Measuring One-Way Speed of Light

[cooperm]

Hey all, first I just want to say that I am by no means a physicist - just someone that is very interested in physics, and I have very little understanding of physics, but I am trying to learn.

I've been reading this article about anisotropic synchrony convention which mentions that we cannot measure the one-way speed of light because you would need 2 perfectly synchronized clocks, and to synchronize them perfectly you would already need to know the one-way speed of light first.

So this leads me to my 2-part question:

1. If you somehow made the light travel in a circle so that it travels back to you without going 2 ways, would you be able to calculate the one-way speed of light?

2. Is it possible to make light travel in a circle without affecting its speed, or at least affecting it in such a way where you would know exactly how much you affected it?


Thank you in advance, I'm very curious about this.

 

[ghwellsjr]

Hey all, first I just want to say that I am by no means a physicist - just someone that is very interested in physics, and I have very little understanding of physics, but I am trying to learn.

I've been reading this article about anisotropic synchrony convention which mentions that we cannot measure the one-way speed of light because you would need 2 perfectly synchronized clocks, and to synchronize them perfectly you would already need to know the one-way speed of light first.

So this leads me to my 2-part question:

1. If you somehow made the light travel in a circle so that it travels back to you without going 2 ways, would you be able to calculate the one-way speed of light?

2. Is it possible to make light travel in a circle without affecting its speed, or at least affecting it in such a way where you would know exactly how much you affected it?


Thank you in advance, I'm very curious about this.

The two-way measurement of the speed of light is a round-trip. Going in a circle is a round-trip. That does not get around the problem of measuring the one-way speed of light.

 

[Wes Tausend]

The two-way measurement of the speed of light is a round-trip. Going in a circle is a round-trip. That does not get around the problem of measuring the one-way speed of light.

George,

First let me say that the link that the OP (cooperm) posted in post #1 seems to have a pretty good explanation of why light can't be measured one way, a subject you so graciously explained to me in the recent past.

Second, it seems there may be a way to measure light one-way something on the order that cooperm queried, but it seems impractical. Since light can be completely absorbed by passing near a black hole, it seems there may be a narrow point of radius where light might not escape, but would not be absorbed either. Whatever this point is called (Schwarzschild radius?), it would be technically an orbit I think.

Hawking has stated something to the effect, in his Brief History of Time, that an orbit proceeds in a straight line because of curved space. So if one could practically (doubtful) measure the speed of one light orbit, the speed should constitute a one-way measurement using a single clock. The light should feel no acceleration. The single clock might run quite slow near such a field but it should display a reliably consistent rate, I think.

The flaw must be that the single clock would either have to also orbit at the speed of light to escape capture (an impossibility in which case the clock would feel no acceleration, nor slow) or perhaps less flawed, the single clock could pick up a specific light beam from afar, a beam that was known to have done a sling-shot around a black hole. Just short of such an orbit would be the ultimate observed gravitational lensing, I believe. Is such a sling-shot path ever possible in any manner, to arrive back at the coordinates where one started?

Before I get too involved, is the above-linked general "RationalWiki" website OK to reference here at physicsforums, or is it considered too controversial? I might like to reference the website in the future for the one-way light explanation, or other carefully chosen subjects.

Thanks,
Wes
...

 

[WannabeNewton]

You can have a light beam freely falling in closed circular orbit at e.g. ##r = 3M## in Schwarzschild space-time (the so-called "photon radius") but a measurement of the average speed of the circulating light beam after a complete period, using a stationary (hence accelerating) clock at the same radius, would not constitute a measurement of the one-way speed of light as it involves a round-trip light circuit starting and ending at the same clock. A one-way speed of light "measurement" requires two spatially separated synchronized clocks and since clock synchronization is purely conventional, you cannot actually measure the one-way speed of light in the same way one measures the two-way speed of light. Rather the one-way speed of light is defined by the choice of synchronization convention.

 

[ghwellsjr]

Wes,

I limit my discussions to Special Relativity. I don't know General Relativity. Maybe someone else can respond.

As far as the link goes, it is full of clutter, I would recommend the wikipedia article on the one-way speed of light.

EDIT: Looks like somebody already did. Thanks, WBN.

 

[Wes Tausend]

Wes,

I limit my discussions to Special Relativity. I don't know General Relativity. Maybe someone else can respond.

As far as the link goes, it is full of clutter, I would recommend the wikipedia article on the one-way speed of light.

EDIT: Looks like somebody already did. Thanks, WBN.

Thanks for responding and the link advice, George. The Wikipedia link is pretty good without some of the apparent slants of the OP's link, and I never thought to specifically look for it. It helped me see WBN's point.

Sorry it took so long to get back and acknowledge this.

Thanks,
Wes
...

 

[Wes Tausend]

You can have a light beam freely falling in closed circular orbit at e.g. ##r = 3M## in Schwarzschild space-time (the so-called "photon radius") but a measurement of the average speed of the circulating light beam after a complete period, using a stationary (hence accelerating) clock at the same radius, would not constitute a measurement of the one-way speed of light as it involves a round-trip light circuit starting and ending at the same clock. A one-way speed of light "measurement" requires two spatially separated synchronized clocks and since clock synchronization is purely conventional, you cannot actually measure the one-way speed of light in the same way one measures the two-way speed of light. Rather the one-way speed of light is defined by the choice of synchronization convention.

I think I see your point WannabeNewton. The difference is partly accepted definition, and partly that the light would still suffer from the impossibilty of separating speed in one direction from that in the opposite (return) and knowing they are certainly identical.

Such an obtuse method might allow a single clock to be used, but the logical conclusion would be the same as using a mirror and a single clock. In thinking it over, one might be able to someday do such a measurement by passing light in such an orbit as to pass close to the black hole in perihelion and measuring it at a less stressful point of aphelion. But there is no reason to wish to do so at this time because of reasons you have stated.

As a bit of trivia, I did see such a sling-shot set-up mentioned before. A similar point came up once before on some forum, or another, where it was supposed that the traveling twin of Einstein's Twin Paradox would not undergo a discernable acceleration by carefully sling-shooting around a star in a u-turn, and could thereby return to Earth without "feeling a return" acceleration and affecting his aging. (If I recall that scenario correctly.)

One other way-out experimental method might have occurred in a once-imagined closed universe where a beam of light could be supposed to leave the universe in a single direction and reappear from behind still traveling the same direction. This could then be repeated in the opposite direction and times compared as of a single clock. I believe the first flaw would be, that we are quite certain that we do not presently live in a closed universe. That, and secondly, the light might take forever to return.

Thank you kindly for your reply, WannabeNewton.

Wes
...

 

[Nugatory]

There's some history at work in the terminology here.

The fundamental issue is actually the difference between two-clock and one-clock measurements of the speed of light; the former require a synchronization convention and the latter do not. When this issue first came up, general relativity and the possibility of curved light paths were decades in the future; only straight-line light paths in flat space-time were considered so a one-clock measurement necessarily involved a mirror or equivalent, and therefore was a two-way measurement. In principle GR suggests that there are other ways of making one-clock measurements, ones that don't have an obvious "out" and "back" to make the phrase "two-way" feel natural. But that's just a problem with the terminology, not the physics.

After a century of established practice, I don't expect the terminology to change. Everyone knows what I mean by measuring the "two-way" speed of light, but I'd get blank looks if I started talking about "one-clock" measurements.

 

[DrStupid]

we cannot measure the one-way speed of light because you would need 2 perfectly synchronized clocks, and to synchronize them perfectly you would already need to know the one-way speed of light first.

In theory a one-way measurement of the speed of light would be possible with two parallel slits rotating on the same axis. But in praxis it would be difficult to get the required accuracy.

 

[ghwellsjr]

In theory a one-way measurement of the speed of light would be possible with two parallel slits rotating on the same axis. But in praxis it would be difficult to get the required accuracy.

I don't understand your measurement but I can assure you that it's not an issue of accuracy. There is always some assumption that is made in these kinds of proposals that is tantamount to saying that the light takes the same amount of time to go one way as it takes to go the other way.

 

[DrGreg]

It's worth pointing out that if you use a non-standard synchronisation method, it doesn't just result in an anisotropic speed of light, it affects the coordinate speeds of everything else as well. For example, a rotating disk that appears rigid with standard synchronisation would not appear rigid with a non-standard synchronisation; points on the circumference wouldn't all move with the same, constant coordinate speed. So an assumption of rigidity is tantamount to an assumption of standard synchronisation.

 

[DrStupid]

I don't understand your measurement

I mean something like this:

The distance between the slits can be measured by use of any suitable reference.
The orientation of the slits would be adjusted in rest. After starting rotation any oscillations need to fade out before the measurements starts. Than the angular velocity can be measured locally at any point of the axis.

The maximum sensor signal is reached after n full rotations of the slits. The speed of light results from the corresponding angular velocity and the distance between the slits.

There is always some assumption that is made in these kinds of proposals that is tantamount to saying that the light takes the same amount of time to go one way as it takes to go the other way.

As it is a one-way measurement there is no other way. Therefore no corresponding assumptions are required.

 

[ghwellsjr]

As it is a one-way measurement there is no other way. Therefore no corresponding assumptions are required.

Yes there is. DrGreg already addressed it. You have an assumption of rigidity.

Look at it this way, you either have to drive the shaft at one location and assume that when the oscillations fade away, the slits are synchronized or you have to drive the shaft at more than one location and use some other method to assure that they are synchronized.

 

[DrStupid]

You have an assumption of rigidity.

There is no rigidity required. Elasticity is sufficient.

 

[Wes Tausend]

...
DrStupid,

It seems the above claim of a single clock, from rotating slits on the same axle, stems from the belief of an equivalent of a solid bar locking the hands of two distant clocks together so that the clocks must logically run concurrent. Or, if one must insist it is one long single clock, the speed of light is measured within the contained volume of the one clock. Interesting take.

It does agree with what I once imagined time to fundamentally be. In the most simple system, time can be measured only by a uniform rotation as a periodic event comparison ratio to any other event to be timed. In more complicated systems, other forms of time measurements might be attempted, but all distill to any sine wave or frequency, and they are still only a distended rotation. Therefore time is always a periodic rotation to me, and the direction of rotation does not affect the Arrow of Time being one direction. I am always looking for the root cause, or definition, and I could be wrong here.

Thanks,
Wes
...

 

[WannabeNewton]

There is no rigidity required. Elasticity is sufficient.

That doesn't matter. The "experiment" still overtly requires the use of clock synchronization so you're back to square one. If you have a journal reference attempting to bypass the use of clock synchronization in any and all "measurements" of the one-way speed of light then please link it.

 

[ghwellsjr]

There is no rigidity required. Elasticity is sufficient.

If your shaft is elastic, then from where does you confidence come that the two slits pass the light at the same time?

 

[PeterDonis]

The maximum sensor signal is reached after n full rotations of the slits.

How do you measure ##n##?

 

[DrStupid]

If your shaft is elastic, then from where does you confidence come that the two slits pass the light at the same time?

The slits can not pass the light at the same time because the light needs some time to travel from one slit to the other.

 

[DrStupid]

How do you measure ##n##?

The experiment results in a sensor signal as a function of the corresponding angular momentum. This function is periodic and n is "measured" by counting the maximums: n=0 for the first maximum for the non rotating slits (obviously not very useful), n=1 for the second maximum and so on.

 

[ghwellsjr]

The slits can not pass the light at the same time because the light needs some time to travel from one slit to the other.

Your picture shows that light is passing through both slits at the same time. Of course it's not the same photons passing through both slits at the same time. I thought the idea was that a photon passing through the first slit while it was on the top would pass through the second slit exactly one rotation later while it was on top and you vary the speed of rotation until you see light come through. Isn't that what is supposed to happen? And unless you assume that both slits are on top at the same time, in other words, that the shaft is rigid, then how can you determine when a given photon got from the first slit to the second slit?

 

[PeterDonis]

The experiment results in a sensor signal as a function of the corresponding angular momentum.

You mean angular velocity, correct? That's what you're measuring, according to your description. I'll assume that's what you mean below.

This function is periodic and n is "measured" by counting the maximums: n=0 for the first maximum for the non rotating slits (obviously not very useful), n=1 for the second maximum and so on.

Ok, so the experimental results will be a curve of sensor signal vs. angular velocity. But the angular velocity that appears in the experimental results is measured at some particular point on the axis; there is no guarantee, without an assumption of rigidity, that the angular velocity at the point of measurement equals the angular velocity of the slits, because the whole assembly is elastic.

Even if you let all oscillations damp out as best you can, there is no guarantee, again without an assumption of rigidity, that the relative orientation of the slits under steady rotation is the same as it was in the original rest state. And if you try to measure angular velocity at multiple points, or try to measure the actual relative orientation of the slits while in motion, or try to drive the shaft at multiple points to control the slits' relative orientation (as ghwellsjr pointed out), you have the usual clock synchronization issues.

Finally, you have an obvious clock synchronization issue between the sensor and the measurement point for angular velocity; these two measurements are at spatially separated points, so you can't just assume the two signals are referenced to the same time, which means you can't even generate the experimental result you are describing without making some assumption about clock synchronization.

 

[DrStupid]

You mean angular velocity, correct?

Yes, you are right.

there is no guarantee, without an assumption of rigidity, that the angular velocity at the point of measurement equals the angular velocity of the slits, because the whole assembly is elastic.

The angular velocity is not the problem. It could be measured by Doppler effect. The problem is the same orientation of the slits in their co-rotating rest frame. This is guaranteed because the assembly is elastic. Elasticity implies that the device returns to its position of rest after the accelerating angular momentum is removed. It might start oscillating first but after thermalization of the mechanic energy the slits will be in their original relative position again.

Even if you let all oscillations damp out as best you can, there is no guarantee, again without an assumption of rigidity, that the relative orientation of the slits under steady rotation is the same as it was in the original rest state.

If the construction is sufficiently balanced I do not see why there should be a torsion without angular momentum. However, if such a torsion exists and leads to a wrong result it should be detectable because it would hardly give the same wrong result for any configuration.

Finally, you have an obvious clock synchronization issue between the sensor and the measurement point for angular velocity; these two measurements are at spatially separated points, so you can't just assume the two signals are referenced to the same time

These measurements neither needs to be performed at spatially separated points nor at the same time. Thus I do not see any clock synchronization issue.

 

[DrStupid]

And unless you assume that both slits are on top at the same time, in other words, that the shaft is rigid

As mentioned above the shaft does not need to be rigid. Elasticity is sufficient to guarantee that the slits are in their original relative orientation as soon as the rest position is reached.

 

[ghwellsjr]

As mentioned above the shaft does not need to be rigid. Elasticity is sufficient to guarantee that the slits are in their original relative orientation as soon as the rest position is reached.

Do you accept without question or exception all the tenets of Special Relativity, including the Lorentz Transformation?

 

[PeterDonis]

The angular velocity is not the problem. It could be measured by Doppler effect.

Which requires some assumption about light propagation in order to convert the Doppler measurement to an angular velocity. See further comments below.

The problem is the same orientation of the slits in their co-rotating rest frame.

Which requires the assumption that there *is* a co-rotating rest frame. There is no guarantee that there is one without an assumption of rigidity.

This is guaranteed because the assembly is elastic. Elasticity implies that the device returns to its position of rest after the accelerating angular momentum is removed.

It means no such thing. The implicit definition of "elastic" that you are using here, which is basically that the inter-atomic distances obey Hooke's Law, is a non-relativistic approximation; it does not, and cannot, hold for a fully relativistic system.

If the construction is sufficiently balanced

"Sufficiently" has to mean "perfectly" here, which is not possible. Any imbalance will result in the slits not being aligned in the steady rotating state even if they are aligned in the original rest state. So perfect balance is a necessary condition for the slits to be aligned in the steady rotating state; however, it is *not* a sufficient condition. See below.

I do not see why there should be a torsion without angular momentum.

Um, first of all, in the steady-state rotating case, there *is* angular momentum. The only state with zero angular momentum is the original rest state, before the assembly is spun up.

Second, even if there is no torsion in the steady rotating state, after the disks are spun up and oscillations are allowed to die away, and even if the assembly is perfectly balanced, there is still no guarantee that the slits will be aligned, assuming they were in the original rest state. That's because there is no way to spin up *any* object from rest to a constant angular velocity without changing the relative orientation of at least some of its parts. And unless you precisely control the spin-up process for every single atom of the assembly, you cannot control how the relative orientations of the parts change, even assuming perfect balance to start with.

However, if such a torsion exists and leads to a wrong result it should be detectable because it would hardly give the same wrong result for any configuration.

The wrong result wouldn't be a matter of torsion; as above, there doesn't need to be torsion present for the slits to be misaligned in the steady rotating state. The misalignment just leads to an error in the relationship between measured angular velocity and measured sensor signal.

These measurements neither needs to be performed at spatially separated points

Um, what? Your diagram explicitly shows the sensor, where the sensor measurements are taken, being spatially separated from the axis of the assembly, where the angular velocity measurements are taken. So something has to propagate in order to make the comparison: either a signal (e.g., a Doppler signal, as you suggested) has to propagate from the axis to the sensor (where, say, a Doppler shift measuring device is co-located with the device that senses the laser signal), or a signal from the sensor has to propagate to where the angular velocity of the axis is measured. And any such propagation requires assumptions about how much time it takes, i.e., assumptions about clock synchronization.

nor at the same time.

Yes, they do. Your experimental result is a graph of sensor signal vs. angular velocity. How can you match the two measurements up without a common time reference?

 

[DrStupid]

Which requires some assumption about light propagation in order to convert the Doppler measurement to an angular velocity.

Doppler is just one possibility. The angular velocity can be measured locally as well. If the records for both slits show the same constant value than they are rotating with the same speed.

Which requires the assumption that there *is* a co-rotating rest frame. There is no guarantee that there is one without an assumption of rigidity.

I do not see where rigidity comes into play here. Please explain.

The implicit definition of "elastic" that you are using here, which is basically that the inter-atomic distances obey Hooke's Law, is a non-relativistic approximation; it does not, and cannot, hold for a fully relativistic system.

Please explain how relativistic effects would lead to a torsion.

"Sufficiently" has to mean "perfectly" here

No. It means that the assembly remains radial symmetric within the accuracy of measurement. Radial deformations can easily be detected by an external reference.

Any imbalance will result in the slits not being aligned in the steady rotating state even if they are aligned in the original rest state.

I can't see why. Of course the construction will be deformed by any imbalance but why should it be twisted in any case?

Um, first of all, in the steady-state rotating case, there *is* angular momentum. The only state with zero angular momentum is the original rest state, before the assembly is spun up.

I'm very sorry. That was a translation error. What I mean is moment of force.

there is no way to spin up *any* object from rest to a constant angular velocity without changing the relative orientation of at least some of its parts.

Thats true. But an elastic object will return to its original shape if all forces are removed. You mentioned that you have doubts about that for relativistic conditions but you need to explain that in detail.

And unless you precisely control the spin-up process for every single atom of the assembly, you cannot control how the relative orientations of the parts change, even assuming perfect balance to start with.

If I can measure the angular velocity of both slits with sufficient accuracy I could integrate it to get the resulting relative orientation. But I still do not think that this is necessary.

The wrong result wouldn't be a matter of torsion; as above, there doesn't need to be torsion present for the slits to be misaligned in the steady rotating state. The misalignment just leads to an error in the relationship between measured angular velocity and measured sensor signal.

I can't see why.

Your diagram explicitly shows the sensor, where the sensor measurements are taken, being spatially separated from the axis of the assembly, where the angular velocity measurements are taken.

That's just an example. Obviously it is impossible to show any possible arrangement in a single picture. You can measure angular velocity at any point of the axis and by use of mirrors or optical fibers you can place the sensor to any location.

So something has to propagate in order to make the comparison

Even if the measurement are not performed at the same place the migration of the signals is not time critical. There is no clock synchronization required.

How can you match the two measurements up without a common time reference?

I just need to guarantee that the signals are constant within given time period of time and that the time periods of both records are overlapping. For example:

1. Start recording of the sensor signal.
2. Drink some coffee.
3. Start recording of the angular velocity.
4. Read a newspaper.
5. Stop recording of the angular velocity.
6. Get record and go to the sensor.
7. Stop recording of the sensor signal.
8. Check the records to make sure that there are no oscillations or other fluctuations.
9. If the values are not constant than return to 1.

 

[DrGreg]

I think it's worth examining how a non-isotropic one-way speed of light comes about. Suppose you have a standard inertial coordinate system [itex](t,x,y,z)[/itex] with Einstein-synchronised time. Now define a new coordinate system by[tex]\begin{align}
T &= t + \alpha x \\
X &= x \\
Y &= y \\
Z &= z
\end{align}[/tex]where [itex]\alpha[/itex] is some positive constant. By substituting [itex]x=\pm c t[/itex], it's easy to show that, in the new coordinates, the 1-way speed of light is [tex]
\frac{c}{1 \pm \alpha c}
[/tex]in the positive and negative X directions. It's still c in the Y and Z directions, and the 2-way speed of light is still c in every direction.

Now let's apply this to the spinning slits, with the axis of rotation along the X axis. Let's further suppose the system has been running at constant angular velocity for some time so it is in an equilibrium state therefore behaving in a Born-rigid manner. Furthermore, when analysed in [itex](t,x,y,z)[/itex] coordinates, the time [itex]t_1[/itex] taken for light to pass between the slits in the positive x-direction is exactly the time of one revolution, so light passes through both slits. Now analyse this in [itex](T,X,Y,Z)[/itex]. Now the time taken for light is [itex]T_1 = t_1 + \alpha x_1[/itex]. This is longer than the time [itex]t_1[/itex] taken for one revolution, and therefore, as the light does pass through both slits, we must conclude that the slits are no longer aligned in T-coordinates.

Reversing the argument, if you assume the slits remain aligned after spinning up the system, you are assuming Einstein synchronisation.

 

[Dale]

Please explain how relativistic effects would lead to a torsion.

Consider a cylinder rotating about the x-axis of some inertial frame. Suppose that it has a straight line painted on it parallel to the axis in this frame. Now consider the line in another inertial frame, a quick Lorentz transform will show that the line forms a helix in another frame.

 

[DrStupid]

Now the time taken for light is [itex]T_1 = t_1 + \alpha x_1[/itex]. This is longer than the time [itex]t_1[/itex] taken for one revolution

How do you define "the time taken for light" if time is dependent on a position?

 

[DrStupid]

Consider a cylinder rotating about the x-axis of some inertial frame. Suppose that it has a straight line painted on it parallel to the axis in this frame. Now consider the line in another inertial frame, a quick Lorentz transform will show that the line forms a helix in another frame.

Always use the rest frame of the assembly. Problem solved.

 

[ghwellsjr]

Are you going to answer my question:

Do you accept without question or exception all the tenets of Special Relativity, including the Lorentz Transformation?

 

[DrGreg]

How do you define "the time taken for light" if time is dependent on a position?

For the purpose of this thought experiment, you measure t using two Einstein-synchronised clocks at the two positions and use the equation [itex]T=t+\alpha x[/itex].

However, in a practical scenario where you are given two T-synchronised clocks but you don't know how they have been synchronised, you just read T from the two clocks.

 

[PeterDonis]

DrStupid, we have apparently been talking at cross purposes; I was assuming that you were measuring the sensor signal continuously as the angular velocity of the assembly was continuously changed, but it doesn't look like that's the case:

For example:

1. Start recording of the sensor signal.
2. Drink some coffee.
3. Start recording of the angular velocity.
4. Read a newspaper.
5. Stop recording of the angular velocity.
6. Get record and go to the sensor.
7. Stop recording of the sensor signal.
8. Check the records to make sure that there are no oscillations or other fluctuations.
9. If the values are not constant than return to 1.

In other words, you spin up the assembly to some angular velocity, and keep it constant while you measure the sensor signal. Then you spin the assembly up some more, and hold it constant again while you measure the sensor signal. Then you repeat until you have enough points for a graph. Correct?

Then you have the following problem: how do you correlate the different angular velocity measurements? A spin-up process intervenes between each one, and that process will change the spatial geometry of the assembly (because it will change the internal forces within the assembly, since those forces depend on angular velocity). That includes possible changes in the relative alignment of the slits; in other words, the equilibrium state of the assembly at different angular velocities may have different alignments of the slits.

Also, you are still either assuming that the entire assembly has a single "co-rotating rest frame" for each angular velocity measurement (so an angular velocity measurement at one point applies to the entire assembly), or assuming a clock synchronization between different parts of the assembly for each angular velocity measurement (if you take angular velocity measurements locally at different points of the assembly).

 

[Dale]

Always use the rest frame of the assembly. Problem solved.

Not if the problem is to measure the speed of light in different frames.

If you use the rest frame of the cylinder then you assume the synchronization of that frame. That will lead to anisotropic speed of light as was already described