Did MMX's Assumptions on Light and Sound Waves Affect Their Findings?

[Gadhav]

I am wondering whether MMX was based on faulty assumptions that light waves would behave like sound waves.
1) What if MMX detected a phase shift? It would just mean that speed of light is c and it goes through different distance, with or without Ether justifying the shift.
2) Alternatively they would not detect any shift even when Ether was present since speed of light is always the same as they do not behave as sound waves.
It does not prove existence or non existence of Ether or constant speed of light.

What am I missing here?

 

[ghwellsjr]

I am wondering whether MMX was based on faulty assumptions that light waves would behave like sound waves.

Yes, it was, in the sense that M&M as well as most all scientists of the time believed that light did propagate in a medium (but differently than sound waves).

1) What if MMX detected a phase shift? It would just mean that speed of light is c and it goes through different distance, with or without Ether justifying the shift.

If they did detect a phase shift, then we'd be living in a universe with different physics so anybody's guess is as good (or bad) as anybody else's.

2) Alternatively they would not detect any shift even when Ether was present since speed of light is always the same as they do not behave as sound waves.
It does not prove existence or non existence of Ether or constant speed of light.

What am I missing here?

You're not missing anything.

In fact, Lorentz, et al, came up with a perfectly logical and consistent theory that was based on an absolute rest state for the presumed ether only in which light traveled at c. Since they believed that the surface of the Earth must always be traveling through this ether, length contraction (and later time dilation) of the experimental apparatus would explain the null result.

 

[Nugatory]

I am wondering whether MMX was based on faulty assumptions that light waves would behave like sound waves.
1) What if MMX detected a phase shift? It would just mean that speed of light is c and it goes through different distance, with or without Ether justifying the shift.
2) Alternatively they would not detect any shift even when Ether was present since speed of light is always the same as they do not behave as sound waves.

For #1: The experiment does not observe a phase shift, so it doesn't much matter what it might be telling us if it had observed a phase shift.

For #2: Yes, the M-M experiments are consistent with a constant speed of light, ether or no. These experiments disprove only those theories in which light has a constant speed with respect to a hypothetical ether that would define a universal rest frame and therefore not with respect to other observers.

It does not prove existence or non existence of Ether or constant speed of light.

Experiments never prove any theory. All they do is disprove competing theories.

 

[lugita15]

Yes, it was, in the sense that M&M as well as most all scientists of the time believed that light did propagate in a medium (but differently than sound waves).

What do you mean differently than sound waves? Are you just referring to the fact that they thought light was a transverse oscillation in the aether, as opposed to sound which is a longitudinal oscillation in air?

In fact, Lorentz, et al, came up with a perfectly logical and consistent theory that was based on an absolute rest state for the presumed ether only in which light traveled at c.

I wish you wouldn't put so much emphasis on the "absolute rest" part, because it can be a bit misleading. To be clear, they believed that the principle of relativity was true, which to them meant that the "true" laws of physics were invariant under Galilean transformations. So when they saw that Maxwell's equations weren't Galilean invariant, their conclusion was that these weren't the true laws of physics; instead, they thought these laws were akin to the wave equation for sound, i.e. laws that were only true in one frame, not the real laws of physics that hold for all inertial frames.

Then the Michelson Morley experiment showed that Maxwell's equations were true in all frames despite not being Galilean invariant. This posed a threat to the principle of relativity, and Lorentz resolved this by saying that Maxwell's equations appeared to be true in all frames because of length contraction and time dilation, but the real laws of physics are actually something else, equations that really ARE Galilean invariant and really do hold in all frames. (These modified equations were found by Hertz, and can be found by expressing Maxwell's equations in terms of "uncontracted length" and "undilated time".)

 

[ghwellsjr]

What do you mean differently than sound waves? Are you just referring to the fact that they thought light was a transverse oscillation in the aether, as opposed to sound which is a longitudinal oscillation in air?

Yes.

 

[lugita15]

ghwellsjr, I think you may have replied in the middle of me editing my post. Did you see the rest of it?

 

[Gadhav]

Thanks for replies. As I get it so far:

1) MMX always assumed that speed of light was c in Ether, just like speed of sound in constant in a media. It also assumed that Galileo's relativity was correct.

2) So if Earth moves through it, it will take longer or shorter for it to travel along Ether than perpendicular direction, assuming Galileo's relativity was correct.

3) That was not observed. So the theory suggested that there is no Ether. (I am not clear of this conclusion yet since even if you replace Ether with Vacuum, Galileo's relativity can hold.)

4) But then how do you equate the equations for time in horizontal and perpendicular direction? So the hteory said that if we "assume" time dilation/length contraction they equate. There was no explanation given by MMX. Lorentz tried to explain by saving that electron in direction of motion can contract the size of atom but had no proof.

5) Later Einstein "assumed" that speed of light is not only c but also independent of relative motion of observers and worked back words to come at same result but had a better explanation for length contraction/time dilation. He used invariant of length to come to same result.

Is this correct so far?

 

[nitsuj]

ghwellsjr, I think you may have replied in the middle of me editing my post. Did you see the rest of it?

I read it and learned something from it. Thanks!

 

[nitsuj]

5) Later Einstein "assumed" that speed of light is not only c but also independent of relative motion of observers and worked back words to come at same result but had a better explanation for length contraction/time dilation. He used invariant of length to come to same result.

Is this correct so far?

splitting hairs, but Einstein didn't assume. The assumption was a medium of sorts. Einstein went on what the evidence (experiments) was showing (proving). Minkowski put a pretty bow on it; no Ether, just spacetime.

 

[ghwellsjr]

ghwellsjr, I think you may have replied in the middle of me editing my post. Did you see the rest of it?

Didn't Lorentz, et al, believe in a "luminiferous ether"? Or was Einstein ill-informed?

 

[lugita15]

Didn't Lorentz, et al, believe in a "lumeniferous ether"?

Yes, he definitely did. What in my post contradicts that? Lorentz believed that light was a propagation of the aether, which did not contradict the principle of relativity any more than sound being a propagation of air.

 

[ghwellsjr]

After I said:

In fact, Lorentz, et al, came up with a perfectly logical and consistent theory that was based on an absolute rest state for the presumed ether only in which light traveled at c. Since they believed that the surface of the Earth must always be traveling through this ether, length contraction (and later time dilation) of the experimental apparatus would explain the null result.

...you said:

I wish you wouldn't put so much emphasis on the "absolute rest" part, because it can be a bit misleading.

...and since you now say you agree with my first comment, I don't understand what is misleading about putting an emphasis on the "absolute rest" part which is the significant aspect of the "luminiferous ether", isn't it?

 

[lugita15]

...and since you now say you agree with my first comment, I don't understand what is misleading about putting an emphasis on the "absolute rest" part which is the significant aspect of the "luminiferous ether", isn't it?

When you use the term "absolute rest", it suggests that Lorentz and his contemporaries didn't believe in the principle of relativity, which is emphatically not true. (That kind of absolute rest was what Aristotle believed, not the aether theorists.). They thought that Maxwell's equations were only true in the aether frame, just as the sound wave equation is only true in the air frame, but they thought that neither of these facts contradicted the principle of relativity. This is because they thought that neither of these sets of equations were "true" laws of physics. In their mind, the true laws of physics were still Galilean-invariant and were true in all frames.

 

[ghwellsjr]

When you use the term "absolute rest", it suggests that Lorentz and his contemporaries didn't believe in the principle of relativity, which is emphatically not true.

To me, the term "absolute rest" implies "absolute time" and "absolute space", referring to the concept that a second here is the same as a second there and everywhere, and a foot here is the same as a foot there and everywhere. It doesn't mean that they believed they could ever locate the state of "absolute rest", just that they believed nature operated according to it. In other words, nature conspired to hide the state of "absolute rest" by modifying the rate at which moving clocks ticked and the lengths of moving objects along the axis of motion so that the it gave the illusion of relativity. It never occurred to them to think in terms of time and space being relative in the sense that Einstein did. If you have ever followed my comments, I have always said that the difference between SR and LET is that they both accept the same first postulate of the Principle of Relativity but they accept a different second postulate regarding the propagation of light.

By the way, I agree with the rest of your comments and so I'm wondering if there is a way to express these ideas succinctly without going into all the details every time the subject comes up.

 

[lugita15]

To me, the term "absolute rest" implies "absolute time" and "absolute space", referring to the concept that a second here is the same as a second there and everywhere, and a foot here is the same as a foot there and everywhere.

If all you're saying is that they had absolute notions of space and time, I agree with that wholeheartedly. They thought that the length of an object, and the duration between two events, had definite, objective values, that did not depend on how observers were moving around. But "absolute rest" has a different meaning: it means that there is such a thing as being "truly" at rest, independent of the motion of different observers. That is something that the physicists of the late nineteenth century did not believe. They thought the universe treated all frames equally, in the sense of thinking myself as at rest and you as in motion is equally valid as the other way around.

It doesn't mean that they believed they could ever locate the state of "absolute rest", just that they believed nature operated according to it. In other words, nature conspired to hide the state of "absolute rest" by modifying the rate at which moving clocks ticked and the lengths of moving objects along the axis of motion so that the it gave the illusion of relativity.

If you replaced "the state of absolute rest" with "the rest frame of the aether", I would have no quibbles with it. But the way you say it makes it seem like they thought the universe has a preferred frame, and it's because of length contraction and time dilation that it seems that it doesn't have a preferred frame. But that's the exact opposite of what they believed. They thought the universe *appeared* to have a preferred frame, thus seeming to violate the principle of relativity. But they thought that if you were able to accurately measure lengths and times, then you would find out that the universe really doesn't have a preferred frame. Specifically, you would find that the real laws of electromagnetism are Galilean-invariant and hold in all frames.

It never occurred to them to think in terms of time and space being relative in the sense that Einstein did.

Yes, I agree with that; due to their absolute notions of space and time, they thought the principle of relativity meant Galilean invariance, so they thought that length contraction and time dilation must just be things that lead to inaccurate measurements, as opposed to things that lead to a new, genuinely valid coordinate system.

If you have ever followed my comments, I have always said that the difference between SR and LET is that they both accept the same first postulate of the Principle of Relativity but they accept a different second postulate regarding the propagation of light.

I have absolutely no problem with that, other than the minor proviso that Lorentz's historical theory had physical explanations for length contraction, time dilation, and mass increase.

By the way, I agree with the rest of your comments and so I'm wondering if there is a way to express these ideas succinctly without going into all the details every time the subject comes up.

We do seem to have an awful lot of agreement, but I think there is still something disagree about, because there was something we were arguing about in this thread.

As far as expressing these ideas succinctly, what ideas in particular do you want to express?

 

[ghwellsjr]

If all you're saying is that they had absolute notions of space and time, I agree with that wholeheartedly. They thought that the length of an object, and the duration between two events, had definite, objective values, that did not depend on how observers were moving around. But "absolute rest" has a different meaning: it means that there is such a thing as being "truly" at rest, independent of the motion of different observers. That is something that the physicists of the late nineteenth century did not believe. They thought the universe treated all frames equally, in the sense of thinking myself as at rest and you as in motion is equally valid as the other way around.

I'm saying both. Belief in absolute notions of space and time is the same as belief in an "absolute rest", it's just that they came to realize that they could never identify that state. Thus, as I have repeatedly said, they believed that nature operated on the state of absolute ether rest but conspired to hide that state from us so that it was impossible to perform any experiment that would violate the Principle of Relativity.

If you replaced "the state of absolute rest" with "the rest frame of the aether", I would have no quibbles with it. But the way you say it makes it seem like they thought the universe has a preferred frame, and it's because of length contraction and time dilation that it seems that it doesn't have a preferred frame.

Yes, that is what I'm saying.

But that's the exact opposite of what they believed. They thought the universe *appeared* to have a preferred frame, thus seeming to violate the principle of relativity. But they thought that if you were able to accurately measure lengths and times, then you would find out that the universe really doesn't have a preferred frame. Specifically, you would find that the real laws of electromagnetism are Galilean-invariant and hold in all frames.
Yes, I agree with that; due to their absolute notions of space and time, they thought the principle of relativity meant Galilean invariance, so they thought that length contraction and time dilation must just be things that lead to inaccurate measurements, as opposed to things that lead to a new, genuinely valid coordinate system.

Now that I don't understand and don't agree with. I thought they had a split understanding of the Principle of Relativity, one set of transforms, Lorentzian, that applied to electromagnetism and Maxwell's equations and one set of transforms, Galilean, that applied to mechanics. But in all cases, there were no experiments that violated the Principle of Relativity and so I don't know what you mean by the universe "appeared" to have a preferred frame. Maybe that thought would be the case before MMX, but it never panned out.

I have absolutely no problem with that, other than the minor proviso that Lorentz's historical theory had physical explanations for length contraction, time dilation, and mass increase.

That's because he was trying to resolve the differences in the two sets of transforms that he believed applied to different laws.

We do seem to have an awful lot of agreement, but I think there is still something disagree about, because there was something we were arguing about in this thread.

Yes, that is a very interesting thread and I read it all. I really liked my arguments.

I think the best way to deal with this is to look at Einstein's 1920 book on relativity. If you look at chapter 5, The Principle of Relativity (In the Restricted Sense), you will see that he deals directly with this topic. By the way, when he says, "in the restricted sense", he's talking about the Galilean transformation. And he points out that since there has never been any example of an experimental violation of the PoR, "This is a very powerful argument in favour of the principle of relativity".

Then in chapter 7, The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity, he once again addresses this same issue that he brought up in his first paper on SR. At the end of the second to last paragraph, he says: "Prominent theoretical physicists were therefore more inclined to reject the principle of relativity, in spite of the fact that no empirical data had been found which were contradictory to this principle." So once again, he is pointing out that there has not been any experimental evidence against the Principal of Relativity. But he is stating the exact opposite of what I have been saying, namely that LET affirms Einstein's first postulate, the Principle of Relativity but rejects his second postulate. I believe he is saying this because Lorentz's transformation process when applied to Maxwell's equations are compatible with Einstein's second postulate. However, Einstein's important point is that having two sets of transformations is rejecting the Principle of Relativity on theoretical grounds, even if there is no evidence against it. And this is where it seems we differ, you believe that having two different sets of transforms is compatible with the Principle of Relativity.

Finally, look at chapter 14 where Einstein points out that the resolution to the apparent conflict between his two postulates is to apply the Lorentzian transformation to all laws, not have two sets of transforms for different laws. In other words, change all the laws that previously conformed to the Galilean transformation so that they would now conform to the Lorentzian transformation and that's what they did.

Now getting back to the difference in what Einstein says and what I have been saying, when I'm talking about the moving target called LET, I'm referring to where it ended up, as wikipedia says:

Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. The introduction of length contraction and time dilation for all phenomena in a "preferred" frame of reference, which plays the role of Lorentz's immobile aether, leads to the complete Lorentz transformation (see the Robertson-Mansouri-Sexl test theory as an example). Because of the same mathematical formalism it is not possible to distinguish between LET and SR by experiment.

You correctly identified this as my emphasis in your reference thread. And the reason I'm doing this is because I want to emphasize that Einstein's theory of Special Relativity affirms all Inertial Reference Frames (IRF's) and anyone of them is sufficient to explain any scenario, just like the one illusive LET state of absolute ether rest. Some people think that each observer needs their own IRF to understand what they observe or that it provides additional insight over some other IRF in which they are not at rest. Some people think that SR proves that LET is wrong or that it proves that an absolute ether rest state cannot exist. Some people think that Special Relativity means that you have to have multiple IRF's in any given scenario. In fact, the only difference between (modern) LET and SR is the second postulate: SR says there is no preferred IRF and light propagates at c in all of them whereas LET says that there is a preferred IRF, the only one in which light propagates at c. And there is no experimental evidence to help us decide between these two theories so if we want to choose between them, we choose on philosophical grounds.

So I like to point out that even if someone believed in an "absolute rest" and its inherent "absolute time" and "absolute space", they would still be better off forgetting about LET and wholeheartedly adopting Einstein's theory of Special Relativity as being a simpler theory.

As far as expressing these ideas succinctly, what ideas in particular do you want to express?

You wanted me to use "the rest frame of the aether" instead of "the state of absolute rest" but I'm wondering if you would have any problem with "the absolute rest frame of the aether"?

 

[DrGreg]

I think the historical point that lugita15 is making is that Lorentz and his contemporaries made a subtle distinction between properties of space & time (what we would nowadays call spacetime) and properties of the supposed aether that filled spacetime. That distinction is often lost in modern-day presentations of LET. If my memory is correct, Lorentz interpreted the Lorentz transform as$$\begin{align} \begin{pmatrix}\gamma && - \gamma v \\ -\gamma v && \gamma \end{pmatrix} &= \begin{pmatrix}1 && - v \\0 && 1 \end{pmatrix} \begin{pmatrix}\gamma^{-1} && 0 \\ 0 && \gamma \end{pmatrix} \begin{pmatrix}1 && 0 \\-v && 1 \end{pmatrix} \\ \\ \\ \textbf{L} &=\textbf{T} \cdot \textbf{E} \cdot \textbf{G} \end{align}$$I'm using a matrix notation that Lorentz wouldn't have used, with $c=1$ and $\begin{pmatrix}t\\x\end{pmatrix}$ coordinates.

• G is the Galilean transform, a relative property of Galilean spacetime
• E represents time dilation and length contraction, an absolute property of the supposed aether. Note that EG alone is enough to explain the Michelson-Morley experiment.
• T expresses Lorentz's notion of "local time" (what we would now call a clock synchronisation convention), and I'm not sure if Lorentz had any explanation for it other than something needed to make Maxwell's equations invariant.

 

[lugita15]

I'm saying both. Belief in absolute notions of space and time is the same as belief in an "absolute rest"

No, that's not true. Newton and Galileo believed that there was such a thing as the true length of a rod or the true duration between two events. But they did not believe that there was such a thing as being "truly" at rest or "truly" in motion. (That's what Aristotle believed, though.) They thought that all inertial frames are equally valid. The physicists of the late nineteenth century still shared all these beliefs.

it's just that they came to realize that they could never identify that state. Thus, as I have repeatedly said, they believed that nature operated on the state of absolute ether rest but conspired to hide that state from us so that it was impossible to perform any experiment that would violate the Principle of Relativity.

They did indeed believe that nature used length contraction and time dilation to hide the rest frame of the aether from us. But they did not see the aether as being "truly" at rest. They thought that the universe treated all frames as equal. The role of the aether frame for light seemed no more unusual to them then the role of the air frame for sound.

Now that I don't understand and don't agree with. I thought they had a split understanding of the Principle of Relativity, one set of transforms, Lorentzian, that applied to electromagnetism and Maxwell's equations and one set of transforms, Galilean, that applied to mechanics.

No, they thought the Principle of Relativity exclusively meant Galilean invariance. The fact that the laws of electromagnetism seem Lorentz invariant just indicated to them that their measuring equipment was faulty due to length contraction and time dilation. They were still confident that accurate measuring rods and clocks would show Galilean invariant laws of electromagnetism.

But in all cases, there were no experiments that violated the Principle of Relativity and so I don't know what you mean by the universe "appeared" to have a preferred frame. Maybe that thought would be the case before MMX, but it never panned out.

As I said, to them the Principle of Relativity and Galilenan invariance were the same. So before Michelson-Morley, they put Maxwell's equations in the same category that they put the wave equation for sound: equations that weren't Galilean invariant, and thus were not the true laws of physics. But then Michelson-Morley showed that Maxwell's equations really do seem to be actual laws of physics. But if the actual laws of electromagnetism were not Galilean invariant, in their mind this would mean that the Principle of Relativity was false. That's what I meant when I said the universe appeared to have a preferred frame; Michelson-Morley seemed to indicate that the universe doesn't respect the Principle of Relativity.

Lorentz's solution to this was to say "Don't worry, the laws of physics are Gailiean invariant, but length contraction and time dilation make it seem like they're not. If Michelson-Morley conducted their experiment with accurate equipment, they would find that electromagnetism obeys Galilean invariance. So the Principle of Relativity is still true."

Einstein's solution was to say "Michelson-Morley was accurate, so Galilean invariance really is wrong, but the Principle of Relativity is still true. You just need to throw out your absolute notions of space and time."

That's because he was trying to resolve the differences in the two sets of transforms that he believed applied to different laws.

No, he did not believe that the Lorentz transformations genuinely applied to the laws of electromagnetism. He believed that they appeared to apply, but Galilean transformations are what really applied.

Yes, that is a very interesting thread and I read it all. I really liked my arguments.

I'm sure you do.

Then in chapter 7, The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity, he once again addresses this same issue that he brought up in his first paper on SR. At the end of the second to last paragraph, he says: "Prominent theoretical physicists were therefore more inclined to reject the principle of relativity, in spite of the fact that no empirical data had been found which were contradictory to this principle."

I think he is referring to the fact that after the Michelson-Morley experiment, many physicists (other than Lorentz) started to doubt the Principle of Relativity. That's because Michelson-Morley seemed to show that the speed of light is c in all reference frames, so Maxwell's equations seemed to accurately describe electromagnetic phenomena in all reference frames, which would mean that the real laws of electromagnetism are not Galilean invariant.

So once again, he is pointing out that there has not been any experimental evidence against the Principal of Relativity.

Yes, he is pointing out that even though some physicists thought the Michelson-Morley experiment rejected the Principle of Relativity, it didn't actually identify a preferred frame or show that different laws of physics hold in different frames, which is what you'd expect for a refutation of the Principle of Relativity.

But he is stating the exact opposite of what I have been saying, namely that LET affirms Einstein's first postulate, the Principle of Relativity but rejects his second postulate. I believe he is saying this because Lorentz's transformation process when applied to Maxwell's equations are compatible with Einstein's second postulate. However, Einstein's important point is that having two sets of transformations is rejecting the Principle of Relativity on theoretical grounds, even if there is no evidence against it.

I think Einstein is not referring to Lorentz ether theory. He's referring to Lorentz's analysis of Michelson-Morley, where Lorentz concluded that Maxwell's equations appeared to hold in all frames, so the speed of light appeared to hold in all frames. Of course Lorentz's reaction to this conclusion was to say that this appearance was deceptive, based on length contraction and time dilation.

And this is where it seems we differ, you believe that having two different sets of transforms is compatible with the Principle of Relativity.

When did I say anything like that?

Finally, look at chapter 14 where Einstein points out that the resolution to the apparent conflict between his two postulates is to apply the Lorentzian transformation to all laws, not have two sets of transforms for different laws. In other words, change all the laws that previously conformed to the Galilean transformation so that they would now conform to the Lorentzian transformation and that's what they did.

Lorentz believed that the Lorentz transformations appeared to apply to all laws of physics, but they actually applied to none of them. Einstein's resolution to say that the Lorentz transformations genuinely applied to all laws of physics, which meant that the notions of space and time that gave rise to the Galilean transformations were in need of rethinking.

And the reason I'm doing this is because I want to emphasize that Einstein's theory of Special Relativity affirms all Inertial Reference Frames (IRF's) and anyone of them is sufficient to explain any scenario, just like the one illusive LET state of absolute ether rest.

Once again I'd quibble with the word "absolute" if you mean it in the sense of one frame being truly at rest or one frame being preferred by the universe over all others. But other than that, I agree with you. In Lorentz's theory, if you were in any frame other than the aether frame, then your rods and clocks were inaccurate, but in Einstein's theory you could use the readings from your own rods and clocks without fearing that you were making a mistake.

Some people think that each observer needs their own IRF to understand what they observe or that it provides additional insight over some other IRF in which they are not at rest. Some people think that SR proves that LET is wrong or that it proves that an absolute ether rest state cannot exist. Some people think that Special Relativity means that you have to have multiple IRF's in any given scenario. In fact, the only difference between (modern) LET and SR is the second postulate: SR says there is no preferred IRF and light propagates at c in all of them whereas LET says that there is a preferred IRF, the only one in which light propagates at c. And there is no experimental evidence to help us decide between these two theories so if we want to choose between them, we choose on philosophical grounds.

We're in complete agreement in all that.

EDIT: Except possibly for the part about "preferred". If by "preferred" you mean that the aether frame was the only one in which Maxwell's equations held and light propagates at c, then I'm fine with that. But if by preferred you mean you mean that it's its privileged by the universe over other frames, then that's not quite right. It is true that people in other frames make inaccurate frames according to LET, but that's not due to a problem with the frame, that's due to physical effects from the aether that makes their measurements off. If they were able to use the "true" coordinates of their frame, as opposed to the "apparent" coordinates of their frame, then the universe would treat that frame the same way it treated the aether frame. So in that sense Lorentz saw himself as firmly in the Principle of Relativity camp.

So I like to point out that even if someone believed in an "absolute rest" and its inherent "absolute time" and "absolute space", they would still be better off forgetting about LET and wholeheartedly adopting Einstein's theory of Special Relativity as being a simpler theory.

Again, I disagree that absolute rest is the same as absolute space and time.

You wanted me to use "the rest frame of the aether" instead of "the state of absolute rest" but I'm wondering if you would have any problem with "the absolute rest frame of the aether"?

I'd still object to the word absolute. Would you similarly say "the absolute rest frame of air"?

 

[lugita15]

[*]T expresses Lorentz's notion of "local time" (what we would now call a clock synchronisation convention), and I'm not sure if Lorentz had any explanation for it other than something needed to make Maxwell's equations invariant.
[/LIST]

Lorentz didn't have much of an explanation, but Poincare came up with something: he said that due to length contraction and time dilation, observers in frames other than the aether frame would synchronize their clocks incorrectly if they used light signals (basically Einstein synchronization).

 

[Histspec]

Maybe we should look what Lorentz himself wrote. In 1895 he argued in the introduction of his influential "Versuch..." paper:
http://en.wikisource.org/wiki/Attempt_of_a_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Bodies/Introduction

That we cannot speak about an absolute rest of the aether, is self-evident; this expression would not even make sense. When I say for the sake of brevity, that the aether would be at rest, then this only means that one part of this medium does not move against the other one and that all perceptible motions are relative motions of the celestial bodies in relation to the aether.

However, in 1910 he argued that it is a matter of taste, whether one adopts Lorentz's own view of "true" times and lengths in the "preferred" aether system, or Einstein's and Minkowski's relativistic ones:
http://en.wikisource.org/wiki/The_Principle_of_Relativity_and_its_Application_to_some_Special_Physical_Phenomena

Provided that there is an aether, then under all systems x, y, z, t, one is preferred by the fact, that the coordinate axes as well as the clocks are resting in the aether. If one connects with this the idea (which I would abandon only reluctantly) that space and time are completely different things, and that there is a "true time" (simultaneity thus would be independent of the location, in agreement with the circumstance that we can have the idea of infinitely great velocities), then it can be easily seen that this true time should be indicated by clocks at rest in the aether. However, if the relativity principle had general validity in nature, one wouldn't be in the position to determine, whether the reference system just used is the preferred one. Then one comes to the same results, as if one (following Einstein and Minkowski) deny the existence of the aether and of true time, and to see all reference systems as equally valid. Which of these two ways of thinking one is following, can surely be left to the individual.

So even though Lorentz remained a believer in the aether his entire life, he also admitted that his aether-and-true-time ideas were the cause for the failure of his pre-1905 papers to reach exact Lorentz covariance of electrodynamics. He wrote in 1914:
http://en.wikisource.org/wiki/Two_Papers_of_Henri_Poincar%C3%A9_on_Mathematical_Physics

The formulas (4) and (7) are not in my memoir of 1904. Because I had not thought of the direct way which led there, and because I had the idea that there is an essential difference between systems x, y, z, t and x', y', z', t'. In one we use - such was my thought - coordinate axes which have a fixed position in the aether and which we can call "true" time; in the other system, on the contrary, we would deal with simple auxiliary quantities whose introduction is only a mathematical artifice. In particular, the variable t' could not be called "time" in the same way as the variable t.
In this order of ideas I did not think of describing the phenomena in the system x', y', z', t' exactly in the same way as in system x, y, z, t,...

 

[St_LightStorm]

What am I missing here?

This should clear it up...

http://www.datasync.com/~rsf1/crit/1908k.htm

[Here AB is the length of the arm of the mmx]

For us to render a full account, let's consider two points A and B which move with a constant absolute velocity v in the direction AB. A luminous wave, starting from A at instant t, will arrive at B at instant t'. It will have to travel the distance AB + (t - t')v: with the speed c we have then...​

Therefore,

T_going = (AB + (t - t')v)/c
T_returning = ((AB - (t - t'))/c
​

Note that light travels a distance that is greater than the length of the arm of the arm of the mmx, when going. And when returning, light travels a lesser distance than the length of the arm of the mmx.

Here, (t - t')/c = the distance the Earth travels (at v) during the time it takes light to travel the distance AB. Let us call this distance, d. Since the velocity of the Earth is constant, d is the same when light returns from the reflector. Therefore,

T_going = (AB + d)/c
T_returning = (AB - d)/c

T_going + T_returning = (AB + d)/c + (AB - d)/c = 2(AB)/c​

Null result, per ether theory. No length contraction needed. This was explained by Ritz in 1908 and he explained why Lorentz was wrong and where he was wrong. You should read the chapter, "Absolute Motion", it will help clear your doubts.

Ritz gets the same result, as mine, but he goes into extra algebra by not making substitution I made for (t - t')/v.

 

[russ_watters]

The other arm.

 

[PAllen]

What am I missing here?

This should clear it up...

http://www.datasync.com/~rsf1/crit/1908k.htm

[Here AB is the length of the arm of the mmx]

For us to render a full account, let's consider two points A and B which move with a constant absolute velocity v in the direction AB. A luminous wave, starting from A at instant t, will arrive at B at instant t'. It will have to travel the distance AB + (t - t')v: with the speed c we have then...​

Therefore,

T_going = (AB + (t - t')v)/c
T_returning = ((AB - (t - t'))/c
​

Note that light travels a distance that is greater than the length of the arm of the arm of the mmx, when going. And when returning, light travels a lesser distance than the length of the arm of the mmx.

Here, (t - t')/c = the distance the Earth travels (at v) during the time it takes light to travel the distance AB. Let us call this distance, d. Since the velocity of the Earth is constant, d is the same when light returns from the reflector. Therefore,

T_going = (AB + d)/c
T_returning = (AB - d)/c

T_going + T_returning = (AB + d)/c + (AB - d)/c = 2(AB)/c​

Null result, per ether theory. No length contraction needed. This was explained by Ritz in 1908 and he explained why Lorentz was wrong and where he was wrong. You should read the chapter, "Absolute Motion", it will help clear your doubts.

Ritz gets the same result, as mine, but he goes into extra algebra by not making substitution I made for (t - t')/v.

You have two separate equations using t and t'. You assume, without justification, that t-t' is the same for both of them. In an aether theory they would not be the same. By declaring them the same and substituting d for both, you are assuming your conclusion.

The fact is, for an aether theory, t-t' in one direction is AB/(c-v), and it is AB/(c+v) in the other direction. Thus you really should have d1 = ABv/(c-v) and d2 = ABv/(c+v).

[Edit: Actually, reading your argument more carefully, I think your error is different from above. You define (forgiving typos) that t-t' is the time for light to travel AB. The problem is that that after light has traveled the distance AB + v(t-t') as so defined, the mirror will have moved further. To get the time the light actually catches the mirror you need to solve ct = AB + vt, getting, as I noted AB/(c-v). ]

 

[russ_watters]

I think you were right the first time:
t = leaving time from A.
t' = arrival time at B.
Arrival back at A? Undefined, but assumed to be t' + (t' - t)

 

[PAllen]

I think you were right the first time:
t = leaving time from A.
t' = arrival time at B.
Arrival back at A? Undefined, but assumed to be t' + (t' - t)

I am taking him at his definition of t-t', with a typo corrected:

"Here, (t - t')v = the distance the Earth travels (at v) during the time it takes light to travel the distance AB"

This is well defined, but then the point is that after (AB+v(t-t'))/c, light will not have reached the receding mirror yet.

 

[St_LightStorm]

typo

PAllen: This is well defined, but then the point is that after (AB+v(t-t'))/c, light will not have reached the receding mirror yet.

It would have.

If the Earth did not move at all, then

T_going = d = (t - t')v = 0, since v = 0.
T_going = (AB + d)/c= (AB + 0)/c = AB/c
​

If the Earth moved at v > 0 then

T_going = d (some distance greater than zero), where d = (t - t')v
T_going = (AB + d)/c​

Using the same logic for return, we get T_returning = (AB - d)/c;

T_going + T_returning = (AB + d)/c + (AB - d)/c = 2(AB)/c= Null, without length contraction. Ritz gets the same result, but he goes into extra algebra, which is essentially, saying 2(AB)/c. His way of saying "2" is a little complicated.

 

[St_LightStorm]

PAllen: This is well defined, but then the point is that after (AB+v(t-t'))/c, light will not have reached the receding mirror yet.

It would have.

If the Earth did not move at all, then

T_going = d = (t - t')v = 0, since v = 0.
T_going = (AB + d)/c= (AB + 0)/c = AB/c
​

If the Earth moved at v > 0 then

T_going = d (some distance greater than zero), where d = (t - t')v
T_going = (AB + d)/c​

Therefore, whether the Earth moved or not, T_going = d = (AB + d)/c, where d = (t - t')v.

In other words, in time T_going, light travels a distance of D + d at c and the Earth travels a distance of d at v.

 

[PAllen]

PAllen: This is well defined, but then the point is that after (AB+v(t-t'))/c, light will not have reached the receding mirror yet.

It would have.

If the Earth did not move at all, then

T_going = d = (t - t')v = 0, since v = 0.
T_going = (AB + d)/c= (AB + 0)/c = AB/c
​

If the Earth moved at v > 0 then

T_going = d (some distance greater than zero), where d = (t - t')v
T_going = (AB + d)/c​

Using the same logic for return, we get T_returning = (AB - d)/c;

T_going + T_returning = (AB + d)/c + (AB - d)/c = 2(AB)/c= Null, without length contraction. Ritz gets the same result, but he goes into extra algebra, which is essentially, saying 2(AB)/c. His way of saying "2" is a little complicated.

No, you are wrong. You have also changed your definition. In your first post on this, you said:

t-t' is the time it takes light to go AB.

Using this, it is obvious that light will not reach the mirror in :

AB/c + v(t-t')/c

because by the time light gets to AB + v(t-t') the Earth will have moved a little more.

If you now say d is whatever distance light travels to reach the receding mirror, you have to solve for it in a valid way. Further, you then discover that the increase in time for the receding mirror is not the same as the decreasing time for the approaching mirror. There are then two separate t-t' values and two separate d values.

The claim that d values are the same is simply false.

To solve the outgoing case, you must have ct = AB + vt. This gives t (equivalent to your t-t') of AB/(c-v). Going the other way, you have to solve ct = AB -vt. This gives AB/(c+v). Then the total time is AB/(c-v) + AB/(c+v).

Ritz agrees with everyone else on this. He writes, in Absolute motion section:

t-t' = AB (1/(c-v) + 1/(c+v))

exactly as I have it.