Relativity without the aether: pseudoscience?

[Aether]

If LET makes no such assumption, why is "ether" in the name at all?

I suppose that it is because absolute simultaneity implies some sort of instantaneous connection between events.

By the way, would you say the same sort of thing about the Galilei transform in Newtonian physics? Is it "superstitious" to say that simultaneity is absolute in Newtonian physics, since you could describe Newtonian physics using a coordinate transform where simultaneity is relative? If you really take this argument to its logical conclusion, you'd have to say it's superstitious to say anything at all about absolute vs. relative simultaneity, regardless of what the laws of physics are like, since you always can use coordinate systems where either one is true, even if they are ungainly or unphysical.

It is not superstitious to choose a coordinate system. But when a popular majority of the inhabitants of Salem winds up saying things like "experiments prove that the speed of light is a constant", and then proceeds to burn people at the stake for simply pointing out that "it's just a coordinate system, stupid", then you're into the realm of superstition. Oh, that's exactly what did happen to both Galileo and Newton wasn't it?

 

[Hurkyl]

What's a good book to learn this from, Hurkyl?

I don't know -- I only remember seeing it in an article mathematics journal probably over a decade ago. I worked out the application to Minowski geometry myself a couple years back. (I connected the two through the importance of the hyperbola. Of course, this connection was probably mentioned in the article as well)

You can develop a great deal of it through analogy -- pull out a text on complex numbers, and then work out how things must be modified to work with h²=1 instead of i²=-1. For example, the Euler identity is proven as:

<br /> \begin{equation*}<br /> \begin{split}<br /> e^{h\beta} &amp;= 1 + (h\beta) + \frac{1}{2!}(h\beta)^2<br /> + \frac{1}{3!}(h\beta)^3 + \cdots<br /> \\ &amp;= 1 + h\beta + \frac{1}{2!}h^2\beta^2<br /> + \frac{1}{3!}h^3\beta^3 + \cdots<br /> \\ &amp;= (1 + \frac{1}{2!}\beta^2 + \frac{1}{4!}\beta^4 + \cdots)<br /> + h(\beta + \frac{1}{3!}\beta^3 + \frac{1}{5!}\beta^5 + \cdots)<br /> \\&amp;= \cosh \beta + h \sinh \beta<br /> \end{split}<br /> \end{equation*}<br />

Which is exactly the method used in proving e^z = \cos z + i \sin z.

 

[JesseM]

I suppose that it is because absolute simultaneity implies some sort of instantaneous connection between events.

I doubt that's what most people who discuss the "Lorentz Ether Theory" mean. Also, if you do believe there is some sort of real instantaneous connection between events, then wouldn't that mean there is a single relativistic reference frame whose definition of simultaneity is "really" the correct one? If it was just a matter of coordinate systems, then you'd be free to pick any relativistic reference frame and then make it so all the frames in the LET coordinate transformation used that frame's definition of simultaneity.

It is not superstitious to choose a coordinate system. But when a popular majority of the inhabitants of Salem winds up saying things like "experiments prove that the speed of light is a constant", and then proceeds to burn people at the stake for simply pointing out that "it's just a coordinate system, stupid", then you're into the realm of superstition. Oh, that's exactly what did happen to both Galileo and Newton wasn't it?

I don't think any physicist would disagree that you are free to pick a coordinate system where the speed of light is not constant, but they might argue that such coordinate systems are unphysical (they could not be constructed by observers in windowless boxes using rulers and clocks, for example). After all, you could also pick a weird coordinate system where clock speed varies by location and thus a given particle like a muon would have a different half-life depending on its position in space, but it would seem a bit pedantic to disagree with the statement "experiments show that all muons have the same half life" on this basis.

 

[Perspicacious]

I believe what I have said above is accurate but I'm not certain.

Pete, your comments are totally irrelevant. The title of this thread is "Relativity without the aether: pseudoscience?" The first sentence on page one says, "Special relativity (SR) and Lorentz ether theory (LET) are empirically equivalent systems for interpreting local Lorentz symmetry."

I countered the accusation by assuming a minimal axiom set for SR and adding The Santa-Reindeer Postulate. Russ Watters responded similarly by adding the invisible Purple Elephant conjecture.

The starter of this thread (Aether) doesn't see the absurdity of adding an invisible, empty postulate to SR that has no logical or observable consequences. My position is that if an axiom doesn't generate any quantifiable predictions, then it's worthless and needs to be thrown out.

As a mathematician, I understand games. I can accept definitions, the meaning of words and the logical consequences of adding to SR the silly Santa-Reindeer Postulate or the invisible Purple Elephant conjecture. Where's the logic? How can adding an unobservable Santa or a non-interacting purple elephant to SR turn a pseudoscientific theory into real science? Aether didn't answer this question. You can give it a try if you like.

 

[Aether]

I don't know -- I only remember seeing it in an article mathematics journal probably over a decade ago. I worked out the application to Minowski geometry myself a couple years back. (I connected the two through the importance of the hyperbola. Of course, this connection was probably mentioned in the article as well)

You can develop a great deal of it through analogy -- pull out a text on complex numbers, and then work out how things must be modified to work with h²=1 instead of i²=-1. For example, the Euler identity is proven as:

<br /> \begin{equation*}<br /> \begin{split}<br /> e^{h\beta} &amp;= 1 + (h\beta) + \frac{1}{2!}(h\beta)^2<br /> + \frac{1}{3!}(h\beta)^3 + \cdots<br /> \\ &amp;= 1 + h\beta + \frac{1}{2!}h^2\beta^2<br /> + \frac{1}{3!}h^3\beta^3 + \cdots<br /> \\ &amp;= (1 + \frac{1}{2!}\beta^2 + \frac{1}{4!}\beta^4 + \cdots)<br /> + h(\beta + \frac{1}{3!}\beta^3 + \frac{1}{5!}\beta^5 + \cdots)<br /> \\&amp;= \cosh \beta + h \sinh \beta<br /> \end{split}<br /> \end{equation*}<br />

Which is exactly the method used in proving e^z = \cos z + i \sin z.

Actually, I just started reading my first book on complex analysis yesterday, so I'll print this out and use it as a bookmark for awhile until I understand it better. Thanks!

 

[Aether]

I doubt that's what most people who discuss the "Lorentz Ether Theory" mean. Also, if you do believe there is some sort of real instantaneous connection between events, then wouldn't that mean there is a single relativistic reference frame whose definition of simultaneity is "really" the correct one? If it was just a matter of coordinate systems, then you'd be free to pick any relativistic reference frame and then make it so all the frames in the LET coordinate transformation used that frame's definition of simultaneity.

I am using LET as a label for the ether transformation equations that I posted from Mansouri-Sexl. If we ever find a way to detect a locally preferred frame, then LET takes charge. Failing that, then SR and LET are at least empirically equivalent. That is the state of affairs today, and for the puposes of this discussion I haven't made any predictions for future observations.

I don't think any physicist would disagree that you are free to pick a coordinate system where the speed of light is not constant, but they might argue that such coordinate systems are unphysical (they could not be constructed by observers in windowless boxes using rulers and clocks, for example). After all, you could also pick a weird coordinate system where clock speed varies by location and thus a given particle like a muon would have a different half-life depending on its position in space, but it would seem a bit pedantic to disagree with the statement "experiments show that all muons have the same half life" on this basis.

Why can't such a coordinate system be constructed by an observer in a windowless box? I presume that any coordinate system constructed by an observer in a windowless box is undefined outside the box, and inside the box the lack of windows isn't relevant.

 

[JesseM]

I am using LET as a label for the ether transformation equations that I posted from Mansouri-Sexl. If we ever find a way to detect a locally preferred frame, then LET takes charge.

Why does LET take charge then? This seems like a double standard, since your position is that despite the fact that the laws of nature look much simpler if we use the Lorentz transformation, that isn't a reason to favor it over the LET transformation; so if we discovered some new laws that looked simpler if we used the LET transform, to be consistent you should say that we should have no reason to favor the LET transform over the Lorentz transform in this case. Also, if LET is just a set of transformation equations (why do you call them 'ether' transformation equations if you don't assume a physical substance called 'ether', BTW?) then we'd have no obligation to make the physically preferred frame match the one whose coordinate time ticks the fastest in the LET transform.

Why can't such a coordinate system be constructed by an observer in a windowless box? I presume that any coordinate system constructed by an observer in a windowless box is undefined outside the box, and inside the box the lack of windows isn't relevant.

Unless I am misunderstanding something, the LET coordinate systems can't be constructed by a bunch of observers in a windowless box because they require each observer to know his velocity relative to a particular preferred coordinate system in order to synchronize his clocks correctly. My physical interpretation of the LET transformation equations is that each observer defines coordinates in terms of a network of rulers and clocks just like in SR, except that instead of each observer synchronizing his clocks using the assumption that light travels at the same speed in all directions in his frame, there is only a single observer who synchronizes his clocks this way, and all other observers adjust their clocks so that their definition of simultaneity matches this special frame. This is not possible unless each observer knows his velocity relative to this special frame.

 

[Aether]

Unless I am misunderstanding something, the LET coordinate systems can't be constructed by a bunch of observers in a windowless box because they require each observer to know his velocity relative to a particular preferred coordinate system in order to synchronize his clocks correctly. My physical interpretation of the LET transformation equations is that each observer defines coordinates in terms of a network of rulers and clocks just like in SR, except that instead of each observer synchronizing his clocks using the assumption that light travels at the same speed in all directions in his frame, there is only a single observer who synchronizes his clocks this way, and all other observers adjust their clocks so that their definition of simultaneity matches this special frame. This is not possible unless each observer knows his velocity relative to this special frame.

If you could detect a locally preferred frame from within a windowless box, then everyone could synchronize to that without reference to the walls of the box, and that would be great; everyone inside the box would be synchronized with everyone outside the box. However, the observers in the box can at least all agree on using the rest frame of the box itself as a common reference, and they can all ping the walls of the box with their radars, and they can all synchronize their clocks to maintain absolute simultaneity with each other.

 

[JesseM]

If you could detect a locally preferred frame from within a windowless box, then everyone could synchronize to that without reference to the walls of the box, and that would be great; everyone inside the box would be synchronized with everyone outside the box. However, the observers in the box can all agree on using the rest frame of the box as a common reference, and they can all ping the walls of the box with their radars, and they can all synchronize their clocks to maintain absolute simultaneity with each other.

When I talk about "windowless boxes" I mean that each observer has his own windowless box, not that you have a bunch of observers within the same windowless box. In SR, each observer can construct a network of rulers and clocks in his own windowless box without any knowledge of things outside his box, and if these boxes are moving alongside each other arbitrarily close by in space, then the Lorentz transform will map between the readings on each observer's clock/ruler system as they pass by each other. With the LET transform, there is no way each observer in his own box can physically construct the different coordinate systems unless they have windows and can communicate, so that they can agree on which of them will have the preferred coordinate system and the rest can synchronize their clocks by seeing how fast they're moving relative to this preferred observer.

By the way, I added a little to the beginning of my previous post after you responded to it...

 

[pmb_phy]

Pete, your comments are totally irrelevant. The title of this thread is "Relativity without the aether: pseudoscience?"

Wow! Its like you didn't even read my post!

Its overly obvious from my response is that the answer to "Relativity without the aether: pseudoscience?" is no (if the question posed is even a valid question to ask in the first place). russ and yourself have assumed a definition of "ether" (i.e. ether - that which supports the propagation of light) whose existence has never been detected either directly or indirectly and you both start off with this assumption. I chimmed in. So now you're surelyt asking who these "people" are right? I do recall that the name of one of these chaps is Albert Einstein. Albert Einstein - An address delivered on May 5th, 1920, in the University of Leyden
http://www.mountainman.com.au/aether_0.html

I may have the wrong idea between Eistein's 1920's address but that is just one person who looks at the the term "ether" as being different from that used by Maxwell and the ancient's. The ancient's used the term "ether" to refer to the element which permeated all of, otherwise empty, space.

Pete

 

[Aether]

When I talk about "windowless boxes" I mean that each observer has his own windowless box, not that you have a bunch of observers within the same windowless box. In SR, each observer can construct a network of rulers and clocks in his own windowless box without any knowledge of things outside his box, and if these boxes are moving alongside each other arbitrarily close by in space, then the Lorentz transform will map between the readings on each observer's clock/ruler system as they pass by each other. With the LET transform, there is no way each observer in his own box can physically construct the different coordinate systems unless they have windows and can communicate, so that they can agree on which of them will have the preferred coordinate system and the rest can synchronize their clocks by seeing how fast they're moving relative to this preferred observer.

By the way, I added a little to the beginning of my previous post after you responded to it...

That could turn out be a practical advantage to SR in the absence of a locally preferred frame, but I'm not convinced of that yet. Can you show a simple example using the transformation equations that I provided? There is already an example relating to momentum being discussed in the "Einstein's clock synchronization convention" thread. Until it is proven otherwise, I will assume that LET is empirically equivalent to SR because Mansouri-Sexl say that they are; but if it can be shown not to be exactly so then that would make a real difference to how I look at this.

 

[Perspicacious]

Pete,

I'm not aware of anyone, including Einstein, who successfully defined the meaning of "aether" so that it would result in definite, quantifiable predictions. Aether (the poster) doesn't even want to extend the current range of SR's quantifiable predictions. Aether wants a new theory that is empirically equivalent to SR. He is arguing for the addition of an undetectable absolute frame of reference. I don't see how his revision is any different than adding to SR the Santa-Reindeer Postulate or the invisible Purple Elephant conjecture.

 

[pmb_phy]

I'm not aware of anyone, including Einstein, who successfully defined the meaning of "aether" so that it would result in definite, quantifiable predictions.

The terms "aether," "ether" and "superluminal ether" are all syonyms for the same thing. I used the term because Einstein was using it. I thgought it'd be the least confusing way to get this straight. I guess not. This is a fact which has not escaped aether. Right aether.

Sorry folks but I must leave the board for the rest of the day. If there is something here beyone semantics then please let me know.

Pete

 

[JesseM]

That could turn out be a practical advantage to SR in the absence of a locally preferred frame, but I'm not convinced of that yet. Can you show a simple example using the transformation equations that I provided?

A simple example of what?

There is already an example relating to momentum being discussed in the "Einstein's clock synchronization convention" thread. Until it is proven otherwise, I will assume that LET is empirically equivalent to SR because Mansouri-Sexl say that they are; but if it can be shown not to be exactly so then that would make a real difference to how I look at this.

I think you're confused here--if LET is defined solely in terms of a different coordinate system, without any different assumptions about the laws of physics, then obviously the theory is not predicting any new empirical consequences, because it's assuming the same laws of physics! Changing your coordinate system doesn't change the laws of physics, it only changes the equations used to express the laws of physics in that coordinate system. You can pick any crazy coordinate system you want! (I still doubt that Mansouri and Sexl share your view that the LET refers to nothing more than a coordinate transformation with no new physical assumptions, but that's another issue) But if you want to physically construct a measuring device such that the reading on a clock and the marking on the ruler next to a particular event correspond to the coordinates of the event in that coordinate system, then it should be equally obvious that this measuring device will be different if you choose a different coordinate system. The set of measuring devices that correspond to each coordinate system in the LET transformation are different that the set of measuring devices that correspond to each coordinate system in the Lorentz transformation, and one characteristic that's different is that there's no way (according to the current known laws of physics) for a bunch of observers to construct the coordinate system of their rest frame without knowing their velocity relative to a single preferred frame, whereas in the Lorentz transform each observer's rest frame can be constructed with no knowledge of the outside world (in a windowless box). This is not an "empirical difference" in the sense of the laws of physics being different, it's just a difference in what would be needed to construct a set of measuring devices corresponding to each coordinate system allowed by the transformation. It is a good reason to see the LET transformation as more unphysical than the Lorentz transformation, though.

Speaking of the physical basis for using one coordinate system vs. another, did you have any comment on the part I added to my earlier post after you responded to it?

I am using LET as a label for the ether transformation equations that I posted from Mansouri-Sexl. If we ever find a way to detect a locally preferred frame, then LET takes charge.

Why does LET take charge then? This seems like a double standard, since your position is that despite the fact that the laws of nature look much simpler if we use the Lorentz transformation, that isn't a reason to favor it over the LET transformation; so if we discovered some new laws that looked simpler if we used the LET transform, to be consistent you should say that we should have no reason to favor the LET transform over the Lorentz transform in this case. Also, if LET is just a set of transformation equations (why do you call them 'ether' transformation equations if you don't assume a physical substance called 'ether', BTW?) then we'd have no obligation to make the physically preferred frame match the one whose coordinate time ticks the fastest in the LET transform.

 

[Aether]

A simple example of what?

Of two observers in separate windowless boxes who are able to do something meaningful using the Lorentz transform that they can't do equally well with the ether transform. If you show me something that they can do with the Lorentz transform, then I will try to match it with the ether transform; and if I can't do it, then that will give me a practical reason to think that an impartial observer would prefer the Lorentz transform over the ether transform. (However, the next paragraph may make that unnecessary for now.)

I think you're confused here--if LET is defined solely in terms of a different coordinate system, without any different assumptions about the laws of physics, then obviously the theory is not predicting any new empirical consequences, because it's assuming the same laws of physics! Changing your coordinate system doesn't change the laws of physics, it only changes the equations used to express the laws of physics in that coordinate system. You can pick any crazy coordinate system you want! But if you want to physically construct a measuring device such that the reading on a clock and the marking on the ruler next to a particular event correspond to the coordinates of the event in that coordinate system, then it should be equally obvious that this measuring device will be different if you choose a different coordinate system. The set of measuring devices that correspond to each coordinate system in the LET transformation are different that the set of measuring devices that correspond to each coordinate system in the Lorentz transformation, and one characteristic that's different is that there's no way (according to the current known laws of physics) for a bunch of observers to construct the coordinate system of their rest frame without knowing their velocity relative to a single preferred frame, whereas in the Lorentz transform each observer's rest frame can be constructed with no knowledge of the outside world (in a windowless box). This is not an "empirical difference" in the sense of the laws of physics being different, it's just a difference in what would be needed to construct a set of measuring devices corresponding to each coordinate system allowed by the transformation. It is a good reason to see the LET transformation as more unphysical than the Lorentz transformation, though.

That sounds like a potentially plausible reason to prefer the Lorentz transformation over the ether transformation for all practical purpose unless/until a locally preferred frame is detected. However, it does lead most people to a false belief that the one-way speed of light has been measured by endless numbers of experiments, and in general I think that it tends to warp one's perception of local Lorentz invariance.

Speaking of the physical basis for using one coordinate system vs. another, did you have any comment on the part I added to my earlier post after you responded to it?

Why does LET take charge then? This seems like a double standard, since your position is that despite the fact that the laws of nature look much simpler if we use the Lorentz transformation, that isn't a reason to favor it over the LET transformation; so if we discovered some new laws that looked simpler if we used the LET transform, to be consistent you should say that we should have no reason to favor the LET transform over the Lorentz transform in this case. Also, if LET is just a set of transformation equations (why do you call them 'ether' transformation equations if you don't assume a physical substance called 'ether', BTW?) then we'd have no obligation to make the physically preferred frame match the one whose coordinate time ticks the fastest in the LET transform.

I am still forming my position and how to describe it, but I think that it is this: that the laws of nature are described by the Minkowski metric, but that the Lorentz transformation isn't any different (mathematically at least) from the ether transform. Mansouri-Sexl say that they are also empirically equivalent, not just mathematically equivalent. If we discovered some new laws that enable us to define a locally preferred frame, then I would presume that would mean that the Minkowski metric itself would be asymmetrical in some way and the natural choice of transformation would then resolve into something that maintains absolute simultaneity. I call them ether transformation equations because that is what Mansouri-Sexl call them.

 

[robphy]

Special relativity (SR) SR and Lorentz ether theory (LET) are empirically equivalent systems for interpreting local Lorentz symmetry.

While I don't have the time to contribute to this lively thread, let me just point to
"A Comparison between Lorentz's Ether Theory and Special Relativity in the Light of the Experiments of Trouton and Noble", Michel Janssen's dissertation, which is available at http://www.tc.umn.edu/~janss011/ . Here is the first paragraph in his Introduction

In this dissertation, I want to compare the ether theory of the great Dutch physicist Hendrik Antoon Lorentz (1853–1928) to Einstein’s special theory of relativity. To the end of his life, Lorentz maintained, first, that his theory is empirically equivalent to special relativity, and, second, that, in the final analysis, it is a matter of taste whether one prefers the standard relativistic interpretation of the formalism of the theory or his own ether theoretic interpretation (see, e.g., Nersessian 1984, pp. 113–119). I will argue that Lorentz’s first claim, when understood properly, should be accepted, but that the second should be rejected.

I haven't read the dissertation yet. (I don't have too much free time right now.) However, this and his other papers on the History of Relativity look interesting.

 

[JesseM]

Of two observers in separate windowless boxes who are able to do something meaningful using the Lorentz transform that they can't do equally well with the ether transform. If you show me something that they can do with the Lorentz transform, then I will try to match it with the ether transform; and if I can't do it, then that will give me a practical reason to think that an impartial observer would prefer the Lorentz transform over the ether transform. (However, the next paragraph may make that unnecessary for now.)

OK, but I already did that. The different observers in windowless boxes can create ruler/clock systems such that, when an outside observer looks at the coordinates that two different observers assign to the same event using these systems, he will see that they are related by the Lorentz transform. They do this just by creating a system of rulers with clocks attached to each ruler marking, and synchronizing the clocks using light signals, under the assumption that light moves at c in their own box's rest frame; then to assign coordinates to a given event, they just look at the reading on the ruler and clock that were at the same position as the event at the moment it happened (the Lorentz transformation is usually derived based on the assumption that each observer assigns coordinates to events using exactly this physical setup). In contrast, there's no way for observers in windowless boxes to build measuring devices such that the coordinates different observers assign to the same event are related by the LET transform, although they can do this if they can communicate and agree on which observer has the preferred frame, and then the rest can measure their velocity relative to this preferred observer and use this information to synchronize their clocks.

That sounds like a potentially plausible reason to prefer the Lorentz transformation over the ether transformation for all practical purpose unless/until a locally preferred frame is detected. However, it does lead most people to a false belief that the one-way speed of light has been measured by endless numbers of experiments, and in general I think that it tends to warp one's perception of local Lorentz invariance.

I disagree that this is "false" just because it depends on using a particular coordinate system--you could equally well say it's a false belief that people can measure the speed of anything, like, say, cars. Likewise the same reasoning would force you to say it's "false" that scientists have measured that muons all have the same decay rate regardless of your position in space, since you could in principle pick a weird coordinate system where clocks ticked at different coordinate speeds depending on position. I think it's understood implicitly in statements like this that you're talking in terms of the most physically natural coordinate system, otherwise you'd always have to qualify every single statement about physics that refers to position, time, velocity, acceleration, etc.

I am still forming my position and how to describe it, but I think that it is this: that the laws of nature are described by the Minkowski metric, but that the Lorentz transformation isn't any different (mathematically at least) from the ether transform.

Of course it's different--they're different coordinate systems. The Lorentz transformation transforms time coordinates like t&#039; = \gamma (t - vx/c^2) while the LET transformation transforms them like t&#039; = \gamma t. What else do you think it means to say that two coordinate transformations are mathematically different?

Mansouri-Sexl say that they are also empirically equivalent, not just mathematically equivalent.

Again, I suspect that Mansouri-Sexl don't mean the "Lorentz Ether Theory" to refer just to a coordinate transformation, but to a hypothesis that there is an unobserved physical entity called "ether" out there which has a particular rest frame, and which has the property that clocks slow down and rulers shrink the faster they move relative to this rest frame. To say that this theory was "empirically equivalent" to SR would just be to note that there's no experiment we can do that would tell us our velocity relative to this ether rest frame, even if there is some unknowable objective answer to this question.

If we discovered some new laws that enable us to define a locally preferred frame, then I would presume that would mean that the Minkowski metric itself would be asymmetrical in some way and the natural choice of transformation would then resolve into something that maintains absolute simultaneity.

Like I said, no matter what the laws of physics are you could still use either set of coordinate systems. If you want to say that the LET coordinate systems would be more of a "natural choice" in this case I agree, but then you should agree that in terms of the laws of physics as we know them now, the Lorentz transform is more of a "natural choice", since the known laws of physics will obey the same equations in every reference frame using the Lorentz transform but not using the LET transform, and because observers in windowless boxes could create physical versions of the coordinate systems of the Lorentz transform but not of the LET transform.

 

[Aether]

OK, but I already did that. The different observers in windowless boxes can create ruler/clock systems such that, when an outside observer looks at the coordinates that two different observers assign to the same event using these systems, he will see that they are related by the Lorentz transform.

I don't recall hearing you say anything about an outside observer before.

They do this just by creating a system of rulers with clocks attached to each ruler marking, and synchronizing the clocks using light signals, under the assumption that light moves at c in their own box's rest frame; then to assign coordinates to a given event, they just look at the reading on the ruler and clock that were at the same position as the event at the moment it happened (the Lorentz transformation is usually derived based on the assumption that each observer assigns coordinates to events using exactly this physical setup). In contrast, there's no way for observers in windowless boxes to build measuring devices such that the coordinates different observers assign to the same event are related by the LET transform, although they can do this if they can communicate and agree on which observer has the preferred frame, and then the rest can measure their velocity relative to this preferred observer and use this information to synchronize their clocks.

The outside observer is the one who defines the preferred frame. Now that you have introduced him, and said that he is the one who can actually relate the two coordinate systems from the two windowless boxes, then I suspect that the LET transform might perform equally well. This outside observer merely needs to syncrhonize the clocks in the windowless boxes, and then do an LET transform; this is no different than working the Lorentz transform which has the exact same syncrhonization function embedded within it.

I disagree that this is "false" just because it depends on using a particular coordinate system--you could equally well say it's a false belief that people can measure the speed of anything, like, say, cars.

The speed of anything can be measured to have the same value regardless of direction or clock synchronization using a round-trip radar pulse for example. The round-trip speed of light can also be measured to have the same value regardless of direction or clock synchronization.

Likewise the same reasoning would force you to say it's "false" that scientists have measured that muons all have the same decay rate regardless of your position in space, since you could in principle pick a weird coordinate system where clocks ticked at different coordinate speeds depending on position. I think it's understood implicitly in statements like this that you're talking in terms of the most physically natural coordinate system, otherwise you'd always have to qualify every single statement about physics that refers to position, time, velocity, acceleration, etc.

First we need to establish that SR coordinates really are more physcially natural than LET in the absence of a locally preferred frame, and then we need to establish that SR+LET is not even more physically natural than that. Even if we can eventually come to an agreement that SR is more natural in the absence of a locally preferred frame, we have already agreed that LET is more natural when there is a locally preferred frame. What about coordinate free geometry, and being able to at least see the problem from both the SR and the LET perspectives? I don't think it matters which coordinate system that you use so long as you are aware of its inherent limitations, or at least that it has some.

Of course it's different--they're different coordinate systems. The Lorentz transformation transforms time coordinates like t&#039; = \gamma (t - vx/c^2) while the LET transformation transforms them like t&#039; = \gamma t. What else do you think it means to say that two coordinate transformations are mathematically different?

They are not really any different, but you have obscured that from presenting the equations in a different form than Mansouri-Sexl do and by neglecting to mention that Einstein synchronized clocks are readjusted to LET synchronization before using the LET transform. The -vx/c^2[/itex] term from the Lorentz transform is merely pulled out of the equation and then plugged directly into the clock at x to synchronize it. <br /> <br /> <blockquote data-attributes="" data-quote="JesseM" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> JesseM said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Again, I suspect that Mansouri-Sexl don&#039;t mean the &quot;Lorentz Ether Theory&quot; to refer just to a coordinate transformation, but to a hypothesis that there is an unobserved physical entity called &quot;ether&quot; out there which has a particular rest frame, and which has the property that clocks slow down and rulers shrink the faster they move relative to this rest frame. To say that this theory was &quot;empirically equivalent&quot; to SR would just be to note that there&#039;s no experiment we can do that would tell us our velocity relative to this ether rest frame, even if there is some unknowable objective answer to this question. </div> </div> </blockquote>Do you have a copy of their papers? I can provide you with one if you don&#039;t. They don&#039;t call their ether theory &quot;LET&quot;, I&#039;m just using it as a convenient label. <br /> <br /> <blockquote data-attributes="" data-quote="JesseM" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> JesseM said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Like I said, no matter what the laws of physics are you could still use either set of coordinate systems. If you want to say that the LET coordinate systems would be more of a &quot;natural choice&quot; in this case I agree, but then you should agree that in terms of the laws of physics as we know them now, the Lorentz transform is more of a &quot;natural choice&quot;, since the known laws of physics will obey the same equations in every reference frame using the Lorentz transform but not using the LET transform, and because observers in windowless boxes could create physical versions of the coordinate systems of the Lorentz transform but not of the LET transform. </div> </div> </blockquote>We might be able to come to an agreement along these lines at some point, but now that you have thrown an &quot;outside observer&quot; into the example I&#039;m not yet ready to say that the Lorentz transform is a more natural choice in the absence of a locally preferred frame.

 

[Aether]

The terms "aether," "ether" and "superluminal ether" are all syonyms for the same thing. I used the term because Einstein was using it. I thgought it'd be the least confusing way to get this straight. I guess not. This is a fact which has not escaped aether. Right aether.

It seems to me that these terms all imply that the Minkowski metric is, or at least has the potential to be, asymmetric somehow. I suppose that's what GR is all about (e.g., that the metric is, or at least has the potential to be, asymmetric...asym-metric?), and that Einstein is saying that the metric is the aether (however, all of this may ultimately depend on what your definition of "is" is ).

 

[JesseM]

I don't recall hearing you say anything about an outside observer before.

The outside observer isn't necessary for their coordinates to be related by a Lorentz transform, but since their boxes are all windowless, none of them can see what each other's coordinate readings are--that's the only reason I introduced him. Alternately, you could have each of them build their measuring devices in windowless boxes, then once the devices were up and running the boxes could be opened so they could all see the devices that everyone else built.

The outside observer is the one who defines the preferred frame.

No, certainly not--the outside observer's velocity is irrelevant, all he's doing is noting "hmm, observer A assigned that event coordinates x=3.5 meters, t=9 seconds while observer B assigned the same event coordinates x'=7 meters, t'=2 seconds", something like that.

Now that you have introduced him, and said that he is the one who can actually relate the two coordinate systems from the two windowless boxes, then I suspect that the LET transform might perform equally well. This outside observer merely needs to syncrhonize the clocks in the windowless boxes, and then do an LET transform

See, your outside observer needs to actually interact with the different measuring devices, to take a part in how they are constructed, for them to work right--my outside observer is only noting the readings on measuring devices which have already been completely constructed by the observers inside their windowless boxes. My outside observer can just be a ghost noting facts about the world without being able to have any effect on it (and even if there is no outside observer, it's still true that the coordinates of different observers are related by the Lorentz transform even if none of them are aware of this fact), yours is taking an active role in building the different measuring devices, making use of information he obtains by seeing the velocity of different devices relative to one another.

I disagree that this is "false" just because it depends on using a particular coordinate system--you could equally well say it's a false belief that people can measure the speed of anything, like, say, cars.

The speed of anything can be measured to have the same value regardless of direction or clock synchronization using a round-trip radar pulse for example. The round-trip speed of light can also be measured to have the same value regardless of direction or clock synchronization.

You can't measure the speed of anything in a way that doesn't depend on your choice of coordinate system. For example, suppose a spaceship is flying at 0.8c in the preferred frame of the ether transform, and you want to know how fast it's flying in the ether-transform frame of an observer moving at 0.6c in the same direction relative to the preferred frame. In the preferred frame, two points along the ship's path are x=0,t=0 and x=0.8,t=1, so using the ether transform equations you provided in post #92, we find that these events correspond to x'=0,t'=0 and x'=0.25,t'=0.8 (actually I'm not sure about this last one--you wrote the equation t_1=(1-v^2/c_0^2)^{1/2}T_1 for the time transformation in the ether equation, but then for the Lorentz transform you wrote t_1=(1-v^2/c_0^2)^{1/2}T_1-vx_1/c_0^2 when it's actually supposed to be t_1=(T_1-vx_1/c_0^2)/(1-v^2/c_0^2)^{1/2}, so should we also divide by (1-v^2/c_0^2)^{1/2} rather than multiply by it in the ether transform equation?). This means that the velocity of the ship in this second observer's rest frame would be 0.3125c according to the ether transformation. On the other hand, if you use the Lorentz transform then the coordinates of these same two events are x'=0,t'=0 and x'=0.25,t'=0.65, so the velocity of the ship in this observer's rest frame is 0.3846c according to the Lorentz transformation. So you can see that even for objects moving slower than light, your notion of the speed of slower-than-light objects like spaceships or cars depends on your choice of coordinate system.

Of course it's different--they're different coordinate systems. The Lorentz transformation transforms time coordinates like t&#039;=\gamma(t - vx/c^2) while the LET transformation transforms them like t&#039;=\gamma t. What else do you think it means to say that two coordinate transformations are mathematically different?

They are not really any different, but you have obscured that from presenting the equations in a different form than Mansouri-Sexl do

OK, show me the form that they present the time transformation in then.

and by neglecting to mention that Einstein synchronized clocks are readjusted to LET synchronization before using the LET transform. The -vx/c^2[/itex] term from the Lorentz transform is merely pulled out of the equation and then plugged directly into the clock at x to synchronize it.

I&#039;m still not understanding how this means there is &quot;no mathematical difference&quot; between them. If you synchronize the clocks in a different way, then isn&#039;t that a mathematically different coordinate system? Won&#039;t the actual time-coordinates I assign to particular events be changed as a result? What type of change in the coordinate systems <i>would</i> qualify as &quot;mathatically different&quot; in your use of the term? <blockquote data-attributes="" data-quote="Aether" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Aether said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Do you have a copy of their papers? I can provide you with one if you don&#039;t. </div> </div> </blockquote>I don&#039;t have a copy, so if you could provide one that would be helpful, thanks.

 

[Aether]

(actually I'm not sure about this last one--you wrote the equation t_1=(1-v^2/c_0^2)^{1/2}T_1 for the time transformation in the ether equation, but then for the Lorentz transform you wrote t_1=(1-v^2/c_0^2)^{1/2}T_1-vx_1/c_0^2 when it's actually supposed to be t_1=(T_1-vx_1/c_0^2)/(1-v^2/c_0^2)^{1/2}, so should we also divide by (1-v^2/c_0^2)^{1/2} rather than multiply by it in the ether transform equation?). I don't have a copy, so if you could provide one that would be helpful, thanks.

If anyone else would like to download a copy of the Mansouri-Sexl papers in the future, please let me know and I'll make them available. Let's confirm that you approve of their version of the Lorentz transform equations before going any further.

 

[JesseM]

You can download a copy (8MB) from ... for the next few hours. After that I'll erase this link, and if anyone wants it at a later time all they'll have to do is ask me for it. Let's confirm that you approve of their version of the Lorentz transform equations before going any further.

OK, I've downloaded it. The time transformation in the Lorentz transformation they give in equation 3.4 seems incorrect to me--they do indeed write t = (1 - v^2)^{1/2} T - vx, but if you look anywhere else (like here or here or http://www.bun.kyoto-u.ac.jp/~suchii/lorentz.tr.html or here) you'll see that the usual time transformation is t = \gamma (T - vx/c^2) = (T - vx/c^2)/\sqrt(1 - v^2/c^2).

 

[Aether]

OK, I've downloaded it. The time transformation in the Lorentz transformation they give in equation 3.4 seems incorrect to me--they do indeed write t = (1 - v^2)^{1/2} T - vx, but if you look anywhere else (like here or here or http://www.bun.kyoto-u.ac.jp/~suchii/lorentz.tr.html or here) you'll see that the usual time transformation is t = \gamma (T - vx/c^2) = (T - vx/c^2)/\sqrt(1 - v^2/c^2).

Have a look at post #42 in the "Einstein's clock synchronization convention" thread. DrGreg says that it's OK. There are other confirmed typos in M&S, and it would be good to know for sure if this was yet another one.

Quick poll: What do you think that the metric represents if not a physical thing aka "the aether"?

 

[JesseM]

Have a look at post #42 in the "Einstein's clock synchronization convention" thread. DrGreg says that it's OK. There are other confirmed typos in M&S, and it would be good to know for sure if this was yet another one.

OK, I see what's going on. Instead of showing the formula for t in terms of the (X,T) coordinate system, they're giving the formula for t in terms of the T-coordinate of the (X,T) system and the x-coordinate of the (x,t) system. That seems overcomplicated, but it isn't a mistake. So I was mistaken when I said earlier that time transforms like t&#039; = \gamma t in the ether transform, it should actually be t&#039; = t/\gamma. But this doesn't affect the numerical example I provided in my last long post (#70), because I did use t&#039; = t \sqrt{1 - v^2/c^} in coming up with those numbers.

 

[Aether]

OK, I see what's going on. Instead of showing the formula for t in terms of the (X,T) coordinate system, they're giving the formula for t in terms of the T-coordinate of the (X,T) system and the x-coordinate of the (x,t) system. That seems overcomplicated, but it isn't a mistake.

Perhaps they did it that way to make it clear that the only difference between LET and SR is that in one this -vx/c_0^2 term is embedded in the transformation equation, and in the other this term is plugged into a clock?

 

[JesseM]

Perhaps they did it that way to make it clear that the only difference between LET and SR is that in one this -vx/c_0^2 term is embedded in the transformation equation, and in the other this term is plugged into a clock?

Seems like a plausible reason. Anyway, now that we've got this cleared up, do you have any comments on the rest of my post #70?

 

[DrGreg]

Special Relativity (SR) has two postulates: not only that the speed of light is invariant but also that the laws of physics take the same form in all inertial frames.

The "LET" transformations quoted by Aether provide an alternative to the first postulate. But they do not deal with particle dynamics and the concepts of mass, momentum, energy and force, which, in SR, depend on the second postulate. The relativistic formulas for momentum and energy are based on the assumptions that momentum and energy are both conserved relative to any choice of inertial observer, and the same formulas apply in all frames. In particular, momentum and energy are assumed to be isotropic.

For example, the magnitude of momentum depends only on the magnitude of velocity relative to the observer, and not on the direction. This has a practical consequence: if you take two particles of equal mass and fire them towards each other at equal and opposite velocities, and they collide and stick together, the resultant mass will be stationary. This result is true, according to SR, relative to any inertial observer. I assume that there is plenty of experimental evidence to confirm this. Perhaps other readers can confirm my assumption.

If the same observer uses LET co-ordinates instead of SR co-ordinates, distance is the same but time is different, so the two particles no longer have the same speed, before collision, in LET co-ordinates, yet still they end up stationary. This establishes that, in LET, momentum cannot be isotropic. (See this thread Einstein's Clock Synchronization Convention if you need more details.)

For LET to successfully compete with SR, it needs its own definitions of momentum and energy, and, for these to be conserved, they cannot be isotropic. I don't know if there are formulations of LET which include additional postulates that will cope with momentum and energy relative to a moving observer. The formulas quoted by Aether do not answer this question.

 

[Aether]

Seems like a plausible reason. Anyway, now that we've got this cleared up, do you have any comments on the rest of my post #70?

It is ambiguous to define a velocity as 0.8c because c is a variable in LET. You can define it unambiguously as 0.8c_0, and then it should be the same in both SR & LET. We need to develop a simple but specific example where all of the coordinates are calculated using the Lorentz transform, and then see if the LET transform can't match it. You can't compute the Lorentz transform without providing the -vx/c_0^2 term for each clock, and I'm just going to take it and put it in the clock.

 

[Aether]

Special Relativity (SR) has two postulates: not only that the speed of light is invariant but also that the laws of physics take the same form in all inertial frames.

The "LET" transformations quoted by Aether provide an alternative to the first postulate. But they do not deal with particle dynamics and the concepts of mass, momentum, energy and force, which, in SR, depend on the second postulate. The relativistic formulas for momentum and energy are based on the assumptions that momentum and energy are both conserved relative to any choice of inertial observer, and the same formulas apply in all frames. In particular, momentum and energy are assumed to be isotropic.

For example, the magnitude of momentum depends only on the magnitude of velocity relative to the observer, and not on the direction. This has a practical consequence: if you take two particles of equal mass and fire them towards each other at equal and opposite velocities, and they collide and stick together, the resultant mass will be stationary. This result is true, according to SR, relative to any inertial observer. I assume that there is plenty of experimental evidence to confirm this. Perhaps other readers can confirm my assumption.

If the same observer uses LET co-ordinates instead of SR co-ordinates, distance is the same but time is different, so the two particles no longer have the same speed, before collision, in LET co-ordinates, yet still they end up stationary. This establishes that, in LET, momentum cannot be isotropic. (See this thread Einstein's Clock Synchronization Convention if you need more details.)

For LET to successfully compete with SR, it needs its own definitions of momentum and energy, and, for these to be conserved, they cannot be isotropic. I don't know if there are formulations of LET which include additional postulates that will cope with momentum and energy relative to a moving observer. The formulas quoted by Aether do not answer this question.

The second postulate is automatically satisfied because the LET coordinates transform as a tensor. M&S give the general transformation on page 508, and then whittle it down for convenience sake. I will stipulate that energy and momentum need to be conserved in LET, but suppose that they are since the coordinates transform as a tensor.

 

[DrGreg]

The second postulate is automatically satisfied because the LET coordinates transform as a tensor. M&S give the general transformation on page 508, and then whittle it down for convenience sake. I will stipulate that energy and momentum need to be conserved in LET, but suppose that they are since the coordinates transform as a tensor.

If you assume SR is correct, you can come up with some expressions for momentum and energy relative to LET co-ordinates by application of the transform equations. But if you ignore SR and try to calculate momentum and energy some other way, how do you find the answer? How, for example, do you prove that, relative to the ether, the relativistic form p=\gamma_u m u should be used instead of p= m u?

 

[JesseM]

It is ambiguous to define a velocity as 0.8c because c is a variable in LET.

The speed of light varies depending on your reference frame, but I would think that in the ether transform the symbol "c" no longer refers to the actual speed of light in an arbitrary frame, but only to the speed of light in the preferred frame where light travels at the same speed in all directions. After all, doesn't "c" appear in the transformation equations themselves? Mansouri and Sexl just set it equal to 1, but I think if you include it the ether transform equations would look like:

x&#039; = (x - vt)/\sqrt{1 - v^2/c^2}
t&#039; = t \sqrt{1 - v^2/c^2}

The c that appears here is a constant, no?

You can define it unambiguously as 0.8c_0

OK, if c_0 means the speed of light in the preferred frame, that's what I meant. Also, I did specify that when I said the speed of the ship was 0.8c and the speed of the second observer was 0.6c, these speeds were relative to the preferred frame of the ether transform, which Mansouri and Sexl mean to represent the ether's rest frame (although you do not make this assumption, apparently).

and then it should be the same in both SR & LET. We need to develop a simple but specific example where all of the coordinates are calculated using the Lorentz transform, and then see if the LET transform can't match it.

I don't know what you mean by "can't match it"--match what, exactly? The point of my example in post #70 was not to show that the ether transform is incorrect or that it can't do something that the Lorentz transform can do, but just to show that the speed of a sublight object such as a spaceship or a car depends on whether you choose to use the coordinate systems given by the ether transform or the Lorentz transform, that your earlier statement that "The speed of anything can be measured to have the same value regardless of direction or clock synchronization using a round-trip radar pulse for example" is incorrect because the speed of an object does not always have the same value in an ether transform frame and the corresponding Lorentz transform frame.

You can't compute the Lorentz transform without providing the -vx/c_0^2 term for each clock, and I'm just going to take it and put it in the clock.

I don't know what you mean by "I'm just going to take it and put it in the clock". Put what in the clock? What does this have to do with my point that all velocity measurements depend on your choice of coordinate system? (you can substitute 'depend on your choice of clock synchronization' if you like, although it would be possible to invent wacky coordinate systems which differ in ways that go beyond clock synchronization, like one where the ratio of ruler length to coordinate length is different in different regions of space)

Also, do you have any response to the other points I made in post #70? Do you agree now that the "outside observer" I referred to plays no role in the construction of the different measuring devices that different observers use to assign coordinates to events, for example? What about my question about what you could possibly mean when you say there is "no mathematical difference" between the Lorentz transform and the ether transform?

 

[Aether]

The speed of light varies depending on your reference frame, but I would think that in the ether transform the symbol "c" no longer refers to the actual speed of light in an arbitrary frame, but only to the speed of light in the preferred frame where light travels at the same speed in all directions. After all, doesn't "c" appear in the transformation equations themselves? Mansouri and Sexl just set it equal to 1, but I think if you include it the ether transform equations would look like:

x&#039; = (x - vt)/\sqrt{1 - v^2/c^2}
t&#039; = t \sqrt{1 - v^2/c^2}

The c that appears here is a constant, no?

No. c_0[/itex] is the round-trip speed of light, and c=c(v,\theta).<br /> <br /> <blockquote data-attributes="" data-quote="JesseM" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> JesseM said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> OK, if c_0 means the speed of light in the preferred frame, that&#039;s what I meant. Also, I did specify that when I said the speed of the ship was 0.8c and the speed of the second observer was 0.6c, these speeds were relative to the preferred frame of the ether transform, which Mansouri and Sexl mean to represent the ether&#039;s rest frame (although you do not make this assumption, apparently). I don&#039;t know what you mean by &quot;can&#039;t match it&quot;--match what, exactly? The point of my example in post #70 was not to show that the ether transform is incorrect or that it can&#039;t do something that the Lorentz transform can do, but just to show that the speed of a sublight object such as a spaceship or a car depends on whether you choose to use the coordinate systems given by the ether transform or the Lorentz transform, that your earlier statement that &quot;The speed of anything can be measured to have the same value regardless of direction or clock synchronization using a round-trip radar pulse for example&quot; is incorrect because the speed of an object does <i>not</i> always have the same value in an ether transform frame and the corresponding Lorentz transform frame. I don&#039;t know what you mean by &quot;I&#039;m just going to take it and put it in the clock&quot;. Put what in the clock? What does this have to do with my point that all velocity measurements depend on your choice of coordinate system? (you can substitute &#039;depend on your choice of clock synchronization&#039; if you like, although it would be possible to invent wacky coordinate systems which differ in ways that go beyond clock synchronization, like one where the ratio of ruler length to coordinate length is different in different regions of space)<br /> <br /> Also, do you have any response to the other points I made in post #70? Do you agree now that the &quot;outside observer&quot; I referred to plays no role in the construction of the different measuring devices that different observers use to assign coordinates to events, for example? What about my question about what you could possibly mean when you say there is &quot;no mathematical difference&quot; between the Lorentz transform and the ether transform? </div> </div> </blockquote>This is why I&#039;m asking for a simple example. I would rather develop a simple example so that we can model one simple problem and compare notes on it rather than have too big of a word problem to deal with.

 

[JesseM]

No. c_0[/itex] is the round-trip speed of light, and c=c(v,\theta).

OK, but I didn&#039;t even use c_0 in my version of the ether transform equations. If <i>I</i> define c as the speed of light in the ether frame (which I think is equal to the round-trip speed anyway, assuming each observer uses his own ruler and clock to measure the length and time of the round trip), and then I write the ether transformation as I did in my previous post, are you saying that the equations I wrote there are incorrect? <blockquote data-attributes="" data-quote="Aether" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Aether said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> This is why I&#039;m asking for a simple example. I would rather develop a simple example so that we can model one simple problem and compare notes on it rather than have too big of a word problem to deal with. </div> </div> </blockquote> How will an example make any difference for the issue of the &quot;outside observer&quot; who has no effect on any physical system and thus cannot possibly make a difference in any numerical example? Do you agree or disagree that observers in windowless boxes can set up measuring devices to assign coordinates to different events such that the coordinates two observers assign to the same event will transform according to the Lorentz transform, but that it is impossible to build measuring devices in windowless boxes whose coordinates transform according to the ether transform?<br /> <br /> As for the issue of whether speed depends on your coordinate system, I already provided a numerical example. Again, assume that when <i>I</i> use the symbol &quot;c&quot; it refers only to the speed of light as measured in the preferred ether frame, even if you would use the symbol differently.

 

[Aether]

OK, but I didn't even use c_0 in my version of the ether transform equations. If I define c as the speed of light in the ether frame (which I think is equal to the round-trip speed anyway, assuming each observer uses his own ruler and clock to measure the length and time of the round trip), and then I write the ether transformation as I did in my previous post, are you saying that the equations I wrote there are incorrect?

Not necessarily, but there is an ambiguity with specifying a velocity as 0.8c in LET because that is a function of v and \theta.

How will an example make any difference for the issue of the "outside observer" who has no effect on any physical system and thus cannot possibly make a difference in any numerical example?

It may not make any difference in the end. But you said that the outside observer is the one who computes the Lorentz transform, and that's getting way more complicated than just a windowless box.

Do you agree or disagree that observers in windowless boxes can set up measuring devices to assign coordinates to different events such that the coordinates two observers assign to the same event will transform according to the Lorentz transform, but that it is impossible to build measuring devices in windowless boxes whose coordinates transform according to the ether transform?

Two observers in two different windowless boxes each assigning coordinates to an event that is not within either box...I'm not sure exactly what you're scenario is, it could be anything. I'm looking for an explicit example like: "Two windowless boxes A and B each contain an observer who manufactures his own measuring devices to assign coordinates to all of spacetime including the other windowless box, so that the two coordinate systems overlap, and this is possible using the Lorentz transform, but it is not possible using the LET transform unless both observers can somehow sense their velocity with respect to a preferred frame (or this information is provided to them by a third party). A puts coordinates x=1meter t=1second on an event that B assigns coordinates x=1E8 meters and t=1E10 seconds. Windows form in both windowless boxes, and A and B both measure their velocity realtive to the other to be v=1E6 m/s, and their distance is x_B-x_A=1E12 meters apart (motion and distances taken to be along the x-axis). Something like that. It seems to me that the two coordinate systems can't be reconciled without knowing v. Nothing happens when the windows form in the boxes? A third observer C from outside measured the relative velocities of the A and B and uses the Lorentz transform to compare events within the coordinate systems of A and B. Is that example as good as any other for you? Implicit in the coordinate systems of both A and B is the assumtion of v=0 for the observer, so let's use that same assumption for two LET observers Alpha and Beta. They will construct exactly the same coordinate systems as A and B. The only difference is that they will compute t=T/\gamma+f(x,v) where f(x,v)=-vx/c_0^2 is the synchronization of the clock at x, but the LorentzTransformers will compute t=T/\gamma-vx/c_0^2+f(x,v) where f(x,v)=0. There is no difference, and that's no accident; it is by design. That's why I'm quite confident that all of this talk about LET and SR not being empirically equivalent is missing the simple point that they ARE. My point is "look look, there is no real difference", it is only an illusion created by a choice of clock synchronization convention. The speed of light isn't really something that has been measured to be constant, and the relativity of simultaneity isn't some magical truth about physical reality; it's a consequence of one's choice of clock synchronization convention.

As for the issue of whether speed depends on your coordinate system, I already provided a numerical example. Again, assume that when I use the symbol "c" it refers only to the speed of light as measured in the preferred ether frame, even if you would use the symbol differently.

OK, I'll go back and look at that.

 

[JesseM]

Not necessarily, but there is an ambiguity with specifying a velocity as 0.8c in LET because that is a function of v and \theta.

Again, not if you use "c" the way that I said I was using it.

It may not make any difference in the end. But you said that the outside observer is the one who computes the Lorentz transform, and that's getting way more complicated than just a windowless box.

But it doesn't ultimately matter whether anyone "computes" the Lorentz transform, it will still be true that the coordinates the two observers assign to a given event will be related by the Lorentz transform, even if no one notices this fact.

]Two observers in two different windowless boxes each assigning coordinates to an event that is not within either box...

It's pretty common in discussions of SR to talk about rulers sliding arbitrarily close to each other with clocks placed at each marking, and then you can ask questions like "when the clock at the 5-meter mark of the first ruler reads 10 seconds, what marking on the second ruler is next to it at that moment, and what does the clock at that mark read"? So you can imagine something like that, with arbitarily thin boxes sliding alongside each other, and the "events" just being a clock on a marking on a ruler in one box passing arbitrarily close to a clock on a marking on a ruler in another box. Alternately, you could imagine large ghostly boxes that can pass through each other without colliding, and then the ruler markings/clocks in different boxes could occupy the same point in space. It doesn't really matter, these sorts of details aren't important since it's just a thought-experiment.

I'm not sure exactly what you're scenario is, it could be anything. I'm looking for an explicit example like: "Two windowless boxes A and B each contain an observer who manufactures his own measuring devices to assign coordinates to all of spacetime including the other windowless box, so that the two coordinate systems overlap

Yes, this will do fine.

and this is possible using the Lorentz transform

"This is possible using the Lorentz transform" is ambiguous, it's not like the observers use the Lorentz transform when constructing their measuring devices, it's just that once the devices are completed, it will be true that the coordinates that different observers assign to the same point in spacetime will be related by the Lorentz transformation.

but it is not possible using the LET transform unless both observers can somehow sense their velocity with respect to a preferred frame (or this information is provided to them by a third party).

Right, unless the observers have this knowledge of their velocity relative to the preferred frame, there's no technique they can use in constructing the measuring devices that will insure that the coordinates that different observers assign to given points in spacetime will be related by the LET transform.

A puts coordinates x=1meter t=1second on an event that B assigns coordinates x=1E8 meters and t=1E10 seconds. Windows form in both windowless boxes, and A and B both measure their velocity realtive to the other to be v=1E6 m/s, and their distance is x_B-x_A=1E12 meters apart (motion and distances taken to be along the x-axis). Something like that. It seems to me that the two coordinate systems can't be reconciled without knowing v. Nothing happens when the windows form in the boxes?

No, and like I said it's not even necessary for windows to form, it's still a true fact about nature that their coordinates are related by the Lorentz transform even if none of them are able to verify this.

A third observer C from outside measured the relative velocities of the A and B and uses the Lorentz transform to compare events within the coordinate systems of A and B. Is that example as good as any other for you? Implicit in the coordinate systems of both A and B is the assumtion of v=0 for the observer

Huh? v=0 relative to what? And are you talking about the observer who notes the coordinates that A and B assign to a particular event? How could it possibly matter what his velocity is? Questions about whether two events take place at a single point in spacetime or at different points in spacetime must have a single objective answer that is the same for all observers regardless of their velocity--otherwise you'd have different reference frames making different predictions about objective physical events like whether two asteroids will collide or miss each other! So if one observer says "at the moment the clock on the 12-meter mark of ruler A ticked 13 seconds, it occupied the same position as the clock at the 15-meter mark of ruler B which at that moment ticked 8 seconds", then every observer, regardless of velocity, regardless of what coordinate system they're using, must agree on this fact.

so let's use that same assumption for two LET observers Alpha and Beta. They will construct exactly the same coordinate systems as A and B. The only difference is that they will compute t=T/\gamma+f(x,v)

But they can't compute this if they are constructing their measuring devices in windowless boxes!

That's why I'm quite confident that all of this talk about LET and SR not being empirically equivalent is missing the simple point that they ARE.

Aether, you seem to be very confused about the meaning of "empirically equivalent" and also your other phrase "mathematically equivalent"--the way you are using these phrases seems completely incoherent, and I think you are badly misunderstanding what people like Mansouri and Sexl mean when they say the LET is empirically equivalent to SR. It's clear from the paper you sent me that they are not talking just about a different coordinate system, but a theory with some actual physical assumptions that are different from those of SR, namely the assumption of a physical substance called ether which has its own rest frame and which causes rulers to shrink and clocks to slow down when they move relative to it. To say this theory is "empirically equivalent" to SR is not to make any statements about the coordinate systems being equivalent or the measuring devices used to assign these coordinates being equivalent, it's just to note that the theory doesn't make any physical predictions which are different from those of SR. Do you understand what the difference is between an actual physical prediction and a statement which depends on your coordinate system? A lot of your previous statements, including the one I discussed earlier in this post, suggest you're pretty fuzzy on this point. Keep in mind that both the SR coordinate systems and the LET coordinate systems can be used to analyze the functioning of a set of physical measuring devices of either type--you can use the coordinate systems allowed by the LET transform to analyze the physical situation of observers who synchronize their clocks using the Einstein synchronization convention, and you will correctly predict that the matchup between physical ruler-markings and clocks of different observers will be the same as that given by the Lorentz transform; likewise, you can use the coordinate systems allowed by the Lorentz transform to analyze the physical situation of observers who all synchronize their clocks to a certain preferred frame, and you will correctly predict that the matchup between physical ruler-markings and clocks of different observers will be the one given by the LET transform. You can analyze either physical situation from the point of view of LET or SR, and you will get the same physical predictions regardless of what coordinate system you use, showing that the two theories are empirically equivalent; but the two physical situations (and the two sets of physical measuring devices they involve) themselves are different, they are not "equivalent" in any way.

Mansouri and Sexl themselves seem to understand the fact that the physical construction of SR coordinates can be done without any information exchange between observers, but the physical construction of LET coordinates cannot. That's what I think they mean when they distinguish between "system-internal synchronization" and "system-external synchronization" on pp. 499-500:

Both the Einstein procedure and the transportation-synchronization will be called system-internal synchronization. There are other such procedures, such as shaft synchronization [23-26], and the problem to be solved here is the equivalence of the various synchronization procedures. This problem will be solved in part in this paper.

System-internal methods of synchronization are not the only conceivable ones. In section 3 we shall discuss in detail an alternative procedure belonging to the class of system-external synchronization methods. Here one system of reference is singled out ("the ether system") and clocks in all systems are synchronized by comparing them with standard clocks in the preferred system of reference. Infinitely many inequivalent system-external procedures are possible. Among these, one is of special interest: A convention about clock synchronization can be chosen that does maintain absolute simultaneity. Based on this convention an ether theory can be constructed that is, as far as kinematics is concerned (dynamics will be studied in a later paper in this series) equivalent to special relativity. In this theory measuring rods show the standard Fitzgerald-Lorentz contraction and clocks the standard time dilation when moving relative to the ether. Such a theory would have been the logical consequence of the development along the lines of Lorentz-Larmor-Poincaré. That the actual development went along different lines was due to the fact that "local time" was introduced at the early stage in considering the covariance of the Maxwell equations.

This quote also shows, as I said before, that Mansouri and Sexl are considering a theory which actually involves different physical assumptions than SR--the existence of an ether--rather than just a different coordinate system for analyzing the same physical theory. And again, to say this is "empirically equivalent" is just to note that this additional assumption doesn't lead to any new predictions about coordinate-invariant physical facts--if you analyze a given physical scenario, you'll get the exact same physical predictions.

 

[pmb_phy]

This thread has certainly run on for a while.

Aether - You wrote a lot of things and then implied they were valid definitions that came from somewhere. Is the source of these definitions Aether himself?

To be honest I'm not 100% sure of what this thing is that you call Lorentz theory.

You claimed

..are empirically equivalent systems for interpreting local Lorentz symmetry.

You'll have to explain to me what Lorentz theory" is before I can address that appropriately. However, that said, if "Lorentz theory" is what I think it is (MMX experiment null results) then this Lorentz theory fails at attempting to describe all phenomena. If it fails at anything then its a bad theory. Nobody cares that it can work for a subset of observerations (Lorentz symmetry? What is that an observation of?)

You also stated the following

Why isn't "relativity without the aether" fairly described by the term "pseudoscience"?

Just because theory A does not assume the existence of "stuff Q" it doesn't make the theory A a pseudoscience. I see no logic which would allow one to make this jump. I see it being quite possible to have an ether as it was originally defined (that which fills all of space). It was just and then hijacked by EM later on as "ether = the medium through which EM waves propagate." But with no ether required there is no reason to assume that it doesn't exist. Such a jump in logic would be pseudoscience. However if one insists that it stays in relativity because it is required then it violates Occam's razor.

Unlike the ether, though, the sea of virtual particles is not thought to have its own natural rest frame, so it doesn't violate Lorentz symmetry even in an unobserved way.

Did you, for some reason, assume that I thought that there was a rest frame for this sea? If so then how did you reach the conclusion that this is what I assumed? I do not assume that. I never did in fact. In fact I like this example because of the fact that there is no natural rest frame for such a sea of virtual particles.

Pete

 

[JesseM]

Did you, for some reason, assume that I thought that there was a rest frame for this sea? If so then how did you reach the conclusion that this is what I assumed? I do not assume that. I never did in fact. In fact I like this example because of the fact that there is no natural rest frame for such a sea of virtual particles.

No, I didn't assume you thought that, but since you compared this sea to the ether I thought it was important to point out this very important difference between them, so no one would get confused and think that the virtual particle sea lends support to the ether-based idea of a preferred frame.

 

[Aether]

Aether - You wrote a lot of things and then implied they were valid definitions that came from somewhere. Is the source of these definitions Aether himself?

To be honest I'm not 100% sure of what this thing is that you call Lorentz theory.

You claimed
You'll have to explain to me what Lorentz theory" is before I can address that appropriately. However, that said, if "Lorentz theory" is what I think it is (MMX experiment null results) then this Lorentz theory fails at attempting to describe all phenomena. If it fails at anything then its a bad theory. Nobody cares that it can work for a subset of observerations

Mansouri-Sexl define an ether theory (as a popular test theory of local Lorentz invariance), and I'm working from that. My questions, interpretations of what they are saying, and attempts to work through the math are coming from me. I expect half of that to get swept away, but Mansouri-Sexl should be reliable. MMX experiments verify the rotation invariance component of Lorentz symmetry, and that sweeps away some ether theories, but LET is what is left after all of that. It fails at nothing.

(Lorentz symmetry? What is that an observation of?)

That's what most people think that SR is an observation of. I've been collecting lots of papers on experiments to test local Lorentz invariance, and I don't recall finding statements in any of them saying "and this proves SR once again" because they are scientific papers, and (I am beginning to suspect) SR is merely pseudoscientific.

Just because theory A does not assume the existence of "stuff Q" it doesn't make the theory A a pseudoscience. I see no logic which would allow one to make this jump. I see it being quite possible to have an ether as it was originally defined (that which fills all of space). It was just and then hijacked by EM later on as "ether = the medium through which EM waves propagate." But with no ether required there is no reason to assume that it doesn't exist. Such a jump in logic would be pseudoscience.

Coordinate independent geometry is scientific, but SR and LET are empirically equivalent coordinate systems which, when taken separately, typically lead people to make false claims such as "the constancy of the speed of light is proven by experiments". The speed of light is constant in SR, but it is variable in LET.

However if one insists that it stays in relativity because it is required then it violates Occam's razor

I don't think that it is required for doing engineering work so long as a locally preferred frame remains undetectable, but where its absence leads to wrong answers then it should be restored (or SR and LET can both be thrown out, and coordinate independent geometry will be what remains).

p.s. If I'm wrong about any of this, then I expect you guys/girls to beat it out of me. That's why I come here, because I have faith in you.

 

[pmb_phy]

Mansouri-Sexl define an ether theory (as a popular test theory of local Lorentz invariance), and I'm working from that. My questions, interpretations of what they are saying, and attempts to work through the math are coming from me. I expect half of that to get swept away, but Mansouri-Sexl should be reliable. You can download their papers here for the next few hours (8MB): http://69.13.172.13/Mansouri&Sexl.pdf. MMX experiments verify the rotation invariance component of Lorentz symmetry, and that sweeps away some ether theories, but LET is what is left after all of that. It fails at nothing.[/qupte]Are you saying that you can't tell me what this "Lorentz Ether Theory" is in one paragraph??

That's what most people think that SR is an observation of...

I wasn't suggesting anything by that question since I've yet to know what this theory you're speaking of is.

Coordinate independent geometry is scientific, but SR and LET are empirically equivalent coordinate systems which, when taken separately, typically lead people to make false claims such as "the constancy of the speed of light is proven by experiments". The speed of light is constant in SR, but it is variable in LET.

That is the most incorrect statement that I've seen posted on the internent in months. Where did you get this idea from?

I don't think that it is required for doing engineering work ...

Occam's razor is more of a philosophy than anything else and it is not always clear how it should be taken in a given application. That's why you'll never see me invoke it.

p.s. If I'm wrong about any of this, then I expect you guys/girls to beat it out of me. That's why I come here, because I have faith in you.

That is a false assumption. It takes years of scientific training to learn to become a scientist. Sometimes people will come here and get hung up or confused on the most simplest of points and assume that there is something wrong with science today because they have "bewildered" us in some way. Assuming that is wrong because some people just don't care enough to get a point through to you. There could be a million false assumptions in that person's mind that we are just too tired to want to weed through when there are just so many better ways to spend our times.

E.g. This is not a topic I'd want to continue with. I'm into something much more interesting to me. I.e. the language of the Hopi Indian's has no word for time, i.e. it has been said by an expert in linguistics that --

In particular, he has no general notion or intuition of time as a smooth flowing continuum in which everything proceeds at an equal rate, out of the future, through a present, into a past; or, in which, to reverse the picture, the observer is being carried in the stream of duration continuosly away from a past and into a future.

So I'd love to spend all my time now on trying to answer this question "How does one convert a special relativity text from English to the Hopi language?".

Pete

Pete

 

[Aether]

That is the most incorrect statement that I've seen posted on the internent in months. Where did you get this idea from?

The idea that the constancy of the speed of light can't be proven by experiment?

That is a false assumption. It takes years of scientific training to learn to become a scientist. Sometimes people will come here and get hung up or confused on the most simplest of points and assume that there is something wrong with science today because they have "bewildered" us in some way. Assuming that is wrong because some people just don't care enough to get a point through to you. There could be a million false assumptions in that person's mind that we are just too tired to want to weed through when there are just so many better ways to spend our times.

E.g. This is not a topic I'd want to continue with. I'm into something much more interesting to me. I.e. the language of the Hopi Indian's has no word for time, i.e. it has been said by an expert in linguistics that --
So I'd love to spend all my time now on trying to answer this question "How does one convert a special relativity text from English to the Hopi language?".

OK, but I didn't say that there was anything wrong with science, only with relativity.

 

[JesseM]

I wasn't suggesting anything by that question since I've yet to know what this theory you're speaking of is.

Aether seems not to be describing an alternate theory at all, but just a different set of coordinate systems for describing a spacetime which obeys exactly the same laws as the one in SR. As in relativity, each observer can assign coordinates to events using a network of rulers and clocks, but instead of each observer synchronizing their clocks using the assumption that light travels at c in their own rest frame, only one observer synchronizes his clocks this way, and all other observers synchronize their clocks in such a way that their definition of simultaneity agrees with that preferred observer. If x and t are the coordinates assigned to an event by the preferred observer, then another observer moving at v along his access will assign the same event coordinates x' and t', with the coordinates related by the following "LET transformation":

x&#039; = (x - vt)/\sqrt{1 - v^2/c^2}
t&#039; = t \sqrt{1 - v^2/c^2}

You can compare this with the Lorentz transformation:

x&#039; = (x - vt)/\sqrt{1 - v^2/c^2}
t&#039; = (t - vx/c^2) / \sqrt{1 - v^2/c^2}

Most people who use the term "Lorentz ether theory" would define the theory as saying there's an actual physical substance called "ether" and that the preferred observer should be at rest with respect to this ether, but Aether seems not to think this assumption is important, so he isn't making any new physical assumptions at all, he's just using a different set of coordinate systems. You can see, though, that if there was such a thing as ether, and all rulers moving relative to that ether shrunk by \sqrt{1 - v^2/c^2} while all clocks moving relative to that ether had their ticks extended by 1/\sqrt{1 - v^2/c^2}, then if all observers synchronized their clocks using the Einstein synchronization procedure, different observers' coordinate systems would be related by the Lorentz transform and there'd be no way to actually detect which frame was the ether's rest frame, so such a universe would be empirically equivalent to one where there is no ether but the laws of physics exhibit Lorentz-symmetry. I elaborated on this empirical equivalence a little more in the first two paragraphs of post #36.

 

[Aether]

Aether seems not to be describing an alternate theory at all, but just a different set of coordinate systems for describing a spacetime which obeys exactly the same laws as the one in SR. As in relativity, each observer can assign coordinates to events using a network of rulers and clocks, but instead of each observer synchronizing their clocks using the assumption that light travels at c in their own rest frame, only one observer synchronizes his clocks this way, and all other observers synchronize their clocks in such a way that their definition of simultaneity agrees with that preferred observer. If x and t are the coordinates assigned to an event by the preferred observer, then another observer moving at v along his access will assign the same event coordinates x' and t', with the coordinates related by the following "LET transformation":

x&#039; = (x - vt)/\sqrt{1 - v^2/c^2}
t&#039; = t \sqrt{1 - v^2/c^2}

You can compare this with the Lorentz transformation:

x&#039; = (x - vt)/\sqrt{1 - v^2/c^2}
t&#039; = (t - vx/c^2) / \sqrt{1 - v^2/c^2}

Most people who use the term "Lorentz ether theory" would define the theory as saying there's an actual physical substance called "ether" and that the preferred observer should be at rest with respect to this ether, but Aether seems not to think this assumption is important, so he isn't making any new physical assumptions at all, he's just using a different set of coordinate systems. You can see, though, that if there was such a thing as ether, and all rulers moving relative to that ether shrunk by \sqrt{1 - v^2/c^2} while all clocks moving relative to that ether had their ticks extended by 1/\sqrt{1 - v^2/c^2}, then if all observers synchronized their clocks using the Einstein synchronization procedure, different observers' coordinate systems would be related by the Lorentz transform and there'd be no way to actually detect which frame was the ether's rest frame, so such a universe would be empirically equivalent to one there is no ether but the laws of physics exhibit Lorentz-symmetry. I elaborated on this empirical equivalence a little more in the first two paragraphs of post #36.

That seems to be a fair summary, thanks.

 

[pmb_phy]

... but instead of each observer synchronizing their clocks using the assumption that light travels at c in their own rest frame, only one observer synchronizes his clocks this way, and all other observers synchronize their clocks in such a way that their definition of simultaneity agrees with that preferred observer. ...

That's nuts! There is no meaning to synchronizing one clock! I knew there was a good reason I dropped out of this thread!

Pete

 

[JesseM]

... but instead of each observer synchronizing their clocks using the assumption that light travels at c in their own rest frame, only one observer synchronizes his clocks this way, and all other observers synchronize their clocks in such a way that their definition of simultaneity agrees with that preferred observer. ...

That's nuts! There is no meaning to synchronizing one clock! I knew there was a good reason I dropped out of this thread!

Pete

What are you talking about? I said clocks plural, in all 3 instances that you quoted above. The whole basis of SR is the idea of each observer synchronizing their clocks using light signals, it's right there in Einstein's original 1905 paper.

 

[Aether]

That is the most incorrect statement that I've seen posted on the internent in months. Where did you get this idea from?

I would like to see you try and refute that. However, the main purpose for this post is to ask that you delete the link to my website from your post. I only intended for that to remain visible long enough for you to download the paper if you were interested.

 

[Aether]

Both theories postulate Minowski geometry. However, SR makes no additional postulates, defining everything else from the geometry.

However, a LET requires at least one additional postulate about absolute simultaneity, since that cannot be defined from the geometry.

This sounds like a potentially convincing argument, Hurkyl. I have never seen SR described that way anywhere else though; do you know of a source that teaches SR from that perspective? My objection to "SR without the aether" may arise entirely from the difference between what you wrote and the "two postulates" of SR. Am I likely to find statements like "experiments prove that the speed of light is a constant" in such a text?

 

[DrGreg]

If you assume SR is correct, you can come up with some expressions for momentum and energy relative to LET co-ordinates by application of the transform equations. But if you ignore SR and try to calculate momentum and energy some other way, how do you find the answer? How, for example, do you prove that, relative to the ether, the relativistic form p=\gamma_u m u should be used instead of p= m u?

I have today at long last been able to view of copy of the Mansouri-Sexl papers. The conclusion of paper I is

"A theory maintaining the concept of absolute simultaneity can be obtained ... which is ... empirically equivalent to special relativity, as least as far as kinematics is concerned." (My emphasis)​

I think that supports my point about the difference between kinematics and dynamics.

They also make the point that Einsteinian clock synchronization is the same as synchronization via ultraslow clock transport, in the context of SR and what we have been calling "LET".

By the way, I'm no longer sure whether it is correct to describe their transform as "Lorentz Ether Theory" -- there may be several competing ether theories in circulation.

I think I will have more to say once I've read all three papers in more detail.

 

[Hurkyl]

I have never seen SR described that way anywhere else though; do you know of a source that teaches SR from that perspective?

No -- my perspective is pretty much a synthesis of everything I've leared (from a wide variety of sources), and my working out details on my own as well.

There has to be a textbook on Minowski geometry around someplace, though -- I don't know of any, though.

 

[pmb_phy]

I would like to see you try and refute that. However, the main purpose for this post is to ask that you delete the link to my website from your post. I only intended for that to remain visible long enough for you to download the paper if you were interested.

At the time I wrote that assertion it was at a time when I made a false assumption in that the term "LET" of yours meant something other than what I assuimed it meant. I therefore retract my assertion since I don't want to read that article on LET that you linked to. It may be more widely used than that paper

When you explained to me what you meant by LET I then chose to bow out of this conversation since I'm not in the mood for looking into what appears to be bad physics. Please don't try to analyze my statement here because I have nothing against the notion of looking more deeply into what "appears" to be wrong, since it could very well be right. But I have to make choices on how I spend my time. The problem is sitting in this chair with my back in so much pain. If you're curious as to what my back looks like after the removal of the herniated disk then see the photo in the first post at - http://ubb-lls.leukemia-lymphoma.org/ubb/Forum14/HTML/001089.html

I still do physics now but only in those areas I love. At this time I have zero interest into looking into this LET thing. Hence the reason I bowed out of this conversation. I only came back because I neglected to state that because something is not science it doesn't mean that it should be called pseudoscience. Religion is not science but it'd be wrong to call religion pseudoscience. A wrong theory is not pseudoscience simplyt because its wrong. It must satisfy other criteria which lies beyond the science itself and lies within the minds of the holders of the theory. Its a weird thing and too drenched in debateable terminology to want to get into. There's a book called "Science and Unreason" by Radner and Radner. It was required reading in my philosophy of science course in college. I highly recommend this text for those who wish to learn what pseudoscience is.

As far as removing that link - No can do. First off you shouldn't post in open forum something which you don't want to keep there permenently. It requires me to do things like this where you want me to dig through old posts and delete something I quoted. I did look into removing the link but its too late. A post can only be edited for a day or two.

Pete

 

[DrGreg]

To anyone who is interested: I have found a one-page summary of the Mansouri-Sexl framework that Aether refers to here: http://relativity.livingreviews.org/Articles/lrr-2005-5/articlesu9.html , on the "Living Reviews in Relativity" website. (The notation used in the summary is not quite the same as the notation that M&S use themselves.)

The framework is to interpret the results of experiments testing the accuracy of Special Relativity. It assumes there is at least one frame (the "ether frame") in which the speed of light is isotropic and takes the view that the transformation to other frames is an unknown linear transform, with velocity-dependent coefficients that are to be determined experimentally. The results of experiments that had been performed before publication in 1977 are then analysed to determine how close the coefficients must be to the Lorentz transform.

In the course of their analysis, M&S make the point that there is an arbitrary choice of clock synchronization to be made. Their method effectively ignores any effects that are due to the choice of synchronization.

The particular transformation that Aether has been discussing in this forum (which we have been describing as "LET") is one that can be implemented as "synchronization to the ether" (if you have chosen an ether) but which is, essentially, mathematically equivalent to Special Relativity. This is really the point - the two formulations come from different sets of assumptions but come to essentially the same conclusion, in the sense that one formulation can be mathematically transformed into the other. The two "theories" stand and fall together - they're either both true or both false.

If Aether is hoping to find something to favour an ether theory over SR, it would have to take the more generalised form discussed by Mansouri-Sexl rather than the particular form that has been quoted.


References:

Mansouri, R., and Sexl, R.U., “A test theory of special relativity. I - Simultaneity and clock synchronization”, Gen. Relativ. Gravit., 8, 497-513, (1977).

Mansouri, R., and Sexl, R.U., “A test theory of special relativity. II - First Order Tests”, Gen. Relativ. Gravit., 8, 515-524, (1977).

Mansouri, R., and Sexl, R.U., “A test theory of special relativity. III - Second Order Tests”, Gen. Relativ. Gravit., 8, 809-814, (1977).

Bluhm, R., "Breaking Lorentz Symmetry", Physics World, March 2004.