Consistency of the speed of light

[Aether]

You are inverting (8b), right?

No.

I would expect to see a term in $$\omega_{pq}$$ in (8c). I am not seeing it.

$$\omega_{pq}=[p^2\pi^2\epsilon \mu \frac{c_0^2}{a_0^2}+q^2\pi^2\epsilon \mu \frac{c_0^2}{b_0^2}]^{1/2}$$ Eq. (8b),​

with $$(p,q)=(1,0)$$, and $$\epsilon \mu =1$$:

$$\omega_{10}=\pi \frac{c_0}{a_0}$$.​

$$\omega_{10}$$ is a cutoff angular frequency in the absolute frame, and $$\omega_c$$ is that cutoff angular frequency in a moving frame:

$$\omega_c=\frac{\pi c_0}{a}$$.​

Could you show the steps, at a superficial view, if I look at (8b) and at (1), i would expect to see the exponent $${-1/2}$$ in (8c)

To transform $$\omega_{10}$$ to $$\omega_c$$ using Eq. (1) we need to suppose that $$a_0$$ is a distance along the x-axis, and absolute motion is along the x-axis (this is necessary for now because Eq. (1) can only be used for motion and distance along the x-axis):

$$\omega_{c+}=\frac{\pi c_0}{\gamma (a_0-vt_0)}$$.​

However, $$a_0$$ lays along the x-axis while the wave propagates along the z-axis, and E reciprocates in the $$\pm x$$-direction. So, this last equation only applies while the transverse wave motion is in the $$+x$$ direction; while the transverse wave motion is in the $$-x$$ direction this equation applies:

$$\omega_{c-}=\frac{\pi c_0}{\gamma (a_0+vt_0)}$$.​

Eq. (8c) is an attempt to compute the average of these two equations, and may change slightly if this average turns out not to be done quite right.

$$\omega_c=\frac{2\pi c_0}{\gamma((a_0-vt_0)+(a_0+vt_0))}=\frac{\pi c_0}{\gamma a_0}$$;

$$\omega_c=\frac{2\pi c_0}{(a_0-vt_0)+(a_0+vt_0)}[1-\frac{v_x^2}{c_0^2}]^{1/2}=\frac{\pi c_0}{a_0}[1-\frac{v_x^2}{c_0^2}]^{1/2}$$ Eq. (8c);​

Who are a0 and b0?

$$a_0$$ and $$b_0$$ are the dimensions (in the absolute frame) of the interior cross-section of the waveguide. $$a_0$$ is taken to be along the x-axis, $$b_0$$ is taken to be along the y-axis. The electromagnetic wave propagates longitudinally along the z-axis. In a moving frame, these two dimensions transform to $$a$$ and $$b$$ respectively.

It is possible to compute $$\omega_c$$ and $$k$$ for a waveguide in a moving frame simply by transforming these coordinates (a,b).

 

[clj4]

Thank you, I will check it out. At a quick glance the average doesn't look right, doesn't lok like an average. Have you considered checking ref 9, apparently they did all the support calculations there. Might save you a lot of time.

 

[Aether]

Have you considered checking ref 9, apparently they did all the support calculations there. Might save you a lot of time.

Ref (9) should be very useful later, but it doesn't have anything to say about waveguides, $$k$$, etc. per se.

 

[clj4]

I think I found the error. Omega transforms like 1/t so instead of 1/gama you should have gama in your formula

 

[Aether]

I think I found the error. Omega transforms like 1/t so instead of 1/gama you should have gama in your formula

$$\omega$$ transforms like 1/t, but $$\omega_{pq}$$ is defined by the spatial geometry of the waveguide (and the round-trip speed of light). It does seem strange, I also thought that it should transform like 1/t at first. We could leave that as an open question for now.

 

[clj4]

$$\omega$$ transforms like 1/t, but $$\omega_{pq}$$ is defined by the spatial geometry of the waveguide (and the round-trip speed of light). It does seem strange, I also thought that it should transform like 1/t at first. We could leave that as an open question for now.

No, we cannot leave it open, it is a clear error.

 

[Aether]

No, we cannot leave it open, it is a clear error.

It is a clear error on whose part? The boundary conditions on the waveguide "require the tangential component of the electric field in the laboratory frame to vanish at the waveguide walls", and this identifies

$$\omega_c=\omega_{10}=\frac{\pi c_0}{a}=\frac{2\pi c_0}{\lambda}$$,​

so:

$$\frac{\omega_c}{c_0}= \frac{2\pi}{\lambda}=k^0$$,​

which corresponds to the timelike component of a wave 4-vector $$k^\mu$$ and that transforms like $$t$$, right?

 

[Aether]

That turns the whole idea of physical science on its head. No experiment can be devised that would prove any theory.

Sure there are experiments that can be devised to prove many theories, but this is not possible in the case of the postulate of SR regarding the constancy of the one-way speed of light. That is because all measurements of speed are inherently coordinate-system dependent. Doppler shifts, for example, are measurable in a coordinate-system independent way (e.g., $$\frac{v}{c}$$ is a coordinate-system independent dimensionless ratio), so you could actually prove something (within the limits of the precision of your measurements) by making such a measurement. The difference between coordinate-system dependent vs. independent measurements is what we're talking about here.

 

[Jimmy Snyder]

Sure there are experiments that can be devised to prove many theories.

I deleted my post because it was redundant. Name a theory and the experiment that proves it.

 

[Aether]

I deleted my post because it was redundant. Name a theory and the experiment that proves it.

Theory: The Sun is made up of mostly hydrogen and helium; Experiment that proves it: spectroscopic analysis of sunlight vs. ionized hydrogen and helium. Duh.

You deleted your original post. If you still don't want to have this conversation (at least not here and now), then delete your second post too and I'll delete my responses.

 

[Jimmy Snyder]

Duh.

I don't like the direction this discussion is taking.

All that your experiment proves is that there is something in or on the Sun that produces the same spectral lines as Hydrogen and Helium do on the Earth. An extraordinary coincidence indeed, but I'm afraid that does not prove your theory.

 

[Aether]

All that your experiment proves is that there is something in or on the Sun that produces the same spectral lines as Hydrogen and Helium do on the Earth. An extraordinary coincidence indeed, but I'm afraid that does not prove your theory.

OK, Theory #2: There is something in or on the Sun that produces the same spectral lines as Hydrogen and Helium do on the Earth; Experiment that proves it: spectroscopic analysis of sunlight vs. ionized hydrogen and helium.

 

[Jimmy Snyder]

OK, Theory #2: There is something in or on the Sun that produces the same spectral lines as Hydrogen and Helium do on the Earth; Experiment that proves it: spectroscopic analysis of sunlight vs. ionized hydrogen and helium.

The experiment that you cite cannot have taken place since light from the sun is slightly red-shifted. The lines coming from the sun do not exactly match those of Hydrogen and Helium on the earth.

 

[Aether]

The experiment that you cite cannot have taken place since light from the sun is slightly red-shifted. The lines coming from the sun do not exactly match those of Hydrogen and Helium on the earth.

The experiment has taken place, and as I said before "you could actually prove something (within the limits of the precision of your measurements) by making such a measurement".

 

[Jimmy Snyder]

The experiment has taken place.

But the results were not as you claim. The spectral lines were not the same, just similar.

No amount of experimentation can ever prove me right; a single experiment can prove me wrong. -- Albert Einstein

 

[masudr]

An experiment can change the status of an assertion from "hypothesis" to "likely to be true".

Note that this is in NO WAY WHATSOEVER a proof. Proof of some conjecture, in the mathematical (and the only relevant) sense, implies there is no way that some conjecture can ever be false.

Your statements about the spectral line merely say that at the time the experiment was done the measurements agreed with those that occurred on Earth (even assuming the light wasn't redshifted). However, to PROVE the conjecture, you would need to show that no matter when you did the experiment and under WHATEVER circumstance, you would still get the same results. There is no experiment that can ever do that to any theoretical conjecture or hypothesis. That is the status of theory or postulate in ANY empirical science.

 

[Jimmy Snyder]

An unexplained center-to-limb variation of solar wavelength has been known for 75 years.

http://www.Newtonphysics.on.ca/Chromosphere/CHROMOSPHERE.html

 

[Aether]

But the results were not as you claim. The spectral lines were not the same, just similar.

No amount of experimentation can ever prove me right; a single experiment can prove me wrong. -- Albert Einstein

An experiment can change the status of an assertion from "hypothesis" to "likely to be true".

Note that this is in NO WAY WHATSOEVER a proof. Proof of some conjecture, in the mathematical (and the only relevant) sense, implies there is no way that some conjecture can ever be false.

Your statements about the spectral line merely say that at the time the experiment was done the measurements agreed with those that occurred on Earth (even assuming the light wasn't redshifted). However, to PROVE the conjecture, you would need to show that no matter when you did the experiment and under WHATEVER circumstance, you would still get the same results. There is no experiment that can ever do that to any theoretical conjecture or hypothesis. That is the status of theory or postulate in ANY empirical science.

OK, there is a sense in which what you are saying makes sense: "Scientific theories are never proven to be true, but can be disproven. All scientific understanding takes the form of hypotheses, or conjectures" -- http://en.wikipedia.org/wiki/Theory. However, in the context of this thread and Einstein's quote that isn't what we're talking about at all. We are talking about something very specific, about whether it is possible (or not) to make a coordinate-independent measurement of the one-way speed of light. We all agree (at least for the purposes of this discussion) that we can measure the round-trip speed of light. If you want to argue that we really can't even measure the round-trip speed of light (or anything else for that matter), then please do that in another thread.

I interpret Einstein's quote as a warning that he is assuming that Lorentz symmetry is perfect, that no experiment can ever prove that it is perfect, but a single experiment could prove that it is not perfect. Not some general notion which would also apply to every other scientist in the world just as well.

 

[Jimmy Snyder]

If you want to argue that we really can't even measure the round-trip speed of light, then please do that in another thread.

I didn't say that you can't do experiments. I said that you can't prove theories. It was in response to the original post in this thread.

 

[gregory_]

Hello, I've been watching this topic off and on for quite awhile now and it appears to be getting off track. I'm sorry to finally speak up on a note like this... but if it is possible, can we please focus on the issue at hand again?

We are talking about something very specific, about whether it is possible (or not) to make a coordinate-independent measurement of the one-way speed of light.

It appears that this is what the topic started as. And it appears to be what you keep trying to return to. But I don't understand why all the calculations dealing with Gagnon's experiment are necessary for this topic.

You have argued your point well and clearly. I have seen no mathematically consistent argument against your statement that coordinate independent one-way velocity measurements do not exist.

So, to help clarify this long thread, has everyone come to an agreement on this main point and you have moved onto the specifics of one experiment?

Since it is easy to mathematically prove that coordinate independent one-way velocity measurements do not exist, if there is still a debate on this point, it would seem more appropriate to settle this simple question first instead of trying to do it with the messy details of just one particular experiment. Wouldn't you agree?

 

[Jimmy Snyder]

I interpret Einstein's quote as ... Not some general notion which would also apply to every other scientist in the world just as well.

Here is a small sample of quotes I got off the net indicating that Einstein's quote is accepted in the larger context.

-------------------------------------------------------------------

A theory is an explanation, a coherent set of ideas. They are not "proven," which tends to puzzle non-scientists. Theories can't be proven. They are accepted based on how well they are supported by empirical evidence, which is one of the reasons they change.
http://edstar.ncrel.org/mn/ViewEssay.asp?IssueID=37&EssayID=155

We can never be quite sure that we had indeed found the correct theory, since theories can't be proven.
http://www.spaceandmotion.com/Physics-Stephen-Hawking.htm

Scientific theories are never proven to be true, but can be disproven.
http://en.wikipedia.org/wiki/Theory

 

[Jimmy Snyder]

Your statements about the spectral line merely say that at the time the experiment was done the measurements agreed with those that occurred on Earth (even assuming the light wasn't redshifted). However, to PROVE the conjecture, you would need to show that no matter when you did the experiment and under WHATEVER circumstance, you would still get the same results.

Having slept on this, I came up with some ideas.

I am not a scientist. I agree with you that the theories I am familiar with from reading scientific texts are of such a universal nature that their proof would require the kind of universal experiment you describe. None-the-less, there is nothing preventing me from coming up with a less universal theory. For instance: "Last night, an electron hit the phosphorus on the screen of my TV, and I saw the resulting scintilation." However, the fact that I saw the scintilation does in no way prove the existence of electrons. That remains a theory. I saw a scinitilation. If I report more than what I actually saw, then whether I am aware of it or not, I am stating a theory. And to the extent that my theory differs, even by one iota, from what I actually saw, my theory is not proven. On the other hand, I can be more careful in the statement of my theory.

Snyder's Theory of Everything: "Last night, I saw a scintilation on the screen of my TV."

This won't do either. In the process of limiting my statement to what I actually saw, I have not a theory, but a fact.

Heads you win, tails I lose, for either way I have not proved a theory.

 

[Aether]

It appears that this is what the topic started as. And it appears to be what you keep trying to return to. But I don't understand why all the calculations dealing with Gagnon's experiment are necessary for this topic.

That is because Gagnon et al. have published a paper in a respected physics journal that claims (or seems to) to have measured the one-way speed of light in a coordinate-independent way. There has been no rebuttal to their claims, at least not that has been published by the American Physical Society, so clj4 can point to their paper as evidence until it is refuted.

You have argued your point well and clearly. I have seen no mathematically consistent argument against your statement that coordinate independent one-way velocity measurements do not exist.

Thank-you. That's right, but the Gagnon paper stands until it is refuted, so we're sudying the details of the paper.

So, to help clarify this long thread, has everyone come to an agreement on this main point and you have moved onto the specifics of one experiment?

Not everyone has agreed on this main point. There are a half-dozen (or so) papers like Gagnon et al. that claim to have measured one-way speeds of light, and we may need to deal with each of them in turn.

Since it is easy to mathematically prove that coordinate independent one-way velocity measurements do not exist, if there is still a debate on this point, it would seem more appropriate to settle this simple question first instead of trying to do it with the messy details of just one particular experiment. Wouldn't you agree?

Yes, I agree. If you would like to present such a proof, then please do so. However, these published papers that claim to have actually made coordinate independent one-way veocity measurements have to be properly refuted (especially if someone is insisting); wouldn't you agree?

 

[gregory_]

... so clj4 can point to their paper as evidence until it is refuted.

They measured basically no phase difference. Do we disagree with that? No, I don't believe anyone is disagreeing with their actual phase difference measurements at the moment. Our real complaint is in their calculations that claim this amounts to determining the universe's "real" synchronization convention.

And you have refuted this. You explained very clearly why such a measurement isn't possible. You showed that their paper's conclusions (not measurements) are wrong. Therefore if anyone wants to disagree the next step is for clj4 or others to counter your argument and so on.

Making both parties drag through the details of every paper is to lose sight of the main point. The best part about science is that we can work out the calculations ourselves. So, let's shed the experimental details, and come to agreement on whether a one way velocity can be defined independent of a coordinate system.

Then we can go back and approach the papers at our leisure if we want to nail down their error. To do it in the other order when the argument is so simple is just going to result in debating ad infinitum. Also, if one insists on doing it that way, the result never feels "convincing" since many detailed calculations were required and no insight into "why" it worked out this way can be seen. If one can make a general proof it is always preferred to working out every case individually. Besides, it is always best to understand the easy cases (which also happens to be the general case here) before burying oneself in detailed calculations.


Here, I will even help start this. Let me explain why no experiment can distinguish between "Generalized Galilean Transformations" and "Lorentz transformations".

1] There is one frame in which both theories agree on the form of every physical law. Perform the calculations in this frame to predict the result of the experiment. By definition the two theories must agree on the predictions.

Actually, that's it.


Or, here's a more specific case:
1] The time measured by a moving clock (in arbitrary motion) between two events on its path and coincident with its position are invarients in both theories (and both theories predict the same result).

2] Therefore all experiments measuring time differrences on a clock cannot distinguish between these two theories.

3] The two theories can agree on the spatial coordinates for all events.

4] Therefore any "measurement" of one way velocity which requires measuring time differences and length differences cannot distinguish between the two theories.

I can show the math for those steps if one really wishes, but given the statements from people so far, it appears we agree on those (which makes it confusing why we don't agree on the final conclusion).

------------------

So, clj4, please answer the following:
Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

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.

 

[my_wan]

We are talking about something very specific, about whether it is possible (or not) to make a coordinate-independent measurement of the one-way speed of light.

That does very much sum up the problem. I think you refuse to accept that nature doesn't provide for observing such a measurement because it is all you have.

I don't think anyone can disagree that that aethereal theories of SR can be presented that does not contradict experimental evidence. The impossibility of your quote only expands the possible numbers of them. Choosing such a theory for purely biased reasons is not science but would be a valid logical exercise if your bias wasn't forcing you to cling to a dead horse.

Suppose for the sake of argument I had a theory that technically qualified as an ether theory and I could make the following true statements about.
SR is derivable 'AS IS'.
Mass energy equivalence is trivially derived.
Qualitatively conforms to GR 'AS IS'.
Reproduces the predictions of GR in the special cases checked.
Demands quantization of measurements.
The core equalities of QM trivially derived.
Provides opertional mechanisms for EPR without C violations as long as information is properly defined.
Demands things like DSR.
http://www.physicspost.com/articles.php?articleId=129"
The unobservables prevailant in such theories used instead to define and derive symmetries in the observable physics.
Etc, etc.

Do I have enough? No... Why? Where did I make even one prediction? Even DSR is a retridiction. Even though it's probably in principle falsiable I haven't supplied any method of doing so. Not to mention that I've failed to articulate any problems with it. So come on, back up and rethink your core assumptions. Articulate them PRECISELY right down to what an ether could be at it's most basic level. See if you can make something and quit hanging your hat on one unobservable concept. Or else you can be just another board spammer...

 

[Aether]

We are talking about something very specific, about whether it is possible (or not) to make a coordinate-independent measurement of the one-way speed of light.

I think you refuse to accept that nature doesn't provide for observing such a measurement because it is all you have.

You have this backwards. It is clj4 who has refused (so far) to accept this. Anyone else?

Choosing such a theory for purely biased reasons is not science but would be a valid logical exercise if your bias wasn't forcing you to cling to a dead horse.

Please explain.

Do I have enough? No... Why? Where did I make even one prediction?

I predicted that the paper of Gagnon et al. wouldn't hold up to careful scrutiny, and I further predict that anyone who doesn't heed this lesson and produces a work in contradiction to the principles that we are discussing will fail.

So come on, back up and rethink your core assumptions. Articulate them PRECISELY right down to what an ether could be at it's most basic level. See if you can make something and quit hanging your hat on one unobservable concept. Or else you can be just another board spammer...

I do have a personal theory that leads me to examine these false claims of coordinate independent one-way speed measurements, but this isn't a place for personal theories; and even if it was, there is a long incubation period for such a thing.

 

[Hans de Vries]

Aether,

For havens sake, when are you going to see the light?
Which transformation is right? Lorentz or Mansouri-Sexl?
Do you still consist that they are not experimentally distinguishable?


Regard, Hans

 

[Aether]

Aether,

For havens sake, when are you going to see the light?
Which transformation is right? Lorentz or Mansouri-Sexl?
Do you still consist that they are not experimentally distinguishable?Regard, Hans

Hello Hans,
Please show the details of how you're generating those graphs, and then show how to calculate the output of a hypothetical experiment from the equations. If you can show that different outcomes for an actual (hypothetical and idealized) experiment are predicted by the two sets of transforms, then I'll have to see the light. If you can't do that, then you'll have to see the light. Deal?

If you could set-up a simulation of the experiment as I did in post #164 (e.g., providing both the output and source code), that would be great. If you're not a programmer, then I'll write a program from your Latex (that is, if you still think that you have a valid point after reading what I have to say below about your wave drawings).

What are the horizontal and vertical axes in your drawings? I presume that absolute motion is along the x-axis, so the waves in your drawings are propagating back and forth along the y-axis? You only have the transformation equation for the x-axis to work with at the moment, so for now you must have both the longitudinal axis of wave propagation and the absolute motion along the x-axis in order to transform your experiment using the equations given. If you do that, you will see that the wave's round-trip travel time is predicted to be the same for both transforms. If you do not use a round-trip, then you'll also have to provide either a reference waveguide or a second clock/oscillator at the far end of the first waveguide.

 

[Hans de Vries]

Hello Hans,
Please show the details of how you're generating those graphs, and then show how to calculate the output of a hypothetical experiment from the equations. If you can show that different outcomes for an actual (hypothetical and idealized) experiment are predicted by the two sets of transforms, then I'll have to see the light. If you can't do that, then you'll have to see the light. Deal?

That's OK.

If you could set-up a simulation of the experiment as I did in post #164 (e.g., providing both the output and source code), that would be great. If you're not a programmer, then I'll write a program from your Latex (that is, if you still think that you have a valid point after reading what I have to say below about your wave drawings).

I was thinking in modifying my deBroglie wave program for this purpose
but I can just as well do this from scratch.

What are the horizontal and vertical axes in your drawings? I presume that absolute motion is along the x-axis, so the waves in your drawings are propagating back and forth along the y-axis? You only have the transformation equation for the x-axis to work with at the moment, so for now you must have both the longitudinal axis of wave propagation and the absolute motion along the x-axis in order to transform your experiment using the equations given. If you do that, you will see that the wave's round-trip travel time is predicted to be the same for both transforms. If you do not use a round-trip, then you'll also have to provide either a reference waveguide or a second clock/oscillator at the far end of the first waveguide.

A laser gives a light pulse downwards vertically in the rest frame.
There's a mirror at the bottom which reflects the light back.

The laser can be made to co-move width the moving frame so that
it will stay at the same position in the moving frame.


Regards, Hans

 

[Hans de Vries]

I write the program in the 3D raytracing Povray language which is simple
to follow and gives a very powerful visualization environment.

http://www.povray.org/

You can download and install the program for free here.

http://www.povray.org/download/

Then just copy and paste my program and click the RUN button.


Regards, Hans