Relativity and Lorentz Symmetry: What is the Relationship to Reality?

[JesseM]

[Mentor's note: This thread was extracted from another thread, SR transforms of matter/light interactions at the request of some of the participants because it drifts significantly from the original topic of that thread. You may want to edit some of your postings to reflect the changed context.]
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Suffice it to say that SR is a coordinate-system dependent interpretation of the laws of physics, and as such it should not be confused with "reality" per se.

No, SR is just a statement about the fundamental laws of physics being Lorentz-symmetric. This is still true even if you choose not to use the Lorentz transformation to define your set of inertial coordinate systems. (Also, the choice of what coordinate system to use is not in itself an 'interpretation of the laws of physics', any more than your choice of where to place the origin of your spatial coordinate axes is an interpretation of the laws of physics--it seems to me that the only way the LET can count as a distinct 'interpretation' is if it postulates some unobservable physical entities which are governed by non-Lorentz-symmetric laws.)

 

[nakurusil]

There is a physical difference between objects in relative motion to one another. For example, if two identical atomic clocks are synchronized while co-located and at rest in a first inertial frame; then one clock is moved into a second inertial frame for a time; then returned to the starting position; when the elapsed times on the two clocks are compared they are seen to be physically different.

Why not do the honest thing and admit that you put up a silly post?

 

[Aether]

Ok, first let me say that JesseM, pervect, Hurkyl (and a few others) are my teachers, so what I'm about to say shouldn't be construed as an argument against what JesseM is saying but rather as my exploration of a potential opportunity to learn something new.

No, SR is just a statement about the fundamental laws of physics being Lorentz-symmetric. This is still true even if you choose not to use the Lorentz transformation to define your set of inertial coordinate systems.

When I said "SR" I was referring to the two postulates of SR + what follows from them. So, I am distinguishing between the reality of local Lorentz symmetry vs. the coordinate-system dependent interpretation following from the two postulates.

(Also, the choice of what coordinate system to use is not in itself an 'interpretation of the laws of physics', any more than your choice of where to place the origin of your spatial coordinate axes is an interpretation of the laws of physics--it seems to me that the only way the LET can count as a distinct 'interpretation' is if it postulates some unobservable physical entities which are governed by non-Lorentz-symmetric laws.)

I am distinguishing the different conclusions that can be reached by application of the various simultaneity conventions as "interpretations" vs. the reality of local Lorentz symmetry which is invariant over a change of simultaneity convention.

Why not do the honest thing and admit that you put up a silly post?

If JesseM and pervect both say that I put up a silly post, then I will admit that I did so. Otherwise, I will try to learn anything new that I can while we are on this subject and not admit to such a thing unless my mind is changed about something.

 

[JesseM]

When I said "SR" I was referring to the two postulates of SR + what follows from them. So, I am distinguishing between the reality of local Lorentz symmetry vs. the coordinate-system dependent interpretation following from the two postulates.

Ah, but the two postulates are not coordinate-dependent, they are physical postulates about what will be measured on physical systems of rulers and clocks constructed according to Einstein's specifications. When answering the question of what they will measure, you have no obligation to use a coordinate system that corresponds to their measurements! You could just as well use some other set of coordinate systems like the ones determined by coordinate transformation that Mansouri and Sexl give in their paper, and as long as you make sure to use the correct equations of the laws of physics to go with whatever coordinate system you use, you will still end up predicting that the different systems of rulers and clocks described by Einstein will measure identical results when they do identical experiments in their rest frame.

I am distinguishing the different conclusions that can be reached by application of the various simultaneity conventions as "interpretations" vs. the reality of local Lorentz symmetry which is invariant over a change of simultaneity convention.

Well, I would argue that the theory known as "SR" deals only with physical predictions like the ones described above, it is conventional to use coordinate systems which are based on these systems of rulers and clocks but that isn't a part of the physical theory.

If JesseM and pervect both say that I put up a silly post, then I will admit that I did so. Otherwise, I will try to learn anything new that I can while we are on this subject and not admit to such a thing unless my mind is changed about something.

I think that's a good attitude. I do think your original post showed confusion about which ideas are a core part of the "theory of SR" and which are just commonplace conventions used in solving SR problems, but these issues are somewhat subtle so this kind of confusion is understandable.

 

[Aether]

If I don't take isotropy for granted, what are the other interpretations?

You can take two-way light speed isotropy for granted because Michelson interferometers confirm that, but you can not in general take one-way light speed isotropy for granted because there is no experiment that can measure that in a coordinate-system independent way. This is because there is currently no way to synchronize two clocks at different locations other than to make some coordinate-system dependent assumption. For red-shifts, there is no ambiguity of interpretation due to the conventionality of clock synchronization conventions because the isotropy of v and c are both affected in the say way by an arbitrary choice of clock synchronization conventions.

It's the (in)famous barn and pole paradox about relativity of simultaneity. The linked page shows the calculations as well as the Minkowski diagram of the case. The rocket fits in the barn only for the barn's frame of reference of course.

This page shows an example calculated using the one-dimensional Lorentz transformation. I may come back to this later to show a counter-example using the https://www.physicsforums.com/showpost.php?p=755432&postcount=92", but first let me have this discussion with JesseM to be sure that I am not really confused about something first. However, if you want to go ahead and do the calculations yourself then I will discuss the results with you.

Ah, but the two postulates are not coordinate-dependent, they are physical postulates about what will be measured on physical systems of rulers and clocks constructed according to Einstein's specifications.

The two postulates are not physical. They define a set of coordinate systems wherein relative simultaneity is implied. I can use a different set of postulates to construct an equally valid set of coordinate systems wherein absolute simultaneity is implied. Maybe you can say that the postulates themselves are not coordinate-dependent, but their sole purpose is to construct a particular set of coordinate systems; and at least some of the conclusions drawn from their application are coordinate-system dependent interpretations of physical effects.

When answering the question of what they will measure, you have no obligation to use a coordinate system that corresponds to their measurements! You could just as well use some other set of coordinate systems like the ones determined by coordinate transformation that Mansouri and Sexl give in their paper, and as long as you make sure to use the correct equations of the laws of physics to go with whatever coordinate system you use, you will still end up predicting that the different systems of rulers and clocks described by Einstein will measure identical results when they do identical experiments in their rest frame.

If we express in tensor notation the (currently accepted) equations for the laws of physics within an (preferred) inertial frame, then these equations will correctly predict the results of all experiments (to date) carried out in that frame. There is no question of different "equations for the laws of physics to go with whatever coordinate system you use" for any other frame, the same set of equations for the laws of physics can be used regardless of the coordinate system chosen as long as we do all of the coordinate transformations correctly.

Well, I would argue that the theory known as "SR" deals only with physical predictions like the ones described above, it is conventional to use coordinate systems which are based on these systems of rulers and clocks but that isn't a part of the physical theory.

Hurkyl, pervect, and possibly coalquay4004 all said that LET is a formulation of SR in a different coordinate system, and that the two postulates don't define SR per se but only one formulation of SR in a particular coordinate system. They didn't provide any reference for this though, and I have never seen a statement like that anywhere else. Can you provide a reference to show how SR is generally defined without necessarily implying the relativity of simultaneity?

I think that's a good attitude. I do think your original post showed confusion about which ideas are a core part of the "theory of SR" and which are just commonplace conventions used in solving SR problems, but these issues are somewhat subtle so this kind of confusion is understandable.

Which statement of mine is it that you think showed confusion exactly?

 

[MeJennifer]

Hurkyl, pervect, and possibly coalquay4004 all said that LET is a formulation of SR in a different coordinate system, and that the two postulates don't define SR per se but only one formulation of SR in a particular coordinate system.

While the formulas are identical between LET and relativity their interpretations of reality are very different.
In relativity distance and duration are dynamic and depend on the relative speed of the measured object while in LET distance and duration are static and contraction and dilation are caused by objects moving relative to the ether.
In LET there is absolute space and time, in relativity there is not.

 

[Aether]

While the formulas are identical between LET and relativity their interpretations of reality are very different.
In relativity distance and duration are dynamic and depend on the relative speed of the measured object while in LET distance and duration are static and contraction and dilation are caused by objects moving relative to the ether.
In LET there is absolute space and time, in relativity there is not.

Yes, my point is to beware of such interpretations of reality because they aren't based on observation, and therefore they are outside of the domain of science. I am particularly alarmed by such interpretations of reality because they can fool us into ruling-out theories that we think are contrary to observed facts when they really aren't.

 

[MeJennifer]

Yes, my point is to beware of such interpretations of reality because they aren't based on observation, and therefore they are outside of the domain of science. I am particularly alarmed by such interpretations of reality because they can fool us into ruling-out theories that we think are contrary to observed facts when they really aren't.

Actually I agree with you.

So then that is why I responded to your earlier statement saying:

Although there is a physical (real) difference between objects in these two frames...

There is no experimental evidence for this assertion.
In LET it is believed to be true but not in relativity.

 

[Aether]

Actually I agree with you.

So then that is why I responded to your earlier statement saying:

There is no experimental evidence for this assertion.
In LET it is believed to be true but not in relativity.

Well, I don't disagree with you either.

That's why I said that I don't want to argue over the semantics of this, although if I can find a more precise way to say what I mean in a coordinate-system independent way that would be nice. Poor nakurusil is over there insisting that there is no physical difference between objects in relative motion to one another......I got hit by a baseball one time, and it sure felt real to me.

 

[nakurusil]

Well, I don't disagree with you either.

That's why I said that I don't want to argue over the semantics of this, although if I can find a more precise way to say what I mean in a coordinate-system independent way that would be nice. Poor nakurusil is over there insisting that there is no physical difference between objects in relative motion to one another......I got hit by a baseball one time, and it sure felt real to me.

What I objected to is this statement:

There is a physical difference between objects in relative motion to one another. For example, if two identical atomic clocks are synchronized while co-located and at rest in a first inertial frame; then one clock is moved into a second inertial frame for a time; then returned to the starting position; when the elapsed times on the two clocks are compared they are seen to be physically different.

Your statement was wrong in first place and is still wrong, you are trying to take us through some metaphysical detour of LET vs SR. I explained to you that you picked a wrong example, i.e. you do not understand the fact that you are operating outside SR already. Very simple.

 

[JesseM]

The two postulates are not physical. They define a set of coordinate systems wherein relative simultaneity is implied. I can use a different set of postulates to construct an equally valid set of coordinate systems wherein absolute simultaneity is implied. Maybe you can say that the postulates themselves are not coordinate-dependent, but their sole purpose is to construct a particular set of coordinate systems; and at least some of the conclusions drawn from their application are coordinate-system dependent interpretations of physical effects.

This is the part of your argument that I was referring to as "confused". Of course the postulates are physical--they are a statement that if you build measuring-devices of the type Einstein specified, the laws of physics will be measured to work the same way in each one. Again, this would be true even if you used a different set of coordinate systems (with a different notion of simultaneity) to actually analyze this problem and make predictions about what each of these measuring-devices will measure. How do you think that isn't a physical prediction? And if you agree "the laws of physics are Lorentz-symmetric" is a physical statement, what difference do you imagine there is between that statement and the statement "the laws of physics will work the same way in different measuring-systems whose measurements are related by the Lorentz transform"? How would you express the fact that the laws of physics are Lorentz-symmetric if you were working in some other set of coordinate systems?

If we express in tensor notation the (currently accepted) equations for the laws of physics within an (preferred) inertial frame, then these equations will correctly predict the results of all experiments (to date) carried out in that frame. There is no question of different "equations for the laws of physics to go with whatever coordinate system you use" for any other frame, the same set of equations for the laws of physics can be used regardless of the coordinate system chosen as long as we do all of the coordinate transformations correctly.

That's true, but I wasn't talking about the laws of physics expressed in tensor notation, since any law of physics (including Newtonian mechanics) can be expressed in tensor notation and it will then work the same in all coordinate systems. The easiest and least technical way to understand the concept of Lorentz-symmetry is to say that if you express the laws of physics in terms of algebra/calculus equations (like expressing the equation for time dilation as $$t = t_0 / \sqrt{1 - v^2/c^2}$$), then the equations will be the same for each of the inertial measuring-systems described by Einstein which define the coordinate systems of the Lorentz transformation, while they will not be the same (again, assuming you are expressing them in non-tensor notation) in other types of coordinate systems.

Hurkyl, pervect, and possibly coalquay4004 all said that LET is a formulation of SR in a different coordinate system, and that the two postulates don't define SR per se but only one formulation of SR in a particular coordinate system.

Again, SR is defined by the statement that the laws of physics have a particular symmetry, namely Lorentz-symmetry. I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory, but the way of defining it above is a perfectly valid one that's easy to understand without knowing a lot of advanced math, and it is a physical definition that doesn't require that you yourself use the coordinate systems defined by the Lorentz transformation, you can use whatever coordinate system you like to predict what would be measured in the type of physical ruler-clock system described by Einstein.

They didn't provide any reference for this though, and I have never seen a statement like that anywhere else. Can you provide a reference to show how SR is generally defined without necessarily implying the relativity of simultaneity?

The way I defined it above does not "imply the relativity of simultaneity", since you are free to analyze those different ruler/clock systems from the perspective of a set of inertial coordinate systems which all agree on simultaneity, like the ones defined in the Mansouri-Sexl paper.

Which statement of mine is it that you think showed confusion exactly?

You seem to be rather confused about the difference between coordinate-dependent statements and "physical" or coordinate-independent ones. The fact that you don't understand that the question "what would be measured by a system of physical rulers and clocks constructed according to Einstein's specifications in his 1905 paper" is a physical question, not a coordinate-dependent one, is the prime example of this confusion.

 

[Aether]

This is the part of your argument that I was referring to as "confused". Of course the postulates are physical--they are a statement that if you build measuring-devices of the type Einstein specified, the laws of physics will be measured to work the same way in each one. Again, this would be true even if you used a different set of coordinate systems (with a different notion of simultaneity) to actually analyze this problem and make predictions about what each of these measuring-devices will measure. How do you think that isn't a physical prediction?

I think that by building measuring-devices of the type Einstein specified that you have necessarily embedded a https://www.physicsforums.com/showpost.php?p=973915&postcount=129" into many of the "measurements" that you could make with them.

And if you agree "the laws of physics are Lorentz-symmetric" is a physical statement, what difference do you imagine there is between that statement and the statement "the laws of physics will work the same way in different measuring-systems whose measurements are related by the Lorentz transform"?

I agree that the known laws of physics are Lorentz-symmetric is a physical statement, but also seek-out possible observable violations of this which may define a locally preferred frame. I don't mind ignoring a potential locally preferred frame by using the Lorentz transforms, but I do object to ruling-out the possible existence of one by other than observational means.

How would you express the fact that the laws of physics are Lorentz-symmetric if you were working in some other set of coordinate systems?

I would express the laws of physics in tensor (spinor) notation, note that they agree with all experiments in at least one (locally preferred) inertial reference frame, and then transform to the other set of coordinate systems; requiring that any transformations preserve an invariant line-element may be the key step in expressing Lorentz symmetry. I would go to this trouble only because I am trying to examine the fundamental laws of physics themselves while trying to avoid costly coordinate-system dependent detours when designing experiments and writing-up results/predictions.

That's true, but I wasn't talking about the laws of physics expressed in tensor notation, since any law of physics (including Newtonian mechanics) can be expressed in tensor notation and it will then work the same in all coordinate systems. The easiest and least technical way to understand the concept of Lorentz-symmetry is to say that if you express the laws of physics in terms of algebra/calculus equations (like expressing the equation for time dilation as $$t = t_0 / \sqrt{1 - v^2/c^2}$$), then the equations will be the same for each of the inertial measuring-systems described by Einstein which define the coordinate systems of the Lorentz transformation, while they will not be the same (again, assuming you are expressing them in non-tensor notation) in other types of coordinate systems.

I have stipulated in other thread(s) that Einstein's simultaneity convention simplifies many practical calculations by collapsing the tensor notation into a simpler notation. I don't have any objection to that until it leads someone to a belief that relativity of simutaneity is an empirically established fact, for example.

Again, SR is defined by the statement that the laws of physics have a particular symmetry, namely Lorentz-symmetry. I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory, but the way of defining it above is a perfectly valid one that's easy to understand without knowing a lot of advanced math, and it is a physical definition that doesn't require that you yourself use the coordinate systems defined by the Lorentz transformation, you can use whatever coordinate system you like to predict what would be measured in the type of physical ruler-clock system described by Einstein.

But it embeds a conventional clock synchroinzation choice that leads people to a belief that the relativity of simultaneity is "real", and that isn't necessarily so.

The way I defined it above does not "imply the relativity of simultaneity", since you are free to analyze those different ruler/clock systems from the perspective of a set of inertial coordinate systems which all agree on simultaneity, like the ones defined in the Mansouri-Sexl paper.

The way you defined it above (actually, there is an ambiguity here because you have talked about several things above) does not imply the relativity of simultaneity because that isn't the Lorentz tranform for the time coordinate, but rather it is the LET transform. The way you defined it above is insconsistent with the two postulates of SR.

You seem to be rather confused about the difference between coordinate-dependent statements and "physical" or coordinate-independent ones. The fact that you don't understand that the question "what would be measured by a system of physical rulers and clocks constructed according to Einstein's specifications in his 1905 paper" is a physical question, not a coordinate-dependent one, is the prime example of this confusion.

Ok, if you will bear with me I would certainly like to dispell any confusion that may be lurking.

 

[Aether]

Your statement was wrong in first place and is still wrong, you are trying to take us through some metaphysical detour of LET vs SR.

My statement may or may not be viewed as "wrong" depending on which coordinate system that you choose to work in; so it is not wrong in reality, though I may learn to phrase it more effectively I'll admit. My reference to the LET transforms as a counter-example to the Lorentz transforms follows their use by Mansouri & Sexl. This is standard mainstream physics, although it is unfamiliar to many in the field. If you do not have access to their papers, I could make them available to you. You can also search this forum for an extensive discussion of them.

I explained to you that you picked a wrong example, i.e. you do not understand the fact that you are operating outside SR already. Very simple.

Ok, I accept the validity of SR within its narrowly defined domain of applicability. Do you accept that LET (aka GGT) is empirically equivalent to SR?

 

[JesseM]

I think that by building measuring-devices of the type Einstein specified that you have necessarily embedded a https://www.physicsforums.com/showpost.php?p=973915&postcount=129" into many of the "measurements" that you could make with them.

Not if I don't use these measuring-devices to define my coordinate system! I am simply treating them as a physical system to be analyzed, no different than the clocks in the twin paradox or any other physical system. Are you really saying that if I analyze any other physical system using, say, the coordinate systems provided by the Mansouri-Sexl, everything is fine and dandy, but if I analyze that particular physical systems consisting of a grid of rulers and clocks constructed according to Einstein's specifications, I am magically forced to abandon the coordinate system I'd been using and adopt the coordinate system defined by these rulers and clocks? How could that possibly make any sense? This is why I said you were confused!

I agree that the known laws of physics are Lorentz-symmetric is a physical statement, but also seek-out possible observable violations of this which may define a locally preferred frame.

OK, SR is simply the theory that all fundamental laws are Lorentz-symmetric, if a law is found that falsifies this, then SR will be falsified. However, the Lorentz Ether theory does not predict that there will be any measurable violations of Lorentz-symmetry, although it may be an interpretation which imagines fundamentally unmeasurable entities which violate it, in the same way that Bohm's interpretation of quantum mechanics imagines fundamentally unmeasurable precise positions for particles at all times.

I don't mind ignoring a potential locally preferred frame by using the Lorentz transforms, but I do object to ruling-out the possible existence of one by other than observational means.

Yes, you're free to imagine whatever you want for future laws of physics. But this is not what we were debating; we were debating whether Einstein's two postulates are purely physical ones, or whether they commit you to using a particular coordinate system and thus would be violated by a restatement of the laws of physics in a different set of coordinate systems which nonetheless made no distinct physical predictions.

How would you express the fact that the laws of physics are Lorentz-symmetric if you were working in some other set of coordinate systems?

I would express the laws of physics in tensor (spinor) notation, note that they agree with all experiments in at least one (locally preferred) inertial reference frame, and then transform to the other set of coordinate systems; requiring that any transformations preserve an invariant line-element may be the key step in expressing Lorentz symmetry. I would go to this trouble only because I am trying to examine the fundamental laws of physics themselves while trying to avoid costly coordinate-system dependent detours when designing experiments and writing-up results/predictions.

I don't know enough about tensor notation to say if "requiring that any transformations preserve an invariant line-element" would be equivalent to the assumption of Lorentz-symmetry, but regardless, you are still confused if you think the mathematically less sophisticated statement that "the laws of physics expressed in non-tensor form will obey the same equations in all the inertial measuring-systems constructed according to Einstein's procedure" is itself a coordinate-dependent statement. This statement could be verified in any arbitrary coordinate system or set of coordinate systems, it's a physical statement about the results of physical measurements made using physical devices.

I have stipulated in other thread(s) that Einstein's simultaneity convention simplifies many practical calculations by collapsing the tensor notation into a simpler notation.

My statement above does not in any way commit you to using Einstein's simultaneity convention, you are free to view the physical clocks in the measuring-devices you're analyzing as being out-of-sync in the coordinate system which you define as their rest frame.

Again, SR is defined by the statement that the laws of physics have a particular symmetry, namely Lorentz-symmetry. I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory, but the way of defining it above is a perfectly valid one that's easy to understand without knowing a lot of advanced math, and it is a physical definition that doesn't require that you yourself use the coordinate systems defined by the Lorentz transformation, you can use whatever coordinate system you like to predict what would be measured in the type of physical ruler-clock system described by Einstein.

But it embeds a conventional clock synchroinzation choice that leads people to a belief that the relativity of simultaneity is "real", and that isn't necessarily so.

This seems to be some sort of pedagogical argument, not an argument against the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric.

The way I defined it above does not "imply the relativity of simultaneity", since you are free to analyze those different ruler/clock systems from the perspective of a set of inertial coordinate systems which all agree on simultaneity, like the ones defined in the Mansouri-Sexl paper.

The way you defined it above (actually, there is an ambiguity here because you have talked about several things above)

I don't think there is any ambiguity--where in that quote do you see it?

does not imply the relativity of simultaneity because that isn't the Lorentz tranform for the time coordinate, but rather it is the LET transform. The way you defined it above is insconsistent with the two postulates of SR.

False, the postulates of SR only involve predictions about physical measurements on physical systems of rulers and clocks. If you want to analyze those rulers and clocks from the perspective of some other set of coordinate systems besides the ones defined in terms of their measurements, nothing is stopping you. In much the same way, we could use the conventional coordinate systems normally used in SR to analyze the behavior of a set of ruler/clock systems whose clocks were "synchronized" using some other convention besides the Einstein synchronization convention, with the consequence that the clocks will appear out-of-sync from the perspective of the coordinate system we are using--this is no different from the idea that you can use these conventional coordinate systems to analyze the accelerating clock in the twin paradox, which will not stay synchronized with the inertial clock in this coordinate system. Analyzing a particular set of physical clocks does not commit you to using a coordinate system in which they are in sync!

 

[Aether]

Not if I don't use these measuring-devices to define my coordinate system! I am simply treating them as a physical system to be analyzed, no different than the clocks in the twin paradox or any other physical system.

Ok, you are talking about a physical system of measuring-devices that are set-up by Einstein's procedure(s), and then you are going to examine that system; but in doing so you may set up a second coordinate system that is not set-up by Einstein's procedure(s)? In that case, your first set-up is a physical system and the second set-up isn't. I was only considering the second set-up 'til now.

Are you really saying that if I analyze any other physical system using, say, the coordinate systems provided by the Mansouri-Sexl, everything is fine and dandy, but if I analyze that particular physical systems consisting of a grid of rulers and clocks constructed according to Einstein's specifications, I am magically forced to abandon the coordinate system I'd been using and adopt the coordinate system defined by these rulers and clocks? How could that possibly make any sense? This is why I said you were confused!

No, of course not. I don't prefer LET/GGT over SR or one simultaneity convention over another. I prefer a coordinate-system independent view in the absence of an observational constraint on the simultaneity convention.

OK, SR is simply the theory that all fundamental laws are Lorentz-symmetric, if a law is found that falsifies this, then SR will be falsified. However, the Lorentz Ether theory does not predict that there will be any measurable violations of Lorentz-symmetry, although it may be an interpretation which imagines fundamentally unmeasurable entities which violate it, in the same way that Bohm's interpretation of quantum mechanics imagines fundamentally unmeasurable precise positions for particles at all times.

LET/GGT and SR stand or fall together. The only reason that I refer to LET/GGT at all is to understand the coordinate-system dependency of SR; this is how Mansouri & Sexl intended I think.

I have to run right now, so I will reply to the rest of your comments here later.

 

[nakurusil]

My statement may or may not be viewed as "wrong" depending on which coordinate system that you choose to work in; so it is not wrong in reality, though I may learn to phrase it more effectively I'll admit. My reference to the LET transforms as a counter-example to the Lorentz transforms follows their use by Mansouri & Sexl.

your repeated references to LET/GGT/ETC are nothing but a red herring, your example is non-inertial because of the turnaround involved. Do you get this? You are outside any of the theories that use inertial frames.
The stuff about coordinate-dependent measurements, one way light speed isotropy, etc is just another red herring, you miss the basic experimental and theoretical stuff. I'll let JesseM set you straight on this subject.

 

[Aether]

your repeated references to LET/GGT/ETC are nothing but a red herring, your example is non-inertial because of the turnaround involved. Do you get this? You are outside any of the theories that use inertial frames.
The stuff about coordinate-dependent measurements, one way light speed isotropy, etc is just another red herring, you miss the basic experimental and theoretical stuff. I'll let JesseM set you straight on this subject.

Any "measurement" that you can make comparing the elapsed times on the two separated clocks without the turnaround is necessarily coordinate-system dependent because it requires a conventional clock synchronization choice. If JesseM disagrees with this, then let him say so. Otherwise, please feel free to be quiet now and try to learn something.

 

[nakurusil]

Any real "measurement" that you can make (comparing the elapsed times on the two separated clocks) without the turnaround is necessarily coordinate-system dependent because it requires a conventional clock synchronization choice. If JesseM disagrees with this, then let him say so. Otherwise, please feel free to be quiet now and try to learn something.

You don't need to be arrogant, let me remind you what you really wrote:

There is a physical difference between objects in relative motion to one another. For example, if two identical atomic clocks are synchronized while co-located and at rest in a first inertial frame; then one clock is moved into a second inertial frame (!) for a time; then returned to the starting position;

Apparently you not only have problems with understanding the basics but also with understanding your own posts.

 

[JesseM]

Ok, you are talking about a physical system of measuring-devices that are set-up by Einstein's procedure(s), and then you are going to examine that system; but in doing so you may set up a second coordinate system that is not set-up by Einstein's procedure(s)?

I'm not treating the physical system of measuring-devices as a "coordinate system" at all, just as a physical system. You can use whatever coordinate system you like to analyze it, provided you pick the correct form of the laws of physics in that coordinate system. And again, the first and second postulates are physical postulates about what will be measured by such measuring-devices, your predictions about what they will measure should be independent of what coordinate system you choose.

Are you really saying that if I analyze any other physical system using, say, the coordinate systems provided by the Mansouri-Sexl, everything is fine and dandy, but if I analyze that particular physical systems consisting of a grid of rulers and clocks constructed according to Einstein's specifications, I am magically forced to abandon the coordinate system I'd been using and adopt the coordinate system defined by these rulers and clocks? How could that possibly make any sense? This is why I said you were confused!

No, of course not. I don't prefer LET/GGT over SR or one simultaneity convention over another. I prefer a coordinate-system independent view in the absence of an observational constraint on the simultaneity convention.

So you agree that analyzing the type of system of measuring-devices and clocks proposed by Einstein does not commit us to the view that their definition of simultaneity is "correct"? And do you agree that the first and second postulate are simply postulates about what would be measured by such systems?

 

[Aether]

I'm not treating the physical system of measuring-devices as a "coordinate system" at all, just as a physical system. You can use whatever coordinate system you like to analyze it, provided you pick the correct form of the laws of physics in that coordinate system. And again, the first and second postulates are physical postulates about what will be measured by such measuring-devices, your predictions about what they will measure should be independent of what coordinate system you choose.

LET and SR (e.g., the first and second postulates) are empirically equivalent, so any predictions about actual measurements will agree; so, for predictions on which these two theories agree I would call "physical". It is only on matters where these two theories disagree that I would raise an issue of coordinate-system dependency.

So you agree that analyzing the type of system of measuring-devices and clocks proposed by Einstein does not commit us to the view that their definition of simultaneity is "correct"? And do you agree that the first and second postulate are simply postulates about what would be measured by such systems?

Let's come back to this and every other issue above after we have examined this statement: "the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric." Can you (or someone else who is reading along) cite a reference for this along the lines of "I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory"?

 

[MeJennifer]

LET and SR (e.g., the first and second postulates) are empirically equivalent, so any predictions about actual measurements will agree; so, for predictions on which these two theories agree I would call "physical". It is only on matters where these two theories disagree that I would raise an issue of coordinate-system dependency.

Again the difference between LET and relativity has nothing to do with coordinate systems.

 

[JesseM]

LET and SR (e.g., the first and second postulates) are empirically equivalent, so any predictions about actual measurements will agree; so, for predictions on which these two theories agree I would call "physical".

So do you agree that the prediction that the two postulates will be satisfied in the type of physical measuring-systems described by Einstein in his 1905 paper is a "physical" prediction?

Let's come back to this and every other issue above after we have examined this statement: "the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric." Can you (or someone else who is reading along) cite a reference for this along the lines of "I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory"?

What do you want a reference for, the claim that Einstein's two postulates are equivalent to the postulate that the laws of physics are Lorentz-symmetric, or the claim that there are "mathematically more advanced" ways of expressing the postulate of Lorentz-symmetry?

 

[Aether]

While the formulas are identical between LET and relativity their interpretations of reality are very different...Again the difference between LET and relativity has nothing to do with coordinate systems.

The https://www.physicsforums.com/showpost.php?p=755432&postcount=92" are not identical between LET and relativity.

 

[Aether]

So do you agree that the prediction that the two postulates will be satisfied in the type of physical measuring-systems described by Einstein in his 1905 paper is a "physical" prediction?

Up to the point that one simultaneity convention is selected based on other than observational criteria. You can not select a simultaneity convention and still claim complete physicality.

What do you want a reference for, the claim that Einstein's two postulates are equivalent to the postulate that the laws of physics are Lorentz-symmetric, or the claim that there are "mathematically more advanced" ways of expressing the postulate of Lorentz-symmetry?

I want a complete standard mainstream definition of Lorentz symmetry, and then we will examine your proposition that Einstein's postulates are a necessary and sufficient condition to satisfy that definition. If the reference discusses this matter directly, then that would be ideal.

 

[JesseM]

Up to the point that one simultaneity convention is selected based on other than observational criteria. You can not select a simultaneity convention and still claim complete physicality.

I'm not talking about a selecting a simultaneity convention, I'm just asking about physical measurements on a physical system of rulers and clocks. How many times do I have to say "you are not obligated to use a coordinate system where the clocks are synchronized" before it sinks in? Again, analyzing a physical situation involving a physical system of rulers and clocks which have been "synchronized" using the physical procedure known as the Einstein synchronization convention does not magically force you to use a coordinate system with a simultaneity convention that says the clocks all read the same time at a given t-coordinate, any more than analyzing the behavior of the physical clocks in the twin paradox would magically force you to use a coordinate system where each twin's clock reads the same time at every t-coordinate (which would be impossible once they reunite anyway).

But I've been saying this over and over and you still don't seem to get it. Can you explain which part of the above is unclear?

I want a complete standard mainstream definition of Lorentz symmetry, and then we will examine your proposition that Einstein's postulates are a necessary and sufficient condition to satisfy that definition. If the reference discusses this matter directly, then that would be ideal.

I'll look around for something like this, although as I said I'm not too knowledgeable about group theory or tensor mathematics. Doing a bit of quick googling, it seems the term "Lorentz covariance" is synonymous with Lorentz symmetry, and this page has a quote by Einstein where he defines Lorentz covariance in terms of the equations of physics being unchanged by a Lorentz transformation (which I hope you'd agree is equivalent to my statement that the laws of physics are measured to work the same in the different inertial systems of rulers and clocks described by Einstein in his 1905 paper, since the two postulates can be used to prove that the positions and times assigned by these systems must be related by the Lorentz transformation):

The heuristic method of the special theory of relativity is characterized by the following principle: only those equations are admissible as an expression of natural laws which do not change their form when the co-ordinates are changed by means of the Lorentz transformation (covariance of equations with respect to the Lorentz transformations). (Albert Einstein, 1934)

And this page from the Springer Encyclopaedia of Mathematics says:

The physical applications of Lorentz transformations are connected with Einstein's relativity principle, according to which all physical laws, except the law of gravitation, are invariant under Lorentz transformations. In a number of cases, for example in axiomatic quantum field theory, the use of this and other equally general postulates makes it possible to make far-reaching deductions about the forms of functional dependencies between different physical quantities.

So both these sources define the notion of Lorentz covariance/invariance simply in terms of the laws of physics being unchanged under a Lorentz transformation, which I would think means they are talking about the non-tensor form of the laws, since I had thought that any physical law (including, say, Newton's laws) could be expressed in a "generally covariant" tensor form in which it would work the same way in all coordinate systems (for example, see the last section of this page), although I could be misunderstanding things here.

 

[Aether]

I'm not talking about a selecting a simultaneity convention, I'm just asking about physical measurements on a physical system of rulers and clocks. How many times do I have to say "you are not obligated to use a coordinate system where the clocks are synchronized" before it sinks in? Again, analyzing a physical situation involving a physical system of rulers and clocks which have been "synchronized" using the physical procedure known as the Einstein synchronization convention does not magically force you to use a coordinate system with a simultaneity convention that says the clocks all read the same time at a given t-coordinate, any more than analyzing the behavior of the physical clocks in the twin paradox would magically force you to use a coordinate system where each twin's clock reads the same time at every t-coordinate (which would be impossible once they reunite anyway).

But I've been saying this over and over and you still don't seem to get it. Can you explain which part of the above is unclear?

It isn't so much that it is unclear, it is that I am unwilling to risk absorbing this while the larger questions of Lorentz symmetry, tensor notation, etc. are still outstanding. When those issues are fully resolved, then I will be in a better position to absorb or reject some of these other notions in an informed way. Let's come back to these lesser issues later.

I'll look around for something like this, although as I said I'm not too knowledgeable about group theory or tensor mathematics. Doing a bit of quick googling, it seems the term "Lorentz covariance" is synonymous with Lorentz symmetry, and this page has a quote by Einstein where he defines Lorentz covariance in terms of the equations of physics being unchanged by a Lorentz transformation (which I hope you'd agree is equivalent to my statement that the laws of physics are measured to work the same in the different inertial systems of rulers and clocks described by Einstein in his 1905 paper, since the two postulates can be used to prove that the positions and times assigned by these systems must be related by the Lorentz transformation): And this page from the Springer Encyclopaedia of Mathematics says: So both these sources define the notion of Lorentz covariance/invariance simply in terms of the laws of physics being unchanged under a Lorentz transformation, which I would think means they are talking about the non-tensor form of the laws, since I had thought that any physical law (including, say, Newton's laws) could be expressed in a "generally covariant" tensor form in which it would work the same way in all coordinate systems (for example, see the last section of this page), although I could be misunderstanding things here.

This is such an important issue that I would like to fully understand it before proceeding with the rest of the discussion. Since Newton's laws are expressed using 3-vectors rather than 4-vectors, I don't see how they could be Lorentz covariant/invariant. Also, if Lorentz covariance/invariance is specifically tied to the Lorentz transforms then it may not be as fundamental of a physical concept as we have given it credit for above (e.g., what about the LET transforms?). I would question whether or not Poincare covariance/invariance isn't the more general physical symmetry; I'm not saying that this is so, but these are questions that I would need to know the answers to before leaving this subject.

 

[JesseM]

It isn't so much that it is unclear, it is that I am unwilling to risk absorbing this while the larger questions of Lorentz symmetry, tensor notation, etc. are still outstanding.

Why? The question of whether the two postulates of relativity can be interpreted as "physical" or not is separate from the question of whether they are equivalent to what is called "Lorentz-symmetry". I think my argument above makes it pretty clear that they are perfectly physical, these "larger questions" that you mention are irrelevant to that argument.

This is such an important issue that I would like to fully understand it before proceeding with the rest of the discussion. Since Newton's laws are expressed using 3-vectors rather than 4-vectors, I don't see how they could be Lorentz covariant/invariant.

They aren't Lorentz covariant, they are generally covariant, which is a separate concept. As I understand it, general covariance basically means the equations work the same way in every possible coordinate system--inertial, non-inertial, whatever--and any law of physics can be expressed in a generally covariant form if you use the right sort of tensor notation, so it is not really a characteristic of the laws of physics like Lorentz covariance is. The link I gave at the end of the last post quotes Michael Friedman's Foundations of Space-Time Theories as saying (and note that when the page refers to 'covariance', they are referring to general covariance rather than Lorentz invariance/covariance):

Looking back on the development of relativity from our present point of view, we can see that there are three distinct notions that have been inadvertently conflated: symmetry, indistinguishability, and covariance. The symmetry group of a space-time theory characterizes the objects of that theory: it tells us which objects are absolute and which dynamical, and the size of the symmetry group is inversely proportional to the number of absolute objects. The indistinguishability group of a space-time theory characterizes the laws of that theory: it determines which reference frames (states of motion) are distinguishable (by a "mechanical experiment") relative to those laws, and in well-behaved theories the indistinguishability group is contained in the symmetry group (indistinguishable models are identical). Covariance, on the other hand, is really a property of formulations of space-time theories rather than space-time theories themselves: it characterizes systems of differential equations ... representing the intrinsic laws of a space-time theory relative to some particular coordinatization ... The covariance group of such a formulation reflects the range of coordinate systems in which that particular system of equations holds good.

In pre-general-relativistic physics these three distinct notions happen to coincide. In well-behaved theories with inertial coordinate systems (flat space-time) the symmetry group = the indistinguishability group = covariance group of the standard formulation (with respect to a subclass of inertial coordinate systems). Thus, for example, in classical electrodynamics the symmetry group = ... = the indistinguishability group = covariance group of the standard formulation ... In relativistic electrodynamics, on the other hand, the symmetry group = the Lorentz group = indistinguishability group = the covariance group of the standard formulation ...

In general relativity, however, our three notions are not interchangeable. As we have seen, we cannot interpret the general principle of relativity as an indistinguishability requirement, for the indistinguishability group of the general theory is just the restricted group of transformations from one local inertial frame to another. Nor can we interpret it as a covariance requirement, for the general theory has no standard formulation in the usual sense, and the covariance group of the theory is the same as the covariance group of every other space-time theory. Hence, in neither of these interpretations is the general principle of relativity any kind of generalization of the special principle of relativity. As Anderson was the first to realize, the only way to interpret the general principle as such is to make it a symmetry requirement. That is, we interpret the general principle of relativity s the requirement that the symmetry group of our theory include all differentiable transformations: in effect, that it be just the group M. This requirement means that our theory can have no absolute objects, for the only geometrical objects invariant under all differentiable transformations are constant-valued scalars. (Friedman 1983, 212-4).

Also, if Lorentz covariance/invariance is specifically tied to the Lorentz transforms then it may not be as fundamental of a physical concept as we have given it credit for above (e.g., what about the LET transforms?).

If you would actually think about my argument above showing why the two postulates are completely physical ones, you would see that the postulates are every bit "as fundamental of a physical concept as we have given it credit for", and from there it is a short step to agreeing that if Lorentz-symmetry is equivalent to the statement that the laws of physics must work the same way in all the physical measuring-systems that Einstein describes in his 1905 paper, as I have claimed and as I think the quotes in my previous post suggest, then Lorentz-symmetry would also be a completely physical statement about the laws of nature. If you are not willing to think about this, but instead insist that we take a course in tensor mathematics and group theory before drawing any conclusions, then this discussion can't go any further.

 

[Aether]

If you are not willing to think about this, but instead insist that we take a course in tensor mathematics and group theory before drawing any conclusions, then this discussion can't go any further.

As always, I appreciate your help; but with all due respect, you do not yourself know the answers to my questions, so you can not possibly know the extent to which they are relevant to this discussion. The fact is that you do not at this time have the answers my questions; that's ok, perhaps someone else who knows the answers will chime in, or after a few days one of us will have the answers. If pervect or Hurkyl advise me that they think this is an unreasonable request, then I will reconsider it. I single them out because I suspect that they already know the answers to these questions.

 

[JesseM]

With all due respect, you do not yourself know the answers to my questions, so you can not possibly know the extent to which they are relevant to this discussion.

Nonsense, the argument about the two postulates being physical is completely clear, the mathematical details of how "Lorentz-symmetry" is defined could not change this conclusion since the argument doesn't even use that term. You might as well say that because I do not know the answers to questions about the metric of a rotating black hole, I "can not possibly know the extent to which they are relevant to this discussion". Do you have an actual argument as to how you think the definition of Lorentz-symmetry could possibly affect our conclusions as to whether questions about the measurements made by a physical system of rulers and clocks are coordinate-dependent or not, or are you just unwilling to give any thought to the issue until I jump through your hoops?

 

[Aether]

Do you have an actual argument as to how you think the definition of Lorentz-symmetry could possibly affect our conclusions as to whether questions about the measurements made by a physical system of rulers and clocks are coordinate-dependent or not, or are you just unwilling to give any thought to the issue until I jump through your hoops?

I am not really ready to make an argument, that is why I am asking these questions; but I will give you my thoughts as they are at this moment so that you will know better why I want to examine one issue before another. I think that the definition of Lorentz-symmetry (at least as you have described it above) may well lead to the conclusions that you are making (e.g., if it is specifically linked to the Lorentz transforms and not equally applicable to the LET transforms). If that is true, then I want to know if the statement that "all known physical laws are Lorentz-symmetric" isn't some sort of subset of a more general statement along the lines of "all known physical laws are Poincare symmetric, and Lorentz symmetry is a subgroup of Poincare symmetry" for example. If that is the case, then Lorentz-symmetry itself could be a coordinate-system dependent concept.

 

[JesseM]

I am not really ready to make an argument, that is why I am asking these questions; but I will give you my thoughts as they are at this moment so that you will know better why I want to examine one issue before another. I think that the definition of Lorentz-symmetry (at least as you have described it above) may well lead to the conclusions that you are making (e.g., if it is specifically linked to the Lorentz transforms and not equally applicable to the LET transforms). If that is true, then I want to know if the statement that "all known physical laws are Lorentz-symmetric" isn't some sort of subset of a more general statement along the lines of "all known physical laws are Poincare symmetric, and Lorentz symmetry is a subgroup of Poincare symmetry" for example. If that is the case, then Lorentz-symmetry itself could be a coordinate-system dependent concept.

OK, but when I asked you if you were willing to think about my argument, I was only talking about the argument which didn't even mention the concept of "Lorentz-symmetry", the one about how the claim that the laws of physics respect Einstein's two postulates is a physical claim which is independent of what coordinate system you choose to use (and therefore independent of how you choose to define simultaneity). Of course once we have addressed this question we can then ask whether "the claim that the laws of physics respect Einstein's two postulates" is identical in meaning to the claim that "the laws of physics are Lorentz-symmetric"; but this is an entirely separate question, you don't need to even touch upon it to address the first one.

 

[Aether]

OK, but when I asked you if you were willing to think about my argument, I was only talking about the argument which didn't even mention the concept of "Lorentz-symmetry", the one about how the claim that the laws of physics respect Einstein's two postulates is a physical claim which is independent of what coordinate system you choose to use (and therefore independent of how you choose to define simultaneity). Of course once we have addressed this question we can then ask whether "the claim that the laws of physics respect Einstein's two postulates" is identical in meaning to the claim that "the laws of physics are Lorentz-symmetric"; but this is an entirely separate question, you don't need to even touch upon it to address the first one.

You said "the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric", so now I want to know what "Lorentz-symmetric" really means. I think that I am diligently pursuing an examination of "the only thing that [you are] claiming here", but I will look at what you just said above first...tomorrow.

 

[JesseM]

You said "the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric", so now I want to know what "Lorentz-symmetric" really means.

OK, but in subsequent posts I narrowed down my question after you questioned whether my definition of "Lorentz-symmetric" was the correct one. What I am asking about now is just the claim that "Einstein's postulates are physical ones" (ie that they are postulates about what will be measured by systems of physical rulers and clocks constructed in a specific way, and that they are therefore coordinate-independent postulates). We don't need to bring up the definition of Lorentz-symmetry to address this.

 

[Aether]

What I am asking about now is just the claim that "Einstein's postulates are physical ones" (ie that they are postulates about what will be measured by systems of physical rulers and clocks constructed in a specific way, and that they are therefore coordinate-independent postulates). We don't need to bring up the definition of Lorentz-symmetry to address this.

Would ideal observers in two different inertial frames ever disagree as to "what will be measured by systems of physical rulers and clocks constructed in a specific way" if those measurements were coordinate-system independent? Don't ideal observers in two different inertial reference frames sometimes disagree as to "what will be measured by systems of physical rulers and clocks constructed in a specific way" (e.g., properly constructed in view of Einstein's postulates)?

 

[JesseM]

Would ideal observers in two different inertial frames ever disagree as to "what will be measured by systems of physical rulers and clocks constructed in a specific way" if those measurements were coordinate-system independent?

No, they would never disagree.

Don't ideal observers in two different inertial reference frames sometimes disagree as to "what will be measured by systems of physical rulers and clocks constructed in a specific way" (e.g., properly constructed in view of Einstein's postulates)?

No, for any given ruler-clock system, all observers will agree what it measures. I'm not talking about each observer constructing their own ruler-clock system according to Einstein's procedure, and then looking only at what is measured by their own system; I'm talking about different observers each looking at the same ruler-clock system, regardless of whether it is at rest relative to themselves, and seeing what is measured by that system. You can also construct multiple such ruler-clock systems in relative motion, give them all labels like "system A" and "system B", and then all observers will agree on what was measured by the physical system A (even if its measurements don't correspond to the coordinates assigned by the observers' own chosen coordinate system), all will agree on what was measured by physical system B, etc. The two postulates of SR amount to the idea that each physical measuring-system constructed according to Einstein's procedure will measure the laws of physics to work the same way, including the speed of light as measured by that system.

If there is some event that I observe to happen right next to the 3-meter mark on a given ruler-clock system, with the clock at the 3-meter mark reading 15 seconds at the moment it happened, do you think other observers might observe the event to happen next to a different mark or a different clock-reading on the same ruler-clock system? Relativity doesn't allow disagreements about local physical events like that, if it did you could get totally different physical predictions (suppose the event was an astronaut sending a radio transmission back to earth, and the clock at the 3-meter mark was programmed to explode when it read 15 seconds--different frames shouldn't disagree on whether the transmission would get cut off by the astronaut's unfortunate demise!)