What evidences of relativity do you find the most compelling

[Aether]

There's a subtle but devastating difference between coordinate-independent and coordinate-free. I think that's where your confusion stems from. Special relativity is automatically (indeed, by construction) coordinate-independent, although the original formulation is not coordinate-free.

I would like to understand this subtlety better.

I'm unaware of what the GGT you speak of is, but your mention of the aether makes my eyes glaze over in resignation.

clj4 insists that the one-way speed of light is measurable in a coordinate-system independent way, and cites http://imaginary_nematode.home.comcast.net/papers/Gagnon_et_al_1988.pdf" paper as proof. GGT is introduced within this paper, and an experiment is described which is supposed to be able to distinguish between GGT and SR. Many other people also think that this is plausible.

What's more, the claim that "they are both the same ... theory using different coordinate systems" sounds, to people who understand the wording, ridiculous. If they are equivalent modulo choice of gauge then your GGT is *not* distinguishable from special relativity and hence should be discarded.

The Gagnon paper claims to be able to distinguish between GGT and SR, and clj4 believes their claim. I am simply pointing out that SR and GGT are *not* distinguishable by any experiment.

 

[clj4]

clj4 insists that the one-way speed of light is measurable in a coordinate-system independent way,

This is nonsense, one way light speed is not measurable, so stop right here.

...and cites http://imaginary_nematode.home.comcast.net/papers/Gagnon_et_al_1988.pdf" paper as proof. GGT is introduced within this paper, and an experiment is described which is supposed to be able to distinguish between GGT and SR. Many other people also think that this is plausible.

This is a gross distortion of the truth. What is shown in the 10-12 papers that I have given you is that while aether theories (a la GGT) claim light speed to be anisotropic, all these experiments, conducted by respected physicists and published in peer refereed journals have shown no detection of such light speed anisotropy within the error bars. As such, they show that there is a distinction between "aether" theories and SR.
You have tried repeatedly, on multiple threads to distort the truth and every time you have just proven that you can't even perform some simple calculations. And though, you persist? Why? Do you need a refresher on "Wrong (and wilfully false) claims"?

The Gagnon paper claims to be able to distinguish between GGT and SR, and clj4 believes their claim. I am simply pointing out that SR and GGT are *not* distinguishable by any experiment.

It isn't just one paper, it is all these papers:1. C.M.Will “Clock Synchronization and isotropy of one-way speed of light”, Phys.Rev. D, 45, 2 (1992)

2. D.R.Gagnon, D.G.Torr, P.T.Kolen, T.Chang “Guided-wave measurement of the one-way speed of light”, Phys.Rev. A, 38, 4 (1988)

3. T.Chang , “Maxwell’s equations in anisotropic space”, Phys.Lett, 70A, 1 (1979)

4. T.Krisher, L.Maleki, G.Lutes, L.Primas, R.Logan, J.Anderson, C.Will, Phys. Rev. D, 42, 2, (1990)

5. S. Herrmann, A. Senger, E. Kovalchuk, H. Müller, A. Peters: "Test of the isotropy of the speed of light using a continuously rotating optical resonator", Phys. Rev. Lett. 95, (2005)

6. T. Chang, D. Torr, “Dual properties of spacetime under an alternative Lorentz transformation”, Found. Of Phys. Lett, 1, 4, (1988)

7. T.Chang, D.Torr, D.Gagnon, “A modified Lorentz theory as a test theory of special relativity”, ”, Found. Of Phys. Lett, 1, 4, (1988)

8. S.Schiller, P.Antonini, M.Okhapkin “A precision test of the isotropy of the speed of light using rotating cryogenic optical cavities” Phys. Rev. Lett. 95, 150401 (2005)

9. Lipa, J. A., Nissen, J. A., Wang, S., Stricker, D. A., and Avaloff, D. “A New Limit on Signals of Lorentz Violation in Electrodynamics” Phys. Rev. Lett. 90, 060403 (2003)

10. Wolf, P., Bize, S., Clairon, A., Santarelli, G., Tobar, M. E., and Luiten, A. N. “Improved Test of Lorentz Invariance in Electrodynamics” Phys. Rev. D 70, 051902(R) (2004)11. Paul L. Stanwix,1 Michael E. Tobar,1 Peter Wolf,2,3 Mohamad Susli,1 Clayton R. Locke,1 Eugene N. Ivanov,1 John Winterflood,1 and Frank van Kann1 "Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators" , Phys. Rev. Lett. 95, 040404 (2005)

 

[Aether]

This is a gross distortion of the truth. What is shown in the 10-12 papers that I have given you is that while aether theories (a la GGT) claim light speed to be anisotropic, all these experiments, conducted by respected physicists and published in peer refereed journals have shown no detection of such light speed anisotropy within the error bars. As such, they show that there is a distinction between "aether" theories and SR.
You have tried repeatedly, on multiple threads to distort the truth and every time you have just proven that you can't even perform some simple calculations. And though, you persist? Why? Do you need a refresher on "Wrong (and wilfully false) claims"?

I have a lot to learn about many things, but I haven't tried to distort the truth nor have I made willfully false claims. The Gagnon paper is wrong, one or two of the others have some relatively minor flaws, and you are misinterpreting the rest.

 

[clj4]

I have a lot to learn about many things, but I haven't tried to distort the truth nor have I made willfully false claims. The Gagnon paper is wrong, one or two of the others have some relatively minor flaws...

The above sounds arrogant, considering the fact that in our interaction over the Gagnon paper you have repeatedly shown that you cannot calculate.

Look what you write:

"clj4 insists that the one-way speed of light is measurable in a coordinate-system independent way"

What credibility do you have with such an patently false and non-sensical opening statement?

 

[Aether]

SR is a coordinate-independent theory, therefore any formulation of it will be coordinate-independent.

Most formulations will not be "manifestly" coordinate-independent: they will formulate SR in a way that apparently depends on the choice of coordinate system. But it is then later proven that if we had started with a different coordinate system, we would still arrive at the exact same theory.

Ok, but this is equally true for GGT, aka Lorentz ether theory (LET), right? GGT/LET is a formulation of SR?

Ah, but 3-velocity is not a physical quantity! The coordinate-free formulations wouldn't say anything at all about 3-velocity, since the very notion of 3-velocity depends on a choice of coordinates (which is one reason why it's called the "coordinate velocity").

The coordinate-free formulation is still SR?

There are all sorts of coordinate systems you can put on Euclidean space, and you can do Euclidean geometry in any of them. But the Euclidean geometry has a "nicest" class of coordiante systems: the orthonormal ones, right?

Right.

The same is true in Minowski space: the geometry picks out a "nicest" class of coordinate charts, and those are what we often call the "inertial reference frames". Those do, indeed, have a constant one-way (coordinate) speed of light. But other affine coordinate charts on Minowski space do not have constant one-way speed of light. The curvilinear charts, of course, don't even have light traveling along a coordinate-line!

Doing SR in a "skew" coordinate system does not change it into another theory -- it's still SR. (Just like Euclidean geometry done in a skew coordinate system is still Euclidean geometry)

Ok. Then GGT/LET is still SR? What then do we call SR when the one-way speed of light is defined as a constant?

 

[Aether]

Look what you write:

"clj4 insists that the one-way speed of light is measurable in a coordinate-system independent away"

What credibility do you have with such an patently false and non-sensical opening statement?

Is this better:

"clj4 insists that the one-way speed of light anisotropy is measurable in a coordinate-system independent way"

 

[clj4]

Is this better:

"clj4 insists that the one-way speed of light anisotropy is measurable in a coordinate-system independent way"

It is not that I "insist", it just is that there are valid experiments that clearly refute the idea of light speed anisotropy.
It has been explained to you numerous times (quite a few times in this thread) that the formalism employed in describing the theory has no bearing on the outcome of the experiments as long as the formalisms are valid and equivalent.
You keep trying to cancel out valid experiments based on the formalism (coordinate dependent vs. independent) used in describing the theories. When you made the feeblest attempt at calculating anything you failed miserably, if you are so convinced that you are right, please rewrite the theory of any of the papers below in your formalism of choice and see what you get.

Why don't you read (& understand & accept) the published papers?

That would perhaps stop you from distorting the scientific truth: 1. C.M.Will “Clock Synchronization and isotropy of one-way speed of light”, Phys.Rev. D, 45, 2 (1992)

2. D.R.Gagnon, D.G.Torr, P.T.Kolen, T.Chang “Guided-wave measurement of the one-way speed of light”, Phys.Rev. A, 38, 4 (1988)

3. T.Chang , “Maxwell’s equations in anisotropic space”, Phys.Lett, 70A, 1 (1979)

4. T.Krisher, L.Maleki, G.Lutes, L.Primas, R.Logan, J.Anderson, C.Will, Phys. Rev. D, 42, 2, (1990)

5. S. Herrmann, A. Senger, E. Kovalchuk, H. Müller, A. Peters: "Test of the isotropy of the speed of light using a continuously rotating optical resonator", Phys. Rev. Lett. 95, (2005)

6. T. Chang, D. Torr, “Dual properties of spacetime under an alternative Lorentz transformation”, Found. Of Phys. Lett, 1, 4, (1988)

7. T.Chang, D.Torr, D.Gagnon, “A modified Lorentz theory as a test theory of special relativity”, ”, Found. Of Phys. Lett, 1, 4, (1988)

8. S.Schiller, P.Antonini, M.Okhapkin “A precision test of the isotropy of the speed of light using rotating cryogenic optical cavities” Phys. Rev. Lett. 95, 150401 (2005)

9. Lipa, J. A., Nissen, J. A., Wang, S., Stricker, D. A., and Avaloff, D. “A New Limit on Signals of Lorentz Violation in Electrodynamics” Phys. Rev. Lett. 90, 060403 (2003)

10. Wolf, P., Bize, S., Clairon, A., Santarelli, G., Tobar, M. E., and Luiten, A. N. “Improved Test of Lorentz Invariance in Electrodynamics” Phys. Rev. D 70, 051902(R) (2004)

 

[coalquay404]

I would like to understand this subtlety better.

The best way to understand it is to simply consider exactly what physical quantities are. In all of physics, physical quantities are represented by tensorial quantities (there are various subtleties involved in quantization, pointed out initially by Van Hove, which relate to our inability to completely quantize a classical space of observables without accepting either an O(h^2) correction term or quantizing only a subset of the space of classical observables, but I digress. Now, in some old-fashioned books, tensors are defined in terms of the fact that their coordinates transform according to certain rules. This isn't a wrong way to think about tensors, but it is certainly a very limited way to think about them.

In general, a coordinate-independent theory will produce the same fundamental physical laws regardless of which system of coordinates (and, by extension, which observer) is used. This is equivalent to the statement that physics should be "gauge invariant" (a choice of gauge is roughly equivalent to a choice of coordinate system). This is very different, however, from formulating a theory in a coordinate-free way.

Perhaps the best example I can give centres on general relativity. The majority of old-fashioned books on GR (Weinberg's foremost among them) describe general relativity in a manifestly coordinate-invariant way. However, they do use coordinates to describe things. For example, in these books the Riemann tensor is usually defined as something with the following components:

R^a_{\phantom{a}bcd}<br /> = 2\partial_[c\Gamma^a_{\phantom{a}d]b} + 2\Gamma^a_{\phantom{a}e[c}\Gamma^e_{\phantom{e}d]b}

Now, while this description makes explicit use of coordinates in order to describe physical quantities, it is manifestly coordinate-independent since using a different system of coordinates should lead to an equivalent set of physical laws. The flip side of this is the more modern description which uses a coordinate-free philosophy. In this system, the Riemann tensor would be defined by a map R:\mathfrak{X}(M)\times\mathfrak{X}(M)\times\mathfrak{X}(M)\to\mathfrak{X}(M), R:(X,Y,Z)\mapsto R(X,Y)Z, where

R(X,Y)Z = \nabla_X\nabla_YZ - \nabla_Y\nabla_XZ - \nabla_{[X,Y]}Z.

This is manifestly coordinate free; the vectors and tensors are explicitly viewed as things which exists independently of any coordinate systems which we may use to describe them. This is the more modern, and to my eyes far more elegant, way in which physics is described. You don't need to worry about coordinates or indices on tensors: you just do the damn physics. Special relativity can be formulated in just this way if you're willing to forego some clarity in favour of mathematical sophistication.

The advantage of the coordinate-free descriptions is that the possible types of physical theory which you can construct are very clear. For example, many different types of string and brane models are based on things called p-forms. These are just totally antisymmetric tensors of order p. The nice thing about the coordinate-free approach is that you can view all of the acceptable free theories as being based on an exact p-form F with an action of the form

S=-\frac{1}{2p!}\int F\wedge\star F,

where \star is the Hodge dual operator. This stuff seems really abstract and difficult to understand the first time you see it but, trust me, this coordinate-free approach is the only sane way to do theoretical physics. Anything else will involve so much brute force calculation that it becomes unfeasible.

 

[pervect]

Ok, but this is equally true for GGT, aka Lorentz ether theory (LET), right? GGT/LET is a formulation of SR?

The coordinate-free formulation is still SR?

Right.

Ok. Then GGT/LET is still SR? What then do we call SR when the one-way speed of light is defined as a constant?

I think we call SR "SR with a coordinate system that is compatible with Newtonian physics", and LET "SR with a coordinate system that is incompatible with Newtonian physics".

But it's a bit long :-), so the names haven't caught on.

Seriously, the motivation for Einstein clock synchronization is ultimately compatibility with Newtonian physics. This is a very useful property of SR, something that will be lacking if clock synchronization conventions are changed.

 

[Hurkyl]

LET "SR with a coordinate system that is incompatible with Newtonian physics", and LET "SR with a coordinate system that is incompatible with Newtonian physics".

Well, remember that there's a philosophical difference. (I say philosophical because it doesn't manifest itself in any measurable way)

SR works in a Minowski space-time, and all physical quantities are geometric.

LET works in the pre-relativistic setting where space and time are independent. (but the laws of physics conspire to prevent us from ever being able to figure out how they are split!)