Standing light waves if the one-way speed of light were not constant?

[greypilgrim]

Hi.

According to Wikipedia: The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector.

Mid 20^th century, the most precise measurements of the speed of light were done using cavity resonance. But how could standing waves form if the speeds were different for both ways, wouldn't either $\lambda$ or $f$ (or both) be different?

Also: Leaving the cavity away and just using a laser and a far away mirror, couldn't I just measure $\lambda$ for the leaving and reflected beam (e.g. with a diffraction grating) and $f$ (e.g. using the photoelectric effect) and if they both are the same, so must be $c=\lambda\cdot f$?

 

[Ibix]

See here. Changing the one way speed of light is just messing with your synchronization convention. It just changes your interpretation of what's going on in the cavity, nothing else.

 

[greypilgrim]

What would be wrong with my proposal, i.e. measure wavelength and frequency of a leaving and the reflected beam separately?

 

[Vanadium 50]

What would be wrong with my proposal,

Apart from the fact that it is a personal theory and therefore off-limits on PF? Or that the one-way speed of light is not a defined quantity but depends on your measuring convention - as has been said over and over again on PF including this very thread? Or something else.

 

[cianfa72]

I would add that the 2nd postulate of Einstein's SR is actually two folded. Namely in any inertial frame:

1. the (two-way) speed of light doesn't depend on source motion, is isotropic (as MMX experiment shows) and has the same invariant value $c$
2. there exists a consistent way to synchronize clocks at rest in any given inertial frame in a such way that the one-way speed of light is isotropic with invariant speed $c$ (Einstein's synchronization convention)

The condition to be consistent in 2. does mean that Einstein's synchronization convention is actually an equivalence relation. BTW it can be shown that from assuming 1. for every closed path then it follows that 2. is actually an equivalence relation (applied to spacetime events).

 

[greypilgrim]

Apart from the fact that it is a personal theory and therefore off-limits on PF? Or that the one-way speed of light is not a defined quantity but depends on your measuring convention - as has been said over and over again on PF including this very thread? Or something else.

All I read is that the problem is about the synchronization or simultaneity convention. But this is only an issue if the measurements are performed at different places. My two wavelength and frequency measurements would be done at the same place.

I don't have a personal theory at all, I just wondered why none of all those suggested one-way speed measurement methods try to make use of the properties of light as a wave, that seemingly allows to measure $\lambda$ and $f$ of two oppositely directed beams at one single place.

Well – maybe not quite... I guess a wavelength measurement always requires some distance between the grating and the screen, and a frequency measurement will take finite time, so I suspect that those more complicated equations of length contraction and time dilation will come in here somewhere such that both measurements will lead to the same $\lambda$ and $f$.

 

[Ibix]

Well – maybe not quite... I guess a wavelength measurement always requires some distance between the grating and the screen, and a frequency measurement will take finite time, so I suspect that those more complicated equations of length contraction and time dilation will come in here somewhere such that both measurements will lead to the same $\lambda$ and $f$.

Yes. That's what the sheared Minkowski diagram shows in the thread I linked. The nodes aren't moved by a change in one way speed, just whether the antinodes are in phase or not - and that's simultaneity biting you as it always will.

 

[PeterDonis]

My two wavelength and frequency measurements would be done at the same place.

Then you are not measuring the one-way speed of light. So any claim you make about the one-way speed of light in such a scenario isn't based on measurements. It's based on some choice of simultaneity convention. As has already been pointed out to you multiple times.

 

[greypilgrim]

I think Ibix already answered my question, but I'm curious:

Then you are not measuring the one-way speed of light.

The leaving and reflected beams go opposite directions. Why would $\lambda_1\cdot f_1$ and $\lambda_2\cdot f_2$ not be the one-way speeds of light?

 

[Ibix]

The leaving and reflected beams go opposite directions. Why would $\lambda_1\cdot f_1$ and $\lambda_2\cdot f_2$ not be the one-way speeds of light?

They would be. But you can't measure them without assuming a synchronisation convention somewhere, and hence assuming your answer.

 

[PeterDonis]

The leaving and reflected beams go opposite directions. Why would $\lambda_1\cdot f_1$ and $\lambda_2\cdot f_2$ not be the one-way speeds of light?

If you are doing this:

My two wavelength and frequency measurements would be done at the same place.

Then no, $\lambda_1 \cdot f_1$ and $\lambda_2 \cdot f_2$ are not one-way speeds of light. You are measuring both at the same place.

Please stop and think very carefully. You do not appear to be doing that when considering this scenario.

 

[greypilgrim]

Please stop and think very carefully. You do not appear to be doing that when considering this scenario.

Well, that just got harder since #10 and #11 are conflicting.

 

[PeterDonis]

Well, that just got harder since #10 and #11 are conflicting.

I think in #10 @Ibix forgot that you said, in what I quoted in post #11, that you were measuring both sets of wavelength/frequency in the same place. Which, as I pointed out, is in contradiction to you saying you want to measure the one-way speed of light.

So ultimately the conflict is coming from you: you need to make up your mind which scenario you want to talk about. Do you want to talk about measuring both sets of wavelength/frequency in the same place? Or do you want to talk about measuring the one-way speed of light (and making the required choice of synchronization convention to do that, since you would be making measurements in two different places)? You can't do both.

 

[greypilgrim]

I'm getting more and more confused. Is your point that a wavelength measurement cannot be done at a single place, but needs a finite distance (e.g. between diffraction grating and screen)? Or something entirely different?

 

[PeterDonis]

I'm getting more and more confused.

That's because you're not taking my advice and stopping to think carefully.

Is your point that a wavelength measurement cannot be done at a single place, but needs a finite distance (e.g. between diffraction grating and screen)? Or something entirely different?

Something entirely different. For this discussion there is no problem idealizing a wavelength/frequency measurement as happening at a single place.

But you are talking about two wavelength/frequency measurements. Do they both happen at the same place? Or at different places?

If they happen at the same place, then you cannot use them to measure the one-way speed of light.

If they happen at different places, then, while you can use them to measure the one-way speed of light, doing that requires adopting a synchronization convention, so the results will depend on what convention you adopt.

 

[greypilgrim]

If they happen at the same place, then you cannot use them to measure the one-way speed of light.

Is there a difference between a one-way speed of light measurement and a one-direction speed of measurement? Is that where I go wrong? If not, I really don't see it.

 

[PeterDonis]

Is there a difference between a one-way speed of light measurement and a one-direction speed of measurement?

I don't think so. One-way speed means speed going one way. That means in one direction.

If not, I really don't see it.

Don't see what?

 

[Dale]

What would be wrong with my proposal, i.e. measure wavelength and frequency of a leaving and the reflected beam separately?

The main thing that is wrong with your proposal is that you did not do the math. If you did the math then you would have found the following:

As a quick summary of the actual math for this experiment, use Minkowski coordinates $(t,x,y,z)$ and Anderson coordinates $(T,X,Y,Z)$ with parameter $\kappa$. This leads to the following coordinate transforms (in units where $c=1$) $$T = t-\kappa x$$ $$X=x$$ $$Y=y$$ $$Z=z$$ with the corresponding one way speeds of light (in the $x$ direction) $$c_+=\frac{1}{1-\kappa}$$ $$c_-=\frac{1}{1+\kappa}$$

The position four-vectors are $r^\mu=(t,x,y,z)$ and $R^\mu=(T,X,Y,Z)$. Now for a travelling plane wave in the $x=X$ direction the wave four-vector is $$k^\mu(r) = (\omega, k, 0, 0) $$ $$K^\mu(R)=(\omega-\kappa k, k, 0,0)$$ The travelling waves in the $-x=-X$ directions are obtained by setting $k=-k$, and the standing wave is the sum of the two.

The phase of the forward travelling wave is denoted $\phi_+$ and the phase of the backward travelling wave is denoted $\phi_-$ which are obtained as $$\phi_\pm = k^\mu r_\mu = \pm k x - t \omega$$ The nodes are obtained by solving the equation $$\phi_+ - \phi_- = n 2\pi$$ $$x=\frac{n \pi}{k}$$ Similarly in the Anderson coordinates $$\phi_\pm = K^\mu R_\mu = \pm k X - (T + X \kappa) \omega$$ And again the nodes are obtained by solving the equation $$\phi_+ - \phi_- = n 2\pi$$ $$X=\frac{n \pi}{k}$$

Since $x=X$ the position of the nodes is not a function of $\kappa$ and their values are unchanged when changing the one way speed of light.

It might help to take a step back for a moment. In order to measure something, anything, you need to make some sort of a physical experiment whose value depends on the quantity you want to measure. In this case you want to measure the one way speed of light, which is given by $\kappa$ in the description above. So you need to find some experiment whose value depends on $\kappa$. Yours does not (nor does any other experiment).

 

[PeterDonis]

For this discussion there is no problem idealizing a wavelength/frequency measurement as happening at a single place.

Actually, on looking at the Wikipedia page referenced in the OP, this is not true, at least for wavelength, for the cavity measurement. The cavity measurements described there used the dimensions of the cavity as the "measurement" of the wavelength. But that requires measurements at different places; "same place" in this case would mean a cavity of zero size, which is of course useless.

 

[PeterDonis]

Leaving the cavity away and just using a laser and a far away mirror, couldn't I just measure $\lambda$ for the leaving and reflected beam (e.g. with a diffraction grating) and $f$ (e.g. using the photoelectric effect) and if they both are the same, so must be $c=\lambda\cdot f$?

If you measure both wavelength/frequency pairs at the same place, which I assume is the source/detector, how do you know they were the same at the far away mirror? You can't just assume that. You would have to measure it.

 

[greypilgrim]

I don't think so. One-way speed means speed going one way. That means in one direction.

And why am I not measuring two one-way speeds then if I do those measurements for a beam going away from me and a beam coming towards me?

 

[PeterDonis]

And why am I not measuring two one-way speeds then if I do those measurements for a beam going away from me and a beam coming towards me?

Because you can't measure one-way speeds using measurements at just one place. Think about it. Think carefully. (And read my post #20.)

 

[greypilgrim]

If you measure both wavelength/frequency pairs at the same place, which I assume is the source/detector, how do you know they were the same at the far away mirror?

I don't, but in all the threads I read it was always about the speed of light being different for different directions, not about it being different at different places. They all assumed it to be constant for one direction, and so did I.

 

[PeterDonis]

I don't

And that is why you can't measure the one-way speed of light using measurements at just one place.

in all the threads I read it was always about the speed of light being different for different directions, not about it being different at different places. They all assumed it to be constant for one direction, and so did I.

They assumed the speed of light to be the same in different places. (At least, that's what you are implying. You haven't actually referenced any other threads you've read.) But assuming is not the same as measuring. In this thread you asked about measuring.

 

[PeterDonis]

in all the threads I read it was always about the speed of light being different for different directions, not about it being different at different places.

But what "speed of light" was discussed as possibly being different for different directions?

In the Michelson-Morley experiment, for example, they rotated the apparatus, which was in effect testing the speed of light in different directions. But they were testing the two-way speed of light: source and detector were at the same place. That's the only kind of test that can give you an invariant result, i.e., a result that doesn't depend on any coordinate choice or simultaneity convention.

Again, you didn't reference any of the other threads, but it's entirely possible that they were only talking about the two-way speed of light, which would make them irrelevant to this thread in any case.

 

[PeterDonis]

the Michelson-Morley experiment

Note also that this experiment was effectively testing for differences in round-trip light travel time. It was not using measurements of frequency and wavelength.

 

[Dale]

And why am I not measuring two one-way speeds then if I do those measurements for a beam going away from me and a beam coming towards me?

See my post 18 above. To do a measurement of the one way speed of light you need an experiment that depends on $\kappa$

 

[greypilgrim]

Okay. Let's assume a universe with only one spatial dimension for which $c_+\neq c_-$ but they are constant everywhere on the axis. If I now measure wavelength and frequency of two opposite beams at a single place, will I find

1. $\lambda_+\neq\lambda_-$ ?
2. $f_+\neq f_-$ ?
3. Both 1. and 2. ?
4. Neither 1. nor 2. ?
5. Situation isn't uniquely defined yet?

 

[PeterDonis]

Let's assume a universe with only one spatial dimension for which $c_+\neq c_-$ but they are constant everywhere on the axis.

$c_+ \neq c_-$ in what coordinates? You continue to ignore this issue. You need to stop ignoring it.

If I now measure wavelength and frequency of two opposite beams at a single place

Then you will not know anything about the one-way speed of light. The question is not what you will observe if you make a particular assumption about the one-way speed of light. The question is what you can infer about the one-way speed of light from a particular set of observations. The only way to answer that is to work from the observations.

 

[Vanadium 50]

it was always about the speed of light being different for different directions, not about it being different at different places. They all assumed it to be constant for one direction, and so did I.

Are you really arguing that the speed of light in Cleveland is different than the speed of light in Houston?

5 points for using a thought experiment that contradicts the results of a real experiment.

 

[greypilgrim]

$c_+ \neq c_-$ in what coordinates? You continue to ignore this issue. You need to stop ignoring it.

Well I copied Dale's notation from #18, and he didn't seem to have an issue defining those two. So why shouldn't there be a clear answer which one of the 5 options in #28 is correct?

Then you will not know anything about the one-way speed of light. The question is not what you will observe if you make a particular assumption about the one-way speed of light. The question is what you can infer about the one-way speed of light from a particular set of observations. The only way to answer that is to work from the observations.

It's absolutely not uncommon to come up with a theoretical model and then try and find an experiment that either confirms or falsifies it.

Are you really arguing that the speed of light in Cleveland is different than the speed of light in Houston?

The very citation of mine you gave says that I'm exactly not doing that.

 

[PeterDonis]

Well I copied Dale's notation from #18, and he didn't seem to have an issue defining those two.

His definition requires a choice of coordinates. Do you understand that?

So why shouldn't there be a clear answer which one of the 5 options in #28 is correct?

Why should anyone care which one of the 5 options in #28 is correct, since, as I have already said, none of them have anything to do with actually measuring the one-way speed of light, which is what you say you are trying to discuss? What's the point in even trying to give an answer to an irrelevant question?

 

[Dale]

Okay. Let's assume a universe with only one spatial dimension for which $c_+\neq c_-$ but they are constant everywhere on the axis. If I now measure wavelength and frequency of two opposite beams at a single place, will I find

1. $\lambda_+\neq\lambda_-$ ?
2. $f_+\neq f_-$ ?
3. Both 1. and 2. ?
4. Neither 1. nor 2. ?
5. Situation isn't uniquely defined yet?

The information is already given in post 18 for you to answer this yourself. You should actually work through the math until you get the answer you are seeking as well as the understanding why it doesn’t matter, as others said.

The main problem with all these proposals is not working through the math

 

[Ibix]

@PeterDonis - I'm not sure I'm entirely following your objections here.

As I understand it, if we have a single beam of light propagating in one direction we can measure its frequency at a single location with just an antenna and a clock (and good reflexes...). We cannot measure its wavelength at a single point. To get wavelength we need two antennae separated by some distance and a pair of clocks, and we measure the phase simultaneously at each point. Naturally, the word "simultaneously" is where we slip in the assumption about the value of the one way speed of light that we will then "measure".

I don't see why we can't use the exact same kit to work with a beam propagating in the opposite direction. I do see why you can't use that kit to simultaneously measure the speed of beams of light in opposite directions, but I'm not clear if you are talking (in #11 et seq) only about standing waves in cavities (in which case we have two beams moving simultaneously in opposite directions - and I agree with you) or just about two beams with the same kit (in which case I don't see the problem beyond the obvious "we slipped in a simultaneity convention" issue).

To put it another way, the problem in a cavity filled with a standing wave is that you can't measure the wavelength in either direction because all you can see is the interference between the two waves. If the pulse in the light cavity is short enough that it doesn't interfere with itself (a light clock, basically) then it does make sense to measure the wavelength in either direction, and you can do at the same location. To me, your objections don't quite seem to fit into either of those positions.

 

[PeterDonis]

I don't see why we can't use the exact same kit to work with a beam propagating in the opposite direction

I didn't say we couldn't. I just said, and you have agreed, that the "kit" in question involves measurements at more than one place, since that's required to measure wavelength. It is impossible to measure the one-way speed of light using measurements at only one place.

If the pulse in the light cavity is short enough that it doesn't interfere with itself (a light clock, basically) then it does make sense to measure the wavelength in either direction, and you can do at the same location.

Aren't you contradicting yourself? Earlier in your post you said you can't measure wavelength using measurements at only one place. Now you're saying you can?

Note that light clock isn't a one-way measurement of anything; the "ticks" are round trips.

Note also that, as I said in an earlier post, in the "standing wave in a cavity" case, you are relying on measurements of the size of the cavity to infer wavelength, which means you are relying on measurements in more than one place.