Can we really ever accurately test SR time dilation?

[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.

 

[TrickyDicky]

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.

First it's good you introduce an appeaser tone.
I actually have no problem with either approach,it's a matter of taste I guess.

I would only ask someone taking your approach to also recommend a name for the general theory of which SR is just an interpretation.

I would like for that theory to be GR but I understand at this point we cannot assert it (maybe when quantum gravity finally arrives).

 

[Dale]

I actually have no problem with either approach,it's a matter of taste I guess.

OK, that makes things easy then.

 

[TrickyDicky]

I was simply concerned about a possible double standard: In that if it is not allowed to talk about a photon's rest frame because it is not possible to attain that frame (frames are also conventional in SR) , we don't obtain any new falsiable prediction by introducing it and it is therefore meaningless, why is it ok to play around with possible one-way speeds of light if it is not possible to measure it and we have a convention that works fine in the sense that all predictions are correct. Isn't this fiddling meaningless too then?

 

[Dale]

I was simply concerned about a possible double standard: In that if it is not allowed to talk about a photon's rest frame

It is allowed to talk about it. There is even a FAQ about it. The FAQ and the discussions are short, but they are allowed.

The reason that the discussions about a photon's rest frame are so short is that it is a logical self-contradiction. After pointing out that it is a self-contradiction there really isn't much left to say.

Different synchronization conventions are not logical self contradictions, so the discussion can be substantially longer. I don't see any double-standard here.

 

[TrickyDicky]

Different synchronization conventions are not logical self contradictions, so the discussion can be substantially longer. I don't see any double-standard here.

Not sure what you exactly mean by logical self contradiction and to what extent different synchronization conventions that make no different predictions but seem to question light isotropy are more or less logically self contradictory, my point was more in the sense of being superfluous just like the ether was in Einstein's reasoning.

 

[Russell E]

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.

I don't think mathpages says the use of light pulses to define synchronization has nothing to do with the physical nature of light. Also, it has everything to do with choosing inertial coordinates... in fact, it is one and the same stipulation, provided you define (as Einstein did, implicitly) inertial coordinates as those in which the laws (plural) of mechanics hold good. You can find a more detailed discussion of this on the mathpages site here

www.mathpages.com/home/kmath684/kmath684.htm

 

[PAllen]

I don't think mathpages says the use of light pulses to define synchronization has nothing to do with the physical nature of light. Also, it has everything to do with choosing inertial coordinates... in fact, it is one and the same stipulation, provided you define (as Einstein did, implicitly) inertial coordinates as those in which the laws (plural) of mechanics hold good. You can find a more detailed discussion of this on the mathpages site here

www.mathpages.com/home/kmath684/kmath684.htm

In has been pointed out, and not under dispute in this thread, that choosing a anisotropic clock synch for coordinates leads to non-orthonormal coordinates, with cross terms in the metric. From this it is obvious that you would have non-vanishing connection even for an inertial observer, thus 'inertial forces'. However, in the formulation I gave in #49 (see also #57), where distances and angles are measured via two way lightspeed, the 3-d projection of world lines is the same as for standard coordinates, while the rate of motion (using the 'skewed' clocks) along 3-paths are adjusted by the 'inertial forces'.

 

[Russell E]

In has been pointed out, and not under dispute in this thread, that choosing a anisotropic clock synch for coordinates leads to non-orthonormal coordinates, with cross terms in the metric.

If you mean that the laws of Newtonian mechanics do not hold good (in the sense of Einstein's 1905 paper) in terms of anisotropic coordinates, then we're in agreement, but I don't agree that this is not under dispute in this thread, because (for example) it was stated in the previous post that "the stipulation has nothing to do with choosing inertial coordinates". What we've just agreed is that the stipulation to use isotropic light speed and the stipulation to use isotropic inertia are one and the same. So I would say this is exactly what is under dispute in this thread.

From this it is obvious that you would have non-vanishing connection even for an inertial observer, thus 'inertial forces'.

I would quibble with the word "observer", because an observer doesn't have a connection, vanishing or otherwise. An observer just exists along a specific worldline. To talk meaningfully about "connections" you need to talk in terms of coordinate systems. If what you're trying to say is that the laws of mechanics (in their homogeneous and isotropic form, i.e., no 'inertial forces') do not hold good in terms of an anisotropic system of coordinates (by definition!), then we're in agreement.

However, in the formulation I gave in #49 (see also #57), where distances and angles are measured via two way lightspeed, the 3-d projection of world lines is the same as for standard coordinates, while the rate of motion (using the 'skewed' clocks) along 3-paths are adjusted by the 'inertial forces'.

I don't see why this is prefaced with "However". It looks like just a re-statement of the preceding comment, i.e., inertia is not isotropic in terms of anisotropic coordinate systems - by definition. The single most important sentence in Einstein's 1905 paper is the very first one (after the preface), in which he says "Let us take a system of coordinates in which the equations of Newtonian mechanics hold good". He doesn't emphasize it, but this automatically entails the synchronization giving isotropic mechanical inertia, which is the basis for Newton's statements of the laws of mechanics. The isotropy of the speed of light in terms of such coordinates is an empirical fact. Of course, we aren't required to use such coordinates, so to that extent the isotropy of light speed is conventional... but the convention is simply the choice to use "coordinates in which the equations of Newtonian mechanics hold good".

To answer the OP's original question, of course it's possible to accurately measure time dilation, once you define what you mean by time dilation. In special relativity it means that if we establish a system of coordinates in which mechanical inertia is homogeneous and isotropic (as Newton taught us), and then compare the characteristic times of moving physical processes (clocks, particle decays, etc) with the time coordinates of that system, the observed difference is time dilation. This is one of the ways we test for Lorentz invariance of physical phenomena. The fact that all phenomena are Lorentz invariant is not at all tautological or conventional, it is an empirical fact.

 

[PAllen]

If you mean that the laws of Newtonian mechanics do not hold good (in the sense of Einstein's 1905 paper) in terms of anisotropic coordinates, then we're in agreement, but I don't agree that this is not under dispute in this thread, because (for example) it was stated in the previous post that "the stipulation has nothing to do with choosing inertial coordinates". What we've just agreed is that the stipulation to use isotropic light speed and the stipulation to use isotropic inertia are one and the same. So I would say this is exactly what is under dispute in this thread.

I don't think the consequences of non-standard clock synch are in dispute between myself, Dalespam, or LastOneStanding. There was no dispute when I mentioned quite early in this thread that you would get non-orthonormal spacetime coordinates. I don't think any us did not understand that that would mean laws of motion take a more complex form.

The statement about whether this is connected to choosing inertial coordinates depends on what you mean by this. There would be no debate about what is meant by standard inertial coordinates. However, one could argue that inertial coordinates encompass something more general.

I would quibble with the word "observer", because an observer doesn't have a connection, vanishing or otherwise. An observer just exists along a specific worldline. To talk meaningfully about "connections" you need to talk in terms of coordinate systems. If what you're trying to say is that the laws of mechanics (in their homogeneous and isotropic form, i.e., no 'inertial forces') do not hold good in terms of an anisotropic system of coordinates (by definition!), then we're in agreement.

I accept the quibble that an observer doesn't have a connection, and agree with the rest (obviously).

I don't see why this is prefaced with "However". It looks like just a re-statement of the preceding comment, i.e., inertia is not isotropic in terms of anisotropic coordinate systems - by definition.

It is not a re-statement. There are many other choices for choosing spatial coordinates which would not have indicated properties. For example, if you use an r coordinate based on proper distance along the surface of constant t, spatial coordinates of event would change (compared to standard inertial) and the metric and laws of motion would be even more complex (for example the two way coordinate speed of light would not be c; and inertial paths would not all be straight lines when projected to 3-surfaces of simultaneity). I am making the explicit point that if we base all spatial measurements on two way light measures, then spatial coordinates can be the same between standard inertial coordinates and non-standard inertial coordinates (with alternate clock synch). Inertial paths may have variations in coordinate speed but not spatial direction

...

To answer the OP's original question, of course it's possible to accurately measure time dilation, once you define what you mean by time dilation. According to special relativity, we simply need to establish a system of coordinates in which mechanical inertia is homogeneous and isotropic, and then compare the characteristic times of moving physical processes (clocks, particle decays, etc) with the time coordinates of that system, and note the time dilation. This is one of the ways we test for Lorentz invariance of physical phenomena. The fact that all phenomena are Lorentz invariant is not at all tautological or conventional, it is an empirical fact.

Even without introducing non-standard clock synch, you cannot say more than:

- you measure that muons created in the upper atmosphere reach the ground
- you measure transverse Doppler

because what these measures 'mean' is frame dependent even restricted to standard inertial coordinates. The first is distance contraction in the frame of the muon. The second is no longer transverse doppler in the emitter frame.

But I agree that it is perfectly correct to say these measure time dilation in a standard inertial coordinates set up by a specified observer. I really doubt anyone had any confusion on this point.

 

[VantagePoint72]

The statement about whether this is connected to choosing inertial coordinates depends on what you mean by this. There would be no debate about what is meant by standard inertial coordinates. However, one could argue that inertial coordinates encompass something more general.

Yes, this was the point I was trying to make, though clearly not well. The synchrony convention is connected to the form your inertial frames take. This is entirely independent from the postulate that the inertial frames (however you've defined them) are special.

 

[Russell E]

The statement about whether this is connected to choosing inertial coordinates depends on what you mean by this. There would be no debate about what is meant by standard inertial coordinates. However, one could argue that inertial coordinates encompass something more general.

There are two different meanings of "inertial coordinate system" in common usage, one of which leaves the synchronization unspecified (so we cannot say that Newton's laws hold good in terms of those coordinates), and one of which specifies the unique synchronization required in order for Newton's laws to hold good. Any time you use a system of coordinates and apply Newton's laws of motion (without 'inertial forces'), you are using the fully specified definition, with the synchronization based on the isotropy of mechanical inertia. This is the de facto "standard inertial coordinate system" for both Newtonian and relativistic physics, and Einstein specifically defined his coordinate systems this way. But most of the discussion in this thread has been based on the other (inadequate) definition of "inertial coordinate system", the one that leaves the synchronization unspecified.

There are many other choices for choosing spatial coordinates which would not have indicated properties...

I don't understand the point of this comment. If you're simply saying we are free to define space and time coordinates in a variety of ways, most of which are not "inertial coordinate systems" (according to either of the definitions), then that's certainly true. But I don't see how that bears on the issue. We're not trying to specify all things that are NOT coordinate systems in which Newton's laws hold good, we are trying to specify the coordinate systems in which they DO hold good. The point is that such coordinate systems possesses a unique synchronization, and it is in terms of these operationally meaningful coordinate systems that we quantify and measure both Newtonian and relativistic effects.

But I agree that it is perfectly correct to say these measure time dilation in a standard inertial coordinates set up by a specified observer. I really doubt anyone had any confusion on this point.

So you agree that "standard inertial coordinate systems" entail the unique synchronization such that mechanical inertia is isotropic? Then we're in agreement... but see below.

The synchrony convention is connected to the form your inertial frames take.

Only if you are using the incomplete definition of inertial coordinate system. (I take the liberty of replacing your word "frame" with "coordinate system", since the meaning of "frame" raises other definitional issues that I think are not central to this discussion.) The point is, Einstein referred to systems of coordinates in which Newton's laws (plural, not just the first law) hold good, and this uniquely specifies the synchronization such that mechanical inertia is isotropic. So there is no ambiguity or flexibility in the form of this class of coordinate systems (which is usually what people mean when they refer to inertial coordinates - even though they may not realize it). These coordinate systems can be operationally established, and the one-way speed of light is empirically equal to c in terms of these coordinates, and time dilation and length contraction and relativistic aberration and every other relativistic effect are directly expressible and measurable in terms of these coordinates.

 

[PAllen]

There are two different meanings of "inertial coordinate system" in common usage, one of which leaves the synchronization unspecified (so we cannot say that Newton's laws hold good in terms of those coordinates), and one of which specifies the unique synchronization required in order for Newton's laws to hold good. Any time you use a system of coordinates and apply Newton's laws of motion (without 'inertial forces'), you are using the fully specified definition, with the synchronization based on the isotropy of mechanical inertia. This is the de facto "standard inertial coordinate system" for both Newtonian and relativistic physics, and Einstein specifically defined his coordinate systems this way. But most of the discussion in this thread has been based on the other (inadequate) definition of "inertial coordinate system", the one that leaves the synchronization unspecified.

I have no disagreement with the above. Further I believe the main participants in the thread understood it.

I don't understand the point of this comment. If you're simply saying we are free to define space and time coordinates in a variety of ways, most of which are not "inertial coordinate systems" (according to either of the definitions), then that's certainly true. But I don't see how that bears on the issue. We're not trying to specify all things that are NOT coordinate systems in which Newton's laws hold good, we are trying to specify the coordinate systems in which they DO hold good. The point is that such coordinate systems possesses a unique synchronization, and it is in terms of these operationally meaningful coordinate systems that we quantify and measure both Newtonian and relativistic effects.

I was responding specifically to your claim that discussion I had following 'However' added no content. I disagree. It was clarifying what must change with choice of synchronization versus what need not change. My further clarification that this is a non-trivial statement is that the arguably most common way to build up distance coordinates given a space-time foliation (using proper distance) will change more things than necessary. By instead using radar distance rather proper distance within spatial slices, more of the features of the standard inertial coordinates can be carried over to non-standard ones. All of this is because you insisted my discussion following 'However' was redundant.

Only if you are using the incomplete definition of inertial coordinate system. (I take the liberty of replacing your word "frame" with "coordinate system", since the meaning of "frame" raises other definitional issues that I think are not central to this discussion.) The point is, Einstein referred to systems of coordinates in which Newton's laws (plural, not just the first law) hold good, and this uniquely specifies the synchronization such that mechanical inertia is isotropic. So there is no ambiguity or flexibility in the form of this class of coordinate systems (which is usually what people mean when they refer to inertial coordinates - even though they may not realize it). These coordinate systems can be operationally established, and the one-way speed of light is empirically equal to c in terms of these coordinates, and time dilation and length contraction and relativistic aberration and every other relativistic effect are directly expressible and measurable in terms of these coordinates.

Everything measurable in one coordinates system is measurable in any other (obviously; coordinates are not part of the physics being modeled, just convention for describing it). Any fully specified coordinate system can be operationally established. Invariant things don't change no matter what the coordinates (clock1 and clock2 show different times when brought together; detector x measures red shift compared to the frequency emitted as measured locally to the emitter; muons created in the upper atmosphere reach ground; muons in accelerators circle a huge number of times on average, before decaying). Note that if you pick a different synchronization, then the one way speed of light empirically not equal to c. Thus, unlike the other things in my list, it is synchronization convention dependent.

Obviously, I agree that Newton's laws (and Maxwell's equations) take simplest form in standard inertial coordinates. They can also, obviously, be written in a general, abstract form which is the same in all coordinates. Not practical for computations, but correct nonetheless.

 

[Russell E]

Everything measurable in one coordinates system is measurable in any other...

Much of this thread has revolved around the claim that things like time dilation and the one-way speed of light are not measurable, because they rely on a convention. Of course, every quantification of a physical parameter relies on a convention (ultimately coming down to a comparison of one thing with another), but the point is that the convention in question here is nothing other than the convention of using inertial coordinates, defined (as Einstein expressed it, somewhat imprecisely) as coordinates in which Newton's laws of mechanics hold good. The fact that the one-way speed of light is c in terms of standard inertial coordinates is not a matter of convention, it is an empirical fact. You say everyone here agrees with this, and yet every time I say it, someone disagrees, and repeats the claim that the one-way speed of light in terms of inertial coordinates is not measurable. They say it depends on the form of the inertial coordinates, so they obviously don't agree that inertial coordinates possesses a unique synchronization such that the numerical value of the one-way speed of light is c, and all other relativistic effects have their expected numerical values.

 

[PAllen]

Much of this thread has revolved around the claim that things like time dilation and the one-way speed of light are not measurable, because they rely on a convention. Of course, every quantification of a physical parameter relies on a convention (ultimately coming down to a comparison of one thing with another), but the point is that the convention in question here is nothing other than the convention of using inertial coordinates, defined (as Einstein expressed it, somewhat imprecisely) as coordinates in which Newton's laws of mechanics hold good. The fact that the one-way speed of light is c in terms of standard inertial coordinates is not a matter of convention, it is an empirical fact. You say everyone here agrees with this, and yet every time I say it, someone disagrees, and repeats the claim that the one-way speed of light in terms of inertial coordinates is not measurable. They say it depends on the form of the inertial coordinates, so they obviously don't agree that inertial coordinates possesses a unique synchronization such that the numerical value of the one-way speed of light is c, and all other relativistic effects have their expected numerical values.

I do not think there is disagreement with any of the following (there is only disagreement on what whether you can talk about non-standard inertial coordinates; you sort of want to say you can't, without quite going so far):

- if you use standard clock synch to set up inertial coordinates, you get standard inertial coordinates in which the coordinate expression of physical laws is particularly simple; this convention defines that the one way speed of light is isotropically c.

- if you set up inertial coordinates such that the Newton's and Maxwell's laws have simplest coordinate expression (alternatively, the the metric is diag(1,-1,-1,-1) in appropriate signature), you will find that one way speed is c.

There was, initially, a substantive disagreement about whether changing clock synch alone could cause transverse doppler to have a different coordinate manifestation than time dilation in inertial coordinates in which the detection apparatus (not the emitter) was at rest. Note, this question cannot even be asked without admitting non-standard inertial coordinates. I believe consensus was reached that changing clock synch alone could cause particular measure of transverse doppler to manifest purely as variation as in the one way speed of light, with the emitter clock agreeing with adjacent inertial frame clocks for the relevant part of its world line.

 

[Russell E]

...there is only disagreement on whether you can talk about non-standard inertial coordinates; you sort of want to say you can't, without quite going so far...

What I want to say - and what I have said - is that there's no ambiguity in the coordinates systems in which "the equations of Newtonian mechanics hold good" (as Einstein put it), and that these are the coordinate systems that people normally have in mind when they think of "inertial coordinates". For this reason, the expression "non-standard inertial coordinates" tends to be misleading, because it suggests that there's some ambiguity in that class of coordinate systems - which there isn't. This gets back to the two different definitions of "inertial coordinates". With the full definition of "inertial coordinates", the expression "non-standard inertial coordinates" is a contradiction in terms. Only if we use the deficient and ambiguous definition of "inertial coordinates" (in which the Newtonian equations of mechanics are not valid) is it permissible to talk about "non-standard inertial coordinates". If we're going to do that, we should at least announce that this is what we're doing. The best approach is just to clearly define whatever systems of coordinates we have in mind (as Einstein did). When we do this, all the misunderstandings evaporate. The important point to convey to students is that the invariance of the one-way speed of light in terms of coordinates in which the Newtonian equations of motion are valid (roughly speaking) is not conventional, it is an empirical fact.

- if you use standard clock synch to set up inertial coordinates, you get standard inertial coordinates in which the coordinate expression of physical laws is particularly simple; this convention defines that the one way speed of light is isotropically c.

It would be more accurate to say "If we impose isotropy of light speed to establish a system of coordinates, we find empirically that mechanical inertia is isotropic in terms of those coordinates, and hence these are inertial coordinates (the full definition)."

- if you set up inertial coordinates such that the Newton's and Maxwell's laws have simplest coordinate expression (alternatively, the the metric is diag(1,-1,-1,-1) in appropriate signature), you will find that one way speed is c.

I don't think it's helpful to include Maxwell's laws in that statement, because that is tantamount to using isotropic light speed (speed of electromagnetic waves), so it's circular. The isotropy and homogeneity of mechanical inertia are the necessary and sufficient conditions to arrive at the full definition of inertial coordinate systems. (It also isn't helpful to talk about the metric being Minkowskian, since that has physical meaning only once we've given operational significance to the coordinates, so it just begs the question.)