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

[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!)

 

[Aether]

No, they would never disagree. 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.

Agreed.

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.

The one-way speed of light is not "measurable" by this system. Each physical measuring-system constructed according to Einstein's procedure will "measure" the laws of physics to work the same way because they are proportional to the one-way speed of light which is put-in by hand using Einstein's procedure.

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?

No.

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!)

Ok. I didn't say that it did. The disagreement that I was referring to was between the two clocks in different frames being in disagreement about the time-stamp to put on a given event.

 

[JesseM]

Agreed.The one-way speed of light is not "measurable" by this system.

Of course it is, although that doesn't mean the one-way speed of light is itself an objective physical quantity. Similarly, this system can measure the distance of any event from the origin of the system, but that obviously isn't an objective physical quantity either. Still, the measurement itself is physical and objective in the sense that for a given measuring-system, all observers will agree on what that particular system measures for the one-way speed of light in that system, or the distance of an event from the origin in that system.

Each physical measuring-system constructed according to Einstein's procedure will "measure" the laws of physics to work the same way because they are proportional to the one-way speed of light which is put-in by hand using Einstein's procedure.

Not at all, if we lived in a universe with Newtonian laws (and with Maxwell's laws only working exactly in the rest frame of the aether), and you constructed systems according to Einstein's procedure, different systems would measure the laws of physics to work differently. Of course they would each measure the one-way speed of light to be the same in all directions (the simultaneity convention guarantees the propagation of light will be isotropic in each system), but different systems would measure different values for the speed of light itself (in this case I believe a system moving at v relative to the aether would measure the speed of light as (c^2 - v^2)/c), and many other laws of physics would be measured to obey different equations when in different systems. This would be true even if we artificially shrunk the length of rulers moving at speed v relative to the aether by a factor of \sqrt{1 - v^2/c^2}, and expanded the length of clock ticks by 1/\sqrt{1 - v^2/c^2}, so that the coordinates of different measuring systems were still related by the Lorentz transform (although I think in this case I think each system would measure the speed of light to be the same).

Ok. I didn't say that it did. The disagreement that I was referring to was between the two clocks in different frames being in disagreement about the time-stamp to put on a given event.

Right, but do you understand now that this has nothing to do with what I was talking about when I said all observers would agree about what each physical measuring-system measures?

 

[nakurusil]

I didn't say that it did. The disagreement that I was referring to was between the two clocks in different frames being in disagreement about the time-stamp to put on a given event.

You mean between the clock in an inertial frame and the other one in a non-inertial frame?

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

Do you understand what it means to give phony examples? Do you understand the very basic difference between an inertial and a non-inertial frame?

 

[Aether]

The one-way speed of light is not "measurable" by this system.

Of course it is, although that doesn't mean the one-way speed of light is itself an objective physical quantity. Similarly, this system can measure the distance of any event from the origin of the system, but that obviously isn't an objective physical quantity either. Still, the measurement itself is physical and objective in the sense that for a given measuring-system, all observers will agree on what that particular system measures for the one-way speed of light in that system, or the distance of an event from the origin in that system.

Such a quantity is not an objective physical quantity. Such a "measurement" is coordinate-system dependent.

Ok. I didn't say that it did. The disagreement that I was referring to was between the two clocks in different frames being in disagreement about the time-stamp to put on a given event.

Right, but do you understand now that this has nothing to do with what I was talking about when I said all observers would agree about what each physical measuring-system measures?

I see that there is a distinction to be made between who's clock we are referring to when we make such a "measurement". I would rather say that "all observers would agree about what each physical measuring-system indicates". There is a class of measurements for which each physical measuring-system will agree (e.g., fine-structure constant, two-way speed of light, etc.), and there is a class of measuring-system indications for which each physical-measuring system will not agree (e.g., the one-way speed of light, the length of an object, etc.). I do not see you making such a distinction.

 

[Aether]

that doesn't mean the one-way speed of light is itself an objective physical quantity

nakurusil, do you agree with JesseM that the one-way speed of light is not itself an objective physical quantity?

 

[nakurusil]

nakurusil, do you agree with JesseM that the one-way speed of light is not itself an objective physical quantity?

This is not the subject of the OP nor is it the subject of the discussion between the two of us. The subject of the discussion between the two of us is your lack of understanding of the differences between inertial and non-inertial frames and how mixing them into your example rendered it irrelevant. Can we get a clear answer from you on this issue?

 

[Aether]

This is not the subject of the OP nor is it the subject of the discussion between the two of us.

This is the subject of the OP:

I'm trying to picture various light based experiments as described from a frame that is in motion with respect to the experiment devices.

For instance the reflection of a photon in a light clock: the atoms (and their fields) that constitute the surface of the mirror are squashed. How is the reflected photon adapted to match this reality?

The subject of the discussion between the two of us is your lack of understanding of the differences between inertial and non-inertial frames and how mixing them into your example rendered it irrelevant. Can we get a clear answer from you on this issue?

Please answer my question: do you agree with JesseM that the one-way speed of light is not itself an objective physical quantity?

 

[nakurusil]

This is the subject of the OP:Please answer my question: do you agree with JesseM that the one-way speed of light is not itself an objective physical quantity?

The subject of the discussion between the two of us is your lack of understanding of the differences between inertial and non-inertial frames and how mixing them into your example rendered it irrelevant. Can we get a clear answer from you on this issue?

 

[Aether]

The subject of the discussion between the two of us is your lack of understanding of the differences between inertial and non-inertial frames and how mixing them into your example rendered it irrelevant. Can we get a clear answer from you on this issue?

I will ignore you from now on unless and until you answer my question. Please feel free to ignore me as well.

 

[JesseM]

Such a quantity is not an objective physical quantity. Such a "measurement" is coordinate-system dependent.

Irrelevant to my argument. The quantity being measured is coordinate-system-dependent, but all coordinate systems will agree on what a particular physical measuring system will get as a result for that measurement. Do you not see the distinction here?

I see that there is a distinction to be made between who's clock we are referring to when we make such a "measurement". I would rather say that "all observers would agree about what each physical measuring-system indicates".

Fine, use the word "indicates" rather than "measures", although I'm pretty sure it is standard terminology to talk about all the inertial coordinate systems "measuring" the same laws of physics. But anyway, we can say that each physical measuring-system designed according to Einstein's procedure will "indicate" that the laws of physics obey the same equations. And this is a property of the laws of physics themselves--it wouldn't be true if the laws were Newtonian, for example. Do you disagree?

There is a class of measurements for which each physical measuring-system will agree (e.g., fine-structure constant, two-way speed of light, etc.), and there is a class of measuring-system indications for which each physical-measuring system will not agree (e.g., the one-way speed of light, the length of an object, etc.). I do not see you making such a distinction.

Now you're talking about a generalized notion of "physical measuring-systems" which goes beyond the ones constructed according to Einstein's procedure--that's what I've been referring to just as "coordinate systems". You don't even need to physically construct a measuring system whose measurements will correspond to a coordinate system, you could just take some other measuring-system (like the ones described by Einstein), then pick some arbitrary mathematical transformation on that system's coordinates, then call the result "your" coordinate system (in this sense, even the two-way speed of light could be disagreed on, although it would be the same in all coordinate systems if you restrict your allowable coordinate systems to ones where differences in position coordinates would match measurements of physical rulers at rest in that coordinate system and differences in time coordinates between events with the same position-coordinates would match measurements of a physical clocks at rest at that position-coordinate).

Anyway, no matter what coordinate system you choose to work in, local physical facts like "when this event occurred, it was right next to this physical clock, which read 30 seconds at the moment it occurred" will be agreed upon by all coordinate systems. And the fact that all the physical ruler-clock systems constructed according to Einstein's procedure will indicate the same "laws of physics" is itself a statement that can be broken down into a bunch of such local physical facts, so it's a fact that's agreed upon by all coordinate systems as well (including ones whose coordinates don't match any of Einstein's ruler-clock systems).

 

[JesseM]

This is the subject of the OP

No it isn't, the original post was simply assuming we were using the same types of inertial coordinate systems used in SR, and asking how the same mirror would look in different frames at an atomic level, and why all frames would agree on their predictions about the behavior of light when analyzing things at the atomic level. Your bringing up the whole issue of the "reality" of statements made in SR was irrelevant to the OP, and I think it'd be better if this side-issue were split into a different thread so there'd be a better chance someone would actually address Leo.Ki's question.

 

[Aether]

This is the subject of the OP

No it isn't, the original post was simply assuming we were using the same types of inertial coordinate systems used in SR, and asking how the same mirror would look in different frames at an atomic level, and why all frames would agree on their predictions about the behavior of light when analyzing things at the atomic level.

The OP didn't specify that we were using the same type of inertial coordinate systems used in SR. More than three days went by with no response to his question before I replied to him with an explanation of precisely what an inertial frame is.

Your bringing up the whole issue of the "reality" of statements made in SR was irrelevant to the OP, and I think it'd be better if this side-issue were split into a different thread so there'd be a better chance someone would actually address Leo.Ki's question.

The OP specifically asked "How is the reflected photon adapted to match this reality?". Nevertheless, I agree that our discussion here may not be exactly what the OP needs to hear in order to answer his question. Would you (or a moderator) care to start a new thread for this side-issue, or do you want me to do it?

 

[JesseM]

The OP didn't specify that we were using the same type of inertial coordinate systems used in SR.

Not in those precise words, but the OP said "a frame that is in motion with respect to the experiment devices", and since it was asked in the context of SR I think we can assume the question was based on the usual SR convention of "frames" rather than some other convention.

The OP specifically asked "How is the reflected photon adapted to match this reality?"

From the context, I don't think "reality" was being used in any deep philosophical sense, just as a way of asking the practical question about how the atoms look in that frame, and how their squashed length affects the way they reflect photons as predicted in that frame.

Anyway, I'm not really blaming you for taking the thread off-topic since you didn't know that your post would lead to such a lengthy discussion, but at this point I do think it would be good if the mods split off the discussion about whether SR is a theory about "reality" into its own thread. Until then, we might as well keep discussing it here, since the mods can split off any new posts we make too if they decide to do a thread split.

 

[Aether]

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

Actually, I too rather prefer to suppose that "matter is spherically spatially extended, and thus to reject the concept of the particle" in a classical sense at least. Nevertheless, "the Logic of Relativity is founded on, and completely consistent with, an Absolute Space. (Contrary to current opinions)". I am so glad to see that I do not have to justify this position at all, as it has been Einstein's own position all along. Though I may now have to consider changing my name from "Aether", to "Extended Particle" or something.

Most profoundly, Lorentz first deduced the foundations of Albert Einstein's Relativity from the assumption of a rigid Space (ether), and that the cause of the electromagnetic field effect that he was using was in fact vibrations in this Space/Ether.

Though Albert Einstein related relative motions of matter only to other matter and not back to an absolute Space like Lorentz did, (which is mathematically simpler) the important point is that the Logic of Relativity is founded on, and completely consistent with, an Absolute Space. (Contrary to current opinions)

From Lorentz's purely mathematical foundation Albert Einstein then developed his Theory of Relativity, which assumed that matter existed as a spherical spatially extended field which changes ellipsoidal shape with motion and thus also with acceleration (which leads to the ellipsoidal geometry which underpins General Relativity and gravitation).

Albert Einstein took one further step than Lorentz though, and assumed (like Leibniz and Mach) that all motion of matter was relative only to other matter, he writes;

"It has, of course, been known since the days of the ancient Greeks that in order to describe the movement of a body, a second body is needed to which the movement of the first is referred." (Albert Einstein, 1919)

By doing this Albert Einstein effectively renounced the concept of a fundamental Space separate from matter (as a field), as he explains below;

"Since the field exists even in a vacuum, should one conceive of the field as state of a 'carrier', or should it rather be endowed with an independent existence not reducible to anything else? In other words, is there an 'aether' which carries the field; the aether being considered in the undulatory state, for example, when it carries light waves? The question has a natural answer: Because one cannot dispense with the field concept, it is preferable not to introduce in addition a carrier with hypothetical properties." (Albert Einstein, 1950)

"Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. The field thus becomes an irreducible element of physical description, irreducible in the same sense as the concept of matter (particles) in the theory of Newton." (Albert Einstein, 1954)

Albert Einstein had many valid reasons for asserting that matter is spherically spatially extended, and thus to reject the concept of the particle (which always had the problem of explaining action-at-a-distance);

 

[nakurusil]

Actually, I too rather prefer to suppose that "matter is spherically spatially extended, and thus to reject the concept of the particle" in a classical sense at least. Nevertheless, "the Logic of Relativity is founded on, and completely consistent with, an Absolute Space. (Contrary to current opinions)".

Are you quoting yourself?
Are you aware that all attempts in detecting Absolute Space have failed?

 

[JesseM]

Actually, I too rather prefer to suppose that "matter is spherically spatially extended, and thus to reject the concept of the particle" in a classical sense at least. Nevertheless, "the Logic of Relativity is founded on, and completely consistent with, an Absolute Space. (Contrary to current opinions)". I am so glad to see that I do not have to justify this position at all, as it has been Einstein's own position all along.

The parts you are quoting are just the opinions of the author of that website, not quotes from Einstein himself. And all this is irrelevant to what we've debating on this thread--let's not take a thread that was split for being off-topic and make it off-topic again, OK? The only section of that page that was relevant to our debate was the one I quoted, where Einstein gave a definition of Lorentz covariance.

 

[Aether]

The parts you are quoting are just the opinions of the author of that website, not quotes from Einstein himself.

There are three quotes from Einstein himself there.

And all this is irrelevant to what we've debating on this thread--let's not take a thread that was split for being off-topic and make it off-topic again, OK? The only section of that page that was relevant to our debate was the one I quoted, where Einstein gave a definition of Lorentz covariance.

Ok.

Here are a set of articles that seem to address the subject of this thread "Relativity, LET, and Reality" more or less directly. For example, from page 84 of Ref. 2: "An examination of these effects will help to clarify the status of the physical "reality" of length-contraction and time-dilation in the Special Theory."

It would be helpful if you would try to reference your argument directly to something within these papers, or else to something in some other published reference of your choosing; and I will try to do the same.

1. C.B. Giannoni, Special Relativity in Accelerated Systems, Philosophy of Science, Vol. 40, No. 3. (Sep., 1973), pp. 382-392.

2. J.A. Winnie, Special Relativity without One-Way Velocity Assumptions: Part I, Philosophy of Science, Vol. 37, No. 1. (Mar., 1970), pp. 81-99.

3. J.A. Winnie, Special Relativity without One-Way Velocity Assumptions: Part II, Philosophy of Science, Vol. 37, No. 2. (Jun., 1970), pp. 223-238.

4. A. Grunbaum, Simultaneity by Slow Clock Transport in the Special Theory of Relativity, Philosophy of Science, Vol. 36, No. 1. (Mar., 1969), pp. 5-43.

5. W. Salmon, The Conventionality of Simultaneity, Philosophy of Science, Vol. 36, No. 1. (Mar., 1969), pp. 44-63.

6. B.C. van Fraassen, Conventionality in the Axiomatic Foundations of the Special theory of Relativity, Philosophy of Science, Vol. 36, No. 1. (Mar., 1969), pp. 64-73.

7. B. Ellis and P. Bowman, Conventionality in Distant Simultaneity, Philosophy of Science, Vol. 34, No. 2. (Jun., 1967), pp. 116-136.

 

[JesseM]

There are three quotes from Einstein himself there.

None are supporting the notion that "the logic of relativity is founded on absolute space" though.

Here are a set of articles that seem to address the subject of this thread "Relativity, LET, and Reality" more or less directly. For example, from page 84 of Ref. 2: "An examination of these effects will help to clarify the status of the physical "reality" of length-contraction and time-dilation in the Special Theory."

I'm not talking about the physical reality of length contraction or time dilation, but only of the physical reality of the statement that "the laws of physics will work the same way in each inertial ruler/clock statement constructed according to Einstein's procedure" (which does not constrain you to use a coordinate system based on these ruler/clock systems, and thus does not mean you will see length contraction or time dilation work the same way that it does in those coordinate systems). Unless your references address this specifically, I'm not interested, I'd rather you responded in your own words to my arguments, like the ones in post #45.

I also wonder--if you don't think the symmetry of the laws of physics as measured by different inertial ruler/clock systems qualifies as a "physical truth" about the laws of nature, then would you also say that rotation invariance and translation invariance (the fact that the laws of physics don't change in an inertial system if you rotate the spatial coordinate axes or move the origin) aren't physical truths either? Note that by theorem[/url], conservation of linear and angular momentum is a direct consequence of these symmetries, and likewise energy conservation is a direct consequence of time-translation invariance (the idea that the laws of physics don't change in an inertial system if you change the moment defined as t=0).

 

[Aether]

I'm not talking about the physical reality of length contraction or time dilation, but only of the physical reality of the statement that "the laws of physics will work the same way in each inertial ruler/clock statement constructed according to Einstein's procedure" (which does not constrain you to use a coordinate system based on these ruler/clock systems, and thus does not mean you will see length contraction or time dilation work the same way that it does in those coordinate systems). Unless your references address this specifically, I'm not interested, I'd rather you responded in your own words to my arguments, like the ones in post #45.

Ok. 1. Conservation of linear momentum is one of the laws of physics implicitly referred to in your statement; 2. this law of physics does "work the same way in each inertial ruler/clock statement (sic?) constructed according to Einstein's procedure"; 3. but linear momentum is not an objective physical quantity, so this law of physics is not an objective physical law; 4. therefore your statement does not seem to be about objective physical reality.

I also wonder--if you don't think the symmetry of the laws of physics as measured by different inertial ruler/clock systems qualifies as a "physical truth" about the laws of nature, then would you also say that rotation invariance and translation invariance (the fact that the laws of physics don't change in an inertial system if you rotate the spatial coordinate axes or move the origin) aren't physical truths either?

I think "that a conservation law can be derived from any continuous symmetry", and that these are physical truths within the limits of experimental error iff they are based on the observation of objective physical quantities to begin with. My complaint (whether or not it stems from my own confusion remains to be seen) about the standard formulation of SR is not that Lorentz-symmetry doesn't contain some grain of truth, it is that it also contains at least one non-physical limitation. Poincare symmetry is in fact the full symmetry of special relativity, and not Lorentz symmetry.

Note that by theorem[/url], conservation of linear and angular momentum is a direct consequence of these symmetries, and likewise energy conservation is a direct consequence of time-translation invariance (the idea that the laws of physics don't change in an inertial system if you change the moment defined as t=0).

Linear momentum is not an objective physical quantity (e.g., it is coordinate-system dependent); so, the conservation of linear momentum is apparently associated with a coordinate-system dependent symmetry; namely, Lorentz symmetry.

 

[Aether]

Irrelevant to my argument. The quantity being measured is coordinate-system-dependent, but all coordinate systems will agree on what a particular physical measuring system will get as a result for that measurement. Do you not see the distinction here?

No. Consider one particular measuring system that comprises an ideal atomic clock, and wherein the quantity being measured is the time on the clock when some well defined signal event occurs at the same location as the clock. For a first arbitrary synchronization of this clock, all coordinate systems will agree on the time indicated by this clock when the signal event occurs. The same would also be true for a second arbitrary synchronization of the clock and the time indicated by this clock when the same signal event occurs. In fact, the only difference between what all coordinate systems agree on as to the particular readings on this clock between the first and second abitrary synchronizations of the clock is in fact only the difference between these two synchronizations of the clock. Every coordinate system will agree on how we arbitrarily syncrhonized this clock, so what? The empirical content of special relativity has nothing whatsoever to do with this trivial agreement of all coordinate systems on how we arbitrarily synchronized this clock, but rather on anything but this that happens to the indicated time on the clock.

Fine, use the word "indicates" rather than "measures", although I'm pretty sure it is standard terminology to talk about all the inertial coordinate systems "measuring" the same laws of physics. But anyway, we can say that each physical measuring-system designed according to Einstein's procedure will "indicate" that the laws of physics obey the same equations. And this is a property of the laws of physics themselves--it wouldn't be true if the laws were Newtonian, for example. Do you disagree?

Yes I disagree. Einstein's procedure did nothing more for us in the above example than to synchronize our clock in an arbitrary way, and therefore it is shown to be completely irrelevant to the empirical content of special relativity.

Now you're talking about a generalized notion of "physical measuring-systems" which goes beyond the ones constructed according to Einstein's procedure--that's what I've been referring to just as "coordinate systems". You don't even need to physically construct a measuring system whose measurements will correspond to a coordinate system, you could just take some other measuring-system (like the ones described by Einstein), then pick some arbitrary mathematical transformation on that system's coordinates, then call the result "your" coordinate system (in this sense, even the two-way speed of light could be disagreed on, although it would be the same in all coordinate systems if you restrict your allowable coordinate systems to ones where differences in position coordinates would match measurements of physical rulers at rest in that coordinate system and differences in time coordinates between events with the same position-coordinates would match measurements of a physical clocks at rest at that position-coordinate). Anyway, no matter what coordinate system you choose to work in, local physical facts like "when this event occurred, it was right next to this physical clock, which read 30 seconds at the moment it occurred" will be agreed upon by all coordinate systems. And the fact that all the physical ruler-clock systems constructed according to Einstein's procedure will indicate the same "laws of physics" is itself a statement that can be broken down into a bunch of such local physical facts, so it's a fact that's agreed upon by all coordinate systems as well (including ones whose coordinates don't match any of Einstein's ruler-clock systems).

Einstein's procedure is completely irrelevant to any measurement that you can possibly make because the only thing it does is to arbitrarily synchronize clocks which is fully equivalent to uniquely determining the one-way speed of light. In J.A. Winnie, Special Relativity without One-Way Velocity Assumptions: Part I, Philosophy of Science, Vol. 37, No. 1. (Mar., 1970), p. 81 he states: "According to the CS thesis [conventionality of simultaneity], this situation reveals a structural feature of the Special Theory, and thereby of the universe it purports to characterize, which not only makes the one-way speed of light indeterminate, but reveals that its unique determination could only be at the expense of contradicting the nonconventional content of the Special Theory".

What I am after is the nonconventional content of the Special Theory, and Einstein's procedure is completely irrelevant to that. It is useful, but not for making empirical measurements.

Now I will ask you once again, please cite a published reference to support your argument.

 

[JustinLevy]

Are you quoting yourself?
Are you aware that all attempts in detecting Absolute Space have failed?

clj4, it is probably best that you stop trying to evade your ban. Your bizarre method of debating by insinuating insults and refusing to answer direct questions always points you out.

Moderators, if you check the IP addresses nakurusil has used, they should match some used by clj4. Thank you.