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## Summary:

- Referencing a YouTube Video

Does this video even make sense? And if so, is it right or wrong?

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- #1

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## Summary:

- Referencing a YouTube Video

Does this video even make sense? And if so, is it right or wrong?

- #2

Paul Colby

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with that said, you can’t muck with the isotropy of the speed of light arbitrarily without modifying Maxwells equation. The type or functional form of any isotropy is limited. Within these limits, it’s a matter of conversion.

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I suggest a forum search if you want more discussion. The topic has beaten to death numerous time here on PF.Does this video even make sense? And if so, is it right or wrong?

There are numerous links at the bottom of this page.

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It is correct. The one way speed of light is indeed a convention.Summary::Referencing a YouTube Video

Does this video even make sense? And if so, is it right or wrong?

I would disagree a bit with him about some of his statements to the effect that we cannot know the one way speed of light. Because it is a convention, not only can we know but we do know with certainty simply by choosing our convention.

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I wonder what the FLRW spacetime would look like under an anisotropic c synchronization.

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If you're really curious, choose your favorite line element for the FLRW metric, pick an approrpirate diffeomorphism to remap t (isotropic) to t' (non-isotropic), and compute the new line element.I wonder what the FLRW spacetime would look like under an anisotropic c synchronization.

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The second measurement of speed of light by James Bradley in 1726 using Stellar Aberration was also a one way measurement.

Another possible approach is to use Doppler effect - we can use source that emits light with known frequency and receiver that is moving with the known speed.

We can measure frequency of received light and calculate speed of light using Doppler formula.

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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.As far as I understand, historicaly the very first measurement of speed of light - in 1676 by Olaus Roemer using Jupiter's satellites was a one-way measurement.

The second measurement of speed of light by James Bradley in 1726 using Stellar Aberration was also a one way measurement.

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Just too ugly compared to the standard coordinates with the proper time of the comoving observers (comoving with the "cosmic substrate" or the rest frame of the cosmic microwave radiation).I wonder what the FLRW spacetime would look like under an anisotropic c synchronization.

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It is easy to set up experiments where the light path is one way. The issue is that all such experiments depend on some method of clock synchronization. Your assumption about clock synchronization determines the speed you get. In the case of Romer’s measurement he was using slow clock transport and assumed the isotropy of slow clock transport. This is equivalent to assuming the Einstein synchronization convention.the very first measurement of speed of light - in 1676 by Olaus Roemer using Jupiter's satellites was a one-way measurement.

This analysis is described here:

https://openlibrary.org/books/OL689312M/Special_relativity_and_its_experimental_foundations

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Paul Colby

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I’m skeptical. One could use a pulsed light source and two partially silvered mirrors separated by some distance. A single distant observer with a single clock could reside equally distant from each mirror. The distant observer would see two pulses separated by the time of flight of the pulse between the mirrors. The source is moved and the pulse sent along the reverse direction.It is easy to set up experiments where the light path is one way. The issue is that all such experiments depend on some method of clock synchronization.

Now this experiment doesn’t solve the problem as usually discussed because the equal length paths to the distant observer each contain a lateral component in opposite directions. However, the magnitude of these contributions depends on the functional form of the speed anisotropy.

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Are you basically suggesting sending light pulses along one edge and the other two edges of a closed triangular path? That's a two-way measurement.I’m skeptical. One could use a pulsed light source and two partially silvered mirrors separated by some distance. A single distant observer with a single clock could reside equally distant from each mirror. The distant observer would see two pulses separated by the time of flight of the pulse between the mirrors. The source is moved and the pulse sent along the reverse direction.

More generally, choosing an anisotropic speed of light just leads to a non-orthogonal coordinate system on spacetime. That doesn't have any measurable consequences beyond making the maths nastier.

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Paul Colby

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How so? Only one observer and only one clock.sending light pulses along one edge and the other two edges of a closed triangular path? That's a two-way measurement.

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To measure a one-way speed of light you need two clocks, one at the place of the emission and one at the place of detection of the light signal. To make sense of the clock readings as a "one-way speed of light" the clocks must be somehow synchronized, and it depends on the synchronization procedure you use, which "one-way speed of light" you measure.

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This is assumes already that the one way speed of light is isotropic.I’m skeptical. One could use a pulsed light source and two partially silvered mirrors separated by some distance. A single distant observer with a single clock could reside equally distant from each mirror. The distant observer would see two pulses separated by the time of flight of the pulse between the mirrors. The source is moved and the pulse sent along the reverse direction.

That is actually the identifying feature of a two way measurement. Actual one way measurements require two clocks so they require an assumption about simultaneity.How so? Only one observer and only one clock.

Two way measurements don’t assume simultaneity since they use a single clock, but to infer a one way speed they have to assume isotropy. What you are describing assumes isotropy, so it is a two way measurement, as also evidenced by the use of a single clock.

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Paul Colby

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Paul Colby

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Only if one defines a partiality reflective mirror as a clock in this case.That is actually the identifying feature of a two way measurement. Actual one way measurements require two clocks.

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This doesn’t work. In the limit the directions become arbitrarily close but the distance becomes arbitrarily long. The time difference from any anisotropy in the speed of light decreases as the directions become close, but it increases as the distance increases. The two effects together mean that even in the limit of a distant observer the anisotropy assumption is still non-negligible.In the limit the observer is infinitely far away the path directions become identical.

It has nothing to do with that. The mirror isn’t a clock. The experiment is a two way experiment because the direction of the light is changed, a single clock is used, and the calculation of the speed of light depends on an assumption about the isotropy of the speed of light. All of those are characteristics of two way measurements.Only if one defines a partiality reflective mirror as a clock in this case.

I recommend that you actually work through the math of your proposed experiment. Either you will see where the isotropy assumption comes in or I can point it out.

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- #20

Paul Colby

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We place two beam splitters (1,2) of negligible dimension, 1 at ##x=-W, y=0## and 2 at ##x=W, y=0##. The detector, D, is placed at ##x=0,y=L##. The beam splitters are adjusted so pulses from each will be directed to the detector and to the other beam splitter. Now, the time of flight depends on distance and direction. Now, we fire a pulse through 1 to 2. The pulse is split at 1 and then at 2. The time of flight between 1 to 2 is

##\Delta_{12} = \frac{2W}{c(0)}##

##\Delta_{21} = \frac{2W}{c(\pi)}##

The split pulses travel along different legs of the triangle to the detector. Their time of flights are,

##\Delta_{1D} = \frac{\sqrt{(L^2+W^2)}}{c(\frac{\pi}{2}-\alpha)}##

##\Delta_{2D} = \frac{\sqrt{(L^2+W^2)}}{c(\frac{\pi}{2}+\alpha)}##

##\alpha = \arctan{\frac{W}{L}}##

The time between received pulses is,

##\Delta_A = \Delta_{12} + \Delta_{2D} - \Delta_{1D}##

Reversing the direction of the pulse (sending through 2 then 1)

##\Delta_B = \Delta_{21} + \Delta_{1D} - \Delta_{2D}##

So, my question / observation is; will ##\Delta_A = \Delta_B## for all ##c(\theta)##? Clearly not since there are choices which make ##\pm(\Delta_{2D} - \Delta_{1D})## negligible while ##\Delta_{12} - \Delta_{21}## is not.

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There is a further condition that you have neglected. That is that the function ##c(\theta)## must have the two way speed of light equal to ##c##. In other words, for any constant path (in an inertial frame) of length ##s##, the time for light to traverse that path forward plus the time to traverse the same path backward is ##2s/c##. This is required because the two-way speed of light is measurable and is ##c##.We make the following further assumptions that c(θ) is a real single valued analytic function of θ.

Any such choices are ruled out by the two way speed of light condition.So, my question / observation is; will ##\Delta_A = \Delta_B## for all ##c(\theta)##? Clearly not since there are choices which make ##\pm(\Delta_{2D} - \Delta_{1D})## negligible while ##\Delta_{12} - \Delta_{21}## is not.

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- #22

Paul Colby

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What is the origin of this requirement?There is a further condition that you have neglected.

Ah, MM. So, If I produce a function ##c(\theta)+c(\theta+\pi) = 2c## which yield ##\Delta_A \ne \Delta_B##. then what?

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Paul Colby

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Okay, tryAny such choices are ruled out by the two way speed of light condition.

##c(\theta) = c + \epsilon\cos^7\theta##

This function meets the requirement, ##c(\theta)+c(\theta+\pi)=2c##, yet yields ##\Delta_A \ne \Delta_B##.

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That's not the requirement. For example, one requirement is:This function meets the requirement, ##c(\theta)+c(\theta+\pi)=2c##, yet yields ##\Delta_A \ne \Delta_B##.

##\Delta_{12} + \Delta_{21} = \frac{4W}{c}##

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Paul Colby

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Good catch.That's not the requirement. For example, one requirement is:

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

also, we’re discussing the actual measurements which are ##\Delta_A## and ##\Delta_B##.