Is the Principle of Relativity Valid for Faster-than-Light Propagation?

[ghwellsjr]

I was under the impression that LET postulates the existence of an aether such that:

• light speed is isotropic relative to the aether

The Principle of Relativity therefore becomes a derived result rather than a postulate.
...
I may be wrong, but I suspect there may never have been a rigorous statement of LET's postulates because the theory was abandoned before it gained much momentum.

One thing is for sure, LET does not accept Einstein's second postulate and whether or not any of its promoters prior to Einstein ever even considered it, they probably wouldn't have given it a second thought because they believed it was irreconcilable with the principle of relativity, whether or not that principle was formulated as a postulate or derived. But the LET that we talk about today does affirm the principle of relativity which Einstein said he raised to the status of a postulate (his first).

So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

 

[Saw]

Woot! 10k posts!

Beware, you are becoming wordy!

LET views the principle of relativity in the same way that NASA conspiracy theorists view the moon landings. They recognize that there is a lot of evidence for it, but they believe that all of the evidence is faked, and it irritates them that they can't prove it. I wouldn't call that "accepting".

I do not know why you think so. Conspiracy theorists argue that NASA did NOT land on the Moon. LET affirms that the PoR DOES apply. A different thing is that LET thinks the PoR applies for a physical reason, which generates a fortunate compensation of effects.

Lorentz's historical theory was "deeper" than SR in at least one sense: it tried to provide physical underpinnings for relativistic effects. For instance, Lorentz believed that a moving electron was compressed by its own electromagnetic field.

Yes, with that I agree. As you imply, "deeper" here does not mean "better" since the underpinning may be wrong. An example to reinforce your point: you may model how hot a body is by measuring temperature and mass; for most purposes, that is good enough, but to gain a better understanding of the phenomenon, you may try to find a deeper-level explanation; in this sense, you may hypothesize that the physical reason is (a) a fluid that goes into the body or (b) the internal motion of particles. Both (a) and (b) are "deeper-level" explanations, although (a) is wrong.

So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

As DrGreg pointed out, the problem with LET is that nobody knows very well what it means since it has never been fully developed. But for the purpose of this discussion, can we make a convention? Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether. Are the two things logically incompatible? I do not think so.

When you say that for LET "light speed is isotropic only relative to the aether", we should clarify what we mean by that. If those concepts ("isotropic", "speed") are fed by absolute measurements of time and distances, then not only LET also I do affirm that light CANNOT be isotropic in any frame. But LET admits that absolute measurements are not in practice possible. We must content ourselves, in real life, with relative measurements. And if you feed the concept of speed with those relative measurements, you forcefully get (also for LET!) isotropic light speed.

 

[harrylin]

This interpretation is based on the concept that the ether is stationary and unmoving. Other interpretarions are possible if the ether is considered to exist and have the ability to move. Why are these other interpretations taboo?

Those other interpretations (presumably all of them, but it's hard to be sure about an undefined group) are incompatible with special and general relativity as well as some key experiments that give support for those theories. Special relativity emerged from Lorentz's electron theory which assumed a stationary ether model and succefully explained such things as the Fizeau "drag".

 

[harrylin]

Yes, but of a different level. Am I wrong if I assume that LET also endorses the two postulates?

There was no "LET". Einstein based the second postulate on Maxwell's theory which also was part of Lorentz's theories. Thus Lorentz didn't disagree with Einstein's 1905 paper, and Einstein clarified that the second postulate is made plausible by Lorentz's preceding theory of electrons. Moreover, Lorentz had next derived the Lorentz transformation equations (although not in their symmetrical form) in order to conform to the first postulate.

Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether. Are the two things logically incompatible? I do not think so.

Neither did Einstein think so, as he explained in a very elaborate way in his Leiden inauguration speech.

 

[harrylin]

[..] So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

No, the isotropy of light in any inertial frame is a derived result, although most textbooks for students skip that. As Einstein put it in 1905:
"We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."

 

[zonde]

I think that problem about LET is not whether or not speed of light is isotropic in all inertial frames (we just construct coordinate systems so that it is so).
I think that problem is about c being universal speed limit. Because Lorentz transform works only for one speed. Any other speed will be different after Lorentz transform. That universality is the unreasonable part. And that universality ensures that principle of relativity holds.

On the other hand we can view principle of relativity as external constraint. Matter that does not follow this principle can not change it's state of motion i.e. it will be fragile and break down when accelerated. If we assume that matter can replicate itself (say pair prodaction can happen only in presence of matter) then more flexible matter will be evolutionary preferable. At least that is my reasoning why principle of relativity holds.

 

[ghwellsjr]

[..]So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

No, the isotropy of light in any inertial frame is a derived result, although most textbooks for students skip that. As Einstein put it in 1905:
"We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."

So you're saying that Einstein's so-called second postulate is also a derived result, just like others on this thread have pointed out that the principle of relativity is a derived result for LET and not a first postulate?

 

[lugita15]

No, the isotropy of light in any inertial frame is a derived result, although most textbooks for students skip that. As Einstein put it in 1905:
"We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."

I think here Einstein is proving the compatibility of the first and second postulates, not the truth of the second postulate, which is of course an assumption of his theory.

 

[lugita15]

On the other hand we can view principle of relativity as external constraint. Matter that does not follow this principle can not change it's state of motion i.e. it will be fragile and break down when accelerated.

What exactly do you mean by this? Why can't an object which does not "follow" the PoR change its state of motion?

 

[zonde]

What exactly do you mean by this? Why can't an object which does not "follow" the PoR change its state of motion?

Object that does not follow PoR would have to have different structure for different states of motion. Well, I am assuming that object can't have many different stable configurations and smoothly slip from one structure to other without breaking down. Something like that.

 

[lugita15]

Object that does not follow PoR would have to have different structure for different states of motion.

I still don't understand what you're talking about. And in any case, it doesn't really make sense to talk about objects "following" the PoR; you can only talk about laws of physics which follow it or not. For example, in Aristotelian physics the law was "An object at rest stats at rest, and an object in motion comes to rest", which is obviously incompatible with the PoR. How could a law of this kind lead to structural instability of physical objects?

 

[Dale]

But LET admits that absolute measurements are not in practice possible.

This is true, but the problem with the rest of your comments is that LET nevertheless asserts the existence and reality of unmeasurable things. Thus, what is real is considered different from what is measured. Conversely, what is measured is considered to be an inaccurate reflection of reality.

Conspiracy theorists argue that NASA did NOT land on the Moon. LET affirms that the PoR DOES apply.

I disagree here. LET argues that the PoR does not apply in reality, but that reality is unmeasurable.

But for the purpose of this discussion, can we make a convention? Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether.

So we should make a convention that we agree you are right? I prefer the convention where we all agree with me.

 

[zonde]

I still don't understand what you're talking about.

Ok, let me try one more time.
Object has different interactions that determine it's structure - different molecular bonds, interactions determining structure of atom and interactions inside nucleons.
Let's say that interactions all happen at different speeds. They have at some distance potential minimum. When we change speed of object this minimum potential distance changes by different amounts for different interactions (because of different interaction speed - you can imagine that we use Lorentz transforms for different interactions with different values of "c"). So if internal distances determining structure of object do not change in unison it should eventually break.

 

[Saw]

I disagree here. LET argues that the PoR does not apply in reality, but that reality is unmeasurable.

Again it depends on what we mean by PoR. If by PoR we mean knowing absolute simultaneity, then, yes, LET argues that we do not have that knowledge. And so do I... Don't you? I would think anybody would agree on that, maybe I am wrong, but it looks quite obvious... (By absolute simultaneity I mean the one that would be established in the eather frame, if the aether existed, or by an instantaneous means of communication, if such thing were possible.)

Instead if by PoR we mean that, even if we do not have such ambitious knowledge (absolute simultaneity), we live quite well without it (we can solve all known practical problems), then LET should agree with that.

 

[ghwellsjr]

So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

As DrGreg pointed out, the problem with LET is that nobody knows very well what it means since it has never been fully developed. But for the purpose of this discussion, can we make a convention? Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether. Are the two things logically incompatible? I do not think so.

The only attribute of the aether of LET is that it is a preferred frame, the one nature operates according to. It does not offer any other explanatory mechanisms regarding how nature interacts with light to cause length contraction or time dilation. So we don't want to conceive of LET as being SR plus something. It's the principle of relativity (which is not SR) plus something just like SR is the principle of relativity plus something else.

When you say that for LET "light speed is isotropic only relative to the aether", we should clarify what we mean by that.

I was using DrGreg's terminology in my quote. I usually use Einstein's terminology such as "light always propagates at c" or "any ray of light moves at c" but they mean the same thing. In LET, light propagates at c only in the aether.

If those concepts ("isotropic", "speed") are fed by absolute measurements of time and distances, then not only LET also I do affirm that light CANNOT be isotropic in any frame. But LET admits that absolute measurements are not in practice possible. We must content ourselves, in real life, with relative measurements. And if you feed the concept of speed with those relative measurements, you forcefully get (also for LET!) isotropic light speed.

There is no measurement that can determine how light propagates. If there were, we wouldn't have the principle of relativity which means we wouldn't have either LET or SR because they are both based on that principle (plus a postulate about how light propagates).

Prior to Maxwell, the principle of relativity was well established. As a result of Maxwell's discovery that his equations describing an electromagnet field predicted waves that happen to travel at c, he (incorrectly) concluded that this would provide a means to experimentally measure the rest state of that field and do away with the principle of relativity. When MMX could not experimentally measure the rest state of that field, the principle of relativity was upheld and LET was formulated to explain what was happening still based on a field at absolute rest. The principle of relativity (again, not to be confused with Special Relativity) was what forced Lorentz, et al, to formulate LET, not the other way around. This resulted in time and space being absolute even though they were aware of the concepts of time dilation and length contraction for objects moving with respect to the aether but it never occurred to them that space itself or time itself, in other word's, nature, could ever be relative. In this sense, absolute time and absolute space are derived results from the experimental evidence of the principle of relative plus the postulate that light travels at c only in one rest state (the one nature operates on).

Einstein's two postulates, along with his definition of a Frame of Reference incorporating the amalgamation spacetime (instead of leaving space and time as independent coordinates) had a derived result of time and space being relative to the defined Frame of Reference rather than an absolute of nature.

 

[harrylin]

So you're saying that Einstein's so-called second postulate is also a derived result, just like others on this thread have pointed out that the principle of relativity is a derived result for LET and not a first postulate?

No, I pointed out that common university textbooks don't properly phrase Einstein's second postulate, instead they make a shortcut for a simplified derivation of the Lorentz transformations. Basically what those textbooks call the second postulate is the second postulate combined with the first postulate.

 

[harrylin]

I think here Einstein is proving the compatibility of the first and second postulates, not the truth of the second postulate, which is of course an assumption of his theory.

Yes indeed; my point was that Einstein's second postulate is not inherently compatible with the first. As a matter of fact those two postulates are, as Einstein put it, "apparently irreconcilable". In contrast, the two postulates of common textbooks are obviously compatible.

 

[harrylin]

[..] LET nevertheless asserts the existence and reality of unmeasurable things. Thus, what is real is considered different from what is measured. Conversely, what is measured is considered to be an inaccurate reflection of reality. [..]

Right - that was also Newton's position. I think that it's a scientifically sound position: we must never assume that appearance equals reality.

LET argues that the PoR does not apply in reality, but that reality is unmeasurable.

"LET"'s argument is moot: the PoR relates to phenomena, not unmeasurable "reality".

 

[Dale]

"LET"'s argument is moot: the PoR relates to phenomena, not unmeasurable "reality".

Hmm, that is an interesting thought. I will have to think about that for a bit.

 

[lugita15]

The only attribute of the aether of LET is that it is a preferred frame, the one nature operates according to. It does not offer any other explanatory mechanisms regarding how nature interacts with light to cause length contraction or time dilation. So we don't want to conceive of LET as being SR plus something. It's the principle of relativity (which is not SR) plus something just like SR is the principle of relativity plus something else.

You are of course talking about the modern construct known as LET. I think historically, a fair characterization of Lorentz's theory would be Newtonian mechanics combined with length contraction, time dilation, and mass increase. And each of these effects would be explained as electromagnetic phenomena.

Prior to Maxwell, the principle of relativity was well established. As a result of Maxwell's discovery that his equations describing an electromagnet field predicted waves that happen to travel at c, he (incorrectly) concluded that this would provide a means to experimentally measure the rest state of that field and do away with the principle of relativity.

As far as I know, Maxwell was a firm believer in Newtonian mechanics and the Galilean principle of relativity. He was also presumably familiar that other wave equations had a preferred frame, like the wave equation for sound waves. Just as one could do an experiment involving sound in order to find the motion of the Earth with respect to air, he found it reasonable that we could use light to find the motion of the Earth with respect to the ether. This wouldn't contradict the PoR at all.

The principle of relativity (again, not to be confused with Special Relativity) was what forced Lorentz, et al, to formulate LET, not the other way around.

I would say that the apparent invariance of the speed of light in all reference frames plus the notion that the speed of light should only equal c in the ether frame is what forced Lorentz to LET; it had nothing to do with the PoR. The fact that the Lorentz transformations are symmetric was not known to Lorentz when he formulated them. The symmetry was a later (mathematical) discovery made by Poincare, and then of course Einstein developed SR in which the symmetry is not a coincidence.

 

[ghwellsjr]

Prior to Maxwell, the principle of relativity was well established. As a result of Maxwell's discovery that his equations describing an electromagnet field predicted waves that happen to travel at c, he (incorrectly) concluded that this would provide a means to experimentally measure the rest state of that field and do away with the principle of relativity.

As far as I know, Maxwell was a firm believer in Newtonian mechanics and the Galilean principle of relativity. He was also presumably familiar that other wave equations had a preferred frame, like the wave equation for sound waves. Just as one could do an experiment involving sound in order to find the motion of the Earth with respect to air, he found it reasonable that we could use light to find the motion of the Earth with respect to the ether. This wouldn't contradict the PoR at all.

What definition of PoR are you using that let's you identify a preferred frame by experiment?

The principle of relativity (again, not to be confused with Special Relativity) was what forced Lorentz, et al, to formulate LET, not the other way around.

I would say that the apparent invariance of the speed of light in all reference frames plus the notion that the speed of light should only equal c in the ether frame is what forced Lorentz to LET; it had nothing to do with the PoR.

I agree with this up to the semicolon, I just don't know why you think "the apparent invariance of the speed of light in all reference frames" has nothing to do with PoR.

The fact that the Lorentz transformations are symmetric was not known to Lorentz when he formulated them. The symmetry was a later (mathematical) discovery made by Poincare, and then of course Einstein developed SR in which the symmetry is not a coincidence.

OK, but what has that got to do with PoR?

 

[lugita15]

What definition of PoR are you using that let's you identify a preferred frame by experiment?

I'm just using the traditional definition "The laws of physics are the same in all inertial reference frames." Maxwell believed that space and time are absolute, so in his mind the principle of relativity implied the Galilean transformations. So the fact that his equations predicted that the speed of light is c led Maxwell to conclude that his equations violated Galilean invariance and thus could only be exactly true in one preferred frame. So he wanted to conduct an experiment to determine that frame. If he was successful, that would not violate the principle of relativity, it would just mean that his equations would have to be modified in order to become Galilean invariant, so that measurements of the speed of light in other frames would be c+v or c-v, where v is the speed of the aether with respect to you.

Think about sound: if you're moving with respect to the air, the speed of sound would be different than what is predicted by the wave equation, only because the wave equation has the air as its preferred frame (which you can determine by doing a Michelson-Morley style experiment with sound instead of light). In order to find out the properties of sound in our moving frame, we have to use a modified wave equation which is Galilean invariant (I'm sure this is a fairly trivial exercise to perform: you can redo the derivation of the wave equation for sound from Newton's laws, just assume that the air molecules are moving rather than stationary).

I agree with this up to the semicolon, I just don't know why you think "the apparent invariance of the speed of light in all reference frames" has nothing to do with PoR.

The constancy of the speed of light is only a consequence of the PoR if it is in fact a law of physics that the speed of light is c. As I said above, Maxwell had no reason to believe that this was the case; he thought his equations would only be exactly accurate in the aether frame.

OK, but what has that got to do with PoR?

Lorentz believed that errors in measuring devices due to length contraction and time dilation were responsible for the apparent invariance of the speed of light. So he thought that speed of light measurements could never reveal the ether frame, but he held out the possibility that some clever experiment might one day find out the ether frame. For instance, if both observer A and observer B were moving with respect to the ether, but at different speeds, perhaps observer A could look at how much observer B's ruler was contracted compared to his own ruler, and use that to find out their speeds with respect to ether. But Poincare proved that was impossible by demonstrating the symmetry of the Lorentz transformations, so that the transformations connected not only observer A and observer B to the ether frame, but also to each other. (EDIT: Actually, you need a little more than just symmetry to show that any two frames are connected by an LT. You need to show that the inverse of an LT is an LT, but you also need to show that the composition of two LT's is an LT. As far as I know, Poincare succeeded in proving both of these facts, but it took Einstein to realize their significance.)

Lorentz would also be shocked to learn that all laws of physics are Lorentz invariant, not just electromagnetism.

 

[Saw]

... Poincare proved that was impossible by demonstrating the symmetry of the Lorentz transformations, so that the transformations connected not only observer A and observer B to the ether frame, but also to each other. (EDIT: Actually, you need a little more than just symmetry to show that any two frames are connected by an LT. You need to show that the inverse of an LT is an LT, but you also need to show that the composition of two LT's is an LT. As far as I know, Poincare succeeded in proving both of these facts, but it took Einstein to realize their significance.)

Lorentz would also be shocked to learn that all laws of physics are Lorentz invariant, not just electromagnetism.

I like this historical description. You succeed in showing that Lorentz and Poincaré were close to formulating SR but only Einstein did. And now that he did and we all believe in the PoR and invariant c, why do we believe so? Of course, because experiment proves it. But is there any physical reason? Well, if someone says, "because light is a wave that propagates through a medium called the aether", we could answer: "you cannot prove it" but we cannot say "you are wrong", either, since neither the PoR nor invariant c are logically incompatible with the aether. I suppose you agree with that.

 

[ghwellsjr]

What definition of PoR are you using that let's you identify a preferred frame by experiment?

I'm just using the traditional definition "The laws of physics are the same in all inertial reference frames."

That is a good definition but it has consequences as Richard Feynman points out in his chapter on Special Relativity from Lectures on Physics:

The principle of relativity was first stated by Newton, in one of his corollaries to the laws of motion: "The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line." This means, for example, that if a spaceship is drifting along at a uniform speed, all experiments performed in the spaceship and all the phenomena in the spaceship will appear the same as if the ship were not moving, provided, of course, that one does not look outside. That is the meaning of the principle of relativity.​

Maxwell believed that space and time are absolute, so in his mind the principle of relativity implied the Galilean transformations.

That's an understatement. At that time, all scientists believed the principle of relativity was embodied in the Galilean transformation.

So the fact that his equations predicted that the speed of light is c led Maxwell to conclude that his equations violated Galilean invariance and thus could only be exactly true in one preferred frame. So he wanted to conduct an experiment to determine that frame.

But violating Galilean invariance is the same as violating the principle of relativity. Here's how Feynman expresses it:

However, the Maxwell equations did not seem to obey the principle of relativity. That is, if we transform Maxwell's equations by the substitution of equations [of the Galilean transformation], their form does not remain the same; therefore, in a moving spaceship the electrical and optical phenomena should be different from those in a stationary ship. Thus one could use these optical phenomena to determine the speed of the ship; in particular, one could determine the absolute speed of the ship by making suitable optical or electrical measurements.​

If he was successful, that would not violate the principle of relativity, it would just mean that his equations would have to be modified in order to become Galilean invariant, so that measurements of the speed of light in other frames would be c+v or c-v, where v is the speed of the aether with respect to you.

No, if he was unsuccessful, it would mean his equations would have to be modified, or so they thought. Here's how Feynman expresses it:

A number of experiments...were performed to determine the velocity of the earth, but they all failed--they gave no velocity at all...something was wrong with the equations of physics. What could it be?...the first thought that occurred was the trouble must lie in the new Maxwell equations of electrodynamics, which were only 20 years old at the time. It seemed obvious that these equations must be wrong, so the thing to do was to change them in such a way that under the Galilean transformation the principle of relativity would be satisfied. When this was tried, the new terms that had to be put into the equations led to predictions that of new electrical phenomena that did not exist at all when tested experimentally, so this attempt had to be abandoned. Then it gradually became apparent that Maxwell's laws of electrodynamics were correct, and the trouble must be sought elsewhere.​

So if an experiment did determine the velocity of the earth, it would mean that the principle of relativity was not valid. But since the experiments were unsuccessful, the principle of relativity survived intact but since Maxwell's equations also survived, it meant that the Galilean transformation must be in error and that's what eventually was discovered to be the case and it was replaced by the Lorentz transformation but this was all done in the context of an absolute ether rest frame.

 

[whosapopstar?]

Could there be any meaning extracted from this question:
Why should ether wind not have such properties that on the contrary, light is a phenomenon that is not influenced by it, while other phenomenon are influenced?

 

[Dale]

I have spent some time thinking about two very interesting points that were raised. I thank both lugita15 and harrylin for their interesting comments. Before addressing them, however, I think that it is important to note two things:

First, the PoR, as I have usually seen it, refers to the equations. E.g. http://en.wikipedia.org/wiki/Principle_of_relativity. It states that the equations of physics have the same form with the same universal constants in all frames of reference.

Second, from Maxwell to Einstein, the leading scientists of the day believed that the PoR was not correct, or at least that it did not apply to EM phenomena. They considered the aether frame to be a preferred frame in the sense of violating the PoR. Specifically, that Maxwell's equations only applied in the aether frame.

Sound waves have a preferred frame, the rest frame of air, yet that doesn't invalid the principle of relativity, because the wave equation for sound waves is not a law of physics and thus does not need to be true in all frames.

I understand your point here, but the difference is that the velocity of the medium for acoustic waves can be detected by non-acoustic phenomena. So, we can say that the speed of sound is isotropic in any frame where a nearby anemometer reads 0, and that is true regardless of if the anemometer is moving in some other frame. Also, Newton's equations would still hold in all frames.

On the other hand, there was supposedly no other way to detect the aether other than its effect on the speed of light. The laws of physics were simply different in that frame. Transforming to another frame would not change anything except the speed of light measurement. Maxwell's equations would only hold in the aether frame.

"LET"'s argument is moot: the PoR relates to phenomena, not unmeasurable "reality".

The PoR relates to the equations. In a theory (like LET) where the equations describe unmeasurable "reality" then the PoR does, in fact, relate to the unmeasurable "reality" also.

LET provides a transformation between the unmeasurable aether frame and the measurable frame. So, LET is an odd mishmash of parts. When you express Maxwell's equations in terms of local time then the equations for all different local frames are the same, reflecting the PoR for all measurable quantities.

However, Lorentz placed a strong fundamental distinction between "time" and "local time". The unmeasurable "time" was only valid in the aether frame, and when Maxwell's equations were expressed in terms of "time" they were therefore only valid in the aether frame. So, the aether still represents an unmeasurable violation of the PoR because the variables in the aether frame only apply to that frame.

 

[Saw]

The PoR relates to the equations. In a theory (like LET) where the equations describe unmeasurable "reality" then the PoR does, in fact, relate to the unmeasurable "reality" also.

LET provides a transformation between the unmeasurable aether frame and the measurable frame. So, LET is an odd mishmash of parts. When you express Maxwell's equations in terms of local time then the equations for all different local frames are the same, reflecting the PoR for all measurable quantities.

However, Lorentz placed a strong fundamental distinction between "time" and "local time". The unmeasurable "time" was only valid in the aether frame, and when Maxwell's equations were expressed in terms of "time" they were therefore only valid in the aether frame. So, the aether still represents an unmeasurable violation of the PoR because the variables in the aether frame only apply to that frame.

I do not know why you insist on sticking to the historical side of the story. I thought it was much more interesting discussing, today, on a simple logical basis, whether aether, PoR and invariant c are intrinsically incompatible or not. But if we are in historical vain, we should not stop there. I am not an expert on the subject, but the little of the direct sources I have had access to, reveals that Lorentz, either alone or prompted by Poincaré or by Einstein's work, ended up accepting everything... Everything that is the essence of SR! That the LT applies between any frame, from aether frame to A, vice versa and from A to B and vice versa. That the aether time, since it is unmeasurable, is not what should feed the equations, but that role should be played by the originally called "local time", which then becomes (since there is nothing else) simply "time". It just happens that, on top of that, Lorentz and Poincaré kept alive the hypothesis of an aether, as a possible root cause for all those things, albeit admitting that Einstein's idea of leaving it aside had been great.

This is one of many possible quotations in that line (from The Einstein Theory of Relativity, by H.A. Lorentz, 1920, available in Project Gutenberg):

It is not necessary to give up entirely even the ether. Many natural philosophers find satisfaction in the idea of a material intermediate substance in which the vibrations of light take place, and they will very probably be all the more inclined to imagine such a medium when they learn that, according to the Einstein theory, gravitation itself does not spread instantaneously, but with a velocity that at the first estimate may be compared with that of light. Especially in former years were such interpretations current and repeated attempts were made by speculations about the nature of the ether and about the mutations and movements that might take place in it to arrive at a clear presentation of electro-magnetic phenomena, and also of the functioning of gravitation. In my opinion it is not impossible that in the future this road, indeed abandoned at present, will once more be followed with good results, if only because it can lead to the thinking out of new experimental tests. Einstein's theory need not keep us from so doing; only the ideas about the ether must accord with it.

Nevertheless, even without the color and clearness that the ether theories and the other models may be able to give, and even, we can feel it this way, just because of the soberness induced by their absence, Einstein's work, we may now positively expect, will remain a monument of science; his theory entirely fulfills the first and principal demand that we may make, that of deducing the course of phenomena from certain principles exactly and to the smallest details. It was certainly fortunate that he himself put the ether in the background; if he had not done so, he probably would never have come upon the idea that has been the foundation of all his examinations.

 

[Dale]

I do not know why you insist on sticking to the historical side of the story.

I think that is a completely incorrect characterization. I definitely addressed the historical side of the story, but I certainly didn't limit my comments to them either.

IMO, the aether is essentially synonymous with a preferred frame and therefore fundamentally incompatible with the PoR.

 

[lugita15]

First, the PoR, as I have usually seen it, refers to the equations. E.g. http://en.wikipedia.org/wiki/Principle_of_relativity. It states that the equations of physics have the same form with the same universal constants in all frames of reference.

I completely agree with this. The fact that you happen to interpret the equations differently does not invalidate the principle of relativity.

Second, from Maxwell to Einstein, the leading scientists of the day believed that the PoR was not correct, or at least that it did not apply to EM phenomena. They considered the aether frame to be a preferred frame in the sense of violating the PoR. Specifically, that Maxwell's equations only applied in the aether frame.

I don't think (based on Whitaker's excellent history of light and aether) that they saw the electromagnetic wave equation as invalidating the PoR, any more than the sound wave equation would. It's definitely true that they believed Maxwell's equations were only true in one frame, but the reason for this was because it violated Galilean invariance. So they concluded that for frames moving with respect to the ether, the equations governing electromagnetic phenomena would be modified slightly, so that they would predict that the speed of light would be c+v or c-v, where v is the speed of the eather.

I understand your point here, but the difference is that the velocity of the medium for acoustic waves can be detected by non-acoustic phenomena. So, we can say that the speed of sound is isotropic in any frame where a nearby anemometer reads 0, and that is true regardless of if the anemometer is moving in some other frame. Also, Newton's equations would still hold in all frames.

On the other hand, there was supposedly no other way to detect the aether other than its effect on the speed of light. The laws of physics were simply different in that frame. Transforming to another frame would not change anything except the speed of light measurement. Maxwell's equations would only hold in the aether frame.

First of all, I think that detecting ether was viewed as a difficult experimental challenge, not physically impossible. Second of all, what do you think would happen if we lived in a world where it was impossible to detect air, and the only way we even knew air existed was by hearing sounds? In that case, I don't think measuring the speed of sound differently in different reference frames, and using that to determine the rest frame of air, would have invalidated the PoR in any way.

The PoR relates to the equations. In a theory (like LET) where the equations describe unmeasurable "reality" then the PoR does, in fact, relate to the unmeasurable "reality" also.

LET provides a transformation between the unmeasurable aether frame and the measurable frame. So, LET is an odd mishmash of parts. When you express Maxwell's equations in terms of local time then the equations for all different local frames are the same, reflecting the PoR for all measurable quantities.

However, Lorentz placed a strong fundamental distinction between "time" and "local time". The unmeasurable "time" was only valid in the aether frame, and when Maxwell's equations were expressed in terms of "time" they were therefore only valid in the aether frame. So, the aether still represents an unmeasurable violation of the PoR because the variables in the aether frame only apply to that frame.

Yes, if we expressed the equations governing electromagnetism in terms of "aether position" and "aether time", the equations would only be Maxwell's equations in the aether frame, and in other frames they would be different. They would be similar, they would just contain extra terms in the Ampere-Maxwell Law and Faraday's law which depend on the speed of the aether. These modified equations were found by Hertz, but they're of course useless from an experimental standpoint because it's impossible to find the aether frame and thus impossible to find out what time and position it would "really" be if our clocks and rulers didn't suffer from relativistic effects. But the important thing to note is that Hertz's modified Maxwell equations are Galilean invariant, so that according to the Lorentz aether theory the Galilean transformations are "really" correct and it is only due to measurement error that the Lorentz transformations seem to be correct. Either way, the principle of relativity survives unscathed.

 

[Saw]

I think that is a completely incorrect characterization. I definitely addressed the historical side of the story, but I certainly didn't limit my comments to them either.

That is true. I was just answering that side of your comments, to go little by little... But would you then admit that the story of LET does not end before Einstein and that Lorentz did defend a theory which is a combination of SR + aether? I think this quotation is quite definitive. Einstein himself was in the best terms with Lorentz and I remember having read something like "that is when Professor Lorentz and I invented the theory of relativity" (special one, of course).

IMO, the aether is essentially synonymous with a preferred frame and therefore fundamentally incompatible with the PoR.

This is for me the most interesting side and where I will try to go a little deeper. I am not going to deny that an aether (if such thing existed at all) would be a privileged frame in the sense that you would obtain there privileged information. Taking the example of simultaneity, I mentioned before that the synchronisation obtained in such frame would be more perfect (more precise!) in as much as it would provide us with very ambitious knowledge: if two events happen by clocks synched in such frame, one can trust that none of them can have causal influence over the other, even if that influence happened to travel at infinite velocity, in no time, instantaneously. Instead, relative simultaneity (or a synch operation done through Einstein convention in any other non-aether frame) does not supply so much information. If two events are simultaneous in a non-aether frame, then the space-time distance between them is space-like, meaning that all frames agree that there can be no causal influence between the two events… as long as we talk about a non-superluminal influence. But what if, for the purpose of discussion, we admit FTL travel? To make things simpler, what if we admit the possibility of instantaneous communication? In that case, the concept of relative simultaneity turns out to be insufficient. Some frames will seem to indicate that the causal influence is impossible, others that it is possible. Who is right? Not all of them, obviously. Here the reasonable answer is that *we do not know*, since the concept of relative simultaneity does not go that far. Fortunately, that is not serious, since FTL travel is impossible. Hence the information provided by the aether frame is in the end unnecessary, since we can solve all known practical problems (with CERN's and neutrinos' permission) on the basis of relative simultaneity.

Conclusion: the aether only leads to a theoretically preferred frame, which is good for nothing practical; it only rules out a fairy-tale PoR where all frames attain a level of information which is as beautiful as unnecessary; however, it is compatible with a realistic PoR, where all frames, based on their empirical measurements, are equally placed to solve all existing practical needs.

 

[Dale]

It's definitely true that they believed Maxwell's equations were only true in one frame, but the reason for this was because it violated Galilean invariance. So they concluded that for frames moving with respect to the ether, the equations governing electromagnetic phenomena would be modified slightly

That is essentially the definition of a violation of the PoR.

Second of all, what do you think would happen if we lived in a world where it was impossible to detect air, and the only way we even knew air existed was by hearing sounds?

Then I think we would conclude that the laws of acoustics are not frame invariant and that there exists a preferred frame.

 

[lugita15]

That is essentially the definition of a violation of the PoR.

It would only be a violation if the Maxwell equations were in fact laws of physics. But they believed that the correct equations of electromagnetism included terms that depended on the speed of the aether, as I discussed in the end of my post (#64).

Then I think we would conclude that the laws of acoustics are not frame invariant and that there exists a preferred frame.

Yes, but I don't think we'd reject the principle of relativity, we would just come up with new laws of acoustics that depended on the speed of air (as undoubtedly people have in real life).

 

[Dale]

It would only be a violation if the Maxwell equations were in fact laws of physics. But they believed that the correct equations of electromagnetism included terms that depended on the speed of the aether, as I discussed in the end of my post (#64).

Which would be a preferred frame!

Look, your idea of the principle of relativity is essentially meaningless. There is simply no way for a law of physics to not obey the principle of relativity in your view. All you would have to do is take any velocity-dependent terms, say that those represent the velocity relative to some otherwise undetectable medium, and claim that therefore it follows the principle of relativity.

You have watered down the principle of relativity so far that it is simply a tautology. Not only all known laws of physics, but all possible laws of physics obey it. So it means nothing to say that a law follows it.

If you disagree with the above then please explain how a law of physics could, in your view, violate the PoR.

 

[Dale]

Conclusion: the aether only leads to a theoretically preferred frame, which is good for nothing practical; it only rules out a fairy-tale PoR where all frames attain a level of information which is as beautiful as unnecessary; however, it is compatible with a realistic PoR, where all frames, based on their empirical measurements, are equally placed to solve all existing practical needs.

Agreed. And LET asserts the existence and reality of said PoR violating fairy-tale.

 

[lugita15]

Which would be a preferred frame!

Look, your idea of the principle of relativity is essentially meaningless. There is simply no way for a law of physics to not obey the principle of relativity in your view. All you would have to do is take any velocity-dependent terms, say that those represent the velocity relative to some otherwise undetectable medium, and claim that therefore it follows the principle of relativity.

You have watered down the principle of relativity so far that it is simply a tautology. Not only all known laws of physics, but all possible laws of physics obey it. So it means nothing to say that a law follows it.

If you disagree with the above then please explain how a law of physics could, in your view, violate the PoR.

This might end up to be a philosophical issue; I apologize in advance if it is. I have to admit that according to my conception of the PoR, for any theory T which violates the PoR there exists a theory T' experimentally indistinguishable from T which obeys the PoR. You might view this as a great indictment of my view, but I think what I said is equally applicable to any physical principle, e.g. conservation of momentum. Suppose you had a theory T that said any collision involving a neutrino does not conserve momentum. Then you could have an experimentally indistinguishable theory T' that says that whenever a neutrino has a collision, an undetectable fairy gains or loses momentum which exactly compensates for the violation of the conservation law. Or it could say that whenever a neutrino has a collision, the fairy provides an external force which explains why the momentum of the system was not conserved. This isn't an indictment of the conservation of momentum; a theory can follow a fundamental physical principle like the principle of relativity or the conservation of momentum and still violate other things we want theories to satisfy, like Occam's Razor.

Getting back to my hypothetical situation, in which air has never been detected: If we were confronted with the fact that the speed of sound is isotropic in only one reference frame I think it would be reasonable to construct a theory in which sound was a longitudinal wave in an invisible medium called air whose rest frame is the reference frame we've found in our experiments. This would be a sound working hypothesis, and tomorrow we would go out and try to see whether we can get even more confirmation, holding out the possibility that we might one day be able to detect this mysterious air or find some indirect side effects of air, just as in the nineteenth century people thought that electromagnetism was an effect of the ether.

Anyway, I go back to what I talked about in the end of post #64: LET only violates the PoR if you use measurable quantities like local time to express your equations; if you instead used the unmeasurable "real position" and "real time", then it is a Galilean-invariant theory albeit one that violates Occam's Razor. But I think we already knew that LET is a severe Occam violator.