A critique of Mike Fontenot's CADO scheme

[ghwellsjr]

JesseM, I don't know how you manage to whip up so many comments in such a short time. It takes me days to digest what you are saying and formulate my responses but I'm finally ready to take a stab at your comments but I want to do it in a general sense rather than specifically quote each of your statements.

In both Einstein's 1905 paper and his 1920 book which we have been quoting from in this thread, Einstein is starting with the two postulates or principles as he sometimes calls them. The first is the Principle of Relativity (which is not his theory of relativity) and the second is the Principle (also called the Law) of Constancy of the One-way Speed of Light. See the beginning of article 2 of his 1905 paper and the end of Chapter VII of his 1920 book where he elucidates these two Principles. Although these two Principles are "apparently irreconcilable" (as he says in the introduction of his paper) or suffer "apparent incompatibility" (as he says in the title of chapter VII of his book), his Theory of Special Relativity affirms both of them by redefining the concepts of space and time from their commonly held definitions prior to the introduction of his theory.

So, when you ask me if his definition of simultaneity can be changed from one based on the one-way speed of light to the slow transport of clocks, it misses the whole point of what he is doing. He is holding to the one-way speed of light in order to define the meaning of time. He does this by defining the time it takes for light to travel in each of the two identical directions to be equal. He is not measuring this time nor measuring the velocities.

The slow transport of clocks doesn't start with the one-way speed of light or have anything to do with the speed of light. If Einstein had postulated that slow moving clocks do not change their tick rates, then he could have used that as the basis for his argument. But the problem with that is that no one would have suggested that slow moving (or maybe even fast moving) clocks should change their tick rates and thus be apparently irreconcilable or have any apparent incompatibility with the Principle of Relativity. If there's no problem, there's no need for a theory to solve the problem.

Now, on to the subject at hand: Mike Fontenot claims that the Principle of the Constancy of the One-way Speed of Light is something that every observer can measure (using slow transport of clocks) and so he uses this as his basis for claiming, in effect, that time is absolute for that observer and this is why he can talk about a "now" when addressing the Current Age of a Distant Object.

 

[GrayGhost]

JesseM, I don't know how you manage to whip up so many comments in such a short time. It takes me days to digest what you are saying and formulate my responses but I'm finally ready to take a stab at your comments but I want to do it in a general sense rather than specifically quote each of your statements.

Well, noone's perfect, but JesseM is pretty good although he's likely not to admit it anytime soon.

So, when you ask me if his definition of simultaneity can be changed from one based on the one-way speed of light to the slow transport of clocks, it misses the whole point of what he is doing. He is holding to the one-way speed of light in order to define the meaning of time. He does this by defining the time it takes for light to travel in each of the two identical directions to be equal. He is not measuring this time nor measuring the velocities.

Ghwells ... if slow clock transport works as advertised, then it supports an invariant 1-way speed of light. The slowly moving clock (from twin A) will always (essentially) be synchronised with twin A's clock (per all) as it goes.

The slow transport of clocks doesn't start with the one-way speed of light or have anything to do with the speed of light.

The fundamental notion is that a slowly moving clock will (almost) never deviate in synchronicity, and range won't matter. Am I correct in that range matters, if the 1-way speed of light varies?

If Einstein had postulated that slow moving clocks do not change their tick rates, then he could have used that as the basis for his argument. But the problem with that is that no one would have suggested that slow moving (or maybe even fast moving) clocks should change their tick rates and thus be apparently irreconcilable or have any apparent incompatibility with the Principle of Relativity. If there's no problem, there's no need for a theory to solve the problem.

I'm not sure whether Einstein considered the slow clock transport back in 1905? He very well may have. It seems hard to believe that he did not consider it. Yet you are right, it seems he would have mentioned it in his 1905 paper had he thought of it. On the other hand, the slow clock transport should be upheld under LET theory, which throws a wrench in it. So maybe that's why he never mentioned it? Hard to say.

Now, on to the subject at hand: Mike Fontenot claims that the Principle of the Constancy of the One-way Speed of Light is something that every observer can measure (using slow transport of clocks) and so he uses this as his basis for claiming, in effect, that time is absolute for that observer and this is why he can talk about a "now" when addressing the Current Age of a Distant Object.

Mike Fontenot does not contend that time is absolute. He merely contends that twin B's spacetime transformation for twin A matches what twin A would predict twin B should predict.

GrayGhost

 

[Dale]

1. what was the A-time-readout at said event?
2. what was the B-range per A at that A-time?​

...

Q1. what did the A-clock actually then read per A himself?
Q2. what did twin A then hold for the current twin B range?​

Hi GrayGhost, sorry I missed this. All of the B observers can use any coordinate system they like and they will all agree on 1 and get Q1 correct. The "per A" of 2 and Q2 requires additionally that they know what method A is using to determine the range. Assuming they know that then all of the B observers can use any coordinate system they like and they will agree on 2 and get Q2 correct.

 

[GrayGhost]

1. what was the A-time-readout at said event?
2. what was the B-range per A at that A-time?

...

Q1. what did the A-clock actually then read per A himself?
Q2. what did twin A then hold for the current twin B range?

Hi GrayGhost, sorry I missed this. All of the B observers can use any coordinate system they like and they will all agree on 1 and get Q1 correct. The "per A" of 2 and Q2 requires additionally that they know what method A is using to determine the range. Assuming they know that then all of the B observers can use any coordinate system they like and they will agree on 2 and get Q2 correct.

Well, everyone knows that twin A will do as Einstein suggested, bounce a radar beam off of twin B, and assume the twin B range was then X=c(T₀+T₂)/2. Here's the thing though ... twin B cannot use that same process to determine where twin A was, because B is not inertial. Therefore, B must use some different method, yet one that is in some way consistent with the twin A process, and one that produces the correct answers to the 2 above questions thereby accurately predicting the twin A experience. Yes?

GrayGhost

 

[Dale]

twin A will do as Einstein suggested, bounce a radar beam off of twin B, and assume the twin B range was then X=c(T₀+T₂)/2. Here's the thing though ... twin B cannot use that same process to determine where twin A was, because B is not inertial.

Yes, B can use that same process, regardless of the fact that B is not inertial. All frames will agree on T0, the time on A's clock when he sent the radar beam, and T2, the time on A's clock when he received the radar beam. Neither A nor B are constrained to be inertial nor to use any specific coordinate system or synchronization convention.

 

[JesseM]

JesseM, I don't know how you manage to whip up so many comments in such a short time. It takes me days to digest what you are saying and formulate my responses but I'm finally ready to take a stab at your comments but I want to do it in a general sense rather than specifically quote each of your statements.

In both Einstein's 1905 paper and his 1920 book which we have been quoting from in this thread, Einstein is starting with the two postulates or principles as he sometimes calls them. The first is the Principle of Relativity (which is not his theory of relativity) and the second is the Principle (also called the Law) of Constancy of the One-way Speed of Light. See the beginning of article 2 of his 1905 paper and the end of Chapter VII of his 1920 book where he elucidates these two Principles. Although these two Principles are "apparently irreconcilable" (as he says in the introduction of his paper) or suffer "apparent incompatibility" (as he says in the title of chapter VII of his book), his Theory of Special Relativity affirms both of them by redefining the concepts of space and time from their commonly held definitions prior to the introduction of his theory.

Sure, he uses the two postulates to derive the Lorentz transformation (or specific consequences of the Lorentz transformation like time dilation), and that's how most textbooks do it too. But that doesn't mean this is the only valid way to derive the Lorentz transformation, you could derive them starting from some different assumptions which don't talk about the one-way speed of light.

So, when you ask me if his definition of simultaneity can be changed from one based on the one-way speed of light to the slow transport of clocks, it misses the whole point of what he is doing.

No, it doesn't. I understand he was not in that case using slow transport to define simultaneity, but just because he was using one particular derivation doesn't mean he would declare any alternate derivation to be invalid! I'm sure he would acknowledge there are multiple distinct set of starting axioms you can use to derive any specific result like time dilation, just like there are multiple valid derivations of a mathematical result such as the Pythagorean theorem. My point all along was that it's meaningful to talk about measuring the one-way speed of light relative to a particular set of starting assumptions, like the assumption that we synchronize clocks using a slow transport method.

If Einstein had postulated that slow moving clocks do not change their tick rates, then he could have used that as the basis for his argument. But the problem with that is that no one would have suggested that slow moving (or maybe even fast moving) clocks should change their tick rates and thus be apparently irreconcilable or have any apparent incompatibility with the Principle of Relativity. If there's no problem, there's no need for a theory to solve the problem.

Sure, I agree that as a historical matter it's unlikely SR would have been first thought up based on axioms which have nothing to do with light. But that's just history, I don't think it has anything to do with the abstract non-historical question of whether it's meaningful to talk about measuring the one-way speed of light.

 

[GrayGhost]

Yes, B can use that same process, regardless of the fact that B is not inertial. All frames will agree on T0, the time on A's clock when he sent the radar beam, and T2, the time on A's clock when he received the radar beam. Neither A nor B are constrained to be inertial nor to use any specific coordinate system or synchronization convention.

It would be interesting to see what happens in the all inertial case, when observer A uses Einstein's convention while observer B uses 2 different conventions ... one being Einstein's and the other something different.

It almost sounds as though you are suggesting that it makes no difference what range you assign to a remotely located luminally moving observer, given any ole convention is assumed as good as the next. Yes?

Also, if it turns out that mother nature allows a 1-way speed of light of only c, would you still say that the convention used makes no difference at all, far as obtaining correct spacetime solutions?

GrayGhost

 

[JesseM]

Also, if it turns out that mother nature allows a 1-way speed of light of only c, would you still say that the convention used makes no difference at all, far as obtaining correct spacetime solutions?

What do you mean by "mother nature allows"? You can use any coordinate system you like, including ones where the 2-way speed of light is different from c and varies by position, as long as you correctly transform the equations representing the laws of physics from an inertial frame into this new system, you're guaranteed to get all the same answers to local physical questions as in the inertial frame.

 

[GrayGhost]

What do you mean by "mother nature allows"?

I mean ... a test is devised that confirms the 1-way speed of light at c.

GrayGhost

 

[ghwellsjr]

Mike Fontenot does not contend that time is absolute. He merely contends that twin B's spacetime transformation for twin A matches what twin A would predict twin B should predict.

Can you provide a linked quote where Mike states your contentions of what he believes?

 

[ghwellsjr]

JesseM, I don't know how you manage to whip up so many comments in such a short time. It takes me days to digest what you are saying and formulate my responses but I'm finally ready to take a stab at your comments but I want to do it in a general sense rather than specifically quote each of your statements.

In both Einstein's 1905 paper and his 1920 book which we have been quoting from in this thread, Einstein is starting with the two postulates or principles as he sometimes calls them. The first is the Principle of Relativity (which is not his theory of relativity) and the second is the Principle (also called the Law) of Constancy of the One-way Speed of Light. See the beginning of article 2 of his 1905 paper and the end of Chapter VII of his 1920 book where he elucidates these two Principles. Although these two Principles are "apparently irreconcilable" (as he says in the introduction of his paper) or suffer "apparent incompatibility" (as he says in the title of chapter VII of his book), his Theory of Special Relativity affirms both of them by redefining the concepts of space and time from their commonly held definitions prior to the introduction of his theory.

Sure, he uses the two postulates to derive the Lorentz transformation (or specific consequences of the Lorentz transformation like time dilation), and that's how most textbooks do it too. But that doesn't mean this is the only valid way to derive the Lorentz transformation, you could derive them starting from some different assumptions which don't talk about the one-way speed of light.

The Lorentz Transformation, time dilation and length contraction had all been derived prior to Einstein's entry onto the scene without the belief in the constancy of the one-way speed of light (and without slow transport) in all inertial frames. But Lorentz and all the others working on these issues believed in an absolute ether rest frame in which time and space were absolute and only in this one frame was the one-way speed of light the same in all directions. They developed Lorentz Ether Theory (LET) to explain the experimental evidence but this theory was one that Einstein was referring to when he stated that there was an inconsistency and incompatibilty between the Principle of Relativity (not his Theory of Relativity) and the Principle of the Constancy of the One-way Speed of Light.

So, when you ask me if his definition of simultaneity can be changed from one based on the one-way speed of light to the slow transport of clocks, it misses the whole point of what he is doing.

No, it doesn't. I understand he was not in that case using slow transport to define simultaneity, but just because he was using one particular derivation doesn't mean he would declare any alternate derivation to be invalid! I'm sure he would acknowledge there are multiple distinct set of starting axioms you can use to derive any specific result like time dilation, just like there are multiple valid derivations of a mathematical result such as the Pythagorean theorem. My point all along was that it's meaningful to talk about measuring the one-way speed of light relative to a particular set of starting assumptions, like the assumption that we synchronize clocks using a slow transport method.

But since LET is just as viable a theory in explaining all the experimental evidence as the Theory of Special Relativity is, the only way to argue against LET in favor of SR is by redefining the meaning of time. Here is how Einstein argues the point from Section IX of his book:

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.​

If Einstein had postulated that slow moving clocks do not change their tick rates, then he could have used that as the basis for his argument. But the problem with that is that no one would have suggested that slow moving (or maybe even fast moving) clocks should change their tick rates and thus be apparently irreconcilable or have any apparent incompatibility with the Principle of Relativity. If there's no problem, there's no need for a theory to solve the problem.

Sure, I agree that as a historical matter it's unlikely SR would have been first thought up based on axioms which have nothing to do with light. But that's just history, I don't think it has anything to do with the abstract non-historical question of whether it's meaningful to talk about measuring the one-way speed of light.

Slow transport of clocks is handled perfectly well in either LET or SR and cannot be used in favor of either one nor to discredit the other one. Neither can any other measurement or experimental evidence. According to Einstein, if you don't mind the inconsistency between the two Principles stated earlier, then you can go with LET and use the concept of absolute time and the constancy of the speed of light in one elusive frame or you can go with SR and keep both Principles and redefine the meaning of time so that it is relative.

Einstein's brand new idea that no one else had ever thought of, redefining time to maintain the Principle of Relativity and the Principle of the Constant Speed of Light is the reason he gets all the credit for Special Relativity even though many of the concepts that he derives in his 1905 paper had already been derived prior to the introduction of his new theory.

 

[Dale]

It almost sounds as though you are suggesting that it makes no difference what range you assign to a remotely located luminally moving observer, given any ole convention is assumed as good as the next. Yes?

Yes, that is exactly what I am saying. This should be clear simply by considering length contraction.

Also, if it turns out that mother nature allows a 1-way speed of light of only c, would you still say that the convention used makes no difference at all, far as obtaining correct spacetime solutions?

I don't know how that would even be logically possible, but if that were the case then I think a non-inertial observer would be required to use the Dolby and Gull convention, and CADO would be untenable.

 

[GrayGhost]

It almost sounds as though you are suggesting that it makes no difference what range you assign to a remotely located luminally moving observer, given any ole convention is assumed as good as the next. Yes?

Yes, that is exactly what I am saying. This should be clear simply by considering length contraction.

Interesting. Well, it seems to me that length contraction is a separate issue, as compared to the determination of where someone is in space at some time.

While non-inertial, let's say twin B does use Einstein's convention as he would in an all-inertial scenario ... and so he determines that twin A was cT₁=c(T₀+T₂)/2 downrange upon the reflection event based on the most recently received bounced EM, call it the event. When it's all done and said, and everyone is sitting around the table analysing the data, it will be clear that if twin B then had his wonder-ruler stretched out in the direction of the event, and physically extended for precisely the length predicted by the above determination (cT₁) via light signals, that twin A would not be anywhere near the other end of his wonder-ruler at that moment T₁ ... and instead would be short or long, possibly and likely massively.

It seems to me that whatever convention is used by twin B, the predicted twin A range must theoretically match what an extended B-ruler would measure at that time. Yes? Only then would the convention used be considered good, and it would conform to what mother nature has dealt us. Now I realize that it takes time for energy to propagate down a wonder-ruler, but there really should be some realtion between a measurement made by a physical ruler and the process used to determine range via EM.

GrayGhost

 

[Dale]

Interesting. Well, it seems to me that length contraction is a separate issue, as compared to the determination of where someone is in space at some time.

No, it is the same thing. Length is nothing more than the difference in the position of the ends of the object at some time.

While non-inertial, let's say twin B does use Einstein's convention as he would in an all-inertial scenario ... and so he determines that twin A was cT₁=c(T₀+T₂)/2 downrange upon the reflection event based on the most recently received bounced EM, call it the event. When it's all done and said, and everyone is sitting around the table analysing the data, it will be clear that if twin B then had his wonder-ruler stretched out in the direction of the event, and physically extended for precisely the length predicted by the above determination (cT₁) via light signals, that twin A would not be anywhere near the other end of his wonder-ruler at that moment T₁ ... and instead would be short or long, possibly and likely massively.

But that is not what we are talking about, we are talking about what B would say about the distance per A. Because all reference frames will agree on the outcome of all physical experiments both B and A will agree on the reading of A's clock at T0 and at T2 and therefore on the range determined by A. B will not agree that that number is the correct number for the range, but will agree that that is the range per A.

You are really confusing yourself here. There is no intrinsic physical meaning to coordinates. By themselves they are simply labels, like your street address and zip code, which is why you are free to change them as you wish. The metric is the thing which connects the labels to the physics, and determines distances, times, and angles as measured physically. As long as you correctly express the metric in your coordinate system all of the physics will work out correctly.

 

[JesseM]

The Lorentz Transformation, time dilation and length contraction had all been derived prior to Einstein's entry onto the scene without the belief in the constancy of the one-way speed of light (and without slow transport) in all inertial frames.

True, but no one had really emphasized the idea that all laws of physics should be invariant under the Lorentz transformation (though Lorentz did bring up this notion in a somewhat offhand way, see [post=3134496]here[/post]), which would transform the notion of an ether frame into a sort of philosophical postulate that would be irrelevant to all possible experiments.

But since LET is just as viable a theory in explaining all the experimental evidence as the Theory of Special Relativity is, the only way to argue against LET in favor of SR is by redefining the meaning of time.

If by LET you mean a theory where the ether frame might eventually be detectable, then I'd say the principle that all laws of physics are symmetric under the Lorentz transform is the only good argument against it (if this wasn't true, and the ether frame was detectable, then 'redefining the meaning of time' wouldn't change the fact that LET was correct and SR incorrect). On the other hand if by LET you refer to an "interpretation" which claims there is such a thing as absolute time but admits the absolute frame would forever be invisible to all experiments due to the Lorentz-symmetry of physical laws, then I would say that this is just an interpretation of SR, what most physicists mean by "SR" is not any sort of philosophical notion about time but just the testable aspects of the theory, all of which can be boiled down to the idea that the fundamental laws of physics are all locally Lorentz-symmetric. Certainly Einstein would have disapproved philosophically of postulating a totally unobservable ether, see http://www.tu-harburg.de/rzt/rzt/it/Ether.html for example:

For if K be a system of co-ordinates relatively to which the Lorentzian ether is at rest, the Maxwell-Lorentz equations are valid primarily with reference to K. But by the special theory of relativity the same equations without any change of meaning also hold in relation to any new system of co-ordinates K' which is moving in uniform translation relatively to K. Now comes the anxious question: Why must I in the theory distinguish the K system above all K' systems, which are physically equivalent to it in all respects, by assuming that the ether is at rest relatively to the K system? For the theoretician such an asymmetry in the theoretical structure, with no corresponding asymmetry in the system of experience, is intolerable. If we assume the ether to be at rest relatively to K, but in motion relatively to K', the physical equivalence of K and K' seems to me from the logical standpoint, not indeed downright incorrect, but nevertheless inacceptable.

But you see here his argument doesn't specifically involve time or simultaneity or the speed of light, but just the Lorentz-symmetry of all fundamental laws. And he says that an undetectable ether is "not indeed downright incorrect", so I think he would probably have agreed that his reasons for finding such an idea "inacceptable" are based on philosophical arguments along the lines of razor[/url]. His 1905 paper and his 1920 book may have partly been intended to advance philosophical views like this, but I think you misinterpret him if you see any major line of argument (like the one about clock synchronizations) as being primarily about philosophical questions, rather than primarily about deriving testable physics conclusions such as time dilation or Lorentz-symmetry.

Here is how Einstein argues the point from Section IX of his book:

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.​

Slow transport of clocks is handled perfectly well in either LET or SR and cannot be used in favor of either one nor to discredit the other one. Neither can any other measurement or experimental evidence.

Well, see above, I think you are just misunderstanding him if you think the primary point of that quote was to argue for one of two experimentally indistinguishable philosophical views. The main point, I think, is just to argue that it is possible to have laws of physics which respect both the principle of obeying the same equations in different inertial frames and the principle that light travels at c in all inertial frames, if we allow different inertial frames to define simultaneity differently. Even an advocate of a philosophical LET would agree with this point, and would probably further agree that it's useful to define inertial frames in the way Einstein suggests, because the Lorentz-symmetry of the fundamental laws of physics implies that this is the only way to have the laws of physics obey the same equations in different inertial frames.

 

[ghwellsjr]

JesseM, I don't think Einstein would agree with your crediting him with more than he is taking credit for himself in the address you quote a small portion of. If you had started a few paragraphs earlier, you would have read:

Such was the state of things when H. A. Lorentz entered upon the scene. He brought theory into harmony with experience by means of a wonderful simplification of theoretical principles. He achieved this, the most important advance in the theory of electricity since Maxwell, by taking from ether its mechanical, and from matter its electromagnetic qualities. As in empty space, so too in the interior of material bodies, the ether, and not matter viewed atomistically, was exclusively the seat of electromagnetic fields. According to Lorentz the elementary particles of matter alone are capable of carrying out movements; their electromagnetic activity is entirely confined to the carrying of electric charges. Thus Lorentz succeeded in reducing all electromagnetic happenings to Maxwell's equations for free space.

As to the mechanical nature of the Lorentzian ether, it may be said of it, in a somewhat playful spirit, that immobility is the only mechanical property of which it has not been deprived by H. A. Lorentz. 1t may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility. How this is to be understood will forthwith be expounded.

The space-time theory and the kinematics of the special theory of relativity were modeled on the Maxwell-Lorentz theory of the electromagnetic field. This theory therefore satisfies the conditions of the special theory of relativity, but when viewed from the latter it acquires a novel aspect.​

And so from the context, we can see that the only thing Einstein is claiming that is different between LET and SR is giving up an absolute ether rest frame. And how did he do that? By expanding the concept of a co-ordinate system to include a time component. So when he is talking about the K and the K' systems in the part of the discussion you quoted, he has already redefined the concept of time to be relative, as described in his 1905 paper and his 1920 book, written in the same year as this talk you've quoted from. He's not saying anything different in any of these three references.

 

[JesseM]

And so from the context, we can see that the only thing Einstein is claiming that is different between LET and SR is giving up an absolute ether rest frame.

Why do you say that? He does not in that quote credit Lorentz with the idea that all laws of physics should be symmetric under the Lorentz transformation, making the ether into a purely metaphysical notion that could never be verified by any possible experiment. As I said earlier Lorentz did in fact mention the idea that all laws might be Lorentz-symmetric like electromagnetism (and Poincare also picked up on this idea from the paper where Lorentz casually mentioned the idea), but I don't think he made any strong claims about it being true, and definitely didn't make the complete symmetry between frames the centerpiece of any of his papers like Einstein did.

And how did he do that? By expanding the concept of a co-ordinate system to include a time component.

Lorentz already came up with the full Lorentz transformation, including the time component and the fact that different frames disagree about whether two events have the same t-coordinate.

 

[GrayGhost]

No, it is the same thing. Length is nothing more than the difference in the position of the ends of the object at some time.

But that is not what we are talking about, we are talking about what B would say about the distance per A. Because all reference frames will agree on the outcome of all physical experiments both B and A will agree on the reading of A's clock at T0 and at T2 and therefore on the range determined by A. B will not agree that that number is the correct number for the range, but will agree that that is the range per A.

You are really confusing yourself here. There is no intrinsic physical meaning to coordinates. By themselves they are simply labels, like your street address and zip code, which is why you are free to change them as you wish. The metric is the thing which connects the labels to the physics, and determines distances, times, and angles as measured physically. As long as you correctly express the metric in your coordinate system all of the physics will work out correctly.

I've given your post here some careful consideration.

I disagree that we were talking only Lorentz transformations. We were also talking about how one accurately determines the current location of a moving body, which most would say does not require any knowledge as to the extent of length contraction. I on the other hand, would not be one of those folks. Yet, one needs an accurate location of the moving body to then apply the LTs, for otherwise one transforms a point that represents something other than the moving body ... and so what then is the point?

Noone disagrees that 2 observers in relative motion disagree on the matter of simultaneity, and hence the range of remotely located moving bodies. However, here's the thing ...

You have made the point that twins A and B may each use their own conventions, and that it doesn't matter in the end. Yet the Minkowski metric was defined for the all-inertial case in flat spacetime, not for acceleration and/or gravitation. To just assume that non-inertial twin B can simply assume that T₁ = (T₀+T₂)/2, or that twin B may use the LTs in the usual all-inertial way (with no extra efforts), is at the very best an unreasonable assumption. IMO, whatever one assumes twin B can or cannot do, must at the very least be consistent with what all-inertial observers claim via SR.

Anyway, I'll think about it further and see if I reconsider.

GrayGhost

 

[ghwellsjr]

Why do you say that? He does not in that quote credit Lorentz with the idea that all laws of physics should be symmetric under the Lorentz transformation, making the ether into a purely metaphysical notion that could never be verified by any possible experiment. As I said earlier Lorentz did in fact mention the idea that all laws might be Lorentz-symmetric like electromagnetism (and Poincare also picked up on this idea from the paper where Lorentz casually mentioned the idea), but I don't think he made any strong claims about it being true, and definitely didn't make the complete symmetry between frames the centerpiece of any of his papers like Einstein did.

Lorentz already came up with the full Lorentz transformation, including the time component and the fact that different frames disagree about whether two events have the same t-coordinate.

In Einstein's http://www.tu-harburg.de/rzt/rzt/it/Ether.html , he never once relegates the ether to a metaphysical notion. In fact, he discusses three different positions that can be taken with regard to the ether.

The first is covered in the quotes that you and I made from his talk, which is the view of Lorentz, which Einstein calls the "Lorentzian ether". This is the one that is commonly referred to as LET in which there is a primary frame, K, in which the ether is at rest and many other frames, K', in which the ether is in motion. This is the position that Einstein calls "inacceptable" in your quote of his talk in post #45.

Immediately after that, Einstein discusses the next possible position to take on the ether which is that it doesn't exist at all. He concludes that discussion with a line in bold from his talk, "the special theory of relativity does not compel us to deny ether."

Then, he launches into the third possible position to take on the ether which is, "We may assume the existence of an ether,; only we must give up ascribing a definite state of motion to it" and he explains why. His argument goes like this:

"Think of waves on the surface of water." He says "we can observe how the position of the separate particles of water alters in the course of time" or we could observe "the shape of the space occupied by the water as it varies in time" [emphasis mine]. In other words, we can observe, see, measure, identify, etc, the one-way speed of the waves. We can know where in space each wave is at each moment in time.

By analogy, "We have something like this in the electromagnetic field. For we may picture the field to ourselves as consisting of lines of force." Here he is talking about the motion of light in the ether as lines of force. He then says, "we are tempted to interpret the dynamic processes as motions of these lines of force, such that each separate line of force is tracked through the course of time." Here he is describing our desire to know the one-way speed of light but he says "It is well known, however, that this way of regarding the electromagnetic field leads to contradictions."

"We must say", according to Einstein, that what happens out there in the ether, cannot be "tracked through time". And all this is before we get to SR, it's just a description of what we can and cannot do with our observations and measurements. And then he concludes, "The special theory of relativity forbids us to assume the ether to consist of particles observable through time, but the hypothesis of ether in itself is not in conflict with the special theory of relativity. Only we must be on our guard against ascribing a state of motion to the ether."

And he goes on to state some good reasons for taking up this last of his three possible positions concerning the ether.

So the bottom line is that, once again, as I said in my first post and in contradiction to what Mike Fontenot says, Einstein is stating that we cannot know, observe, or measure the one-way speed of light. He does not in this talk describe the process that leads to his theory of Special Relativity, but we know from his 1905 paper and his 1920 book that it involves defining time in such a way that we can also define the one-way speed of light.

Please note also throughout this talk that Einstein repeatedly discusses many other great scientists of the past and of his present, some of which he disagrees with and some of which he agrees with, and he never once says anything in disagreement with Lorentz, rather always affirming Lorentz, except this one issue with regard to his concept that the ether is immovable.

 

[Dale]

I disagree that we were talking only Lorentz transformations.

I don't know why you think this is a point of disagreement. I agree, we are not talking only about Lorentz transformations, we are talking about a much more general class of transformations called diffeomorphisms.

You have made the point that twins A and B may each use their own conventions, and that it doesn't matter in the end. Yet the Minkowski metric was defined for the all-inertial case in flat spacetime, not for acceleration and/or gravitation.

You have to be a little careful with your wording here. "The metric" can either refer to the coordinate expression of the metric or it can refer to the coordinate-independent geometry. Usually when people say "Minkowski metric" they are referring to the coordinate expression of the flat spacetime metric in inertial coordinates, in which case your statement is correct and I agree with it completely. In accelerated coordinate systems, as we are discussing here, you need to use a different algebraic form of the metric to express the same underlying geometry. You always need to use the correct form of the metric for the coordinate system you are using.

 

[JesseM]

In Einstein's http://www.tu-harburg.de/rzt/rzt/it/Ether.html , he never once relegates the ether to a metaphysical notion. In fact, he discusses three different positions that can be taken with regard to the ether.

The first is covered in the quotes that you and I made from his talk, which is the view of Lorentz, which Einstein calls the "Lorentzian ether". This is the one that is commonly referred to as LET in which there is a primary frame, K, in which the ether is at rest and many other frames, K', in which the ether is in motion. This is the position that Einstein calls "inacceptable" in your quote of his talk in post #45.

Yes, but I would say he considers it "inacceptable" for philosophical reasons along the lines of Occam's razor...he first says that "from the logical standpoint" this view is "not indeed downright incorrect", just that he finds it "inacceptable". This notion of ether is indeed a "metaphysical notion" which we can never prove wrong logically, or falsify experimentally.

He does go on to talk about a different notion of ether in the remainder of the talk, but this isn't relevant to our discussion of whether he intended to rule out what is now known as a "Lorentz ether theory" (i.e. the metaphysical notion above, which involves a metaphysically preferred frame which defines "true" simultaneity), instead he's expanding the definition of ether to mean that space has definite properties of its own even when empty of observable matter/energy, which of course is true in general relativity.

 

[ghwellsjr]

Yes, but I would say he considers it "inacceptable" for philosophical reasons along the lines of Occam's razor...he first says that "from the logical standpoint" this view is "not indeed downright incorrect", just that he finds it "inacceptable". This notion of ether is indeed a "metaphysical notion" which we can never prove wrong logically, or falsify experimentally.

He does go on to talk about a different notion of ether in the remainder of the talk, but this isn't relevant to our discussion of whether he intended to rule out what is now known as a "Lorentz ether theory" (i.e. the metaphysical notion above, which involves a metaphysically preferred frame which defines "true" simultaneity), instead he's expanding the definition of ether to mean that space has definite properties of its own even when empty of observable matter/energy, which of course is true in general relativity.

But before he goes on to talk about the ether of general relativity, which I didn't comment on, he first goes on to talk about what he considers to be an acceptable ether of special relativity, which is what I discussed in my previous post.

What I would like for you to focus on in my previous post is Einstein's discussion about the ether of special relativity and his statements that we cannot track light's progress through it as a function of time.

 

[JesseM]

"Think of waves on the surface of water." He says "we can observe how the position of the separate particles of water alters in the course of time" or we could observe "the shape of the space occupied by the water as it varies in time" [emphasis mine]. In other words, we can observe, see, measure, identify, etc, the one-way speed of the waves. We can know where in space each wave is at each moment in time.

He says absolutely nothing about the "one way speed of the waves" here. He's just making the point that even if there was no way to measure the motion of particles of water, one could still measure the shape of waves in water.

By analogy, "We have something like this in the electromagnetic field. For we may picture the field to ourselves as consisting of lines of force." Here he is talking about the motion of light in the ether as lines of force. He then says, "we are tempted to interpret the dynamic processes as motions of these lines of force, such that each separate line of force is tracked through the course of time." Here he is describing our desire to know the one-way speed of light

No he isn't, he's saying nothing about one-way speeds or our desire to know them. I think your own interest in the subject of one-way speed is badly distorting your reading of his words, he's really just making the very simple point that we are still free to think of electromagnetic waves as compression of an "ether" as long as we give up any notion that this ether is an ordinary physical substance (like water) made up of particles that have their own rest frame (see the next paragraph where he says "There may be supposed to be extended physical objects to which the idea of motion cannot be applied. They may not be thought of as consisting of particles which allow themselves to be separately tracked through time.")

So the bottom line is that, once again, as I said in my first post and in contradiction to what Mike Fontenot says, Einstein is stating that we cannot know, observe, or measure the one-way speed of light.

And once again your interest in this subject is causing you to see things that aren't there, his comments in this talk have nothing whatsoever to do with the one-way speed of light, if he was concerned with that subject he would have used some phrase like "speed of light" but he doesn't in those paragraphs about the SR "ether", in fact he doesn't even bother mentioning electromagnetic waves in the paragraph about the electromagnetic field, he just talks about lines of force which are present even in field with no accelerating charges and therefore no electromagnetic waves.

Please note also throughout this talk that Einstein repeatedly discusses many other great scientists of the past and of his present, some of which he disagrees with and some of which he agrees with, and he never once says anything in disagreement with Lorentz, rather always affirming Lorentz, except this one issue with regard to his concept that the ether is immovable.

Why do you want me to note this? Do you think my own arguments should somehow lead me to think he would express disagreement with Lorentz about things other than the purely philosophical question about whether we should continue to believe in an ether with its own rest frame even though no experiment could ever determine what its rest frame is?

 

[ghwellsjr]

Thank you for responding as I requested. Let me see if I understand what you are saying.

With regard to Einstein's paragraph concerning "waves on the surface of water", he is only talking about the up and down motion of the waves and not the forward progression of the waves, because the particles of water are not actually moving laterally, merely up and down, and so when he says the shape of the waves, he's referring to the vertical displacement as a function of the lateral distance and not as a function of time, correct?

And the next paragraph about the electromagnetic field is not concerned with waves at all, but merely static lines of force caused by stationary charges, and so when he talks about "the dynamic processes as motions of these lines of force", he doesn't mean as a function of lateral position but as a function of "pressure" or "compression", correct?

 

[JesseM]

Thank you for responding as I requested. Let me see if I understand what you are saying.

With regard to Einstein's paragraph concerning "waves on the surface of water", he is only talking about the up and down motion of the waves and not the forward progression of the waves, because the particles of water are not actually moving laterally, merely up and down, and so when he says the shape of the waves, he's referring to the vertical displacement as a function of the lateral distance and not as a function of time, correct?

No, I didn't mean that, my point was just that describing how "the shape of the space occupied by the water as it varies in time" is just a normal physical question, it does not require some kind of odd philosophical belief that there must be a "true" value to coordinate-dependent aspects or our description of shape vs. time, such as one-way speed. Different observers describing a set of water waves can use different coordinate systems which give different values for speeds, time intervals between events, etc., but if they know the coordinate transformations that relate their different coordinate systems, they can see that all their descriptions are physically equivalent, so they are not saying anything different from one another about "the shape of the space occupied by the water as it varies in time."

And the next paragraph about the electromagnetic field is not concerned with waves at all, but merely static lines of force caused by stationary charges, and so when he talks about "the dynamic processes as motions of these lines of force", he doesn't mean as a function of lateral position but as a function of "pressure" or "compression", correct?

Not saying he was excluding waves or talking only about static lines of force, just that waves weren't central to his comments as your notion that he was talking specifically about one-way speed of electromagnetic waves would suggest.