Consistency of the speed of light

[gregory_]

Okay, I read the Krisher paper. I don't understand the issue here. They are constraining only a particular form of the one-way speed of light. They are NOT ruling out GGT theories. In fact, they specifically (and correctly) state "Notice that the result [(the predicted variation)] is independent of the synchronization procedure". GGT differs from Lorentz transformations only in the synchronization procedure. It is not ruled out here.

So now it is your turn. Please go back and read the post https://www.physicsforums.com/showpost.php?p=942326&postcount=214" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

 

[clj4]

Of course we still have $$\bar{K}^\mu = q \bar{n}^a \bar{g}^{\mu b}\bar{F}_{b a}$$ but this will correspond to the same dependence on the velocity and fields ONLY if $$g^{\mu b}=\bar{g}^{\mu b}$$. In special relativity, the metric is frame independent, so the force law maintains the same form (as expected). However, this is not true for GGT. In GGT the metric is frame dependent and thus the Lorentz force law changes form when we change frames (the metric is worked out in reference 9, so you can calculate the horrid form of the Lorentz force law using GGT if you so wish).

How does this affect Gagnon's paper? It means the boundary conditions they invoke when solving for the fields in the wave-guide are not correct. So their calculations are flawed right at the beginning.

Thank you,

GGT is in effect a Mansouri-Sexl theory, it uses the same exact space-tiime transforms. So, the way it affects the Gagnon paper is that it proves a contradiction between the Mansouri-Sexl predictions and the result of the experiment (see the conclusion of the paper).

 

[clj4]

It took me awhile to figure out what the other paper was (apparrently you made a small typo above?). I assume the next paper is:
Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards
Krisher, T.P.; Maleki, L.; Lutes, G.F.; Primas, L.E.; Logan, R.T.; Anderson, J.D.; Will, C.M.
Physical Review D (Particles and Fields), v 42, n 2, 15 July 1990, p 731-4

I'll take a look at it.


As a side note, I tried to look up that Gagnon paper where he contradicts and says that no effect to second order should be seen according to GGT. The library records show it should be there, but the first three volumes of Foundations of Physics Letters are missing. So I can't even read the whole article myself. Oh well. I guess it doesn't matter now anyway.

So how did you get the quote if you cannot find the paper? How could you tell us about the content of the paper? How do you know that Gagnon spends 20 pages "analizing other experiments"? as per your post #238.

 

[clj4]

Okay, I read the Krisher paper. I don't understand the issue here. They are constraining only a particular form of the one-way speed of light. They are NOT ruling out GGT theories. In fact, they specifically (and correctly) state "Notice that the result [(the predicted variation)] is independent of the synchronization procedure". GGT differs from Lorentz transformations only in the synchronization procedure. It is not ruled out here.

So now it is your turn. Please go back and read the post https://www.physicsforums.com/showpost.php?p=942326&postcount=214" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

Aren't you missing a few things?

1. they are using the most general form of the MS spacetime transformation, with all the parameters in place

2. the result of the experiment puts a very hard boundary on the parameters (makes them effectively zero within the experimental error bars)

3. so the NET effect is a light speed anisotropy of 100m/s !

In case you missed it , the subject of the discussion is:
- the validity of one way speed measurement (do such experiments exist? yes, they do and they are valid)
- the possibility of explaining such experiments from the perspective of a Mansouri-Sexl theory (sure you can , if as a result of analyzing the experimental data all the parameters come out zero or as near to zero as the equipment permits- this is the main role of a test theory)

 

[clj4]

In special relativity, the metric is frame independent, so the force law maintains the same form (as expected). However, this is not true for GGT. In GGT the metric is frame dependent ...

You sure about that? This is where you stop calculating and you start talking. Based on the formulation of GGT I would be inclined to believe that the metric is frame independent. Can you prove the above statement mathematically? It should be simple.

 

[clj4]

The generalized Galilean transformations "mimic" SR in the sense that we still restrict ourselves to inertial frames (for this discussion I will define an inertial coordinate system as one in which a freely moving body moves at a constant velocity). It turns out that being an inertial coordinate system is fairly restrictive and the only freedoms we have are: origin, axis placement, and simultaneity convention.

a. Aren't you forgetting the parametrization of the transforms?

In summary, yes there are compelling reasons to choose Lorentz transformations over generalized galilean transformations. "Unfortunately" experimental proof is not one of them.

b. The correct and complete statement is that all the experiments meant to prove the Mansouri-Sexl (or GGT) reformulations of relativity result into severely constraining the parameters, i.e. they are proven to be zero within the experimental error bars.

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

yes, this is a silly question

if not
Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

Thank you.

See points (a,b) above: because your statements tend to be incomplete and your resulting questions are misleading (if you get incorrect or incomplete initial conditions there is no solution to your problem).

 

[clj4]

1. However, this is not true for GGT. In GGT the metric is frame dependent and thus the Lorentz force law changes form when we change frames (the metric is worked out in reference 9, so you can calculate the horrid form of the Lorentz force law using GGT if you so wish).

2. How does this affect Gagnon's paper? It means the boundary conditions they invoke when solving for the fields in the wave-guide are not correct. So their calculations are flawed right at the beginning.

A. Can you prove statement 1 to be true?

B. Can you prove the connection between the two statements (1 and 2)? In my experience many "horrid forms" tend to cancel out when it matters and to produce nice symmetrical results. Look at the "horrid form" of the Mansouri-Sexl transforms...

 

[clj4]

Only two papers. I will hold you to that.

Okay, I spent time on the Gagnon paper. The error is fairly obvious, but I wasted hours brushing up on this and that in order to feel confident enough to state it here.

The error is this: electrodynamics cannot be formulated with Maxwell's equations alone. It is Maxwell's equations (how the fields interact and are produced by the sources) _AND_ Lorentz's force law (how the fields act back on the sources). Gagnon used the transformed Maxwell's equations from reference 9 without using the transformed Lorentz force law. Reference 9 doesn't calculate it, so they must have (incorrectly) assumed that it retained the same form. This is incorrect.

Lorentz force law:
$$K^\mu = q n_\nu F^{\mu \nu}$$
where K is the Minkowski force, q the charge, n the proper velocity, F the field tensor.

Reference 9 chose the components of the covarient field tensor to define the electric and magnetic fields (instead of the contravarient field tensor, which is why the two source dependent Maxwell's equations come out horrid while the non-source dependent ones come out fairly clean). So we need to rewrite the equation to depend on that, as well as depend on the contravarient proper velocity (corresponds to the physical velocity as opposed to the covarient proper velocity).

$$K^\mu = q (g_{\nu a} n^a) (g^{\mu b}F_{b c}g^{c\nu})$$

Rearranging and noting that $$g^{c\nu} g_{\nu a} = \delta_{ca}$$ we have:

$$K^\mu = q n^a g^{\mu b}F_{b a}$$

Let's move to another frame and see how the dependence of the force on the fields and the velocity changes. (I'll use a bar to denote quantities in this other frame.)

Of course we still have $$\bar{K}^\mu = q \bar{n}^a \bar{g}^{\mu b}\bar{F}_{b a}$$ but this will correspond to the same dependence on the velocity and fields ONLY if $$g^{\mu b}=\bar{g}^{\mu b}$$. In special relativity, the metric is frame independent, so the force law maintains the same form (as expected). However, this is not true for GGT. In GGT the metric is frame dependent and thus the Lorentz force law changes form when we change frames (the metric is worked out in reference 9, so you can calculate the horrid form of the Lorentz force law using GGT if you so wish).

How does this affect Gagnon's paper? It means the boundary conditions they invoke when solving for the fields in the wave-guide are not correct. So their calculations are flawed right at the beginning.

Ahh, just a moment, what allows you to permute the expressiion:$$(g_{\nu a} n^a) (g^{\mu b}F_{b c}g^{c\nu})$$

i.e. what makes it commutative? You moved the tensor $$g_{\nu a}$$ all the way to the right end of the expression.

 

[masudr]

Ahh, just a moment, what allows you to permute the expressiion:


$$(g_{\nu a} n^a) (g^{\mu b}F_{b c}g^{c\nu})$$

i.e. what makes it commutative? You moved the tensor $$g_{\nu a}$$ all the way to the right end of the expression.

These quantities are just components and components are just numbers. As far as I know, numbers have always been commutative. It's the ordering of the indices and the fact that a certain index is contracted over another that preserves the original operations between the tensors.

 

[Aether]

What would each of you say if I told you with absolute certainty that the speed of light can be tested and proven to reach every observable angle by doing one simple experiment within a 3 dimensional mathematical formula?

That depends on what sort of litlbunny is telling me this.

Would any of you be interested in testing out this simple experiment to prove it to yourself?

No.

If you agree to do this experiment I must warn you, you will need to create a computer program in which to measure this experiment, and follow the guidelines I will be suggesting.

Now I'm scared.

If you agree to both of those requirements, would you like me to explain how?

No.

Because the experiment I will be suggesting is not within “normal” theoretical teaching, I will not be able to post the experiment parameters within this forum, unless the moderators of this forum will allow for a little latitude with regards to a experimental suggestion. If not however, I could send you the “How To” in a PM

If you are interested either respond here or through a private PM.

You could post it to the Independent Research forum. However, if you haven't done your "homework" on this already, you should try to develop the concept on your own as far as possible before submitting it to that forum. If you need to learn some things along the way, you can ask questions and get all the help that you need here at PF.

 

[russ_watters]

Because the experiment I will be suggesting is not within “normal” theoretical teaching, I will not be able to post the experiment parameters within this forum, unless the moderators of this forum will allow for a little latitude with regards to a experimental suggestion. If not however, I could send you the “How To” in a PM.

Experiments are not theories - you are welcome to post any experiment you wish. However, when you go and start predicting outcomes that don't mesh with what physics predicts, then you may have a problem.

My gut: the experiment you are thinking of has either already been done or is already covered by other similar but not exactly the same experiments. So predicting a different outcome from what physics would predict would require that other experimental results be different.

 

[Aether]

Thanks for locating these papers gregory, they really help!

Here's an interesting paper appearing right before the new Gagnon paper:

T. Chang and D. G. Torr, Dual properties of spacetime under an alternative Lorentz transformation, Foundations of Physics Letters 1(4), 343 (1988); http://www.springerlink.com/(hnie2i...l,100,103;browsepublicationsresults,484,1560;

Abstract:
In flat spacetime, the fourth space coordinate in special relativity (SR) is equivalent to the coordinate time $$t_E$$. We will show, however, that this definition of physical time is not unique. Another natural choice of coordinate time, $$t_A$$, with absolute synchronization is allowed. Spacetime would exhibit dual properties, namely relativistic and absolute. In an arbitrary inertial frame, the relationship of the above two kinds of coordinate time corresponds to a resynchronization, and the Lorentz transformations can be written in an alternative form, which is called the generalized Galilean transformation (GGT). Although the absolute property is still hidden in nearly all types of experiments, the advantages of the above approach are as follows: (1) It will give us a deeper understanding of SR, including the basis of length contraction, time dilation and the interaction between moving objects and the physical vacuum. (2) It will provide a wider research domain than SR; for example, superluminal motion is predicted and has obtained growing experimental support.

Here is the more recent Gagnon paper:

T. Chang, D. G. Torr and D. R. Gagnon, A modified Lorentz theory as a test theory of special relativity, Foundations of Physics Letters 1(4), 353 (1988); http://www.springerlink.com/(hnie2i...l,100,103;browsepublicationsresults,484,1560;

Abstract:
A modified Lorentz theory (MLT) based on the generalized Galilean transformation has recently received attention. In the framework of MLT, some explicit formulas dealing with the one-way velocity of light, slow-clock transport and the Doppler effect are derived in this paper. Several typical experiments are analyzed on this basis. The results show that the empirical equivalence between MLT and special relativity is still maintained to second order terms. We confirm recent findings of other works that predict the MLT might be distinguished from special relativity at the third order by Doppler centrifuge experiments capable of a fractional frequency detection threshold of $$10^{–15}$$.

 

[clj4]

Excellent , thank you.

Doesn't sound as a retraction, does it? Sounds as a confirmation of the earlier paper we are discussing.

The results show that the EMPIRICAL equivalence between MLT and special relativity is still maintained to second order terms.

EMPIRICAL, as in EXPERIMENTAL. This is exactly what the Gagnon (Phys Rev) claims. EMPIRICAL (experimental) yes. THEORETICAL=no.(see the gagnon paper we are talking about)

We CONFIRM recent findings of other works that PREDICT the MLT MIGHT be distinguished from special relativity at the third order by Doppler centrifuge experiments capable of a fractional frequency detection threshold of 10^(–15)

Aha, now the assault on Mansouri-Sexl resumes. This time is on the theoretical plane, at third order of : $$\frac{v}{c}$$.

A very interesting paper, anyone has a scan that would care to share?
Gregory, how did you get the idea that it might be a retraction?

 

[Aether]

Doesn't sound as a retraction, does it? Sounds as a confirmation of the earlier paper we are discussing.

It sounds like a retraction (or at least a contradiction) to me, but we can hold that judgement in reserve until we're looking at the full paper(s). I'll try to buy both of these papers and post them (sharing for educational purposes only as allowed under the "fair use" provision of the copyright law as I understand it -- someone correct me if I'm wrong).

EMPIRICAL, as in EXPERIMENTAL. This is exactly what the Gagnon (Pghys Rev) claims. EMPIRICAL (experimental) yes. THEORETICAL=no.(see the gagnon paper we are talking about)

Wrong.

Aha, now the assault on Mansouri-Sexl resumes. This time is on the theoretical plane, at level : $$(\frac{v}{c})^3$$.

Sure, we can talk about violations of Lorentz symmetry, and refining models all we want later, but that is not the issue at hand.

 

[clj4]

It sounds like a retraction to me, but we can hold that judgement in reserve until we're looking at the full paper. I'll try to buy both of these papers and post them (sharing for educational purposes only as allowed under the "fair use" provision of the copyright law as I understand it -- someone correct me if I'm wrong).

Appreciate it.

 

[chroot]

What would each of you say if I told you with absolute certainty that the speed of light can be tested and proven to reach every observable angle by doing one simple experiment within a 3 dimensional mathematical formula?

I'd say you deserve another warning for posting crackpot crap on our website. Computer simulations aren't experiments, either.

- Warren

 

[Aether]

Quoting from p. 370 of: T. Chang and D. G. Torr, Dual properties of spacetime under an alternative Lorentz transformation, Foundations of Physics Letters 1(4), 343 (1988); http://www.springerlink.com/(hnie2i...l,100,103;browsepublicationsresults,484,1560;

The theoretical results derived from MLT [modified Lorentz (ether) theory] are consistent with experiments to the same degree as SR. Therefore, MLT and SR are empirically equivalent to date. Furthermore, the above analysis has shown that the relativistic time is not the only possible definition of physical time in flat spacetime. Besides the relativistic time, a natural choice of coordinate time with absolute synchronization is allowed, whether or not violations of SR at the third order are found...This implies that physics is not necessarily limited to a domain defined by SR. The physics may be extended to a domain defined by MLT.

Quoting from p. 350 of: T. Chang, D. G. Torr and D. R. Gagnon, A modified Lorentz theory as a test theory of special relativity, Foundations of Physics Letters 1(4), 353 (1988); http://www.springerlink.com/(hnie2i...l,100,103;browsepublicationsresults,484,1560;

As is well known, all kinds of elementary particles have the dual properties of particles and waves. Historically formal recognition of this more complete and more correct description was a slow process. A similar situation may prevail with spacetime theories; namely, both Newton's purely absolute view and Einstein's purely relative view seem incomplete. We suggest here that spacetime has dual properties: both absolute and relative. The defintion of physical time is not unique.

This is the mainstream view! So, please, get with the program.

 

[clj4]

Quoting from p. 370 of: T. Chang and D. G. Torr, Dual properties of spacetime under an alternative Lorentz transformation, Foundations of Physics Letters 1(4), 343 (1988); http://www.springerlink.com/(hnie2i...l,100,103;browsepublicationsresults,484,1560;

The theoretical results derived from MLT [modified Lorentz ether theory] are consistent with experiments to the same degree as SR. Therefore, MLT and SR are empirically equivalent to date. Furthermore, the above analysis has shown that the relativistic time is not the only possible definition of physical time in flat spacetime. Besides the relativistic time, a natural choice of coordinate time with absolute synchronization is allowed, whether or not violations of SR at the third order are found...This implies that physics is not necessarily limited to a domain defined by SR. The physics may be extended to a domain defined by MLT.

Quoting from p. 350 of: T. Chang, D. G. Torr and D. R. Gagnon, A modified Lorentz theory as a test theory of special relativity, Foundations of Physics Letters 1(4), 353 (1988); http://www.springerlink.com/(hnie2i...l,100,103;browsepublicationsresults,484,1560;

As is well known, all kinds of elementary particles hae the dual properties of particles an waves. Historically formal recognition of this more complete and more correct description was a slow process. A similar situation may prevail with spacetime theories; namely, both Newton's purely absolute view and Einstein's purely relative view seem incomplete. We suggest here that spacetime has dual properties: both absolute and relative. The defintion of physical time is not unique.

This is the mainstream view! So, please, get with the program.

I just skimmed thru the papers.

1. Neither quotes Gagnon (Phys Rev) , nor do they contain any retraction of it. This is the main point. So you cannot use any of the two papers against Gagnon (Phys Rev)

2. The authors actually raise the stakes by showing that MLT predicts a third order effect in (v/c) (chapter 6) that "does not reduce the result to SR as might have been intuitively expected" (page 368).Ref (25) shows that Gagnon had already done this experiment (in 1984) with a precision of 10^(-15). (page 369)

In conclusion it looks like you bought yourself another Gagnon et al paper to refute.

 

[Aether]

I just skimmed thru the papers.

1. Neither quotes Gagnon (Phys Rev) , nor do they contain any retraction of it. This is the main point. So you cannot use any of the two papers against Gagnon (Phys Rev)

Yes, and that seems strange. They do clearly contradict the first paper however which claims that GGT predicts a 19-degree phase shift, a second order effect.

2. The authors actually raise the stakes by showing that MLT predicts a third order effect in (v/c) (chapter 6) that "does not reduce the result to SR as might have been intuitively expected" (page 368).

On page 370 they say: "Besides the relativistic time, a natural choice of coordinate time with absolute synchronization is allowed, whether or not violations of SR at the third order are found". So, while this may be an interesting issue for a later discussion, it doesn't have any impact on what we're talking about here.

Ref (25) shows that Gagnon had already done this experiment (in 1984) with a precision of 10^(-15). (page 369)

He seems to be saying that he actually dectect a violation of Lorentz symmetry at that precision. Again, this may be an interesting issue for a later discussion, but it doesn't have any impact on what we're talking about here.

In conclusion it looks like you bought yourself another Gagnon et al paper to refute.

No, that's not what it looks like to me at all.

 

[clj4]

Yes, and that seems strange. They do clearly contradict the first paper however which claims that GGT predicts a 19-degree phase shift, a second order effect.

On page 370 they say: "Besides the relativistic time, a natural choice of coordinate time with absolute synchronization is allowed, whether or not violations of SR at the third order are found". So, while this may be an interesting issue for a later discussion, it doesn't have any impact on what we're talking about here.

He seems to be saying that he actually dectect a violation of Lorentz symmetry at that precision. Again, this may be an interesting issue for a later discussion, but it doesn't have any impact on what we're talking about here.

No, that's not what it looks like to me at all.

Looks like you want to split hairs, so we'll get to business: neither of the papers retracts gagnon (Phys Rev). This is how this got started. So, please refute Gagnon (Phys Rev). Would be a good idea to deal with Kirshner as well.

 

[clj4]

Yes, and that seems strange. They do clearly contradict the first paper however which claims that GGT predicts a 19-degree phase shift, a second order effect.

You mean 1.9 degrees, I think that we established that together.
Can you point the direct quote (like I did), not thru inferences?



Looks like you want to split hairs, so we'll get to business: neither of the papers retracts Gagnon (Phys Rev). This is how this side conversation got started. So, please refute Gagnon (Phys Rev). Would be a good idea to deal with Kirshner as well while you are at it.

 

[Aether]

You mean 1.9 degrees, I think that we established that together.
Can you point the direct quote (like I did), not thru inferences?

Page 370: "The theoretical results derived from MLT are consistent with experiments to the same degree as SR. Therefore, MLT and SR are empirically equivalent to date." This paper was submitted on 8/22/1988, and the first Gagnon paper was published on 8/15/1988 (submitted 8/12/1986; revised manuscript received 3/11/1988).

Looks like you want to split hairs, so we'll get to business: neither of the papers retracts Gagnon (Phys Rev). This is how this side conversation got started. So, please refute Gagnon (Phys Rev). Would be a good idea to deal with Kirshner as well while you are at it.

I think it is a good idea to examine both of those papers (and I think it's Krisher), but the quote that I just gave above from three of the same four authors as Gagnon et al. (Phys Rev A) seems entirely sufficient (to me) to settle the issue at hand once and for all.

 

[clj4]

Page 370: "The theoretical results derived from MLT are consistent with experiments to the same degree as SR. Therefore, MLT and SR are empirically equivalent to date." This paper was submitted on 8/22/1988, and the first Gagnon paper was published on 8/15/1988 (submitted 8/12/1986; revised manuscript received 3/11/1988).

I think it is a good idea to examine both of those papers (and I think it's Krisher), but the quote that I just gave above from the same three authors as Gagnon (Phys Rev) seems entirely sufficient (to me) to settle the issue at hand once and for all.

Not at all. You would like to get off the hook that easily. The authors are simply examining experiments DIFFERENT from the Gagnon (Phy Rev) with a set of transforms DIFFERENT from Gagnon (Phy Rev).
In the conclusion of Gagnon (Phys Rev, top of page 1772) the authors say:

"Our results are consistent with the special theory of relativity and do not tend to support the semiclassical theory of the existence of a preferred frame of reference". The authors assumed by absurd that such a frame existed, they predicted a second order effect, they got none. Refute that.
Mathematically, not by waiving another paper.

 

[Aether]

The authors are simply examining experiments DIFFERENT from the Gagnon (Phy Rev) with a set of transforms DIFFERENT from Gagnon (Phy Rev).

On p. 355 they actually present the general Mansouri-Sexl transformation, and Gagnon et al. (Phys Rev A) they do not even reference Mansouri-Sexl. So what is your point?

In the conclusion of Gagnon (Phys Rev, top of page 1772) the authors say:

"Our results are consistent with the special theory of relativity and do not tend to support the semiclassical theory of the existence of a preferred frame of reference". The authors assumed by absurd that such a frame existed, they predicted a second order effect, they got none. Refute that.
Mathematically, not by waiving another paper.

GGT doesn't predict any second order effect different from SR, three of these same four authors readily admit that.

 

[clj4]

On p. 355 they actually present the general Mansouri-Sexl transformation, and Gagnon et al. (Phys Rev A) they do not even reference Mansouri-Sexl. So what is your point?

GGT doesn't predict any second order effect different from SR, three of these same four authors readily admit that.

Disprove Gagnon (Phys Rev). With your own calculations.
If you cannot do it (there has been already three weeks of failed attempts, errors, missteps), then admit it and we move to Kirshner. Same drill: mathematical disproof. Might be easier for you, it is not as terse as Gagnon.

 

[gregory_]

So how did you get the quote if you cannot find the paper? How could you tell us about the content of the paper? How do you know that Gagnon spends 20 pages "analizing other experiments"? as per your post #238.

Because I can still read the abstract online for free through INSPEC.

Aren't you missing a few things?

1. they are using the most general form of the MS spacetime transformation, with all the parameters in place

2. the result of the experiment puts a very hard boundary on the parameters (makes them effectively zero within the experimental error bars)

As I CLEARLY pointed out to you, they do not constrain the parameter $$\bf{\epsilon}$$. This is the only parameter that differs between GGT and Lorentz transformations.

In case you missed it , the subject of the discussion is:
- the validity of one way speed measurement (do such experiments exist? yes, they do and they are valid)

No. One way speed measurements are not valid.
If you'd take the time to step back and think about it you'd see this. I really think we should focus on the basics.

In special relativity, the metric is frame independent, so the force law maintains the same form (as expected). However, this is not true for GGT. In GGT the metric is frame dependent ...

You sure about that? This is where you stop calculating and you start talking. Based on the formulation of GGT I would be inclined to believe that the metric is frame independent. Can you prove the above statement mathematically? It should be simple.

Um, are you kidding? Of course the metric is frame dependent in GGT.

In reference 9 of your Gagnon experiment paper, they explicitly work out the metric in GGT. I'm not going to bother working that out for you. Read it yourself if you refuse to think about it and see why the metric has to be frame dependent in GGT (this should be obvious before even doing any calculations).

1. However, this is not true for GGT. In GGT the metric is frame dependent and thus the Lorentz force law changes form when we change frames (the metric is worked out in reference 9, so you can calculate the horrid form of the Lorentz force law using GGT if you so wish).

2. How does this affect Gagnon's paper? It means the boundary conditions they invoke when solving for the fields in the wave-guide are not correct. So their calculations are flawed right at the beginning.

A. Can you prove statement 1 to be true?

B. Can you prove the connection between the two statements (1 and 2)? In my experience many "horrid forms" tend to cancel out when it matters and to produce nice symmetrical results. Look at the "horrid form" of the Mansouri-Sexl transforms...

A] The fact that the metric is frame dependent is not only self evident, but is shown explicitly in reference 9 of Gagnon's experimental paper. Additionally, I have shown that if the metric changes, so too does the Lorentz force law.

B] The Lorentz force law is different. I have shown that.

The boundary conditions on a metal are such that: there is no force on charges in the material, there can only be a force on the surface charges perpendicular to the surface. Because the Lorentz force law normally looks like $$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$ this is equivalent to the boundary condition on the fields of $$\bf{E}_\parallel=0, \bf{B}_\perp=0$$. Because the force law is not the same in GGT frames, the boundary condition is not the same either.

[in reference to another gagnon paper]
Gregory, how did you get the idea that it might be a retraction?

Because he stated that experiments could not distinguish between the theories at second order. But his previous paper claimed the exact opposite.

------------------------
Summary:

The calculations in the Gagnon experiment have been shown to be wrong on their starting assumptions. They are wrong. Krisher has also been shown to not be relavent to this discussion in regards to GGT. So let's move on.

clj4, you skipped a question:
Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

 

[Aether]

Disprove Gagnon (Phys Rev). With your own calculations.

I still want to do that and learn how to do PDE's in anisotropic space, but that doesn't mean I'm going to let you get away with posting crackpottery of the second kind at PF in the mean time.

If you cannot do it (there has been already three weeks of failed attempts, errors, missteps), then admit it and we move to Kirshner. Same drill: mathematical disproof. Might be easier for you, it is not as terse as gagnon.

I cannot do any more with the PDE's in Gagnon et al. right now. I'll continue to study my new textbooks, gregory's analysis, and the two new papers from T.Chang et al.. I'll also read Krisher.

 

[clj4]

No. One way speed measurements are not valid.








B] The Lorentz force law is different. I have shown that.






The calculations in the Gagnon experiment have been shown to be wrong on their starting assumptions. They are wrong.

Your tensor proof is flawed. you skipped the challenge on the commutation of the product. Therefore your so-called disproof of Gagnon is also flawed. Could you please address it?

 

[clj4]

I still want to do that and learn how to do PDE's in anisotropic space, but that doesn't mean I'm going to let you get away with posting crackpottery of the second kind at PF in the mean time.

No need to resort to personal attacks. You know very well that this thread started elswhere with YOUR claim that there are no valid one-way light speed experiments. I gave you a list of experiments, you started working on disproving Gagnon, we moved it here because of the use of LatEx, in order to facilitate your disproof. Once yoiu get personal it is a sign that you lost the argument

 

[gregory_]

Your tensor proof is flawed. you skipped the challenge on the commutation of the product. Therefore your so-called disproof of Gagnon is also flawed. Could you please address it?

This has already been adressed by another poster. I can show you more explicitly if you wish. But first I need to know something...

I'm not sure how to ask this nicely. And I am not trying to put you down or anything. But, do you understand Einstein summation?

If not, then we can start there as that seems to be your issue.

 

[clj4]

This has already been adressed by another poster. I can show you more explicitly if you wish. But first I need to know something...

I'm not sure how to ask this nicely. And I am not trying to put you down or anything. But, do you understand Einstein summation?

If not, then we can start there as that seems to be your issue.

Thank you, I understand it. So please explain your derivation, contrary to what you say it was not addressed in any other post that we can see.
while you are at it, please explain to all of us how could you apply the Minkowski formalism that is derived for SR to GGT? What makes you think that it is even applicable?

 

[gregory_]

Thank you, I understand it. So please explain your derivation, contrary to what you say it was not addressed in any other post that we can see.

If you understand Einstein summation, then I don't understand your issue here. Each of those components is just a number. Numbers commute. (And yes this WAS explained to you already https://www.physicsforums.com/showpost.php?p=944396&postcount=254".) Furthermore, I can do the summations in any order I choose.

while you are at it, please explain to all of us how could you apply the Minkowski formalism that is derived for SR to GGT? What makes you think that it is even applicable?

Umm... tensor notation is not limited to SR or GR. It can be used for any theory with coordinate systems.

I can't believe I am even having this discussion.
(For your information, Gagnon's results are based on exactly such derivations using tensor notation to derive the electric and magnetic fields in GGT ... again starting with the DEFINITION that GGT agrees with SR on the physical laws in one "special frame".)

 

[clj4]

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

Looks like we now have THREE Gagnon/Torr/etc papers that fly in the face of your explanation. Plus a few more referenced by the above mentioned papers.
I think your explanation is not an explanation at all, it is pure belief. When the equipment got sensitive enough to detect second (and third) order effects, people started questioning this belief. Now, you countered by questioning the Gagnon paper claiming that they don't set the boundary conditions correctly (questionable demonstration). In the meanwhile, let me remind you that your question 3 is not the main topic of the thread.
The main topic is the validity of one way light speed experiments. So , now that I answered all your questions I have just one for you:

1. Do you question the validity of the one way light speed experiments, especially Kirshner?

 

[clj4]

Because I can still read the abstract online for free through INSPEC.As I CLEARLY pointed out to you, they do not constrain the parameter $$\bf{\epsilon}$$. This is the only parameter that differs between GGT and Lorentz transformations.

The above answer is not correct. You know very well that a,b and d can be and also are different. Come on, the authors (and this is the standard approach) assume them to be present and end up constraining them (see bottom of page 733).
They do not constrain $$\epsilon$$ because of their simplifying choice of clock synchronization. Had they chosen a more complex clock synchro they might just as well derived constrains for $$\epsilon$$.

Besides, let me point out to you one more time: the main issue of this thread is the validity of one way light speed experiments.(see my question to you)

No. One way speed measurements are not valid.
If you'd take the time to step back and think about it you'd see this. I really think we should focus on the basics.

Well, with this kind of biased answer I suggest that our discussion is done. You may wish to take your findings on Gagnon and Kirshner and write a report to Phys Review. Be careful how you cook up your math in order to support your point. Good bye,

 

[gregory_]

Now, you countered by questioning the Gagnon paper claiming that they don't set the boundary conditions correctly (questionable demonstration).

Not so fast. Seems like you can never admit you are wrong (or keep your word).

You said you would believe me if I showed you mathematically where Gagnon made a mistake. I was skeptical, but I decided to give you the benefit of the doubt. So I showed you where Gagnon made a mistake, and, even without finding an error you feel I "must" be wrong because of some bizarre unstated reason / internal belief.

It does not work this way.
Gagnon is wrong. I showed you why. Either admit this or point out where you feel I made a mistake.

In the meanwhile, let me remind you that your question 3 is not the main topic of the thread.
The main topic is the validity of one way light speed experiments. So , now that I answered all your questions I have just one for you:

1. Do you question the validity of the one way light speed experiments, especially Kirshner?

Okay, if you wish to word it that way. If we constrain ourselves to inertial frames (which we shall define as frames in which all freely moving object move at a constant velocity), then we can use experiment to constrain the one-way speed of light to either the form according to GGT or the Lorentz transformations. It should be pointed out that while this constrains the form, it doesn't constrain the value of the one-way speed of light (as the "special frame" is arbitrary). Further constraint is not possible (and constraint this far was possible only because we restricted ourselves to inertial frames), because, as you admitted yourself, the one-way speed of light is a coordinate system dependant number (there is no way to define a one-way velocity without defining a coordinate system).

As I CLEARLY pointed out to you, they do not constrain the parameter $$\bf{\epsilon}$$. This is the only parameter that differs between GGT and Lorentz transformations.

The above answer is not correct. You know very well that a,b and d can be and also are different.

No. Read the definition of the "generalized galilean transformations". Only the $$\bf{\epsilon}$$ parameter differs between them. Krishner does not distiguish between them.


Because theories invoking GGT agree with SR on the physical laws in one special frame BY DEFINITION, they cannot be distinuighed by experiment BY DEFINITION (unless we find some physical law that is not lorentz invarient, which we both know hasn't happenned as of yet).

Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?