Can we determine the one way speed of light by combined measurements?

[HansH]

TL;DR Summary

The measurement of the 1 way speed of light is impossible because you use the time between 2 clocks while synchronisation of the 2 clocks is a problem. My idea is to measure it differently by combining 2 measurements: the 2 way speed of light and the measurement under a 90 degrees angle, together with a symmetrical synchronisation of both clocks

The idea is to have 2 clocks at position A and B. The clocks are synchronized by sending a light pulse from position S over 2 equal distances x.
The receiver is at position R at a distance y rectangular to the direction AB and exactly in the middle between A and B and right below S.
for proofing that the 1 way speed of light is always c in every direction we first need to create a situation whare c can vary per direction and then as next step proove based on measurements that this is not possible.

Assuming the light speed is not c but depends on the direction that a light wave travels in space, it is already clear that at least the 2 way speed of light is c.

This means that we can define a lightspeed c1 in the positive x direction and a speed d1 in the negative x direction. It can then easily be derived that the two way speed of light being c, this results in the following relation between c1 and d1:

as we assume the possibiity that c depends on the direction, it is not clear on beforehand what is the speed of light in the direction from the clocks to the receiver R. (speed is c3 and c4 in the figure.)

However it is assumed that the speed of light is at least the same in the same direction. if we could realize that we can measure if the lightpulse to synchronize the clocks needs a different time to come from S to A or B. But to do that we must be sure that the time for the light to come from A to R is the same as from B to R. This can be realized by making y>>x such that AR and BR are supposed to be in parallel effectively giving the same lightspeed . so then this time to get from A and B to R is the same and falls out of the measurement.
so this allows to measure the 1 way speed of light as a combination of equations:
c1=x/deltat1 with deltat1 is the time to come from S to B
d1=x/deltat2 with deltat2 is the time to come from S to A
2x/(deltaT1+deltaT2)=c
2x/(deltaT1-deltaT2)=(c1-d1)
This gives 4 equations with 4 unknown so could be solved.
as we already know from measurements that deltaT1-deltaT2=0 always, we know that this can only be true if c1=d1 as this is the only way to create a time difference to come from S to R as AR and BR were already concluded to take same time t pass due to same direction, so same lightspeed and same length.

In a separate mathcad sheet I made some calculations based on an assumed relation between the speeds in x and y directions and resulting counterspeeds in -x and -y directions and all speeds in arbitrary directions in between. Based on that I couls calculate the deltaT1-deltaT2 for different angle alpha. (alpha sets the ratio y/x)
next picture shows the result for different speeds in x and y direction (c,2c,0.8C in x direction and c,2c in y direction and linear changeover between speeds for arbitrary directions in between)
x=1 meter and from the picture it follows that for y larger than say 200meter, deltat significantly reaches its final value. so if we measure deltat=0 this prooves that c1=d1=c.

 

[HansH]

here the mathcad calculation used to make picture above.

 

[Orodruin]

This can be realized by making y>>x such that AR and BR are supposed to be in parallel effectively giving the same lightspeed . so then this time to get from A and B to R is the same and falls out of the measurement.

This assumption is faulty. While the speeds necessarily tend to the same value as y grows, the distance traveled also increases with y - counteracting the decrease in the difference of speeds. If you do the math correctly, you should find that this is exactly the effect needed to offset the difference in the arrival times at A and B. This is because the one-way speed of light is a coordinate effect from picking a simultaneity convention and therefore not physical.

 

[HansH]

Thanks a lot for this answer. This sounds like there is a much deeper thought behind this subject than I was aware of. From your answer I understand that you can never find the actual one way speed because you cannot get rid of its components in a direction of base vectors having its effects in other direcitons also so if light goes in 1 direction and finally effectively same distance back in the opposite direciton but via another path it could be that the light does that with speed different than c but you cannot detect that. so than it does not make sense to talk about it either?

 

[Dale]

There is no possible measurement, no matter how clever, that can measure this. The one way speed of light is just an anisotropic synchronization convention. In other words, it is just a choice of coordinates. No physical measurement can depend on your choice of coordinates, so no physical measurement can depend on the one way speed of light.

 

[Orodruin]

The point is: This is why I knew there was something awry somewhere in the reasoning. Once you know that, it is only a matter of having the willpower and time to find it. The more contrived the setup is, the more the reason may be obfuscated and hidden out of sight, but it is there. Sometimes it is a fun puzzle to go looking for it, other times I will just ignore it.

 

[Michael Thorpe]

Here's a thought:
How about comparing the speed of light in two directions with sound pulses?
Use two light and sound pulse detector/generators say, a kilometre apart, bouncing pulses back and forth (based on light detection) and listen with a microphone in the middle. If the speed of light is the same in each direction, then the sound pulses will be exactly 180 degrees out of phase.

 

[HansH]

@ Orodruin: Thanks again. I really appreciate your approach to first follow the reasoning of the other and then within half an hour exactly focus on the point where the problem is. I think not much people have the capacity (and/ or will) to do that.
For me this helps to get up to speed in the most effective way (although it was not light speed). Finding this out myself starting in the wrong direction by discussing it on another Dutch forum took me a week while still not clear, while you did it within 1 hour. (and clear after 5 seconds after I read your input)

 

[HansH]

bouncing pulses back and forth (based on light detection)

This means you measure the 2 way speed of light.

 

[Ibix]

Here's a thought:
How about comparing the speed of light in two directions with sound pulses?

As already stated on this thread, the one way speed of light is a convention. No experimental result can depend on convention.

Choosing an anisotropic light speed means choosing to make all other speeds anisotropic in the same way.

 

[cianfa72]

There is no possible measurement, no matter how clever, that can measure this. The one way speed of light is just an anisotropic synchronization convention

Anisotropic in the sense that it does not involve a two-way synchronization process/procedure.

 

[Ibix]

Anisotropic in the sense that it does not involve a two-way synchronization process/procedure.

No, of course it involves two way synchronisation. You synchronise your clock to another one by bouncing a radar pulse off it and setting your clock to the time you see on the other clock when the pulse returns, plus the travel time of light on the return leg. (There are other ways of doing it, like slow clock transport, but they reduce to the same thing.) The one way speed of light is assumed in the addition step.

The other clock may synchronise to your clock or other clocks by the same process, as long as they use the same assumptions about the (an)isotropy of lightspeed.

 

[cianfa72]

plus the travel time of light on the return leg. (There are other ways of doing it, like slow clock transport, but they reduce to the same thing.) The one way speed of light is assumed in the addition step.

Ah ok, so assuming a 'value' for the one-way speed of light basically boils down to pick the 'travel time' for the return leg that we decide to sum up to the time we see on the remote clock when the pulse returns.

The other clock may synchronise to your clock or other clocks by the same process, as long as they use the same assumptions about the (an)isotropy of lightspeed.

i.e. as long as they sum up the value $S/c$ where $S$ is the distance between clocks and $c$ is the value of the isotropic one-way speed of light we decided to pick for it.

 

[Michael Thorpe]

Here's a thought:
How about comparing the speed of light in two directions with sound pulses?
Use two light and sound pulse detector/generators say, a kilometre apart, bouncing pulses back and forth (based on light detection) and listen with a microphone in the middle. If the speed of light is the same in each direction, then the sound pulses will be exactly 180 degrees out of phase.

If microphone detects *this*, the each-way speeds are the same:
--I----I----I----I----I----I----I----I--

But *this* means they're different:
--I---I-----I---I-----I---I-----I---I---

 

[Ibix]

If microphone detects *this*, the each-way speeds are the same:
--I----I----I----I----I----I----I----I--

But *this* means they're different:
--I---I-----I---I-----I---I-----I---I---

Have you read my reply pointing out why this is wrong? If not, do so. If you have, what did you not understand about it?

 

[Michael Thorpe]

"the one way speed of light is a convention" is a new concept for me.
I suppose that's like saying, "It doesn't matter if it's different in each direction", but that doesn't sound right, because if the speeds *are* different, it would mean that stars in the South could be a lot closer than stars in the North, for example.

 

[cianfa72]

No, of course it involves two way synchronisation. You synchronise your clock to another one by bouncing a radar pulse off it and setting your clock to the time you see on the other clock when the pulse returns, plus the travel time of light on the return leg. (There are other ways of doing it, like slow clock transport, but they reduce to the same thing.) The one way speed of light is assumed in the addition step.

Sorry we can do actually the other way around. Knowing the length of the leg from a clock (say A) to a remote clock (B) we send a radar pulse from A to B encoding the time shown by clock A when it sends the pulse. Then assuming/picking a value for the one-way speed of light, clock B adds such a value to the time value encoded in the radar pulse from A as it arrives at it.

 

[Michael Thorpe]

Sorry we can do actually the other way around. Knowing the length of the leg from a clock (say A) to a remote clock (B) we send a radar pulse from A to B encoding the time shown by clock A when it sends the pulse. Then assuming/picking a value for the one-way speed of light, clock B adds such a value to the time value encoded in the radar pulse from A as it arrives at it.

RADAR and light are both electromagnetic radiation, so travel at the same speed (in a vacuum).

 

[Ibix]

"It doesn't matter if it's different in each direction"

That is exactly what it means.

because if the speeds *are* different, it would mean that stars in the South could be a lot closer than stars in the North, for example.

I have no idea why you think this follows.

 

[Ibix]

Sorry we can do actually the other way around. Knowing the length of the leg from a clock (say A) to a remote clock (B) we send a radar pulse from A to B encoding the time shown by clock A when it sends the pulse. Then assuming/picking a value for the one-way speed of light, clock B adds such a value to the time value encoded in the radar pulse from A as it arrives at it.

Fair point. The outbound leg of the radar pulse doesn't enter into it unless the other clock also needs to confirm synchronisation.

 

[Michael Thorpe]

That is exactly what it means.

I have no idea why you think this follows.

I'm thinking red-shift should indicate a different distance if light speed is different.

 

[Dale]

Here's a thought:
How about comparing the speed of light in two directions with sound pulses?
Use two light and sound pulse detector/generators say, a kilometre apart, bouncing pulses back and forth (based on light detection) and listen with a microphone in the middle. If the speed of light is the same in each direction, then the sound pulses will be exactly 180 degrees out of phase.

There is no possible measurement, no matter how clever, that can measure the one way speed of light. It is just a synchronization convention. In other words, it is just a choice of coordinates. No physical measurement can depend on your choice of coordinates, so no physical measurement can depend on the one way speed of light.

 

[Grinkle]

I'm thinking red-shift should indicate a different distance if light speed is different.

I expect you are taking as axiomatic that light from the south is equivalent to the return leg of some thought experiment and light from the north is equivalent to the outbound leg of some thought experiment.

 

[Michael Thorpe]

I expect you are taking as axiomatic that light from the south is equivalent to the return leg of some thought experiment and light from the north is equivalent to the outbound leg of some thought experiment.

Yes..

 

[Grinkle]

Yes

Set aside Doppler shift for the moment, that is a frame dependent measurement, unlike c. Cosmologists don't use Doppler shift to measure the speed of light, they take the one-way speed of light and the frequency of the emitted light as measured in the frame of the emitter as a given and then use Doppler shift to measure the relative speed between the light source and the earth-bound detector. It isn't any measurement of the one-way speed of light.

That aside, consider this early (imo brilliant) experiment -

https://en.wikipedia.org/wiki/Michelson–Morley_experiment

Measuring the 2-way speed of light in different directions is just that - it is not somehow establishing the one way speed of light.

 

[HansH]

Today I did some further adaption of the descriptin of the one way speed of light components in my earlier presented version. the adaption was based on the input I got from Orodruin at #3. I changed my equations according to the rules that hold and I can now calculate the one way speed in every direction based on the assumed speed in 2 base vector directions.
and indeed the result is that whatever speed you choose it does not make any difference on the measurements you can do. and my idea of measuring from a large distance rectangular to the source and the clocks or mirrors does indeed not work because although the paths are almost parallel, due to the long distance there is still the same horizontal component that cancels out the measurement I wanted to do, so give no information about the one way speed of light.

 

[wnvl2]

The question of HansH was about the speed of light in vacuum. I assume the same conclusion is valid for the speed of light in matierials? Do materials exist in which the speed of light differs from the speed of light in the reverse direction?

 

[Vanadium 50]

There is no one-way speed of light. Sorry to disappoint.

(This is what us meant by it's a convention).
In a non-relativistic universe, with absolute time and space, measuring the one-way speed of light (or anything) is easy. Measure and time where a light beam starts and stops, and divide distance by time. You have one equation in one unknown.

If you allow different observers to have unsynchronized clocks, now you have one equation in two unknowns. One unknown is the speed of light, and the other is a measure of how out of sync the two clocks are. If you pick a convention of clock synchronization, you've effectively picked a one-way speed of light.

Making it more complicated doesn't fix the problem: instead of one equation in two unknowns, maybe you have 99 equations in 100 uniknowns. Same problem.

 

[wnvl2]

Another try. Let us assume I have a vacuum. I synchronize my clocks using Einstein synchronisation. Now I replace the vacuum by a material. I don't touch the clocks anymore after this substitution. Is it possible that I measure now a different speed in one direction in comparison to the reverse direction?

 

[jbriggs444]

Another try. Let us assume I have a vacuum. I synchronize my clocks using Einstein synchronisation. Now I replace the vacuum by a material. I don't touch the clocks anymore after this substitution. Is it possible that I measure now a different speed in one direction in comparison to the reverse direction?

You mean like https://en.wikipedia.org/wiki/Fizeau_experiment

 

[wnvl2]

Like Fizeau but in a medium that is standing still.

 

[Dale]

Do materials exist in which the speed of light differs from the speed of light in the reverse direction?

Not to my knowledge. There are birefringent crystals where the index of refraction is anisotropic, but as far as I know it is always the same on antiparallel lines.

 

[Vanadium 50]

Do materials exist in which the speed of light differs from the speed of light in the reverse direction?

Such a material could be used to build a perpetual motion machine. So no.

 

[wnvl2]

Can you clarify that further?

 

[cianfa72]

On the basis of the discussion above consider the Einstein's statement: "light is always propagated in empty space with a definite velocity $c$ which is independent of the state of motion of the emitting body."

Does it have an actual physical content about a property of the light or is it just a re-statement of the Einstein's synchronization procedure/convention?