Measuring the One Way Speed of Light

[Ibix]

Shouldn't it theoretically work?

No. The point is that if you tap one edge of your disc, the other edge can't possibly react to that until light has had time to cross the disc - otherwise you can communicate faster than light and all bets are off. But if the other edge can't start moving for that long, the other pulse must have got there first. So there can never be a time when the whole disc is moving due to one impact.

And I am skeptical that exactly 100.00% of the energy is lost into stretching/heating the material and exactly 0.00% is converted into kinetic energy.

Are you claiming to be able to violate the conservation of momentum? Or are you proposing that one edge of your disc might randomly emit a photon or two, giving an impulse to the disc? If the former, you will need a lot of proof. If the latter, photon rockets are uncontroversial but don't help you with your simultaneity measurement.

 

[PeterDonis]

No motion detectors are needed in my simplified version. We only observe whether the disk moves or not.

Um, measuring whether the disk moves requires a motion detector. And a detector attached to the disk will measure zero motion regardless of what you do with light sources or lasers.

@Ibix is also making valid points regarding the behavior of the disk when there is an impulse applied to one point of it.

 

[beamthegreat]

No. The point is that if you tap one edge of your disc, the other edge can't possibly react to that until light has had time to cross the disc - otherwise you can communicate faster than light and all bets are off. But if the other edge can't start moving for that long, the other pulse must have got there first. So there can never be a time when the whole disc is moving due to one impact.

I understand, but if one end starts moving first, the net effect should result in the entire disk moving in that direction. Or we can apply just enough impulse so that the material fails when the internal forces meet, and observe where the material fails.

 

[beamthegreat]

Um, measuring whether the disk moves requires a motion detector. And a detector attached to the disk will measure zero motion regardless of what you do with light sources or lasers.

Or a very very precise ruler.

 

[Nugatory]

The radiation pressure from the photons will make the entire disk move.

There's a hidden assumption here, namely that the disk behaves as a classically rigid object. But any displacement of one part of the disk will propagate to the rest of the disk at the speed of sound in the disk material; not only this necessarily less than the speed of light, but the disturbance is taking the long way around the circumference of the disk. That is, the disk is not rigid and the entire thing will not move as one.

Rigidity is a classical approximation that only works when light travel time across an object is negligible; in relativistic problems like this one that assumption fails and there are no rigid objects. You might want to take google for "bug rivet paradox" and look at our FAQ on why you can't send a faster-than-light signal by pushing on one end of a rigid steel rod.

Although it will take us well beyond a B-level thread, you can also google for "Born rigid motion". Ultimately all of this can be traced back to the relativity of simultaneity; rigidity means that all parts of the body accelerate "at the same time" and relativity says those words don't mean what they sound like.

 

[beamthegreat]

There's a hidden assumption here, namely that the disk behaves as a classically rigid object. But any displacement of one part of the disk will propagate to the rest of the disk at the speed of sound in the disk material; not only this less necessarily less than the speed of light, but the disturbance is taking the long way around the circumference of the disk. That is, the disk is not rigid and the entire thing will not move.

Rigidity is a classical approximation that only works when light travel time across an object is negligible; in relativistic problems like this one that assumption fails and there are no rigid objects. You might want to take google for "bug rivet paradox" and look at our FAQ on why you can't send a faster-than-light signal by pushing on one end of a rigid steel rod.

Although it will take us well beyond a B-level thread, you can also google for "Born rigid motion". Ultimately all of this can be traced back to the relativity of simultaneity; rigidity means that all parts of the body accelerate "at the same time" and relativity says those words don't mean what they sound like.

I fully understand that rigid bodies do not instantaneously react to external forces but rather propagate slowly through the material. But couldn't we apply just enough force so that the material fails when the internal forces meet? We can determine whether c is constant by the location of the failure.

 

[Nugatory]

Or a very very precise ruler.

No, that won't work. No matter how you set up your experiment, and no matter what anistropy may or may not be present, you will measure an outwards displacement at both points of impact. Because these points are spacelike-separated there is no frame-independent way of saying which one happened first or whether they both happened at the same time.

(The initial outwards displacements will be followed by some very complicated oscillatory behavior; as this is damped everything will return to its initial position.)

 

[Ibix]

I understand, but if one end starts moving first, and the net effect should result in the entire disk moving in that direction.

The entire disc cannot possibly start moving because most of it is too far away from the impact point of one laser pulse to have time to react before the other laser pulse lands. The net effect is to stretch the disc, not make it move.

Or we can apply just enough impulse so that the material fails when the internal forces meet, and observe where the material fails.

You could do this, but it will fail at the midpoint since this is a two-way speed measure. The speed of light isn't just the speed at which light propagates - remember that atoms are held together by electromagnetic forces, and changing the speed of light changes your description of their behaviour and hence the speed of sound in the material. You end up with the same breaking point whatever your choice of one way speed of light.

 

[Dale]

No motion detectors are needed in my simplified version. We only observe whether the disk moves or not.

How can you observer whether the disk moves without motion detectors? Any thing that can tell you whether the disk moves or not is a motion detector by definition.

if light travels faster to the right, then it should impact right side of the disk first, causing the disk to move to the right. Once the left beam impacts the left side of the disk, it will impart an equal and opposite momentum, stopping the disk.

You cannot claim this without doing the math.

 

[beamthegreat]

The entire disc cannot possibly start moving because most of it is too far away from the impact point of one laser pulse to have time to react before the other laser pulse lands. The net effect is to stretch the disc, not make it move.

You could do this, but it will fail at the midpoint since this is a two-way speed measure. The speed of light isn't just the speed at which light propagates - remember that atoms are held together by electromagnetic forces, and changing the speed of light changes your description of their behaviour and hence the speed of sound in the material. You end up with the same breaking point whatever your choice of one way speed of light.

Wait.. changing c also changes the speed of sound? How?

 

[Ibix]

Wait.. changing c also changes the speed of sound? How?

It's all electromagnetism when you get right down to it. How do you think atoms affect each other if it isn't through their electromagnetic fields?

 

[Dale]

Wait.. changing c also changes the speed of sound? How?

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 $0.8 c$.

 

[beamthegreat]

Alright, thanks for the all responses. Not that I thought I understood relativity, but knowing that I understand so little of it is humbling and brain-breaking. What about the CMBR? If the speed of light is instantaneous in one direction surely there should be a huge hole in the sky in the microwave spectrum.

 

[Dale]

What about the CMBR? If the speed of light is instantaneous in one direction surely there should be a huge hole in the sky in the microwave spectrum.

Surely? Shouldn't you do the math before you claim to be sure? @pervect provided an outline of how to calculate this back on the first page:

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 don't know how this would look. But I for one am not at all sure that there would be a huge hole. I would expect that there would be some cosmological time dilation that would exactly counteract the $c(\theta)$ but without actually doing the calculations I cannot know.

 

[PeterDonis]

What about the CMBR? If the speed of light is instantaneous in one direction surely there should be a huge hole in the sky in the microwave spectrum.

Remember what I pointed out earlier: changing "the speed of light" is a coordinate choice; it doesn't affect the real-world data at all. The microwave spectrum is what it is regardless of what coordinate choice you make for the speed of light.

 

[PeterDonis]

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 $c(\pi)=0.5 c$

Note that any coordinate choice that makes $c = \infty$ in some direction requires using a null coordinate chart--i.e., your chart will no longer have the intuitively desirable property that one coordinate is timelike and the other three are spacelike. Having $c = \infty$ in some direction means that any two events along the worldline of a light ray in that direction will have the same "time" coordinate--but those events are not spacelike separated, they're null separated, which means any coordinate that is the same for both of them must be a null coordinate.

 

[beamthegreat]

Surely? Shouldn't you do the math before you claim to be sure? @pervect provided an outline of how to calculate this back on the first page:
I don't know how this would look. But I for one am not at all sure that there would be a huge hole. I would expect that there would be some cosmological time dilation that would exactly counteract the $c(\theta)$ but without actually doing the calculations I cannot know.

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

 

[Dale]

your chart will no longer have the intuitively desirable property that one coordinate is timelike and the other three are spacelike

Sure, but null coordinates are perfectly acceptable. You just cannot have a tetrad with a null vector. So your coordinate basis is not a tetrad in those coordinates, but they are perfectly valid coordinates.

 

[PeterDonis]

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

Please read my post #85. You keep mixing yourself up by thinking of $c = \infty$ as somehow changing the real-world data. It doesn't.

 

[PeterDonis]

null coordinates are perfectly acceptable

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.

 

[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?