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

[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.

 

[Ibix]

Aren't you contradicting yourself?

I'm being slightly sloppy - I meant you could use the same pair of probes to measure wavelength in either direction without moving them.

If all you are saying is that you need to measure the E field in two places to be able to measure wavelength, I agree. However you said in #15:

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

Which led me to think you had something else in mind that I couldn't quite grasp.

 

[PeterDonis]

you said in #15

I retracted the wavelength part of that in a later post.