B Measuring the One Way Speed of Light

[Paul Colby]

Since the time around any closed loop equals the length (perimeter) of the loop divided by c we have

Yeah, I don’t accept this as a requirement. It may well be a valid result given the usual velocity anisotropy but I believe it need not hold for those being considered here.

 

[Dale]

Yeah, I don’t accept this as a requirement. It may well be a valid result given the usual velocity anisotropy but I believe it need not hold for those being considered here.

You are not free to reject it. It is required by experiment. Any convention that does not satisfy this requirement is experimentally falsified.

 

[Paul Colby]

You are not free to reject it. It is required by experiment. Any convention that does not satisfy this requirement is experimentally falsified.

Fine, which experiment.

 

[Dale]

Fine, which experiment.

Any non-rotating ring interferometer experiment

 

[Paul Colby]

Any non-rotating ring interferometer experiment

Like all things these are done to finite precision. So, we’ve established the point I was trying to make which is the class of acceptable $c(\theta)$ is really rather narrow. One is restricted to ones that are not measurable. The ones I proposed are measurable and therefore disallowed for some value of the paramete $\epsilon$.

 

[Dale]

the class of acceptable c(θ) is really rather narrow.

But it is neither empty nor unique. That is the point of the conventionality argument. For instance $$c(\theta)=\frac{c^2}{c+a \cos(\theta)}$$ where $0\le a \le c$.

Any choice of $a$ matches all experimental data. So you are free to set it as an arbitrary convention. The usual convention is $a=0$, but $a$ is not measurable.

 

[Paul Colby]

But it is not empty. That is the point of the conventionality argument. For instance $$c(\theta)=\frac{c^2}{c+a \cos(\theta)}$$ where $0\le a \le c$.

Any choice of $a$ matches all experimental data. So you are free to set it as an arbitrary convention. The usual convention is $a=0$, but $a$ is not measurable.

Never said it was empty. For experiment my point is not vacuous. I’ve shown one can construct measurable anisotropies which are measurable and, therefore eliminated by existing experiments. I suspect the functional form you gave is close to exhausting ones vacuous choices. To read the many threads on PF this point seems completely submerged.

 

[Dale]

I’ve shown one can construct measurable anisotropies which are measurable and, therefore eliminated by existing experiments.

Sure. But that is not what people are talking about when they are discussing the conventionality of the one way speed of light.

The fact that something is conventional means that there are at least two possibilities for that thing which are experimentally indistinguishable. It does not mean that all possibilities must be experimentally indistinguishable. There are at least two values of $0\le a \le c$, so the one way speed of light is indeed conventional.

 

[Paul Colby]

Sure. But that is not what people are talking about when they are discussing the conventionality of the one way speed of light.

Well it my sincere hope that the people who come to this forum who don’t understand this conventionality will leave with a better understanding of the limitations of the arguments.

 

[PAllen]

Many threads on this include the observation that only “conspiratorial anisotropy” is allowed by experimental results, and this is a taken as a very good reason to assume exact isotropy; which still doesn’t mean it is not an assumption..

 

[Sagittarius A-Star]

Try $c(\theta) = \frac{c}{1+\epsilon\cos^7\theta}$

That fits to the formula in Wikipedia, consitent with the video in posting #1:

$$c_{\pm} = \frac {c}{1_{\pm} \kappa}$$
κ can have values between 0 and 1. In the extreme as κ approaches 1, light might propagate in one direction instantaneously, provided it takes the entire round-trip time to travel in the opposite direction.

Source:
https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

 

[lerus]

The problem with any one-way measure, including the ones you cite, is that they assume that the speed of light is the same in both directions. Romer, for example, effectively looks at a distant clock (the Jovian moons) and attributes apparent rate variation solely to changing light travel time due to its changing distance. In a relativistic analysis, this turns out to mean that he assumed the Einstein clock synchronisation convention, which is to say that he assumed that the speed of light was isotropic. One could re-analyse the results using a non-isotropic synchronisation convention and get a different result.

In this experiment light moves only in 1 direction - from Jovian moons to the Earth - that's why this is a true one-way measure of speed of light. We don't need to synchronize any clock here, but to interpret results of this experiment we do need to assume that space is isotropic. But on the other side if we try to imagine how extremely complicated this space anysotropy needs to be to satisfy experiment results (we can repeat this experiment from Mars or from Saturn or from whatever) than I'd say that probability of such results is very low.

 

[beamthegreat]

Just a thought, instead of trying to directly measure the one-way speed of light, could we try and see
whether there is a preferred direction for the speed of light?

I am by no means an expert but one idea is to set up a carousel with a lightbulb in the middle and a detector at the end. The lightbulb is rigged to pulse every second, and the disk is set to slowly rotate at a constant speed. We then read the time stamps and see whether there is any offsets between each interval. If the speed of light is constant, there will be no differences in the intervals. If the speed of light is different we should see fluctuations in the intervals. The trick is to have the disk slowly rotating. If the disk is stationary the intervals would always be constant in all directions regardless of the speed of light.

Another idea is to observe the cosmic background radiation. If the speed of light is instantaneous in one direction then there should be a gap in the CMB but to know my knowledge the CMB is uniform in every direction.

 

[Dale]

We don't need to synchronize any clock here

Yes, you do. One clock is the mechanical clock on Earth and the other is the astronomical clock formed by the Jovian moons.

to interpret results of this experiment we do need to assume that space is isotropic. But on the other side if we try to imagine how extremely complicated this space anysotropy needs to be to satisfy experiment results

This assumption of isotropy is precisely the one that is a matter of convention. As I said above one possible form of the anisotropy is $$c(\theta)=\frac{c^2}{c+a \cos(\theta)}$$ This form of isotropy is consistent with experimental results including the Romer experiment.

 

[Dale]

The trick is to have the disk slowly rotating.

Assuming the isotropy of slow clock transport is equivalent to assuming the Einstein synchronization convention.

 

[Paul Colby]

That fits to the formula in Wikipedia, consitent with the video in posting #1:

Yes, at a fixed $\theta$. A key point in the argument I presented uses more than one angle and no reverse paths for the measurement I defined.

The proof Dale provided of $\Delta_A=\Delta_B$ didn’t make use of this form of $c(\theta)$ which is why I failed to replicate his results. His proof is based on an observed fact and is consistent with measurement but quite beside the point being made.

 

[lerus]

Just a thought, instead of trying to directly measure the one-way speed of light, could we try and see
whether there is a preferred direction for the speed of light?

I am by no means an expert but one idea is to set up a carousel with a lightbulb in the middle and a detector at the end. The lightbulb is rigged to pulse every second, and the disk is set to slowly rotate at a constant speed. We then read the time stamps and see whether there is any offsets between each interval. If the speed of light is constant, there will be no differences in the intervals. If the speed of light is different we should see fluctuations in the intervals. The trick is to have the disk slowly rotating. If the disk is stationary the intervals would always be constant in all directions regardless of the speed of light.

Another idea is to observe the cosmic background radiation. If the speed of light is instantaneous in one direction then there should be a gap in the CMB but to know my knowledge the CMB is uniform in every direction.

You don't need to rotate anything - Earth rotates for you

 

[Dale]

but quite beside the point being made.

How so?

 

[Paul Colby]

How so?

Read #2.

 

[Dale]

Read #2.

I have no disagreement with that post.

 

[Paul Colby]

I have no disagreement with that post.

Didn’t say you did. It does state the point I was making.

 

[Dale]

Didn’t say you did. It does state the point I was making.

Your point in post 2 is not the only point to this thread. So the fact that my proof does not address that one specific post hardly makes it “quite beside the point being made”.

 

[Paul Colby]

Whatever. I’ve done far too much pulling teeth here.

 

[beamthegreat]

Assuming the isotropy of slow clock transport is equivalent to assuming the Einstein synchronization convention.

Not sure if I fully understand but we are not attempting to measure the speed of light, just trying to observe whether or not there's a preferred direction for the speed of light. There are no "clocks" to synchronize. The time the lights start blinking have no effect on the experimental results.

 

[Dale]

There are no "clocks" to synchronize.

You have time stamps so you must have a clock, yes? That clock is moving around the circle slowly, right? Since it is moving then it is subject to time dilation.

If you assume that its time dilation is isotropic then you have already assumed the Einstein synchronization convention which is the same as assuming that the speed of light is isotropic.

If the one way speed of light is anisotropic then time dilation is anisotropic. If so then the fact that the anisotropically time dilated clock measures the pulses to be isotropic shows that the speed of light is anisotropic.

It is completely silly to assume this “conspiratorial anisotropy”, but it is consistent with the data.

 

[beamthegreat]

You have time stamps so you must have a clock, yes? That clock is moving around the circle slowly, right?

Since it is moving then it is subject to time dilation. If you assume that its time dilation is isotropic then you have already assumed the Einstein synchronization convention which is the same as assuming that the speed of light is isotropic.

If the one way speed of light is anisotropic then time dilation is anisotropic. If so then the fact that the anisotropically time dilated clock measures the pulses to be isotropic shows that the speed of light is anisotropic.

It is a completely silly declaration, but it is consistent with the data.

Thanks for the response, I think I get it. What if instead of a lightbulb we use a rotating laser that etches a stationary disk? Then there are no clocks and nothing is moving.

 

[Dale]

What if instead of a lightbulb we use a laser that is stationary but rotates around and etches a stationary disk? Then there are no clocks and nothing is moving.

There are also no time stamps.

 

[beamthegreat]

There are also no time stamps.

Then we add one that measures when a photon impact the disk. Both the disk and the clock is stationary. The laser is rotating but stationary.

 

[Dale]

Then we add one that measures when a photon impact the disk. Both the disk and the clock is stationary. The laser is rotating but stationary.

How is one stationary clock supposed to measure the time that a light pulse hits the disk at different locations? Look, you can come up with new variants faster than I can analyze. So why don’t you try your hand at analyzing this one yourself. You can use this transformation as a generalization of the Lorentz transform which allows for anisotropic c:

https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

This transformation will allow you to determine both the speed of light and also the time dilation as needed.

 

[Nugatory]

Then we add one that measures when a photon impact the disk

The measurement we’re making is “what would a clock at the point of impact read at the moment of impact”. If we’re going to compare that value with the time that something else (such as the light leaving the laser) happens somewhere else we need a clock at that point as well, and we’re back to needing synchronized clocks.