B Measuring the One Way Speed of Light

[Dale]

I could be wrong but if c is infinity then wouldn't we be seeing it in real time regardless of the distance?

Yes.

And considering the big bang happened a couple billion years ago we shouldn't be able to see it unless light travels at a finite speed.

Are you sure that it happened a couple billion years ago everywhere in a non-isotropic c convention? Why would the age of the universe be isotropic if c is not isotropic? What about time dilation?

 

[Ibix]

I could be wrong but if c is infinity then wouldn't we be seeing it in real time regardless of the distance?

Yes. But only because you redefined "now at the CMB" to mean "at the same time light left the CMB". The choice of the one way speed of light is inextricably tangled up with your choice of what "now" means.

 

[Dale]

I understand that they are perfectly acceptable mathematically, but the physical interpretation is different. And physical interpretation of coordinates seems to be an issue that @beamthegreat is having difficulty with, so I wanted to make clear what the implications of a coordinate choice that makes $c = \infty$ are. It means the coordinate in that direction does not work like he thinks coordinates work.

Yes, good point. Under these non-isotropic c conventions I think that people need to give up the idea of assigning any physical significance of the coordinates. Personally, I think that is a good thing because coordinates should not be assigned physical significance anyway. It only leads to trouble in GR.

 

[PeterDonis]

Yes.

No, this is wrong. This is an example of how the difference in coordinate choices matters for physical interpretation.

"Seeing in real time" means that there is a time coordinate (i.e, surfaces of constant value of this coordinate are spacelike) which is the same at both the emission event and the reception event.

Choosing coordinates in which $c = \infty$ does not give you that; it can't, since the worldline of a light ray is null, not spacelike (as it would have to be for "seeing in real time" to be true, as above). That is the physical fact that no coordinate choice can change. Which means that no coordinate choice can make you see distant events "in real time". Coordinate choices can't change the physics.

 

[PeterDonis]

only because you redefined "now at the CMB" to mean "at the same time light left the CMB". The choice of the one way speed of light is inextricably tangled up with your choice of what "now" means.

It's worse than that. Defining "now" this way means events that happen "now" are not spacelike separated from you. Which violates the intuitive assumption that underlies the very use of the word "now".

It's better to state right up front that no choice of coordinates can make you see distant events "in real time". Not even a choice that makes $c = \infty$ in some direction. All that does is make your coordinates work differently from what your intuition would think. It doesn't change the physics at all.

 

[Dale]

"Seeing in real time" means that there is a time coordinate (i.e, surfaces of constant value of this coordinate are spacelike) which is the same at both the emission event and the reception event.

Or "seeing in real time" could simply mean that the t coordinate of emission is the same as the t coordinate of reception. As far as I know there is no "textbook" definition that requires your usage. Certainly, in the literature on the Reichenbach synchronization convention (which is the most directly relevant to this thread) it is contemplated to have such null surfaces for your t coordinate. So at least in this narrow instance it is with good precedence.

Again, I think that the resolution for the issue you raise is simply to not assign any physical significance to coordinates to begin with.

EDIT: hmm, now looking back they may use $<$ rather than $\le$ as I recalled

 

[PeterDonis]

"seeing in real time" could simply mean that the t coordinate of emission is the same as the t coordinate of reception.

But then $t$ would be a very bad choice as a name for this coordinate, since it would not be timelike and surfaces with a constant value of the coordinate would not be spacelike, and $t$ to the average lay person implies both of those things (the average lay person might not know enough to state the implications that way, but that's what their intuitive concept of a $t$ coordinate amounts to).

I think that the resolution for the issue you raise is simply to not assign any physical significance to coordinates to begin with.

I agree that this is the best outcome; but getting there often requires careful choices of nomenclature in between, to avoid confusions that are likely to arise when a lay person hasn't yet fully grasped what not assigning any physical significance to coordinates means. (Even physicists who do grasp this often carefully choose coordinate symbols to avoid possible confusion; there's a reason why null coordinates are usually called things like $u$ and $v$ instead of $t$.)

 

[Dale]

surfaces with a constant value of the coordinate would not be spacelike, and t to the average lay person implies both of those things (the average lay person might not know enough to state the implications that way, but that's what their intuitive concept of a t coordinate amounts to).

While I don’t dispute this, I don’t think it is relevant here. This entire topic is completely contrary both to a lay person’s intuition and to an expert’s good sense. Therein is the real problem here.

Veritasium is usually quite good. But his audience is lay people. This topic is just not a lay-person-compatible topic. Lay people have no need to dive into any of the conventions of physics.

He talks about the one way speed of light with this wholly ridiculous sense of wonderment. Where is his video with the same amazement describing that electrons could have been positively charged or B fields could use the left handed rule? He conveys the impression to his audience that this is a great mystery instead of merely a useful convention like any of the other many conventions we use.

 

[MikeeMiracle]

Just a thought regarding clock synchronisation and I am sure this has been considered by people far more clever than me but...

We talk about exchanging lights signals to synchronise clocks...could we not use a pair of entagled particles instead?

 

[Dale]

We talk about exchanging lights signals to synchronise clocks...could we not use a pair of entagled particles instead?

No. There are hundreds of threads on this topic in the QM sub-forum. It is off topic here.

 

[Sagittarius A-Star]

By changing the electromagnetic interaction the produces sound waves in a material. Suppose that you have a material whose speed of sound is $0.8 c$ under the isotropic convention. Then if you use the convention that $c(0)=\infty$ and $c(\pi)=0.5 c$ then clearly the speed of sound in the $\theta=\pi$ direction can no longer be $0.8 c$.

Yes. In this case, the speed of sound in the $\theta=\pi$ (negative x-)direction is $v_{-}' = \frac{4}{9}c$, and that in the opposite direction $v_{+}' = 4c$.

Proof: I use the following transformation, with $k = 1$:

$x' = x \ \ \ \ \ \ \ \ \ \ y' = y \ \ \ \ \ \ \ \ \ \ z' = z \ \ \ \ \ \ \ \ \ \ t' = t+ \frac{kx}{c}$
...
$\frac{c'}{c} = \frac{1}{1-k \cos(\theta)}$

Source:
https://www.mathpages.com/home/kmath229/kmath229.htm

From the transformation for $t'$ follows: $\frac{-x'}{0.8 c} = \frac{-x}{v_{-}'} + \frac{x}{c}$
and with $x' = x$ follows:
$$v_{-}' = \frac{4}{9} c$$

From the transformation for $t'$ follows: $\frac{x'}{0.8 c} = \frac{x}{v_{+}'} + \frac{x}{c}$
and with $x' = x$ follows:
$$v_{+}' = 4 c$$

 

[Flatland]

Can't you theoretically measure the one way speed of light using a black hole? You shoot a beam of light at the black hole at a geodesic path that curves the light beam back to your detector.

Also if the speed of light is directional wouldn't we see this in the CMB where the universe will appear younger in one direction as opposed to another?

 

[Nugatory]

Can't you theoretically measure the one way speed of light using a black hole? You shoot a beam of light at the black hole at a geodesic path that curves the light beam back to your detector.

That’s a two-way measurement that uses a massive gravitating body (actually, you will need more than one to get the path you want) instead of a mirror to send the light signal back to the source.

 

[Dale]

Can't you theoretically measure the one way speed of light

No. (None of the details are relevant)

 

[cmb]

I was thinking about this conundrum recently and didn't realize there was a recent thread going on about it.

Here are two thoughts/questions;
1) Would a viable experiment exist which deliberately introduces speed variation and then uses that as the reference calibration? Thus; Take a multi-km of optical cable and, when in a spiral in the lab, measure its propagation delay. Then lay it out straight and measure the differential time of signals one end to other compared with a beam of light. If the differential propagation delay is, say, 0.3c then 0.3 times instantaneous speed would be zero delay. Do that in both directions and if the delay is the same, would this not show light is isotropic in that axis, in those two tested directions?

2) Best to do this experiment vertically, because the most likely direction that light speed would be anisotropic seems to me to be when it is crossing a gravitational field gradient. If the speed of light varies according to gradient of the gravitational field it is passing through then this seems logical either as a consequence of relativity, or in an philosophical way relativity would be an effect of such anisotropy?

 

[Vanadium 50]

Measuring the "one way speed of light" is equivalent to solving one equation in two unknowns. No amount of Rube Goldebergery will change that.

 

[Dale]

Would a viable experiment exist

No. Again the details are irrelevant.

 

[Nugatory]

and if the delay is the same, would this not show light is isotropic in that axis, in those two tested directions?

It would show that the hypothetical anistropy affects light and the signal speed in the cable similarly.

 

[Vanadium 50]

the details are irrelevant.

Right. Just like in a perpetual motion machine. You can tart it up all you like, but energy is still conserved.
Let me repost what I wrote two weeks ago the last time this came up:

...people who say they have found a way to measure the one-way speed of light should be treated the same as people who claim they can solve one equation in two unknowns.

Specifically, the one-way speed of anything (not just light) going from A to B is:

v = \frac{x_B-x_A}{(t_B - \delta t)-t_A}

where δt is the difference in clock syncronization from A to B. In Newtonian physics, δt = 0. In Relativity, you tell me what one-way speed you want, and I'll tell you the clock syncronization convention to use. It's one equation in two - count 'em, two - unknowns.

 

[cmb]

Measuring the "one way speed of light" is equivalent to solving one equation in two unknowns. No amount of Rube Goldebergery will change that.

Adding in a calibrated delay is providing the second unknown.

Using calibrated delays to determine transmission speeds is quite a normal thing, I think?

 

[cmb]

It would show that the hypothetical anistropy affects light and the signal speed in the cable similarly.

Only if the delay was a constant addition of delay rather than a factor addition.

 

[cmb]

No. Again the details are irrelevant.

Could we possibly spend a moment to discuss, rather than write it off without thought?

If it was found that there was a 50% delay factor in the propagation speed down an optic fibre, and one sets up an experiment with a photon emitter timed to traverse a straight 10,000 feet, then at 1ft/ns (approx c) it'd take 10us for the light to get there and 15us for the delayed path, being uncoiled and laid out straight along the 10,000 test path.

The speed of light is then the distance divided by difference of the two arrival times and times the delay factor. Without any delays in that one direction, this would then be (10,000'/5us) * 50% = 1'/ns, as expected.

If there was a whole-sale slowing down of 25% such that it'd take 12.5us for light and 18.75us for the delay, thus (10,000'/6.75us) * 50% = 0.74'/ns.

The delay factor is the 2nd unknown.

The delay factor being calibrated in a lab with a coil in which the direction is an average of both.

The experiment does not, and probably does not need, to be trying to prove/disprove the whole thing in one go, but if one does this experiment in each direction and one gets a different 'absolute' delay it would disprove that light behaves the same in both directions.

 

[Dale]

Could we possibly spend a moment to discuss, rather than write it off without thought?

Can you spend a moment to read the previous material that has already answered your question over and over and over. We have already spent over 100 posts in this thread alone plus many other posts in many other threads. The details of your scenario are absolutely 100% irrelevant. It is impossible as a matter of definition.

 

[cmb]

We have already spent over 100 posts in this thread alone plus many other posts in many other threads. Can you spend a moment to read the previous material that has already answered your question over and over and over. The details of your scenario are absolutely 100% irrelevant.

I did, and I noted nothing that excludes the matters in my last post.

If you might simply identify the error of physics/maths, then may I please propose that this would be preferable rather than jumping to an instant bias that there is no possible answer.

With a calibrated delay, which is calibrated in a manner which is not biased towards either one way or two way speed measurements because it takes an average, I submit one can then use thsi calibrated relative delay to measure the speed of light.

 

[Dale]

I noted nothing that excludes the matters in my last post.

Then read again.

This is impossible as a matter of definition. The definition of the one way speed of light is the distance that light travels (in a single straight line path) divided by the time that it takes for the light to travel that distance. Since that time is measured by clocks at two different locations then the time depends on your synchronization convention. Let me repeat that for emphasis:

The one way speed of light depends on your synchronization convention by definition.

Your choice of synchronization convention determines the one way speed of light. In other words, BY DEFINITION, the one way speed of light requires that you make an assumption and that assumption determines the one way speed of light. You cannot avoid making that assumption because it is part of the definition, and once you make that assumption you have determined the one way speed of light.

Your experimental details are irrelevant. This is not a matter of clever experimental design.

 

[cmb]

Then read again.

This is impossible as a matter of definition. The definition of the one way speed of light is the distance that light travels (in a single straight line path) divided by the time that it takes for the light to travel that distance.

I have used a different definition of speed, avoiding the conundrum that you say I have not read. I propose that I have just avoided it, but if I am wrong and not avoided it at all then surely it is so obviously a fallacy? If so, please just tell me where the logic breaks down.

Say;
D = known test distance
V1 = unknown speed of 1st measurand
V2 = unknown speed of 2nd measurand
average{V1} = k * average{V2}, by local calibration of each measurand following an identical loop circuit whose test radius << D {and using the same clock}

I propose there no longer a need for any time synchronisation between two distant points.

Instead, let dt = observed time interval between 1st measurand and 2nd measurand passing the end of test distance D, having started off together, and only time-measured at end of D, not requiring any prior synchronisation reference to any other point {and using the same clock}.

then V1 = (D/dt) * (k-1)

'IF' I can perform that calibration, then thereafter this definition of velocity is only using a time measurement made at one singular point and not synchronised to any other clock or any other time reference anywhere else.

There may be some fallacy embedded in the calibration procedure, but I am not seeing it as it does not favour any particular velocity direction prior to the actual one way measurement.

I can do the test run along D, one way, with nothing more than one singular time piece. I do not need two timepieces, thus there is no synchronisation error.

 

[Sagittarius A-Star]

The delay factor is the 2nd unknown.

The delay factor being calibrated in a lab with a coil in which the direction is an average of both.

That calibration does not work. You find a similar scenario in my above posting #101. You need only to replace your speed of light in an optical cable ($0.5 c$) by the hypothetical speed of sound in a material ($0.8 c$) in the isotropic case. In my scanario you can easily calculate, that for example on a distance of 300,000 km in x-direction, the difference of arrival time between light and sound will be $0.25 s$, in both, the isotropic and the anisotropic example.

 

[iVenky]

I have a question. If the velocity of light from a point source of light depends on the direction, doesn't the intensity of light (which is a one-way measurement) change with direction? Clearly, we don't observe this, which means velocity is constant as well regardless of the direction.

 

[Ibix]

'IF' I can perform that calibration, then thereafter this definition of velocity is only using a time measurement made at one singular point and not referenced to any other clock or any other time reference anywhere else.

I find it difficult to work out what you think you are doing. However, I think you are firing two light pulses simultaneously, one through free space and one through an optical fibre. This is essentially synchronising clocks except that the "receiving" clock has an offest of $D/c$ compared to Einstein synchronisation. It is therefore subject to the same synchronisation problems as any other one way speed measure.

I have a question. If the velocity of light from a point source of light depends on the direction, doesn't the intensity of light (which is a one-way measurement) change with direction?

No. Why would it?

 

[Dale]

I have used a different definition of speed

Then it is not what anyone else is talking about when we say “one way speed of light”

You don't get to redefine it. Here on PF we use the standard definition as accepted by the professional scientific community.

There may be some fallacy embedded in the calibration procedure, but I am not seeing it as it does not favour any particular velocity direction prior to the actual one way measurement.

Your calibration is a two way measurement. You then simply assume that the two way speed is the same as the one way speed, which is the Einstein synchronization convention.