B Measuring the One Way Speed of Light

[beamthegreat]

To clarify,

The measurement we’re making is “what would a clock at the point of impact read at the moment of impact”. If we’re going to compare that value with the time that something else (such as the light leaving the laser) happens somewhere else we need a clock at that point as well, and we’re back to needing synchronized clocks.

My idea is not to measure the speed of light, but to see whether there is a preferred direction for light to travel. There is no need for different clocks at the point of impact. The radiation pressure from the photons will make the entire disk move. Only one stationary clock is needed to timestamp every moment of impact.

 

[beamthegreat]

How is one stationary clock supposed to measure the time that a light pulse hits the disk at different locations?

The radiation pressure from the photons will make the entire disk move. Only one clock is needed.

https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

From what I understand, the physics works out to be exactly the same whether c is isotropic or anisotropic, what we need is real world experimental data. Working out equations will not reveal how light actually behaves in reality.

 

[PeterDonis]

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

What does that have to do with "a preferred direction for light to travel"?

Only one stationary clock is needed to timestamp every moment of impact.

This is impossible, since the impacts occur at different points.

From what I understand, the physics works out to be exactly the same whether c is isotropic or anisotropic, what we need is real world experimental data.

No, you have it backwards. The correct statement is that the real world experimental data is the same whether your choice of coordinates in your mathematical model makes the one-way speed of light isotropic or anisotropic. So trying to look for real world experimental data that will tell you whether the one-way speed of light is isotropic or anisotropic is a fool's errand; that property is a property of your mathematical model, not reality, and the real-world experimental data is the same either way.

 

[beamthegreat]

What does that have to do with "a preferred direction for light to travel"?

Alright, a simplified version of that experiment is to shine a laser at opposite directions to ablate the disk. No clocks are needed. If light travels faster in one direction it should hit one side of the disk first and cause it to move in that direction before the other one hits on the opposite side with equal momentum stopping the disk from moving. If the disk does not move, then there is no preferred direction, if it does, then light travels faster in one direction.

 

[Dale]

From what I understand, the physics works out to be exactly the same whether c is isotropic or anisotropic, what we need is real world experimental data. Working out equations will not reveal how light actually behaves in reality.

This is an unscientific assertion. Without working out the equations you cannot compare your real world experimental data with the theory. The heart of the scientific method is the comparison of a theory with experimental data. Both are essential, and if you leave out either one of them you are not doing science.

The radiation pressure from the photons will make the entire disk move. Only one clock is needed.

In your case, the thing that you need to calculate is the radiation pressure assuming anisotropic one way speed of light. The usual expression for the momentum of light is based on the isotropic assumption. Until you calculate that you cannot know if a given set of experimental data would agree or disagree with the theory.

Alright, a simplified version of that experiment is to shine a laser at opposite directions to ablate the disk. No clocks are needed. If light travels faster in one direction it should hit the disk first and cause it to move in that direction before the other one hits on the opposite side with equal momentum stopping the disk from moving.

That is an assumption, not a calculation. This calculation will be horrendously complicated by the fact that the disk cannot be considered rigid in an experiment like this.

 

[PeterDonis]

a simplified version of that experiment is to shine a laser at opposite directions to ablate the disk

Reading your original description of the setup again, you have both the light source and the detectors (impact points) attached to the same disk. This means your whole idea is useless for measuring impacts on the disk, since the light exchanges the same momentum with the disk when it is emitted as when it is absorbed on impact and everything moves together--which means your "motion detector" attached to the disk will measure no motion.

Lasers shining in opposite directions will have the same issue.

 

[beamthegreat]

Reading your original description of the setup again, you have both the light source and the detectors (impact points) attached to the same disk. This means your whole idea is useless for measuring impacts on the disk, since the light exchanges the same momentum with the disk when it is emitted as when it is absorbed on impact and everything moves together--which means your "motion detector" attached to the disk will measure no motion.

Lasers shining in opposite directions will have the same issue.

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

 

[beamthegreat]

For example, 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. We then measure whether the disk moved to the left or the right. No clocks are needed. Nothing is moving. Nothing needs to be synchronized.

 

[Ibix]

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

Further to @PeterDonis' comment, the disc can't be rigid on the timescales that are needed for measuring lightspeed differences. So "the whole disc" never moves, it just stretches, and you're back to clock synchronisation and/or two-way speed methods to determine which end started stretching first.

 

[beamthegreat]

Further to @PeterDonis' comment, the disc can't be rigid on the timescales that are needed for measuring lightspeed differences. So "the whole disc" never moves, it just stretches, and you're back to clock synchronisation and/or two-way speed methods to determine which end started stretching first.

Shouldn't it theoretically work? 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.

 

[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.