B One-Way Speed of Light

[shawnhcorey]

TL;DR

The one-way speed of light can be measure with the use of a transparent medium.

To measure the two-way speed of light, a pulse of light is sent thru a vacuum to bounce off a mirror and return. By knowing the distance to the mirror and how long the pulse takes to travel, the two-way speed of light can be calculated. To measure the one-way speed of light, place a transparent medium in one side of the path and measure the time. Then repeat for the other side. The difference in the times can be use to calculate the difference in the speed of light (if any) in both directions.

Example

Set up the mirror so that it is 29.9792458 cm from the emitter and the detector. It will take 2.00 ns for the pulse to travel to the mirror and back. Place a transparent medium in one side that slows light by 10%.

Same Speed

If light travels at the same speed in both directions, it takes 1.00 ns for one direction. By slowing the light by 10% on one side, it will take 1.10 ns. Same for the other side. Total travel time is 2.10 ns.

Different Speed

For the sake of argument, assume light takes 0.50 ns in one direction and 1.5 ns in the other. Total round-trip time is 2.00 ns.

Place the medium in the side of 0.50 ns. This slows the speed to 0.55 ns and has a total round-trip time of 2.05 ns. Placing it in the other side slows light to 1.65 ns for a round-trip time of 2.15 ns.

If the times for the medium in each side is the same, the light travels the same speed in both directions. But what if the amount the medium slows light down is dependent on the direction?

Snell's Law

Snell's law states that the ratio of the sine of angle of incident to the sine of the angle of refraction is equal to the ratio of the corresponding speed of light in the mediums. Set up an apparatus so that the light in the vacuum is in the same direction as one direction of the pulse of light and then in the other direction. If the angles remain the same, then the medium slow light by the same factor.

 

[Ibix]

No. The choice of the one-way speed of light represents your freedom to choose non-orthogonal axes in your reference frame. It has no detectable physical consequences because it's a personal choice.

I suspect you haven't realised that selecting a different one-way speed of light also changes your definition of the speeds of everything else, including the speed of light in a medium. If you account for that speed change (which is also anisotropic, so needs to be handled differently for the different directions) correctly then the flight time differences will disappear.

 

[shawnhcorey]

No. The choice of the one-way speed of light represents your freedom to choose non-orthogonal axes in your reference frame. It has no detectable physical consequences because it's a personal choice.

I suspect you haven't realised that selecting a different one-way speed of light also changes your definition of the speeds of everything else, including the speed of light in a medium. If you account for that speed change (which is also anisotropic, so needs to be handled differently for the different directions) correctly then the flight time differences will disappear.

Physics is not about choice. It's about measurements. Your comment is unclear. Please specify which measurements you think are wrong.

 

[shawnhcorey]

It is easy to accept a one-way speed of light if you are willing to assume that the clocks on both ends are perfectly synchronized. But that is not a legitimate assumption to people in another inertial reference frame. You should consider the relativity of simultaneity.

True, the one-way speed of light cannot be measured with two clocks. The above experiment uses only one clock.

 

[Ibix]

Physics is not about choice.

Correct. But you may choose to use orthogonal or non-orthogonal axes to express the maths, and the one-way speed of light is an artefact of that choice.

Please specify which measurements you think are wrong.

None of them are wrong, but you implicitly chose to use orthogonal axes to interpret your measurements. Thus you will get an isotropic one-way speed of light because that is an assumption hidden in your analysis.

 

[Ibix]

The above experiment uses only one clock.

...but assumes that the one-way speed of light in glass (or perhaps the refractive index) is isotropic, thereby assuming that the one-way speed of light in vacuum is isotropic

 

[FactChecker]

True, the one-way speed of light cannot be measured with two clocks. The above experiment uses only one clock.

Oh. I stand corrected. I didn't understand the experiment.

 

[PeroK]

Physics is not about choice. It's about measurements. Your comment is unclear. Please specify which measurements you think are wrong.

The one-way speed of anything depends on your synchronization convention for spatially separated clocks.

The question is whether the Einstein synchronization convention - which is the default- is the only option. It isn't the only option. Other coordinate systems, where the one-way speed of light is not isotropic, are regularly used in physics.

 

[shawnhcorey]

Correct. But you may choose to use orthogonal or non-orthogonal axes to express the maths, and the one-way speed of light is an artefact of that choice.

None of them are wrong, but you implicitly chose to use orthogonal axes to interpret your measurements. Thus you will get an isotropic one-way speed of light because that is an assumption hidden in your analysis.

Most physics is described using orthogonal axes. You still haven't specified what is wrong.

 

[shawnhcorey]

...but assumes that the one-way speed of light in glass (or perhaps the refractive index) is isotropic, thereby assuming that the one-way speed of light in vacuum is isotropic

By using Snell's law, this possibility is removed.

 

[shawnhcorey]

The one-way speed of anything depends on your synchronization convention for spatially separated clocks.

The question is whether the Einstein synchronization convention - which is the default- is the only option. It isn't the only option. Other coordinate systems, where the one-way speed of light is not isotropic, are regularly used in physics.

There is only one clock in the experiment.

 

[PeroK]

Most physics is described using orthogonal axes. You still haven't specified what is wrong.

The difference between the time taken for light to travel in vacuum and through a medium with refractive index of 1.1, say, will not be a percentage of the speed but a fixed amount. If you use the Einstein convention and find the difference to be 1 ns, say. Then, with a different synchronization convention the difference must still be 1 ns. This time interval cannot depend on the clock synchronization.

 

[Ibix]

None of them are wrong, but you implicitly chose to use orthogonal axes to interpret your measurements.

To be a bit more precise, you are assuming an isotropic refractive index. That means you are assuming orthogonal time- and space-like axes and hence an isotropic speed of light. To get an anisotropic speed of light you need to consider non-orthogonal coordinates, which would (if done correctly) lead to an anisotropic refractive index and probably a modified version of Snell's law.

You are simply assuming that you can have an anisotropic speed of light without carrying through all of the other changes. That might be consistent with something like a mechanical ether theory with an ether wind, but is not consistent with relativity.

You still haven't specified what is wrong.

I have, at least twice. You are assuming you can use orthogonal axes for some of your maths and non-orthogonal axes for other parts without accounting correctly for the different expressions of physics in the two systems. That mis-match is where your analysis is in error.

 

[PeroK]

There is only one clock in the experiment.

Yes, but if your analysis were valid, it would establish the Einstein synchronization convention as the only viable convention. Which it isn't. So, something must be wrong with your analysis.

The mistake is the assumption about refractive index for non-isotropc coordinates.

 

[PeroK]

Here's a thought experiment. Imagine we have a Moon base. A light signal is sent from Earth saying "the time is $t =0$". The signal is received on the Moon and they have to decide what to do in terms of setting their clocks.

One option is to set the Moon clock to $t' =0$ when the signal arrives. The other option is to set it to $t' = 1.2s$, because the Moon is $1.2$ light-seconds from Earth.

The second option is the Einstein synchronization convention. What about the first option? Is that just totally wrong?

It's not immediately obvious whether that option is valid or not. But, it turns out that it is valid. However, it means that one way speeds between the Earth to the Moon are not the same. That includes most clearly the one way speed of light - which is effectively measured to be infinite in one direction.

No experiment with mirrors and refractive media is going to change this.

Now, you might imagine that for most practical purposes the first convention is awkward and makes life difficult. E.g. it changes how to calculate the effect of a refractive medium on the speed of light.

But, in another context (experiments involving light or objects falling into a black hole) having an alternative synchronization convention is invaluable.

In any case, you can read more about this here:
https://en.m.wikipedia.org/wiki/One-way_speed_of_light

 

[shawnhcorey]

The difference between the time taken for light to travel in vacuum and through a medium with refractive index of 1.1, say, will not be a percentage of the speed but a fixed amount. If you use the Einstein convention and find the difference to be 1 ns, say. Then, with a different synchronization convention the difference must still be 1 ns. This time interval cannot depend on the clock synchronization.

Snell's law states that it is a percentage.

 

[shawnhcorey]

To be a bit more precise, you are assuming an isotropic refractive index. That means you are assuming orthogonal time- and space-like axes and hence an isotropic speed of light. To get an anisotropic speed of light you need to consider non-orthogonal coordinates, which would (if done correctly) lead to an anisotropic refractive index and probably a modified version of Snell's law.

You are simply assuming that you can have an anisotropic speed of light without carrying through all of the other changes. That might be consistent with something like a mechanical ether theory with an ether wind, but is not consistent with relativity.
I have, at least twice. You are assuming you can use orthogonal axes for some of your maths and non-orthogonal axes for other parts without accounting correctly for the different expressions of physics in the two systems. That mis-match is where your analysis is in error.

Snell's law states that the refractive index is isotropic.

 

[shawnhcorey]

Yes, but if your analysis were valid, it would establish the Einstein synchronization convention as the only viable convention. Which it isn't. So, something must be wrong with your analysis.

The mistake is the assumption about refractive index for non-isotropc coordinates.

Snell's law measures if it is isotropic.

 

[shawnhcorey]

Here's a thought experiment. Imagine we have a Moon base. A light signal is sent from Earth saying "the time is $t =0$". The signal is received on the Moon and they have to decide what to do in terms of setting their clocks.

One option is to set the Moon clock to $t' =0$ when the signal arrives. The other option is to set it to $t' = 1.2s$, because the Moon is $1.2$ light-seconds from Earth.

The second option is the Einstein synchronization convention. What about the first option? Is that just totally wrong?

It's not immediately obvious whether that option is valid or not. But, it turns out that it is valid. However, it means that one way speeds between the Earth to the Moon are not the same. That includes most clearly the one way speed of light - which is effectively measured to be infinite in one direction.

No experiment with mirrors and refractive media is going to change this.

Now, you might imagine that for most practical purposes the first convention is awkward and makes life difficult. E.g. it changes how to calculate the effect of a refractive medium on the speed of light.

But, in another context (experiments involving light or objects falling into a black hole) having an alternative synchronization convention is invaluable.

In any case, you can read more about this here:
https://en.m.wikipedia.org/wiki/One-way_speed_of_light

Your example has two clocks. The above experiment has only one clock. The Wikipedia page discusses the problem of synchronizing two clocks. Not a problem here since there is only one clock.

 

[Ibix]

Snell's law states that the refractive index is isotropic.

In orthogonal coordinates, yes. But in those coordinates the one-way speed of light is isotropic. You'd need to re-write Snell's Law in non-orthogonal coordinates if you want to consider an anisotropic speed of light.

If you want to consider an anisotropic speed of light you need to consider all of the consequences of your coordinate choice, not just the ones you want to.

 

[Ibix]

Your example has two clocks. The above experiment has only one clock. The Wikipedia page discusses the problem of synchronizing two clocks. Not a problem here since there is only one clock.

But if you could measure the one-way speed of light in an assumption-free way then you could synchronise clocks remotely in an assumption-free way. The two things are two sides of the same coin.

If you accept that you cannot synchronise remote clocks without assumptions then you accept that your experiment cannot measure the one-way speed of light without assumptions. Or you contradict yourself.

 

[Ibix]

Snell's law measures if it is isotropic.

It's worth noting, of course, that Fizeau's discovery of the failure of the refractive index to behave in a Newtonian fashion is now understood to be one of the first pieces of evidence for relativity.

 

[shawnhcorey]

In orthogonal coordinates, yes. But in those coordinates the one-way speed of light is isotropic. You'd need to re-write Snell's Law in non-orthogonal coordinates if you want to consider an anisotropic speed of light.

If you want to consider an anisotropic speed of light you need to consider all of the consequences of your coordinate choice, not just the ones you want to.

If Snell's law wasn't isotropic, then all the optics in the world would need constant adjustment as the world spins around. Since this is not necessary, Snell's law is isotropic.

 

[shawnhcorey]

But if you could measure the one-way speed of light in an assumption-free way then you could synchronise clocks remotely in an assumption-free way. The two things are two sides of the same coin.

If you accept that you cannot synchronise remote clocks without assumptions then you accept that your experiment cannot measure the one-way speed of light without assumptions. Or you contradict yourself.

No, you're assume that the one-way speed of light cannot be measured without two clocks.

 

[shawnhcorey]

It's worth noting, of course, that Fizeau's discovery of the failure of the refractive index to behave in a Newtonian fashion is now understood to be one of the first pieces of evidence for relativity.

Fizeau's experiment is about a moving medium. The medium does not move in the above. Not relevant.

 

[PeroK]

Fizeau's experiment is about a moving medium. The medium does not move in the above. Not relevant.

Well, then, you'd better publish and claim the Nobel Prize!

 

[PeterDonis]

place a transparent medium in one side of the path

If you are using only one clock, as you say, that means the light has to return to the same point that it started from, since it has to come back to the same clock. Which means you can't place a transparent medium in "one side" of its path and not the other. Both legs of the light's path--outbound and return--cover the same path in space. So if the medium is there on one leg, it's there on the other as well.

If, on the other hand, you insist on having the light hit the mirror at an angle so that the two legs of its path are in different parts of space, then you can't measure the light's flight time using just one clock. You need two.

Either way, your claim to have discovered a way to make an invariant (independent of any conventions) measurement of the one-way speed of light is not valid.

 

[Ibix]

If Snell's law wasn't isotropic, then all the optics in the world would need constant adjustment as the world spins around. Since this is not necessary, Snell's law is isotropic.

You fail to understand. In a system where the speed of light is anisotropic, you need an anisotropic Snell's Law to balance the anisotropic speed of light and avoid exactly those adjustments that, as you yourself note, we do not see.

 

[Ibix]

No, you're assume that the one-way speed of light cannot be measured without two clocks.

Again, you aren't understanding. If you can measure the one-way speed of light then you can synchronise remote clocks without assumptions. You seem to understand that this synchronisation is impossible, but then contradict yourself by claiming a one-way speed measure that would allow it.

 

[Nugatory]

If Snell's law wasn't isotropic, then all the optics in the world would need constant adjustment as the world spins around. Since this is not necessary, Snell's law is isotropic.

The form of Snell’s law is isotropic when expressed in isotropic coordinates, not isotropic when expressed in non-isotropic coordinates. That’s how we can analyze the behavior of light using either coordinates and arrive at the same physical result (namely, that these optics adjustments are not required).

This might also be a good time to mention that angles are inherently frame-dependent; the classical example is a ball bouncing up and down on the deck of a ship.