A 1-Way Speed of Light

[Dale]

That is why in my original post I was trying to avoid that flaw by making R large so the angle <AOB is very small, so that effectively R is one direction. R can be very large if O is far away, say on earth while A and B are on the ISS.

R doesn’t matter. The distance can be as large or small as you like. It doesn’t change the amount of desynchronization if the OWSOL is not isotropic.

You should work out the math. The desynchronization depends on Anderson’s kappa, but not R.

 

[PeterDonis]

the angle <AOB is very small

No, it isn't. Read my post #5.

 

[Ibix]

No, it isn't. Read my post #5.

I don't think O is in the plane of the wheel - it's meant to be on the axis but far outside the plane, so AOB is small. Not that it makes any difference to this problem.

 

[Ibix]

@James Hasty - here's why all attempts to measure the one way speed of light fail.

This is a Minkowski diagram - it shows the position of objects at different times. If you came across displacement-time graphs in high school physics, this is the same thing except we usually draw position horizontally and time vertically.

This one shows two clocks, one red and one blue. Initially (at the bottom of the diagram) they are at $x=-2$ and $x=+2$ respectively. At $t=-4$ a light pulse (yellow) is emitted from $x=0$ in both directions. It arrives at the clocks at $t = -2$ an they immediately set themselves to zero and begin moving, swapping places. They complete the manoeuvre at $t=3$, come to a stop and immediately emit light pulses back to the origin, which arrive there simultaneously at $t=5$.

The interesting point about Minkowski diagrams is that we take them pretty literally as maps of spacetime (at least, one space dimension and the time dimension). So the clocks (which are just point-like objects on this scale) are really the lines - points extended in time.

Note the assumption that the speed of light is equal in both directions in the diagram above. Can we consider an anisotropic one way speed of light? Yes - like this:

Notice how the horizontal grid lines are now slanted? That means that the initial light pulse leaves at $t=-4$ but arrives at one clock slightly before $t=-2$ and the other slightly after $t=-2$ - the speed of light is slightly higher in the $+x$ direction than in the $-x$ direction. And a similar thing happens at the top of the diagram with the returning light pulses which are not emitted at the same time but arrive at the origin at the same time.

But notice that none of the red, blue or yellow lines has changed. The only thing that's changed are the grey lines which are not there in reality. They are just things I added to the diagram to make interpretation easier. So there is no actual physical difference between the isotropic and anisotropic cases - the actual physical measurements will always be the same.

And that is the important bit. It does not matter how many bells and whistles you add to your experimental design, nor whether you have a 2d or 3d setup, whether you use wheels or bananas or whatever. The difference between the isotropic and anisotropic cases is always and only in the shape of the grid you imagine drawing on spacetime. This has no physical consequences.

 

[cianfa72]

As @Ibix showed, the orthogonal grey grid lines in the diagram actually correspond/represent straight lines orthogonal in spacetime (note that the notion of straight line in spacetime is a geometric notion). The isotropy of coordinate one way speed of light corresponds to pick orthogonal grid lines in spacetime (or in the spacetime diagram itself).

 

[James Hasty]

Very good points, thanks all of you for your comments. I know it took time out of your days to respond back to me, and I appreciate it. (I have learned along the way.) Thanks again. Live long and prosper.

 

[James Hasty]

R doesn’t matter. The distance can be as large or small as you like. It doesn’t change the amount of desynchronization if the OWSOL is not isotropic.

You should work out the math. The desynchronization depends on Anderson’s kappa, but not R.

I have Google searched for "Anderson's kappa" but not readily found. What specifically is it?

 

[Dale]

I have Google searched for "Anderson's kappa" but not readily found. What specifically is it?

This is the OWSOL convention used in Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998), "Conventionality of synchronisation, gauge dependence and test theories of relativity", Physics Reports, 295 (3–4): 93–180. doi:10.1016/S0370-1573(97)00051-3

Anderson is not particularly a seminal author in this field. I would say that is Reichenbach. But Anderson’s convention is easier to actually use for real calculations.

 

[Ibix]

$\kappa$ is the thing that controls how slanted the lines in my second diagram are, IIRC.

 

[robphy]

Possibly useful (for conventions and links to references to theories and experiments):
https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

 

[Sagittarius A-Star]

I have Google searched for "Anderson's kappa" but not readily found. What specifically is it?

Here is a similar thing, Reichenbach's $\epsilon$
https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/significance_conv_sim/index.html#epsilon

Here is another explanation:
https://www.mathpages.com/home/kmath229/kmath229.htm

 

[James Hasty]

This is the OWSOL convention used in Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998), "Conventionality of synchronisation, gauge dependence and test theories of relativity", Physics Reports, 295 (3–4): 93–180. doi:10.1016/S0370-1573(97)00051-3

Anderson is not particularly a seminal author in this field. I would say that is Reichenbach. But Anderson’s convention is easier to actually use for real calculations.

Thank you.

 

[cianfa72]

As @Ibix showed, the orthogonal grey grid lines in the diagram actually correspond/represent straight lines orthogonal in spacetime (note that the notion of straight line in spacetime is a geometric notion). The isotropy of coordinate one way speed of light corresponds to pick orthogonal grid lines in spacetime (or in the spacetime diagram itself).

It is worth noting that in some specific cases the two family of "slanted" grid lines drawn in the diagram may result as orthogonal w.r.t. Minkowski inner product even though they do not intersect at 90 degree in the diagram. This is the case when one transforms into a new coordinate system by using Lorentz transformations.