Isotropic and anisotropic propagation of light

[ZapperZ]

Hans. I won't was your time discussing this with you but someone has done this simple water test, see: -

1. You refused to show where the cahill paper has been published. It means that you don't care if such a thing has been accepted as a valid enough paper in a peer-reviewed journal.

2. You are now citing someone's personal cranky website as "evidence" for such a thing.

You obviously do not consider the PF Guidelines as something that applies to you.

Zz.

 

[clj4]

Well, looking at this paper,

Reginald T. Cahill claims that the MM experiment can be used after all
to measure the absolute motion through the aether, it however should
be done in a medium with a refractive index higher than 1.00 (vacuum)

He then claims that he can read the absolute speed through the aether
from MM's 1887 (120 year old) experiment because it was done in air
with a refractive index of 1.00029.

According to Cahill, the effect becomes more visible with $\sqrt{n-1}$
Why doesn't he just put the simplest MM setup in water which makes
it more than 30 times more sensitive as in air. Even the simplest
table-top experiment would reveal the absolute speed with better
than 1% accuracy.

Running LIGO without a vacuum would measure the absolute speed
with what? one-in-a-million? one-in-a-billion?
http://www.ligo.caltech.edu/docs/G/G040436-00/G040436-00.ppt

Aether, please don't let me waste my time with reading this stuff.Regards, Hans

Hans and ZapperZ

The "paper" cited by "Aether" would be a perfect example of physics fraud.
It is a beatiful case to set in front of the graduate students and let them have at it.
It should be a new thread, since it was thrown in by "Aether" as a diversion from the OWLS discussion.
Here are a few points to start the new thread (ZapperZ , can you move this in a new thread?)

1. As both of you have asked: how come that no one has tried a MMX experiment in a medium with refrigency higher than 1? Well, there have been at least TWO such experiments, by reputed scientists with...NULL results:

[1]Shamir and Fox, N. Cim. 62B no. 2 (1969), p258.
A repetition of the MMX with the optical paths in perspex (n = 1.49), and a laser-based optics sensitive to ~0.00003 fringe. They report a null result with an upper limit on $$V_aether$$ of 6.64 km/s.

[2]Trimmer et al., Phys. Rev. D8, p3321 (1973); Phys. Rev. D9 p2489 (1974).
A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of 0.025 m/s. This is about one-millionth of the Earth's orbital velocity and about 1/10,000 of its rotational velocity.

So, "Aether" may be working on yet another such experiment. The result (if the experiment is not going to be forged) should be null, contradicting Cahill. Kind of strange that Cahill wrote his paper in 2002 but did not do any experiment. He seemed content to fake the explanation of the MM and Miller experiments.

2. What is the deal with the Reg Cahill paper?
Aside from being a well known kook, his paper is dead wrong. Can you spot the error? Hint: the light speed in the moving refringent medium is not c/n when calculated wrt to the CMBR frame. Cahill does not understand the elementary speed composition! He doesn't even understand the old Fizeau law for speed of light in moving bodies (which agrees with the relativistic explanation!)

3. How about "Aether's" recent follow-up on the Cahill paper? (see post 61). I think I found it here:

http://arxiv.org/ftp/physics/papers/0603/0603267.pdf

It is nothing less than an attempt to resurect the long dead "Lorentz-FitzGerald contraction", the long dead 1904 Lorentz theory.

We should really separate this from the current thread. On the other hand, should we even discuss kooky theories?

 

[wisp]

You obviously do not consider the PF Guidelines as something that applies to you.
Zz.

OK, I’ll try and stick with papers that have been published in a peer-reviewed journal, but it limits the scope to be able to challenge mainstream views.

 

[wisp]

Re: clj4 link
****
http://prola.aps.org/abstract/PRD/v42/i2/p731_1?qid=6c4ab66eee46e0e8&...


Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards
Timothy P. Krisher, Lute Maleki, George F. Lutes, Lori E. Primas, Ronald T. Logan, and John D. Anderson
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
Clifford M. Will
McDonnell Center for the Space Sciences, Department of Physics, Washington University, St. Louis, Missouri 63130
Received 25 September 1989
A new test of the isotropy of the one-way velocity of light has been performed using NASA’s Deep Space Network (DSN). During five rotations of the Earth, we compared the phases of two hydrogen-maser frequency standards separated by 21 km using an ultrastable fiber optics link. Because of the unique design of the experiment, it is possible to derive independent limits on anisotropies that are linear and quadratic in the velocity of the Earth with respect to a preferred frame. Assuming that the anisotropies have not been partially canceled by systematic environmental effects on the instrumentation, the best limits that can be inferred from the data are Δc/c<3.5×10-7 and Δc/c<2×10-8 for linear and quadratic dependencies, respectively, on the velocity of the Earth with respect to the cosmic microwave background. The theoretical interpretation of the experiment is discussed.

****

Why don’t physicists write in plain English? What exactly are they saying here?

I understand this as: - They tested for a variation in the one-way speed of light and reported a negative result.
But this negative result was only with respect to the cosmic microwave radiation (CMR) frame. Do they not want to report the variation in the one-way speed of light in the earth-frame in which their test equipment resides?

What was the point in stating an upper limit on the one-way linear anisotropy of 100 m/s for an earth-based test, when the limit only applies to a frame moving at 400km/s relative to the earth?
If the CMR is an ether frame, then all they are saying is that light moves at constant speed through the ether.

 

[ZapperZ]

OK, I’ll try and stick with papers that have been published in a peer-reviewed journal, but it limits the scope to be able to challenge mainstream views.

Well tough! That's the rule you have agreed to. Would you like me to quote some crackpot website to challenge YOUR views?

Zz.

 

[clj4]

Re: clj4 link
****
http://prola.aps.org/abstract/PRD/v42/i2/p731_1?qid=6c4ab66eee46e0e8&...Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards
Timothy P. Krisher, Lute Maleki, George F. Lutes, Lori E. Primas, Ronald T. Logan, and John D. Anderson
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
Clifford M. Will
McDonnell Center for the Space Sciences, Department of Physics, Washington University, St. Louis, Missouri 63130
Received 25 September 1989
A new test of the isotropy of the one-way velocity of light has been performed using NASA’s Deep Space Network (DSN). During five rotations of the Earth, we compared the phases of two hydrogen-maser frequency standards separated by 21 km using an ultrastable fiber optics link. Because of the unique design of the experiment, it is possible to derive independent limits on anisotropies that are linear and quadratic in the velocity of the Earth with respect to a preferred frame. Assuming that the anisotropies have not been partially canceled by systematic environmental effects on the instrumentation, the best limits that can be inferred from the data are Δc/c<3.5×10-7 and Δc/c<2×10-8 for linear and quadratic dependencies, respectively, on the velocity of the Earth with respect to the cosmic microwave background. The theoretical interpretation of the experiment is discussed.

****

Why don’t physicists write in plain English? What exactly are they saying here?

I understand this as: - They tested for a variation in the one-way speed of light and reported a negative result.
But this negative result was only with respect to the cosmic microwave radiation (CMR) frame. Do they not want to report the variation in the one-way speed of light in the earth-frame in which their test equipment resides?

What was the point in stating an upper limit on the one-way linear anisotropy of 100 m/s for an earth-based test, when the limit only applies to a frame moving at 400km/s relative to the earth?
If the CMR is an ether frame, then all they are saying is that light moves at constant speed through the ether.

You are understanding it incorrectly. Your bias prevents you from understanding it. Tough.

 

[Aether]

Re: clj4 link
****
http://prola.aps.org/abstract/PRD/v42/i2/p731_1?qid=6c4ab66eee46e0e8&...


Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards
Timothy P. Krisher, Lute Maleki, George F. Lutes, Lori E. Primas, Ronald T. Logan, and John D. Anderson
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
Clifford M. Will
McDonnell Center for the Space Sciences, Department of Physics, Washington University, St. Louis, Missouri 63130
Received 25 September 1989
A new test of the isotropy of the one-way velocity of light has been performed using NASA’s Deep Space Network (DSN). During five rotations of the Earth, we compared the phases of two hydrogen-maser frequency standards separated by 21 km using an ultrastable fiber optics link. Because of the unique design of the experiment, it is possible to derive independent limits on anisotropies that are linear and quadratic in the velocity of the Earth with respect to a preferred frame. Assuming that the anisotropies have not been partially canceled by systematic environmental effects on the instrumentation, the best limits that can be inferred from the data are Δc/c<3.5×10-7 and Δc/c<2×10-8 for linear and quadratic dependencies, respectively, on the velocity of the Earth with respect to the cosmic microwave background. The theoretical interpretation of the experiment is discussed.

****

Why don’t physicists write in plain English? What exactly are they saying here?

I understand this as: - They tested for a variation in the one-way speed of light and reported a negative result.
But this negative result was only with respect to the cosmic microwave radiation (CMR) frame. Do they not want to report the variation in the one-way speed of light in the earth-frame in which their test equipment resides?

What was the point in stating an upper limit on the one-way linear anisotropy of 100 m/s for an earth-based test, when the limit only applies to a frame moving at 400km/s relative to the earth?
If the CMR is an ether frame, then all they are saying is that light moves at constant speed through the ether.

Do you have a copy of the paper, or are you only looking at the abstract? The paper describes a series of measurements made in the laboratory frame, and their analysis boils this down to the more concise statements made in the abstract. Their claim about "measuring" the "one-way speed of light" is coordinate-system dependent, and needlessly confusing. What they actually "measure" is the Mansouri-Sexl parameter $$\alpha$$.

 

[clj4]

Do you have a copy of the paper, or are you only looking at the abstract? The paper describes a series of measurements made in the laboratory frame, and their analysis boils this down to the more concise statements made in the abstract. Their claim about "measuring" the "one-way speed of light" is coordinate-system dependent, and needlessly confusing. What they actually "measure" is the Mansouri-Sexl parameter $$\alpha$$.

You don't understand what you read either. In addition , you willfully and shamelessly distort what the authors say, the authors never claim to be "measuring" the "one-way speed of light" Here is exactly what they say:

"A new test of the isotropy of the one-way velocity of light has been performed using NASA’s Deep Space Network (DSN)."

ISOTROPY, this is what they measured (more exactly they put constraint bars on ANISOTROPY). For a while I thought I was discussing with a person interested in scientific truth. Not after I found out what you stand for in your web page:

http://levynewphysics.com/

You are not here to discuss science, you are here to push your anti-science, antirelativistic views.

 

[Aether]

You don't understand what you read either. In addition , you willfully and shamelessly distort what the authors say, the authors never claim to be "measuring" the "one-way speed of light" Here is exactly what they say:

"A new test of the isotropy of the one-way velocity of light has been performed using NASA’s Deep Space Network (DSN)."

ISOTROPY, this is what they measured (more exactly they put constraint bars on ANISOTROPY).

Ok, their claim about "measuring" the "isotropy of the one-way velocity of light" is coordinate-system dependent, and needlessly confusing. What they are actually trying to "measure" is the Mansouri-Sexl parameter $$\alpha$$.

For a while I thought I was discussing with a person interested in scientific truth. Not after I found out what you stand for in your web page:

http://levynewphysics.com/

You are not here to discuss science, you are here to push your anti-science, antirelativistic views.

This isn't my web page. I've never seen it before.

 

[wisp]

You don't understand what you read either... the authors never claim to be "measuring" the "one-way speed of light" Here is exactly what they say:

"A new test of the isotropy of the one-way velocity of light has been performed using NASA’s Deep Space Network (DSN)."

ISOTROPY, this is what they measured (more exactly they put constraint bars on ANISOTROPY).

Thanks for your reply in defining the purpose of this test – it’s as clear as mud.
This is confusing. If you look up the definitions of ISOTROPY, ISOTROPIC, ANISOTROPIC, ANISOTROPY they are defined as: -

http://en.wikipedia.org/wiki/Isotropic

http://www.pcmag.com/encyclopedia_term/0,2542,t=isotropic&i=45480,00.asp

Isotropic: Definition of: isotropic
Refers to properties, such as transmission speed, that are the same regardless of the direction that is measured. Contrast with anisotropic.

Definition of: anisotropic :-
Refers to properties, such as transmission speed, that vary depending on the direction of measurement. Contrast with isotropic.

So to sum up – This test doesn’t measure the one-way speed of light (your words).

 

[wisp]

Some clj4 quotes

#13

Secondly, contrary to what you think, one way speed of light has been measured repeatedly to be equal to c INDEPENDENT of the RELATIVE movement of the observer and the source.

#21

The third paper, while it only "suggests" a means of executing one way light speed measurements looks awfully close in approach to the one way experiment of Gagnon.

Obviously there’s confusion in the wording used. So for the benefit of all, can anyone explain in plain English explain what the difference are between the two statements: -

1) Experiments that measure variations in the one-way speed of light
2) Experiments that measure anisotropy in the one-way speed of light.

 

[clj4]

Ok, their claim about "measuring" the "isotropy of the one-way velocity of light" is coordinate-system dependent, and needlessly confusing. What they are actually trying to "measure" is the Mansouri-Sexl parameter $$\alpha$$.

This isn't my web page. I've never seen it before.

..and neither is this "masterpiece" of antirelativism that you are boasting about here:

https://www.physicsforums.com/showpost.php?p=970766&postcount=61

The one that is collecting dust at arxiv.org:

http://arxiv.org/ftp/physics/papers/0603/0603267.pdf

The one endorsed by Reg Cahill.

 

[Aether]

..and neither is this "masterpiece" of antirelativism that you are boasting about here:

https://www.physicsforums.com/showpost.php?p=970766&postcount=61

Correct.

The one that is collecting dust at arxiv.org:

http://arxiv.org/ftp/physics/papers/0603/0603267.pdf

The one endorsed by Reg Cahill.

This is not my paper. I'll offer to make my paper on this subject immediately available to Zz, pervect, JesseM, Hurkyl, Tom Mattson, or Garth (sorry if I left anyone out) if any or all of them want to help referee it. Btw, this subject has nothing at all to do with my own personal theory that I have mentioned; it is simply an opportunity to do some interesting experiments out of my own pocket.

 

[clj4]

Correct.

This is not my paper. I'll offer to make my paper on this subject immediately available to Zz, pervect, JesseM, Hurkyl, Tom Mattson, or Garth (sorry if I left anyone out) if any or all of them want to help referee it. Btw, this subject has nothing at all to do with my own personal theory that I have mentioned; it is simply an opportunity to do some interesting experiments out of my own pocket.

Yes, you missed me.I'll have a look at it.

 

[quantumdude]

Aether,

If you've written a paper that you'd like to discuss but that hasn't been peer-reviewed you can send it to the IR Forum, where it will go into a moderation queue. Anyone who wears the "PF Admin", "PF Mentor", or "Science Advisor" emblems will be able to review it. All of the people on your list fall into one of those categories.

 

[Aether]

Aether,

If you've written a paper that you'd like to discuss but that hasn't been peer-reviewed you can send it to the IR Forum, where it will go into a moderation queue. Anyone who wears the "PF Admin", "PF Mentor", or "Science Advisor" emblems will be able to review it. All of the people on your list fall into one of those categories.

Thank-you, Tom. I know that, and appreciate the availability of the IR forum. I'm preparing to actually carry out some experiments, and don't want to post my paper in public before I have actual results to share. Is there any way to post the paper, get feedback, and delay public viewing until a later time?

 

[quantumdude]

The only way is to send it to IR and then correspond with the reviewers. It can be held in the moderation queue indefinitely.

 

[Aether]

The only way is to send it to IR and then correspond with the reviewers.

Thanks. I'll review my paper for compliance with IR guidelines, and then drop it into the moderation queue.

It can be held in the moderation queue indefinitely.

No doubt!

 

[quantumdude]

No doubt!

I'm just saying, we advertise a turnaround time of 30 days for action to be taken on IR threads. I didn't want you to think that we would automatically make your paper public after that time. We'll hold it as long as you want.

 

[clj4]

I'm just saying, we advertise a turnaround time of 30 days for action to be taken on IR threads. I didn't want you to think that we would automatically make your paper public after that time. We'll hold it as long as you want.

Aether,
I promise a turnaround of 1 day. If it is correct, I will say so. If it is wrong, you know by now that I can spot errors very fast.

 

[Aether]

Aether,
I promise a turnaround of 1 day. If it is correct, I will say so. If it is wrong, you know by now that I can spot errors very fast.

I know that you have some good skills, better than mine in some areas, but your attitude isn't scientific; at least not the attitude that you have projected here so far, IMHO.

 

[clj4]

I know that you have some good skills, better than mine in some areas, but your attitude isn't scientific; at least not the attitude that you have projected here so far, IMHO.

Come on, Aether

What do you have to loose? I can spot errors in a matter of minutes. I might end up saving you a lot of time and money. And, if the paper is correct, I will say so. I don't play games.

 

[clj4]

I know that you have some good skills, better than mine in some areas, but your attitude isn't scientific; at least not the attitude that you have projected here so far, IMHO.

haven't you already submitted it at arxiv? This is what you told us earlier. Just point us to the correct paper, would you?

 

[Aether]

haven't you already submitted it at arxiv? This is what you told us earlier. Just point us to the correct paper, would you?

This is not what I told you earlier. My paper isn't on arxiv.

 

[clj4]

This is not what I told you earlier. My paper isn't on arxiv.

Hmmm

hard to know what to believe in what you are saying. Here is your own post in this thread, post 61:

I wrote a paper on this subject last year and showed it to Reg Cahill. He made some suggestions, and after I addressed those within the paper he personally endorsed me at arxiv.org to post papers there. The paper discusses an experiment that I am preparing to carry out myself, and I'll post it when I have some definitive results.

Now, you and I both know that M-M experiments are two-way experiments, right? So why are you connecting this subject to one-way experiments?

Are you saying you haven't posted it at arxiv yet?

 

[quantumdude]

Are you saying you haven't posted it at arxiv yet?

I wrote a paper on this subject last year and showed it to Reg Cahill. He made some suggestions, and after I addressed those within the paper he personally endorsed me at arxiv.org to post papers there. The paper discusses an experiment that I am preparing to carry out myself, and I'll post it when I have some definitive results.

See it now?

 

[wisp]

So for the benefit of all, can anyone explain in plain English explain what the difference are between the two statements: -

1) Experiments that measure variations in the one-way speed of light
2) Experiments that measure anisotropy in the one-way speed of light.

I’ll explain it as best I can, as nobody seems up for the challenge or you don’t think it important – correct me if you think I’m wrong.

1) Experiments that measure variations in the one-way speed of light are not possible according to Einstein (and Aether, and others). Consequently no one has carried out a simple one-way experiment using a laser, a start clock and stop clock, because of the issue of synchronizing clocks.

2) Experiments that measure anisotropy in the one-way speed of light are the norm in mainstream physics. Because the coordinate system used is isotropic, light always has the same velocity in all directions, and so there is no need to actually measure the one-way light speed, as it should always be constant.

I believe a simple one-way experiment using a laser and two clocks is possible. And it is possible to correctly synchronize clocks. Results will prove beyond any doubt that the speed of light one-way will vary by +/-V.

The Krisher et al test for anisotropy refers to the cosmic microwave radiation (CMR) frame. There is always a null result in this frame, and it could even be the ether frame, so the test proves nothing. What we really need to know is what is the anisotropy for the Earth frame. If the result for the Earth frame is positive then the whole concept of an isotropic coordinate system is void, and consequently relativity fails.

 

[Ich]

You can synchronize clocks using slow transport and then measure c. This has been done, the constancy of c has been verified. That is a nontrivial result. There could be variation (as in emitter theory, caused by the speed of the light source) or anisotropy (as in early aether theories).
You can´t measure the one way speed only if you doubt that slow transport preserves synchronisation. At the same time you must doubt the validity of Newtonian mechanics in your reference frame, knowing that it would still work if you only had defined your frame reasonably.

 

[clj4]

I’ll explain it as best I can, as nobody seems up for the challenge or you don’t think it important – correct me if you think I’m wrong.

1) Experiments that measure variations in the one-way speed of light are not possible according to Einstein (and Aether, and others). Consequently no one has carried out a simple one-way experiment using a laser, a start clock and stop clock, because of the issue of synchronizing clocks.

2) Experiments that measure anisotropy in the one-way speed of light are the norm in mainstream physics. Because the coordinate system used is isotropic, light always has the same velocity in all directions, and so there is no need to actually measure the one-way light speed, as it should always be constant.

I believe a simple one-way experiment using a laser and two clocks is possible. And it is possible to correctly synchronize clocks. Results will prove beyond any doubt that the speed of light one-way will vary by +/-V.

The Krisher et al test for anisotropy refers to the cosmic microwave radiation (CMR) frame. There is always a null result in this frame, and it could even be the ether frame, so the test proves nothing. What we really need to know is what is the anisotropy for the Earth frame. If the result for the Earth frame is positive then the whole concept of an isotropic coordinate system is void, and consequently relativity fails.

No one is listening to your babbling , wisp.

 

[Aether]

In a nutshell, after hundreds of posts "Aether"+the two sock puppets on one side and I on the other side have agreed that (see https://www.physicsforums.com/showpost.php?p=953407&postcount=394) the correct wave vector in the Gagnon experiment is linearly dependent on the Earth composite speed (orbital and rotational) as in :

$$k(v_z,\omega)=\frac{v_z}{c}*\frac{\omega}{c}+...$$ (1)

In SR, the term in $$v_z$$ does not exist. IN GGT (an aether theory derived from the Mansouri-Sexl theory), the term in $$v_z$$ is present.

What followed in the BAUT ("Against the Mainstream"!) forum was a disagreement as to whether one could extract the quantity $$(k+k')L/2$$ from the two waves of the form :
$$A*cos(kL-\omega*t)$$ and respectively $$A*cos(k'L-\omega*t)$$
There are at least 3 ways to do exactly that : extract $$(k+k')L/2$$ . I am sure that there are more. The quantity $$(k+k')L/2$$, being dependent of $$v_z$$ gives an excellent tool for separating the SR predictions from the GGT (MS) predictions and from the experimental measurements that agree with SR and disagree with GGT. ("Aether" insists on using the term $$(k-k')L/2$$ that is obviously independent of $$v_z$$)

I was thinking about ordering a beamsplitter cube for an optical interferometer today, and was reminded of a loose-end still dangling from this discussion. The RF interferometer described in the Gagnon paper measures the difference between two signal phases $$(k-k')L/2$$, but optical interferometers typically measure the sum of two signal phases $$(k+k')L/2$$.

http://www.bautforum.com/showpost.php?p=723272&postcount=82" you said that:

1. According to the Gagnon experiment (and any standard wave experiment) the authors measure:

Acos (kz-wt)-Acos(k'z-wt)

This quantity vanishes when k=k', and this is always the case in this experiment (see eq. (1) above) for parallel waveguides at rest wrt one another.

 

[clj4]

I was thinking about ordering a beamsplitter cube for an optical interferometer today, and was reminded of a loose-end still dangling from this discussion. The RF interferometer described in the Gagnon paper measures the difference between two signal phases $$(k-k')L/2$$, but optical interferometers typically measure the sum of two signal phases $$(k+k')L/2$$. http://www.bautforum.com/showpost.php?p=723272&postcount=82" you said that:

This quantity vanishes when k=k', and this is always the case in this experiment (see eq. (1) above) for parallel waveguides at rest wrt one another.

Last gasp try, aren't you? Just the way one can arrange to add two waves one can arrange to subtract them, it is good that you finally came to terms with the idea.
Now, the next thing for you to get is that k and k' are NOT equal. In order to figure that you would need to think a lot harder as to what the term "..." represents in eq.1. (Hint, it is a square root of TWO DIFFERENT quantities for k and k' respectively).

 

[Aether]

Last gasp try, aren't you? Just the way one can arrange to add two waves one can arrange to subtract them. Exercise: figure out how to do that.

You already stipulated that subtraction of the two waves gives a result "that is obviously independent of v_z", so now we're considering your proposal to measure the sum of the two signal phases. The result vanishes when k=k'. Is there anything else to consider?

 

[Aether]

Now, the next thing for you to get is that k and k' are NOT equal. In order to figure that you would need to think a lot harder as to what the term "..." represents in eq.1. (Hint, it is a square root of TWO DIFFERENT quantities for k and k' respectively).

Ok, so we agree that by your abbreviated eq. (1) the summing of the signals always yields a null result. Please state the full form of eq. (1) then.

 

[clj4]

Ok, so we agree that by your abbreviated eq. (1) the summing of the signals always yields a null result. Please state the full form of eq. (1) then.

Oh, you always try to twist things.
1. I maintained and maintain that you need to SUBTRACT the WAVEFORMS (which translates into ADDING the phases), so please refrain from your standard diversions.

2. The term that follows in eq. 1 is

sqrt (omega^2-omega_mn^2) for k

sqrt (omega^2-omega_pq^2) for k'

Happy now?

 

[Aether]

2. The term that follows in eq. 1 is

sqrt (omega^2-omega_mn^2) for k

sqrt (omega^2-omega_pq^2) for k'

Happy now?

Please show how SR and GGT make different predictions (from one another) when these terms are included in eq. (1).