because the convention (definition, stipulation, free choice, principle) that Poincare and Einstein were referring to is nothing other than the decision to use inertial coordinate systems, and once this decision has been made, the invariance of light speed is an empirical fact."

 

[VantagePoint72]

Let me quote the mathpages site so you can clarify your confusion:
"Einstein tried to make the meaning of this definition more clear by saying

That light requires the same time to traverse the path A to M (the midpoint of AB) as for the path B to M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.

Of course, this concept of simultaneity is also embodied in Einstein's second "principle", which asserts the invariance of light speed. Throughout the writings of Poincare, Einstein, and others, we see the invariance of the speed of light referred to as a convention, a definition, a stipulation, a free choice, an assumption, a postulate, and a principle... as well as an empirical fact. There is no conflict between these characterizations, because the convention (definition, stipulation, free choice, principle) that Poincare and Einstein were referring to is nothing other than the decision to use inertial coordinate systems, and once this decision has been made, the invariance of light speed is an empirical fact."

Mathpages is correct in saying it's a stipulation I can make of my own free will and has nothing to do with the physical nature of light; however, that stipulation also has nothing to do with choosing inertial coordinates. The two-way invariance of the speed of light is an empirical fact; the one-way is not because it is fundamentally not measurable. In order to measure a one-way speed, you need clocks at two places. Those clocks need to be synchronized. Thus, the synchronization scheme you use determines your one-way speeds, including that of light. Until you have chosen such a scheme, a one-way speed is a meaningless quantity—and even after you've chosen one, it's a coordinate dependent one. It's not that we are ignorant of the "true" one-way speed of light and, if we knew what it really was, we could establish the correct synchrony convention. It's that one-way speeds are intrinsically a matter of definition since they require synchronized clocks. By using the Einstein synchronization scheme, we define the one-way speed of light to be isotropic. It's a nice definition that simplifies a lot of things, but it is not an assumption about the physical propagation of light.

The fact that earlier you thought an anisotropic speed of light would allow rest frames of photons is, for me, pretty good demonstration that you have no idea what you're talking about and are probably Googling this as you go along. So please don't project your own confusion onto other people. In any case, the others are welcome to continue with this if they like. Personally, I find you incredibly obnoxious and I'm not going to waste more time repeating the same things over and over.

 

[TrickyDicky]

Mathpages is correct in saying it's a stipulation I can make of my own free will and has nothing to do with the physical nature of light; however, that stipulation also has nothing to do with choosing inertial coordinates. The two-way invariance of the speed of light is an empirical fact; the one-way is not because it is fundamentally not measurable. In order to measure a one-way speed, you need clocks at two places. Those clocks need to be synchronized. Thus, the synchronization scheme you use determines your one-way speeds, including that of light. Until you have chosen such a scheme, a one-way speed is a meaningless quantity—and even after you've chosen one, it's a coordinate dependent one. It's not that we are ignorant of the "true" one-way speed of light and, if we knew what it really was, we could establish the correct synchrony convention. It's that one-way speeds are intrinsically a matter of definition since they require synchronized clocks. By using the Einstein synchronization scheme, we define the one-way speed of light to be isotropic. It's a nice definition that simplifies a lot of things, but it is not an assumption about the physical propagation of light.

You always dismiss like that what you can't grasp? You missed the part where it says that the definition is embodied in the second postulate which I'd say is considered an assumption about light propagation.

The fact that earlier you thought an anisotropic speed of light would allow rest frames of photons is, for me, pretty good demonstration that you have no idea what you're talking about and are probably Googling this as you go along. So please don't project your own confusion onto other people. In any case, the others are welcome to continue with this if they like. Personally, I find you incredibly obnoxious and I'm not going to waste more time repeating the same things over and over.

It's funny that you base your attack on something I never claimed. Once again you misunderstand (or use a straw man) and the fact that you have to recur to insulting and personal attacks to make your point denotes it. It's always a bad sign when this happens, please refrain from it, otherwise I guess I should report it.

 

[Dale]

You missed the part where it says that the definition is embodied in the second postulate which I'd say is considered an assumption about light propagation.

I think that the discussion is a little bit of a semantic argument.

You have Einstein's postulates (he did emphasize that the second one was "by definition", but he also explicitly gave it the "status of a postulate" so being a definition and being a postulate aren't mutually exclusive according to Einstein). Those postulates lead to the Lorentz transform, which in turn lead to a lot of testable predictions.

There are also alternative ways to derive the Lorentz transform, such as LET. Those derivations lead to the exact same testable predictions, with only different explanations as to the physical causes.

There are also alternative transforms, such as Winnie's, that are not the same as the Lorentz transform, but also lead to the exact same testable predictions, with only different labeling of the physical causes.

So then the semantic argument becomes, what parts of these three sets do we consider to be "SR". If we consider "SR" to be a theory, then all of these are experimentally equivalent and therefore they are all different interpretations or derivations of the same theory, SR. If we consider "SR" to be only Einstein's specific derivation (i.e. his two postulates) then SR becomes merely an interpretation of the unnamed general theory which encompasses all of the experimentally equivalent interpretations.

LastOneStanding appears to take the former approach, and you appear to take the latter approach. I don't have a name for the unnamed general theory for your approach, so I would tend to take LastOneStanding's approach also. But in the end, it is just semantics and hardly worth arguing over. I would only ask someone taking your approach to also recommend a name for the general theory of which SR is just an interpretation.