Relativity without the aether: pseudoscience?

[Aether]

Given the Lorentz metric, the one-way speed of light is a mathematical consequence of the Special Relativistic definition of an inertial reference frame.

OK, it is a postulate, not determined by experiment. If that is what you mean by this, then I agree.

You agree that the Lorentz metric is empirically verifiable, correct?

Essentially yes, up to the point that many physicists are still looking for violations.

Then so must the one-way speed of light in a coordinate chart that is one of Special Relativity's inertial reference frames.

Empirically verifiable, Hurkyl? No, I don't see that yet. I can see that it's in the Lorentz transform \Lambda_\nu^\mu, not in the LET transform T_\nu^\mu, but what has that to do with the metric \eta_{\mu \nu} per se?

Maybe this is a clue to the psychology of those who cling to aether theories? Do they believe that coordinate charts are physical things, rather than simply a choice we make when modelling a problem?

And maybe this is a clue to the psychology of those who cling to SR as well? That was roughly my point in starting this thread.

 

[Aether]

If you insist on the axiom that says that there is only one frame that can use absolute frame coordinates, then I object. I object to any axiom that has no useful consequences.

The freedom to reset clocks in the universe with arbitrary synchronizations is widely regarded as legitimate physics.

I don't insist on such an axiom, no. I am saying that such a postulate is not empirically different from the SR postulate that the speed of light is a constant in all inertial frames; that an impartial observer, not from our culture, would have no reason (today) to prefer one over the other; and that being able to see the world from both perspectives is better than choosing either one arbitrary extreme or the other. However, if someone here actually proves that SR is empirically right and LET is empirically wrong then that's that.

 

[Hurkyl]

And maybe this is a clue to the psychology of those who cling to SR as well?

If you recall, I said very distinctly:

To even begin to say something like "the one-way speed of light is isotropic", it requires one to specify a coordinate chart.

Coordinare charts are nonphysical choices.

You're thinking about the fact that, among all possible rectilinear coordinate charts we could use, SR chooses to define the orthogonal ones as the inertial reference frames.

(Though I've modified the emphasis)

OK, it is a postulate, not determined by experiment.

No, it is not a postulate, it is a definition.

I repeat that a coordinate chart is not a physical object. One does not need to make postulates, one can write down a precise definition and say "in my theory, the words 'inertial reference frame' absolutely, positively, unequivocally means this:".

Now, one might ask the question if there is any such thing satisfying the definition, but let me remind you that even in a LET, you can take this definition to produce a coordinate chart in which the one-way speed of light is isotropic.

Let me say that again:

In a Lorenz Ether theory,
the Special Relativistic definition of "inertial reference frame"
yields a coordinate chart
in which the one-way speed of light is constant.

Of course, since this chart was chosen to satisfy the SR definition of "inertial reference frame" and not the LET definition of "inertial reference frame", there is no reason to expect this coordinate chart to be an LET inertial reference frame (and generally it will not be).

The point stands -- even in a LET, you can prove that SR-inertial reference frames have a constant one-way speed of light.


You focus too much on coordinates, as if they're a fundamental thing -- it's the geometry that matters.

Both theories let you work in whatever coordinates you like. The difference between SR and LET is that SR postulates nothing more than the geometry. Things like "inertial reference frame" are simply defined from the geometry.

Whereas a LET has to make an additional postulate about absolute simultaneity: it cannot be defined from the Minowski geometry alone.

Let me repeat this:

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.


Actually, as I understand it, LETs do not postulate Minowski geometry -- they postulate some other background geometry, postulate some properties of an aether, and then derive the Minowski geometry, or alternatively, let the experimental verification of Minowski geometry constrain the properties of their aether.

 

[Aether]

You focus too much on coordinates, as if they're a fundamental thing -- it's the geometry that matters.

What is the geometrical difference between SR and LET? Or, do you operate in a coordinate independent geometry where there is no SR & LET per se? If so, how do I get there from here?

 

[Perspicacious]

Relativists don't disallow arbitrary clock synchronizations

I don't insist on such an axiom, no. I am saying that such a postulate is not empirically different from the SR postulate that the speed of light is a constant in all inertial frames;

I gave three links to derivations of SR that don't use the constancy of light postulate. Doesn't that prove that both axioms, including yours, are not required?

an impartial observer, not from our culture, would have no reason (today) to prefer one over the other;

Why aren't you holding out the option of rejecting both? Or do you enjoy wasting everyone's time?

and that being able to see the world from both perspectives is better than choosing either one arbitrary extreme or the other.

I reject both extremes. The axiom of a luminiferous aether fluid is a religious belief without scientific consequences.

However, if someone here actually proves that SR is empirically right and LET is empirically wrong then that's that.

As I've already illustrated with The Santa-Reindeer Postulate, LET is SR with an added, meaningless assumption with no observable consequences.

 

[JesseM]

The points in his article would apply to any theory that posits a special reference frame (for example, a theory that says there is only one frame where the speed of light is 'really' c in all directions) and yet does not make any predictions about the results of actual experiments which are different from those of SR (so all observers will measure the speed of light to be c in all directions, even if this is explained as a faulty measurement because their clocks are not ticking the 'correct' time and their rulers are not reading the 'correct' length).

I'm not sure what you mean by the statement in parenthesis.

Well, think of it this way. Suppose we live in a universe governed by purely Newtonian laws, where light always moves at speed c with respect to the rest frame of the aether, and in other frames it is actually possible to measure your velocity relative to the aether by seeing how fast light moves in one direction vs. the other using ordinary rulers and clocks, just like in our actual universe we could measure our velocity relative to the atmosphere by measuring how fast sound waves move in one direction vs. the other. In this hypothetical universe we have two observers, A who is at rest with respect to the aether, and B who is moving at velocity v with respect to the aether. We give both of them a set of rulers and clocks which they use to define their own coordinate systems, but as a joke, observer B is given special gag rulers that are shorter than normal by a factor of \sqrt{1 - v^2/c^2}, and gag clocks whose ticks are longer than normal by a factor of 1/\sqrt{1 - v^2/c^2}. What's more, we tell observer B that he is the one at rest with respect to the aether, so that he can synchronize his clocks using the assumption that light travels at the same speed in both directions relative to himself. The result will be that the coordinate systems of observer A and observer B will be related by the Lorentz transformation equation, no? And that both will measure light to move at c in all directions relative to themselves, using their own rulers and clocks? But isn't it true that in this universe, observer A's frame is the only one where light "really" moves at c in both directions, while B's measurement was faulty because his clocks are not ticking the "correct" time and their rulers are not reading the "correct" length?

Along the same lines, a believer in the Aether could believe that the real situation is pretty close to this, except that instead of having to give any observer rulers and clocks which we know to work incorrectly, it's just a property of the laws of nature that rulers moving at v relative to the aether will naturally shrink by \sqrt{1 - v^2/c^2} and clocks moving at v relative to the aether will naturally have their ticks extended by 1/\sqrt{1 - v^2/c^2}. If this was true there might be no empirical way to decide who was really at rest with respect to the aether and thus whose rulers and clocks were really measuring correctly, but one might believe there was some objective truth about this nonetheless (just like in some interpretations of QM, there is an objective truth about the simultaneous position and momentum of every particle even if there is no way to measure this empirically).

I don't know exactly what you mean by "LET", does it fit both these criteria?

I am using "LET" as a label the ether transformation equations from M&S-I (see my post #92 in the "consistency of the speed of light" thread for details); this may not be exactly what anyone else, particularly H.A. Lorentz, means by LET.

OK, but as Hurkyl says, the choice of coordinate systems is just a convention, simply choosing a different coordinate system does not give you a different theory of physics. I had assumed that LET involved some hypothesis about there being a particular frame which is actually the rest frame of the aether, and that rulers moving relative to this frame shrink and clocks slow down, even if it cannot be determined experimentally which frame this is. Was I misunderstanding?

That quote doesn't say that aether theories don't exhibit local Lorentz-invariance, it just says that it is an unexplained "happenstance" if they do. In aether theories you need a multitude of separate coincidences to explain why every new phenomena happens to exhibit lorentz-invariance, and you have no reason to predict that new phenomena will exhibit it, whereas SR makes a clear prediction that all phenomena must exhibit local lorentz-invariance, and gives a single conceptual explanation for why they all do.

Is this how you would explain the essential differences between the SR and LET transformation equations (from post #92 referenced above)? It seems like a very simple choice of synchronization convention to me when I compare those two sets of equations.

Again, simply choosing a different coordinate system does not give you a different theory; without some physical assumption about there being a particular frame that is "objectively" special in some way (because it is the rest frame of the aether, perhaps), this is just the theory of SR described in terms of a different choice of coordinates.

 

[Perspicacious]

Here's the first two lines from a paper from Kostelecky & Mewes for example: http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:hep-ph/0111026 "Lorentz violation is a promising candidate signal for Planck-scale physics. For instance, it could arise in string theory and is a basic feature of noncommutative field theories...". So, when I say "yet" I simply mean that I am aware of many physicists who expect to find violations eventually.

A violation of Lorentz invariance wouldn't prove that an aether exists. There are trivial models of spacetime where an absolute frame of reference exists without a material aether fluid.
http://groups.google.com/group/sci.physics.research/msg/e19ac8581a6148f2

Simultaneity is relative in the Lorentz transformation, but absolute simultaneity is maintained with a variable speed of light in LET transformation. Both are equally valid.

It's not that easy. Clocks can be resynchronized in Galilean relativity so that events which are simultaneous in one frame are not simultaneous in another frame. Does that mean that instantaneousness is an option in a Newtonian universe?

 

[Chronos]

No. That is naive and thoroughly disproven. You are confusing the concept of simultaneity with the concept of inertial reference frames. You cannot calibrate clocks that way.

 

[JesseM]

No. That is naive and thoroughly disproven. You are confusing the concept of simultaneity with the concept of inertial reference frames. You cannot calibrate clocks that way.

Are you responding to the quote "Clocks can be resynchronized in Galilean relativity so that events which are simultaneous in one frame are not simultaneous in another frame"? You are certainly free to calibrate clocks any way you like, even in a Newtonian universe. For example, I could give a bunch of observers their own sets of rulers and clocks, and tell each one "if your velocity is v relative to the rest frame of the atmosphere, then any two of your clocks lying along your direction of motion and a distance d apart should be set so that the front clock is behind the back clock by vd/(s^2 - v^2), where s is the speed of sound." Then voila, each observer will have a different definition of simultaneity, and each observer will measure sound to travel at the same coordinate speed in both directions, regardless of his velocity relative to the atmosphere (so you could also get this definition of synchronization by telling each observer to synchronize their clocks using the assumption that sound waves travel at the same speed in all directions in their own frame).

 

[Aether]

Why aren't you holding out the option of rejecting both? Or do you enjoy wasting everyone's time? I reject both extremes.

I offered that as my preferred option in post #11. If everyone here agrees with that, then that would be an interesting result.

The axiom of a luminiferous aether fluid is a religious belief without scientific consequences.

Who said anything about a luminiferous aether fluid? We're talking about clock synchronization conventions where aether=absolute syncrhony, and SR=Einstein synchrony.

As I've already illustrated with The Santa-Reindeer Postulate, LET is SR with an added, meaningless assumption with no observable consequences.

LET picks up one assuption, and drops one assumtion for a net zero of assumtions.

 

[Aether]

OK, but as Hurkyl says, the choice of coordinate systems is just a convention, simply choosing a different coordinate system does not give you a different theory of physics. I had assumed that LET involved some hypothesis about there being a particular frame which is actually the rest frame of the aether, and that rulers moving relative to this frame shrink and clocks slow down, even if it cannot be determined experimentally which frame this is. Was I misunderstanding?

I think that describing the difference between SR and LET as a simple choice of coordinate systems is probably accurate.

Again, simply choosing a different coordinate system does not give you a different theory; without some physical assumption about there being a particular frame that is "objectively" special in some way (because it is the rest frame of the aether, perhaps), this is just the theory of SR described in terms of a different choice of coordinates.

SR & LET are empirically equivalent theories, so I suppose that means that they aren't different theories at all but rather different coordinate systems. Nevertheless, teaching one coordinate system to the exclusion of the other leads to widespread and firmly held superstitious beliefs about physical reality: for example, that the speed of light is actually a constant, and that simultaneity is actually relative.

 

[Hurkyl]

What is the geometrical difference between SR and LET?

Once you get to Minowski geometry, there isn't one, but some physical concepts have different definitions.

E.G. in 2-D space, a line of simultaneity in SR is defined by constructing a line perpendicular to the observer's velocity vector. But, in LET, it's defined by being parallel to the postulated "absolute" line.

Of course, in LET, you can still talk about SR-simultaneity, since it's just a geometric definition. And in SR, if you pick out a special line, you could talk about LET-simultaneity, as if the special line is the "absolute" line.

I am of the understanding, though, that LET doesn't really start with Minowski geometry -- it starts with something more Newton like, but postulates that the aether conspires so that things look like a Minowski geometry.

And that is the reason why SR is preferred over LET's: SR's definitions of things like "simultaneous" are geometric, and can be determined by experiment. LET's at least have this additional assumption about what is "absolutely simultaneous" that cannot be defined purely from geometry, and of which no experiment is known that can determine if two things really are absolutely simultaneous.

Or, do you operate in a coordinate independent geometry where there is no SR & LET per se?

That's the point of Minowski geometry.

Just like Euclidean geometry, you can do it analytically (with coordinates), but it is also possible to do Minowski geometry synthetically.

For example, you can still study triangles, and do trigonometry in Minowski geometry. (Of course, there are a lot of cases depending on which sides are space-like and which are time-like. Light-like lines segments are annoying because they have length zero)

For example, in a right-triangle with one space-like leg of length x, and one time-like leg of duration y, you can compute s² = y² - x². If s² is positive, then the hypotenuse has duration |s| and is timelike. Otherwise, it has length |s| and is spacelike.

In a 1+1 space-time plane, the Minowski analog of circles are the hyperbolas with null vectors as asymptotes. Using this, you can introduce trigonometry, but it uses hyperbolic functions (like sinh) instead of the circular functions (like sin). Lorentz boosts are the analog of rotations, since they "rotate" along these hyperbolas.


Of course, it's hard to draw pictures, because your paper is Euclidean -- unfortunately, it seems that trying to draw Minowski geometry on Euclidean paper does single out a special class of (Minowski-)orthogonal coordinate charts -- the ones whose coordinate axes are drawn as Euclidean-orthogonal lines. So, there are essentially different ways of drawing the Minowski plane on Euclidean paper -- if their "special class" of orthogonal charts are different, then you'll get differently-proportioned Euclidean pictures, despite the fact they're both the same Minowski shape.

And while you can physically do the most natural Euclidean transformations to a sheet of paper (translation, reflection, and rotation), you cannot do all of the most natural Minowski transformations in these pictures: (translation, reflection, and Lorentz boost) -- translation is fine, the results of most Minowski reflections would be different than Euclidean reflections, and you simply can't do a Lorentz boost to a sheet of paper.

 

[Aether]

That's the point of Minowski geometry.

Great! Then that's where I want to go, and it underlines the point of this thread. There is a point in their training where physicists must shed SR per se, and it is a mistake to equate SR with physical reality?

LET's at least have this additional assumption about what is "absolutely simultaneous" that cannot be defined purely from geometry, and of which no experiment is known that can determine if two things really are absolutely simultaneous.

It isn't an "additional" assumption, it is an alternate assumption taking the place of the constancy of the speed of light. Which assumption would an impartial observer, not from our culture, choose? Is it not a coin toss (today)?

 

[Hurkyl]

I should warn you that I'm a mathematician, not a physicist!

 

[Hurkyl]

Oh, here's another nifty thing:

You may recall that there is a sort of "map" between Euclidean geometry and the complex numbers.

For example:

The length of the line segment from p to q is given by |q - p|, where |z|^2 := z \bar{z}.

Multiplication by e^{i \theta} is the same thing as rotating (counterclockwise) about the origin by the angle θ.

Addition by z is the same thing as translation by the vector from the origin to z.



Well, there is a number system called the "hyperbolic numbers" that plays the same role for Minowski geometry. It has the hyperbolic unit h, which satisfies h² = 1. (As opposed to i² = -1 of the complex numbers)

The hyperbolic numbers aren't as nice as the complexes: for example, if x is a real number, then it doesn't have a hyperbolic square root if x<0, but if x>0, it has four hyperbolic square roots: √x, -√x, h√x, -h√x. In particular, 1 has four square roots, 1, -1, h, and -h.

You can't divide by all hyperbolic numbers either: for example, 1+h is a "null" hyperbolic number, and you cannot divide by it.

But these numbers do serve the same role as the complexes do. For example, the metric ds² along the line segment from p to q is given by ds²=|p-q|², where |x + hy|^2 = (x + hy) (x + hy)^* = (x + hy) (x - hy) = x^2 - y^2). (I use * to denote hyperbolic conjugation because I can't remember how to make an overbar go over the whole factor)

Multiplication by e^{h\beta} is a Lorentz boost fixing the origin. (the Minowski analog of rotating about the origin)

Addition by z is the same thing as translation by the vector from the origin to z.


(1+h is "null" because |1+h|²=(1+h)(1-h)=1-1=0)


And we have the hyperbolic Euler's identity, as well as the circular one:
e^{i\theta} = \cos \theta + i \sin \theta
e^{h\beta} = \cosh \beta + h \sinh \beta

 

[Perspicacious]

In a Newtonian universe

I could give a bunch of observers their own sets of rulers and clocks, and tell each one "if your velocity is v relative to the rest frame of the atmosphere, then any two of your clocks lying along your direction of motion and a distance d apart should be set so that the front clock is behind the back clock by vd/(s^2 - v^2), where s is the speed of sound." Then voila, each observer will have a different definition of simultaneity, and each observer will measure sound to travel at the same coordinate speed in both directions, regardless of his velocity relative to the atmosphere.

Or, more simply, in a Newtonian universe, clocks can be reset by a fixed amount in every moving frame such that

x' = x-vt
t' = (t - vx/s^2)/(1-v^2/s^2)

where s' = (s^2-v^2)/s is the speed of sound in the frame that moves at speed v wrt the atmosphere.

 

[JesseM]

SR & LET are empirically equivalent theories, so I suppose that means that they aren't different theories at all but rather different coordinate systems.

Not necessarily--like I said, you could have a theory that made no predictions different from relativity, but which assumed there actually was an unobservable physical entity called "the ether" which had its own rest frame. If LET makes no such assumption, why is "ether" in the name at all?

Nevertheless, teaching one coordinate system to the exclusion of the other leads to widespread and firmly held superstitious beliefs about physical reality: for example, that the speed of light is actually a constant, and that simultaneity is actually relative.

The Lorentz transform is the most physical one, since the laws of physics will have the same form in every frame, and each observer can construct a physical version of this coordinate system in isolation (using rulers and clocks inside a windowless box), without having to know his velocity relative to some "special" observer. Neither of these would be true of other coordinate transforms.

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.

 

[pmb_phy]

Special relativity is physics according to the definition of physics whereas adherence to the aether is a religious belief that doesn't generate any physics.

The OP did not speak of ether theory. The OP spoke only of Lorentz ether theory up until this point (and I have yet to read past this). However it was Lorentz himself who believed in an ether until the day that he died. I'm not sure what his thoughts were on the matter after that day.

It should be known that Einstein never proved there was no ether. What he proved was that if there is an either than it plays no role in the laws of physics. You can call infnite space in which there is no matter in the normal sense as a region of space filled with virtual particles. This "sea" of virtual particles are what a few physicists today refer to as the ether.

I believe what I have said above is accurate but I'm not certain. I think that this - http://www.aip.org/history/einstein/essay-einstein-relativity.htm
speaks to it.

Pete

 

[JesseM]

It should be known that Einstein never proved there was no ether. What he proved was that if there is an either than it plays no role in the laws of physics. You can call infnite space in which there is no matter in the normal sense as a region of space filled with virtual particles. This "sea" of virtual particles are what a few physicists today refer to as the ether.

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.

 

[Aether]

Oh, here's another nifty thing:

You may recall that there is a sort of "map" between Euclidean geometry and the complex numbers.

For example:

The length of the line segment from p to q is given by |q - p|, where |z|^2 := z \bar{z}.

Multiplication by e^{i \theta} is the same thing as rotating (counterclockwise) about the origin by the angle θ.

Addition by z is the same thing as translation by the vector from the origin to z.



Well, there is a number system called the "hyperbolic numbers" that plays the same role for Minowski geometry. It has the hyperbolic unit h, which satisfies h² = 1. (As opposed to i² = -1 of the complex numbers)

The hyperbolic numbers aren't as nice as the complexes: for example, if x is a real number, then it doesn't have a hyperbolic square root if x<0, but if x>0, it has four hyperbolic square roots: √x, -√x, h√x, -h√x. In particular, 1 has four square roots, 1, -1, h, and -h.

You can't divide by all hyperbolic numbers either: for example, 1+h is a "null" hyperbolic number, and you cannot divide by it.

But these numbers do serve the same role as the complexes do. For example, the metric ds² along the line segment from p to q is given by ds²=|p-q|², where |x + hy|^2 = (x + hy) (x + hy)^* = (x + hy) (x - hy) = x^2 - y^2). (I use * to denote hyperbolic conjugation because I can't remember how to make an overbar go over the whole factor)

Multiplication by e^{h\beta} is a Lorentz boost fixing the origin. (the Minowski analog of rotating about the origin)

Addition by z is the same thing as translation by the vector from the origin to z.


(1+h is "null" because |1+h|²=(1+h)(1-h)=1-1=0)


And we have the hyperbolic Euler's identity, as well as the circular one:
e^{i\theta} = \cos \theta + i \sin \theta
e^{h\beta} = \cosh \beta + h \sinh \beta

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

 

[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