Synchronized Clocks in Frames boosted by Acceleration

[Jorrie]

I have often thought about how the one-way speed of light can be measured without having to use synchronized clocks, which tends to be controversial because the clocks are normally synchronized by using one-way light in the first place. Recently, Don Lincoln of Fermi-Lab suggested a method to me. To convince myself, I tested it in a thought experiment, using two clocks and two cables in a frame that is boosted by accelerating it to a new inertial frame. I thought it useful to share it and get other opinions.

First, Don Lincoln's test.

Take two photon detectors. These can be arbitrarily thin - less than a millimeter if necessary. Take the two detectors and place them side by side. From each detector take a cable of a convenient length. Put both of those cables into fast electronics (a modern digital oscilloscope will work just fine).

Fire a light pulse through both detectors. Since these two detectors are adjacent to one another, the transit time from one to the other is of order (1 mm)/(speed of light) = (1 x 10-3 m)/(3 x 108 m/s) = 3 x 10-12 seconds. If sub- 3 picosecond speed is needed, there are ways.

Using your oscilloscope, you can calibrate your cables to establish what "simultaneous" means. In the abstract, the cables can be of identical length. This means that the signals from the two detectors will arrive simultaneously at your oscilloscope.

Now move one detector far away...maybe 1000 feet. Do not disconnect the cables, so you have identical conditions. Fire the light pulse (use a laser) through one detector to hit the other. The signals from the two detectors will transit the cables and hit your oscilloscope at a single spatial point. Since you have already established that the transit time in the cables of both detectors are identical, the only difference between the signal arrival time at your detector is the transit time of light from one to the other. If you have measured the distance exactly, you can then determine the speed of light by distance over time.

I expanded Don's test as follows:
Consider two spaceships connected by a taut cable of 600 units long. Add Don’s second identical cable, folded back and strapped at the half-distance point (for ease of presentation) so that the setup becomes equivalent to his scenario, with the cables calibrated for identical transmission times. Accelerate the whole ‘lab’ lengthwise to 0.6c in such a way that the cables do not stretch (Born-rigidity) and let it coast again.

I used the Rindler coordinates equation t = \sqrt{x^2-\sigma^2}, where \sigma is the distance of the start of the curve from the origin (1 and 1.6 units respectively). The origin coincides with the common light cone of Rindler observers with constant proper acceleration (a), where a =1 / \sigma. The other relevant equations are: \tau = \sigmaasinh(a t) and v/c = tanh(a \tau).
The spacetime diagram is a tad busy, but gives an overview of all the values calculated for the acceleration phase and the later cruise phase.

Click on the thumbnail below if you do not see the diagram.

For simplicity, use a cable with a signal speed of exactly 0.6c, so that a signal takes exactly one time unit to travel the length of the cable. After the acceleration, the speed of the pulse relative to the original reference frame is (0.6\pm0.6)/(1+0.36)c, i.e. 0.882c in the forward direction and zero in the return direction.

In the reference frame the acceleration lasts for t=0.75 units for the blue ship and t=1.2 units for the front ship. The corresponding ship proper times are \tau_{blue}=0.69 and \tau_{red}=1.11 units. The latter clock must be set back by 0.42 units to \tau'_{green}=0.69 units in order to be synchronized with blue again.

The pulse in cable 1 is transmitted simultaneously with the laser pulse and arrives back at the oscilloscope at \tau_{blue}=1.69, while the cable 2 pulse arrives at \tau_{blue}=2.29. This gives a time delay of 0.6 units, which is the travel time of the laser pulse. Since we expect the proper length of the cable to remain the same before and after acceleration, this seems to indicate that it is a true clock-sync-independent measurement of the one-way speed of light in an inertial frame. If correct, this also means that calibrated cables can be used to synchronize distant clocks without slow transport involved.

 

[ghwellsjr]

You should read the wikipedia article on the one-way speed of light. You will see that you have misunderstood what Don was telling you or else he has fooled himself and you. You cannot measure the one-way speed of light, period. All attempts, no matter how complicated or subtle, either are measuring the two-way speed of light or are in fact using the equivalent of synchronized clocks.

You and/or Don have made the faulty assumption that the propagation of an electrical signal down a cable is a constant no matter the orientation of the cable. Suppose that in his setup, you start with the two 1000-foot cables stretched out 500 feet away and back. You are assuming that the time it takes for the signals to get 500 feet away is identical to the time it takes for the signals to get back so that when you stretch out one of the cables the full length it will take the same time to go one-way as it did to go both ways for half the distance. Can you see that this is flawed?

 

[Jorrie]

You and/or Don have made the faulty assumption that the propagation of an electrical signal down a cable is a constant no matter the orientation of the cable. Suppose that in his setup, you start with the two 1000-foot cables stretched out 500 feet away and back. You are assuming that the time it takes for the signals to get 500 feet away is identical to the time it takes for the signals to get back so that when you stretch out one of the cables the full length it will take the same time to go one-way as it did to go both ways for half the distance. Can you see that this is flawed?

I think you misinterpret. The equal time for equal distance (both ways) in the 'test' is measured in the frame of the moving medium, not the reference frame. I fail to see any flaw in that.

 

[mfb]

You need the signal speed in the cable to be the same both ways. This is similar to moving objects (or sending light) between the spaceships.

 

[ghwellsjr]

I think you misinterpret. The equal time for equal distance (both ways) in the 'test' is measured in the frame of the moving medium, not the reference frame. I fail to see any flaw in that.

I was talking only about Don's original setup, not your expanded test. His original setup does not measure the one-way speed of light. I haven't paid any attention to your expanded test. It's unnecessary if you see the problem with Don's setup.

 

[Nugatory]

You need the signal speed in the cable to be the same both ways. This is similar to moving objects (or sending light) between the spaceships.

Don Lincoln's version and OP Jorrie's version are interestingly different, and OP's mistake may be in not appreciating this difference.

In the original form, everything is being done in the lab frame, and the calibration process IS a clock synchronization process - the cables are clocks (easily synchronized clocks, but impractical for general use because they only tick twice so can only make a single measurement). The only possibly questionable assumption is the assumption that the signal propagation time won't depend on whether the cable is laid straight or coiled; that assumption can be verified experimentally.

This synchronization process falls apart completely as soon as the cable is set in motion, as in OP's spaceship version. So, although I see nothing wrong with Don Lincoln's one-way measurement, it's still a synchronized-clock measurement; and OP's spaceship variant does not provide a counterexample to teh need for two-way measurements.

 

[mfb]

The only possibly questionable assumption is the assumption that the signal propagation time won't depend on whether the cable is laid straight or coiled; that assumption can be verified experimentally.

It cannot, unless you use some other method to sync clocks (like light... but then your sync relies on the one-way-speed of light again).

 

[ghwellsjr]

Don Lincoln's version and OP Jorrie's version are interestingly different, and OP's mistake may be in not appreciating this difference.

In the original form, everything is being done in the lab frame, and the calibration process IS a clock synchronization process - the cables are clocks (easily synchronized clocks, but impractical for general use because they only tick twice so can only make a single measurement). The only possibly questionable assumption is the assumption that the signal propagation time won't depend on whether the cable is laid straight or coiled; that assumption can be verified experimentally.

This synchronization process falls apart completely as soon as the cable is set in motion, as in OP's spaceship version. So, although I see nothing wrong with Don Lincoln's one-way measurement, it's still a synchronized-clock measurement; and OP's spaceship variant does not provide a counterexample to teh need for two-way measurements.

The synchronization process also falls apart completely as soon as you move one end of the cable, going from coiled (or just folded in half as I suggested) to stretched out, as in Don's original setup. There is no point in proposing an expanded test if you understand the flaw in the original test setup.

 

[Jorrie]

The synchronization process also falls apart completely as soon as you move one end of the cable, going from coiled (or just folded in half as I suggested) to stretched out, as in Don's original setup. There is no point in proposing an expanded test if you understand the flaw in the original test setup.

I would like to hear more about why the sync process falls apart if I move one end of the cable. Apart from the difficulty of measuring the actual speed in cables without synchronized clocks, is there a technical reason why the signal speed (relative to cable) in a perfect cable in free space would be dependent on direction of the signal?

 

[Nugatory]

It cannot, unless you use some other method to sync clocks (like light... but then your sync relies on the one-way-speed of light again).

Why so? I colocate the two ends so that I can use the same clock to measure the send and receive events, drop the signal into one end of the cable and see how long it takes to come out the other... Try switching the sending and receiving ends, drag the cable around my lab, coil it ten times, a hundred times, coil it clockwise and counterclockwise, or both at the same time, rerun the same tests again with my lab rotated 90 degrees... and my one and only lab clock gives me the same transit time every time. Furthermore, I go to the trouble of moving the ends to different locations, use the non-controversial two-way speed of light to establish a simultaneity convention, and still measure the same transmission time.

So I decide that a reasonable simultaneity convention is that the transmission time of a signal (the signal speed need not be, and probably isn't, the speed of light) in the cable is constant provided the cable remains at rest relative to me. Hence my claim that the cable, after appropriate testing, IS a synchronized clock; and in the future I can use my calibrated cable as a pair of synchronized clocks without repeating the calibration process.

But of course all this does is prove that the detectors at the ends of my cables can be used as synchronized clocks. There's no challenge here to the fact that a one-way measurement requires a synchronized clock; instead I claim that a synchronized clock is hidden in Lincoln's formulation of the thought experiment, and OP has inadvertently lost it.

 

[ghwellsjr]

I would like to hear more about why the sync process falls apart if I move one end of the cable. Apart from the difficulty of measuring the actual speed in cables without synchronized clocks, is there a technical reason why the signal speed (relative to cable) in a perfect cable in free space would be dependent on direction of the signal?

Let's say we take two identical parallel straight 500-foot perfect cables that propagate an electrical signal at c. We send a signal down one of them at the same time that we generate a flash of light. At the other end of the 500-foot cables we have a light detector which goes into our scope on one channel and the electrical signal from the cable goes into a second channel of the scope. We see that the light signal arrives simultaneously with the electrical signal. We also put a mirror at the detector to reflect the light back to the source and we put a tee in the cable to transmit the electrical signal back down the other cable. Back at the source we have a second light detector which we put into one channel of another scope along with the signal from the second cable in a second channel of the scope. We see that the light signal and the electrical signal arrive simultaneously.

Why did we bother with the electrical cables? We already know that when we do this experiment with light and a mirror that we cannot say that the time it takes for the light to propagate in both directions is the same unless we arbitrarily define them to be the same. If we cannot say that they are the same for light in free space, then we cannot say that they are the same for the electrical signals in cables.

 

[ghwellsjr]

Why so? I colocate the two ends so that I can use the same clock to measure the send and receive events, drop the signal into one end of the cable and see how long it takes to come out the other... Try switching the sending and receiving ends, drag the cable around my lab, coil it ten times, a hundred times, coil it clockwise and counterclockwise, or both at the same time, rerun the same tests again with my lab rotated 90 degrees... and my one and only lab clock gives me the same transit time every time. Furthermore, I go to the trouble of moving the ends to different locations, use the non-controversial two-way speed of light to establish a simultaneity convention, and still measure the same transmission time.

So I decide that a reasonable simultaneity convention is that the transmission time of a signal (the signal speed need not be, and probably isn't, the speed of light) in the cable is constant provided the cable remains at rest relative to me. Hence my claim that the cable, after appropriate testing, IS a synchronized clock; and in the future I can use my calibrated cable as a pair of synchronized clocks without repeating the calibration process.

But of course all this does is prove that the detectors at the ends of my cables can be used as synchronized clocks. There's no challenge here to the fact that a one-way measurement requires a synchronized clock; instead I claim that a synchronized clock is hidden in Lincoln's formulation of the thought experiment, and OP has inadvertently lost it.

I agree with everything you said here.

The problem is that you earlier said in post #6 that you saw nothing wrong with Don Lincoln's one-way measurement but his claim was that the one-way speed of light can be measured without having to use synchronized clocks. It would have made more sense if you had pointed out that there was something wrong with Don's claim because he was in fact not measuring the one-way speed of light but rather defining it by using the virtual synchronized clocks of his cables.

 

[Jorrie]

Why did we bother with the electrical cables? We already know that when we do this experiment with light and a mirror that we cannot say that the time it takes for the light to propagate in both directions is the same unless we arbitrarily define them to be the same. If we cannot say that they are the same for light in free space, then we cannot say that they are the same for the electrical signals in cables.

I understand what you are saying for light. My understanding is that the speed of a signal in a cable is some factor (less than unity) of c, with c the two-way speed of light. This forms the basis for one argument that I have heard for why a measurement using two cables actually constitutes a two-way measurement (e.g. Zhang 1997). It does not sound very convincing to me.

Secondly, propagation speed in a real cable has different dynamics than a pulse of light in vacuum, e.g. a real observer can co-move with a pulse in a cable. Is it correct to sweep this difference under the carpet when replacing the cables with light pulses? I'm happy either way, but I'm simply not convinced by your argument up to this point.

 

[ghwellsjr]

I understand what you are saying for light. My understanding is that the speed of a signal in a cable is some factor (less than unity) of c, with c the two-way speed of light. This forms the basis for one argument that I have heard for why a measurement using two cables actually constitutes a two-way measurement (e.g. Zhang 1997). It does not sound very convincing to me.

Secondly, propagation speed in a real cable has different dynamics than a pulse of light in vacuum, e.g. a real observer can co-move with a pulse in a cable. Is it correct to sweep this difference under the carpet when replacing the cables with light pulses? I'm happy either way, but I'm simply not convinced by your argument up to this point.

A person can co-move with a slowly transported clock but that doesn't mean that it also isn't following the same standard arbitrary synchronization process that we always use in Special Relativity. Whenever you do any of these things, you are defining time at a remote location, you're not measuring it. Zhang is right, you should pay attention to what he says.

 

[Jorrie]

But of course all this does is prove that the detectors at the ends of my cables can be used as synchronized clocks. There's no challenge here to the fact that a one-way measurement requires a synchronized clock; instead I claim that a synchronized clock is hidden in Lincoln's formulation of the thought experiment, and OP has inadvertently lost it.

OK, I agree that if we stay strictly in one inertial frame, there is no difference between Lincoln's two cables and two synchronized clocks. However, I have attempted to show that when we boost the final setup lengthwise to a new inertial frame, there is a difference in that the clocks go out of sync, while the cables apparently do not lose their definition of simultaneity.

To further illustrate, if we bring the two clocks slowly together after the acceleration, we expect them to be out of sync. If we bring the two ends of the straightened cable together again, I expect the cables to still have the same simultaneity as before the acceleration, i.e. I do not expect to have to adjust their lengths to show local simultaneity, a-la Lincoln's test. I may be wrong on the latter, but then I want to understand why.

 

[Jorrie]

Zhang is right, you should pay attention to what he says.

I'm afraid when I paid my dues to Zhang's chapter 8, especially his equations 8.3.18 to 8.3.25 (and some references to earlier equations), I was left with the distinct impression that he has shown that the one-way speed of the gamma rays were within very close bounds to the two-way speed of light. His conclusion on the Alvager-Farley-Kjellman-Wallin experiment (eq. 3.1.25):

Thus, by definition, the velocity of the \gamma ray is
c' = \frac{L}{t'_B-t'_A} = c
Note that here c is defined in Eq. (8.2.1), which is the two-way velocity of light
in vacuum. Then we conclude that this experiment determined only a value of the
two-way (but not the one-way) velocity of the \gamma rays and the electric signals.

Yes, it determined c' in terms of c, not absolutely, but does this not reveal a deep truth? Isn't any arbitrary selection of simultaneity convention, other than Einstein's, in conflict with experiment?

 

[ghwellsjr]

OK, I agree that if we stay strictly in one inertial frame, there is no difference between Lincoln's two cables and two synchronized clocks. However, I have attempted to show that when we boost the final setup lengthwise to a new inertial frame, there is a difference in that the clocks go out of sync, while the cables apparently do not lose their definition of simultaneity.

To further illustrate, if we bring the two clocks slowly together after the acceleration, we expect them to be out of sync. If we bring the two ends of the straightened cable together again, I expect the cables to still have the same simultaneity as before the acceleration, i.e. I do not expect to have to adjust their lengths to show local simultaneity, a-la Lincoln's test. I may be wrong on the latter, but then I want to understand why.

As Nugatory said in post #6, the cables act as a clock that ticks only twice--good for a single measurement. They are not producing a continual stream of ticks which are being counted which is what happens in a real clock. If they did that, they would go out of sync just like your real clocks, meaning the values of the counters will be different after you accelerate them and bring them together.

 

[ghwellsjr]

Zhang is right, you should pay attention to what he says.

I'm afraid when I paid my dues to Zhang's chapter 8, especially his equations 8.3.18 to 8.3.25 (and some references to earlier equations), I was left with the distinct impression that he has shown that the one-way speed of the gamma rays were within very close bounds to the two-way speed of light. His conclusion on the Alvager-Farley-Kjellman-Wallin experiment (eq. 3.1.25):

Thus, by definition, the velocity of the γ ray is

c' = \frac{L}{t'_B-t'_A} = c

Note that here c is defined in Eq. (8.2.1), which is the two-way velocity of light
in vacuum. Then we conclude that this experiment determined only a value of the
two-way (but not the one-way) velocity of the γ rays and the electric signals.

Yes, it determined c' in terms of c, not absolutely, but does this not reveal a deep truth? Isn't any arbitrary selection of simultaneity convention, other than Einstein's, in conflict with experiment?

I don't have Zhang's book so I can't comment on the details, except that it sounds like he is saying that the measurement was a combination of one way for the gamma rays plus the opposite way for the electric signals, kind of like Don's test. I only know that the wikipedia article I referred you to in post #2 showed Zhang to be a great defender of the impossibility of measuring the one-way speed of light.

If you understand that claiming to be able to measure the one-way speed of light is equivalent to the claim of being able to identify the absolute rest state of ether, then you will not be enticed by any such claim. It may take a lot of detailed analysis to identify the flaw in these claims, which is what Zhang has done, but for me, it's like a claim to have invented a perpetual motion machine--the US patent office has no interest in any such claim--and I have no interest in analyzing the details of these complicated schemes that claim to measure the one-way speed of light. The simple ones, like slow transport of clocks or Don's scheme I'll take on but not much beyond those.

 

[Jorrie]

As Nugatory said in post #6, the cables act as a clock that ticks only twice--good for a single measurement. They are not producing a continual stream of ticks which are being counted which is what happens in a real clock. If they did that, they would go out of sync just like your real clocks, meaning the values of the counters will be different after you accelerate them and bring them together.

OK, I understand, but this seems to imply that cables as 'two tick clocks' establish Einstein's simultaneity in inertial frames independently from clocks in the conventional sense.

Granted, in order to synchronize conventional ticking clocks by means of the cables, we need parameters of the cables that depend on c, like length and propagation speed. I guess that this is where the "hidden two-way speed of light" creeps in.

 

[ghwellsjr]

I don't see why you think that using light signals to synchronize clocks is any different than using cables. Don's method is the same as an observer being midway between a light source and a light target. The observer starts a timer when he sees the flash of light at the source and stops it when he sees the target illuminated. I think you can see that he's really measuring how long it takes for the light to traverse from his location to the target and back to him, in other words, he's measuring the round-trip time for half the distance and calling it the one-way time for the full distance.

If the observer was looking through a medium that slowed the propagation of the light for him equally in both directions but the light going from the source to the target was in free space, then I think you can see that all this would do is add some time to both ends of his measurement and it would come out the same. In fact, this would be no different than if he was equidistant from the source and the target but not in line with them, in other words, he, the source and the target form a triangle. It would also be the same as if his reaction time added some time to both ends of his measurement. As long as they were the same, it won't make any difference. All these deviations from the ideal would be like the cables with a propagation at less than c--it won't make any difference to the measurement--as long as the propagations are the same.

So I hope I have convinced you that electrical signals in cables are not inherently worse or different than light in free space.

 

[Jorrie]

I don't see why you think that using light signals to synchronize clocks is any different than using cables.

OK, I agree with you - the speed of propagation in the cables was an unintentional red herring; this speed does not matter in the test, or for that matter in my extension. I now want to get back to Don's test. Note that he has assumed we know the length of the cable to the distant detector precisely in the inertial frame:

Since you have already established that the transit time in the cables of both detectors are identical, the only difference between the signal arrival time at your detector is the transit time of light from one to the other. If you have measured the distance exactly, you can then determine the speed of light by distance over time.

Since you are claiming Don does not measure the one-way speed of light, are you saying that we cannot know the length of the cables without assuming a one-way speed of light? I have also hinted at this possibility in my prior reply.

 

[ghwellsjr]

Since you are claiming Don does not measure the one-way speed of light, are you saying that we cannot know the length of the cables without assuming a one-way speed of light? I have also hinted at this possibility in my prior reply.

No, you measure the length of the cables with a rigid ruler. This is Einstein's definition of length or distance. It has nothing to do with the speed of light. Here's Einstein's quote from section 1 of his 1905 paper introducing Special Relativity:

If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.

I'm curious: why would you think that the speed of light would have any bearing on a length measurement?

 

[Jorrie]

I'm curious: why would you think that the speed of light would have any bearing on a length measurement?

Because "The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second" (NIST). Does this not make all length measurements a function of the speed of light?

 

[ghwellsjr]

Because "The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second" (NIST). Does this not make all length measurements a function of the speed of light?

Well if you're going to rely on a hundred years of experience with Special Relativity, then there's no point in trying to measure the speed of light, is there? It's defined to be exactly 299792458 meters per second.

Start over again. Pretend like you don't have access to the common standards available to us today. Make up your own unit for length and time. The length of your right foot is your standard for a foot and the time interval between the next two beats of your heart is your standard for a second. Now do all your measurements. When you get all done, you can confirm that your units and measurements can be converted into the standard units and you get the same results.

 

[Jorrie]

Well if you're going to rely on a hundred years of experience with Special Relativity, then there's no point in trying to measure the speed of light, is there? It's defined to be exactly 299792458 meters per second.

George, I think we actually agree on the main point, just stating it from different points of view, or at least in different words...

Recall that I wrote:
"Since you are claiming Don does not measure the one-way speed of light, are you saying that we cannot know the length of the cables without assuming a one-way speed of light? I have also hinted at this possibility in my prior reply."

I think we could rephrase it something like: "we claim that Don did measure the one-way speed of light, but he cannot prove that it is the real (or only possible) value, because his length measurement assumed the value of the one-way speed of light as defined in the 1980s."

Yes, we can go on and argue on whether two cables with two pulses, two detectors and one oscilloscope constitute two clocks, but that is philosophical. We can also argue that he only measured the two-way speed of light, but IMO Don has demonstrated that he can measure the one-way speed of light with only one clock, the oscilloscope.

 

[ghwellsjr]

This is not a philosophical issue. It's not an issue of opinions. You cannot measure the one-way speed of light, period. (Repeating what I said in my first response to you.) I also said, "All attempts, no matter how complicated or subtle, either are measuring the two-way speed of light or are in fact using the equivalent of synchronized clocks."

I really thought we had made a lot of head way here but now you seem to be backtracking. Did you understand my comment in post #20?

Don's method is the same as an observer being midway between a light source and a light target. The observer starts a timer when he sees the flash of light at the source and stops it when he sees the target illuminated. I think you can see that he's really measuring how long it takes for the light to traverse from his location to the target and back to him, in other words, he's measuring the round-trip time for half the distance and calling it the one-way time for the full distance.

Why don't you agree with this?

 

[K^2]

Yes, we can go on and argue on whether two cables with two pulses, two detectors and one oscilloscope constitute two clocks, but that is philosophical.

Not at all. You are using pulses from the two detectors as means of synchronization. You simply happen to keep the single time-keeper in the middle. It's equivalent to two clocks at either detector being synchronized via a third party sitting in the middle. This is still a synchronized clock experiment.

Edit: Just to expand on this. Imagine that instead of detectors you have two clocks at either end. They recorded at what time they saw the speed of light and immediately send the notification to observer in the middle. Observer in the middle compares the two time stamps and compares these to his own clock. He then sends both parties the results and the disagreement with his own clock. This information can then be used at either end to make computations of the speed of light.

Note that a) This is equivalent to experiment performed in every way. b) If instead the two clocks at either end sent an arbitrary time stamp in advance, they could perform the necessary synchronization in advance, but that does not change the experiment.

So the overall setup with two detectors and a single clock still works as a synchronized clock experiment.

 

[Jorrie]

You cannot measure the one-way speed of light, period.

This is the sort of statement that helps the discussion going in circles. If I correctly measure a distance and I correctly measure (in the same inertial frame) the one-way time of propagation over that distance, I define that as being a measurement of one-way speed of something. Whether I have used a calibrated ruler and two synchronized clocks, or I have used two calibrated cables and and one clock, I have performed a one-way measurement of speed. If that speed happens to be c, I have good reason to believe that I have measured the one-way speed of light (or of some other massless particle).

You seem to attach more to 'measure one way speed' than me and disqualifies it as such if there is some two-way propagation used anywhere in the test - it appears as if even replacing the two cables with two extremely accurate runners with pieces of paper, simply saying "pulse detected", will not satisfy you, because at least one of them had to run half-way and back.

I have already admitted that there is an assumption on the one-way speed of light in Lincoln's test (the 1983 definition: "The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second"). This will guarantee the outcome of his measurement to be c in every inertial frame. This may be exactly equivalent to your "two-way" argument, but IMO it's then neither here nor there.

I will rest my case.

 

[K^2]

There is a reason why distinction between one-way measurement and two-way measurement is made. Maybe instead of trying to argue that your definition is just as good, you should try and find out why that distinction is made. What it is that these definitions tell you about the physics, and why measuring one-way speed of light would have been of interest.

 

[ghwellsjr]

Jorrie, I have asked you about a scenario in which no measurement of distance is involved and no measurement of speed, only a measurement of time by a single timepiece:

An observer is midway between a light source and a light target. The observer starts a timer when he sees the flash of light at the source and stops it when he sees the target illuminated. Do you agree that he's actually measuring how long it takes for the light to traverse from his location to the target and back to him?

 

[Jorrie]

An observer is midway between a light source and a light target. The observer starts a timer when he sees the flash of light at the source and stops it when he sees the target illuminated. Do you agree that he's actually measuring how long it takes for the light to traverse from his location to the target and back to him?

George, I obviously agree with this, but I argue that it is not representative of Don's test. He determines the propagation delay difference between two 2-way signals over known distances. If I misunderstand, please show me where I go wrong when calculating things for Don's test. Let the signal speed in his cables of length L be c' in both directions (it obscures things somewhat if we make it c).

The propagation delay difference that he measures is:
\Delta t = L/c+L/c'-(0.5L/c'+0.5L/c') = L/c
Apart from L that may be "unknown", there is only one thing I can see that may prevent this from being a true 1-way speed test: if the the propagation speed c' in the cables are not the same in both directions. I think this can be ruled out if the cables are oriented in various directions to confirm that the cable signals travel isotropically, as Nugatory has discussed in post #10.

So where exactly is the catch?

 

[K^2]

Let the signal speed in his cables of length L be c' in both directions (it obscures things somewhat if we make it c)

How do you know it's c' both ways? What if it's c' one way and c'' the other? If you assume the speed of light is the same in both directions, even in wires, then there is nothing to test. The entire point of one-way speed of light test is to see if it's different in two directions.

 

[ghwellsjr]

George, I obviously agree with this...

Ok, I'm glad you obviously agree with my little scenario and I'd like to take another step along those lines before responding to the rest of your post.

Let's say now that we have two identical cables that are the same length as the distance from the light source to the observer. He knows this because he stretches them out along the distance and they are equal. We don't care what that distance is and he hasn't measured it.

Now he rigs up some fast electronics so that it injects an electrical signal into both cables at the precise moment that the light is flashed. At the other end of the cables are fast detectors that set off a pair of flashes when the signals get to them. When he performs the experiment, he sees all three flashes at the exact same time. He concludes that the cables propagate the electrical signals identically to the propagation of the light over the same distance.

Note once again that we have not identified how long it takes for the light and the electrical signals to make the trip, only that it is the same for light in free space as it is for the electrical signals in the cables.

Do you agree with this?

 

[Jorrie]

Now he rigs up some fast electronics so that it injects an electrical signal into both cables at the precise moment that the light is flashed. At the other end of the cables are fast detectors that set off a pair of flashes when the signals get to them. When he performs the experiment, he sees all three flashes at the exact same time. He concludes that the cables propagate the electrical signals identically to the propagation of the light over the same distance.

Yes, if you have the all three flashes at the same location, e.g. the cables are both folded back to the source. Or what other setup do you have in mind?

 

[Jorrie]

How do you know it's c' both ways? What if it's c' one way and c'' the other?

This is more or less what I have conceded before.

If you assume the speed of light is the same in both directions, even in wires, then there is nothing to test. The entire point of one-way speed of light test is to see if it's different in two directions.

The interesting point seems that you suggest that we can devise schemes to measure the one-way speed of light (or perhaps rather Lorentz invariance); only that we will probably always find it to equal the two-way speed?

 

[ghwellsjr]

Yes, if you have the all three flashes at the same location, e.g. the cables are both folded back to the source. Or what other setup do you have in mind?

No, if the cables are folded back to the source, then the observer will see the flash from the source as soon as it happens but then he will see the "regenerated" flashes from the two cables some time later.

What I have in mind here is the observer is in the same position he was in during the first scenario that you agreed was obviously correct. He is midway between a source of light and a target. Now these two cables stretch from the source to the midway point where the observer is. When the flash is set off, it takes some undetermined amount of time for the light to propagate to the observer but whatever it is, it is the same as it takes for the two electrical signals to propagate down the cables so that he sees the direct flash of light at the same time that he sees the two "regenerated" flashes of light.

Do you agree?

 

[Jorrie]

Now these two cables stretch from the source to the midway point where the observer is.

Yes, I agree; thought you were using cables that run all the way to the target (when taut).

 

[ghwellsjr]

Ok, good. Now the observer takes one of these cables, along with the light detector on the far end and the electrical signal detector/light generator on the near end, and he swings the cable around so that it can pick up the reflection of the light from the target and send an electrical signal down the cable back towards him.

Now he repeats the experiment. The light flashes at the source. The detector immediately generates an electrical signal that travels down the cable parallel to the flash of light outside the cable. When it gets to the near end of the cable, the electrical signal immediately produces a flash of light coincident with the flash the traveled parallel to the cable in free space and the observer sees both of these at the same time and he starts his timer.

Now the flash in free space continues onward toward the target all by itself until it reaches the target. At this point, it reflects off the target and starts back toward the observer and also immediately triggers the detector in the far end of the second cable which generates an electrical signal that travels parallel to the light flash in free space coming back to the observer.

After some time, the light flash and the electrical signal arrive at the observer where the detector/generator in the near end of the cable produces a flash at the same time that he also sees the light flash that got to him in free space at which point he stops his timer.

Do you understand and agree with this assessment?

 

[Jorrie]

Yes George, I think this is equivalent to your original reflection test. I would like to hear why this is equivalent to Don's test.

 

[ghwellsjr]

You previously agreed that the observer was measuring the round trip time for the light to go from his location to the target and back to him. Now with the cables in place, you have agreed that the observer is doing exactly the same thing with cables that he was doing with just light.

Now replace the observer with a fast oscilloscope and remove the two detector/light generators at the receiving end and plug the two calibrated cables into the scope. You can start over and put the detector ends of both cables at the source and recalibrate as Don suggested and then move one end of one cable from the source to the target and you have exactly the test that Don devised so do you agree that his test in this case is measuring the round trip time for the light to traverse the last half of the distance from the source to the target?

 

[Jorrie]

Now replace the observer with a fast oscilloscope and remove the two detector/light generators at the receiving end and plug the two calibrated cables into the scope. You can start over and put the detector ends of both cables at the source and recalibrate as Don suggested and then move one end of one cable from the source to the target and you have exactly the test that Don devised so do you agree that his test in this case is measuring the round trip time for the light to traverse the last half of the distance from the source to the target?

I will have to work through this one carefully to convince myself that all your steps from #33 onwards necessarily make your test equivalent to Don's setup, because to met it is not obvious. Thanks for your patience - I will post my conclusion when I reach it.

 

[Jorrie]

I will have to work through this one carefully to convince myself that all your steps from #33 onwards necessarily make your test equivalent to Don's setup, because to me it is not obvious.

I have some difficulty convincing myself that Don's cable setup, with cable propagation speed less than c, measures the two-way speed of light. Here's how far I got.

His two cables are of arbitrarily, identical lengths, which I define as 1 distance unit and define time so that the 2-way speed of light comes out at c. I then assume that the 1-way speed of light may be c' (outbound) and c'' (inbound) and that the signal speed in the cables is equivalent to a refraction index n, so that

(1) 1/c' + 1/c'' = 2/c (vacuum) and: n/c' + n/c'' = 2n/c (cables).

The time differential that Don measures on his oscilloscope:

(2) \Delta T = 1/c' + n/c'' - n/(2c') - n/(2c'') = 1/c' - n/(2c') + n/(2c'')

This correlates with the 2-way speed of light in vacuum only if n = 1; e.g. if n = 2, then \Delta T = 1/c''.

Or am I making a wrong assumption somewhere?

 

[K^2]

The interesting point seems that you suggest that we can devise schemes to measure the one-way speed of light (or perhaps rather Lorentz invariance); only that we will probably always find it to equal the two-way speed?

The basic assumption usually made is that they are equal. However, on deeper level, it's irrelevant. If there is an experiment that depends on the difference, then there is an experiment to measure one-way speed of light. Even if indirectly so. Measuring difference with two-way speed of light would be an entirely acceptable measurement.

SR is built around assumption that one-way speed of light is equal to two-way speed of light. However, it should be possible to construct an equivalent theory in which they are not. Such a theory will have needless complications which simplify for any possible experiment, giving you exactly the same predictions as SR.

But that's exactly the thing that tells you that you can't measure one-way speed of light. At least, not within the confines of SR. If you do make a measurement, you prove relativity wrong regardless of whether you got the same or different result.

 

[harrylin]

This is the sort of statement that helps the discussion going in circles. If I correctly measure a distance and I correctly measure (in the same inertial frame) the one-way time of propagation over that distance, I define that as being a measurement of one-way speed of something. [..]

It may be just a matter of words - and yes, debates over words can help a discussion go in circles forever. According to SR (and most of physics) such measurements are reproducible. The one-way speed that you measure is the one-way speed that you (or an engineer who set up your system) first defined by free choice - that isotropy has no physical meaning. For example, if in CERN a particle is accelerated to almost the speed of light, then (according to the lab's definition and reference) light following that electron in that same direction is only slowly catching up with it, and light in the opposite direction is approaching it at almost 2c. In contrast, the definition of the electron's rest frame makes light speed isotropically c in that frame.
Note that SR does not claim that either is "right" (and both would even be contradictory); it claims that if we use that definition then the laws of physics such as that of Maxwell work wrt any inertial frame.

I have already admitted that there is an assumption on the one-way speed of light in Lincoln's test (the 1983 definition: "The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second"). This will guarantee the outcome of his measurement to be c in every inertial frame. This may be exactly equivalent to your "two-way" argument, but IMO it's then neither here nor there.

Indeed. that definition only works if the synchronization convention was used which makes the one-way speed equal to the two way speed.

I will rest my case.

Oops, sorry that makes my remarks like mustard after the meal... but perhaps it's still useful for you or someone else.

 

[ghwellsjr]

I have some difficulty convincing myself that Don's cable setup, with cable propagation speed less than c, measures the two-way speed of light. Here's how far I got.

His two cables are of arbitrarily, identical lengths, which I define as 1 distance unit and define time so that the 2-way speed of light comes out at c. I then assume that the 1-way speed of light may be c' (outbound) and c'' (inbound) and that the signal speed in the cables is equivalent to a refraction index n, so that

(1) 1/c' + 1/c'' = 2/c (vacuum) and: n/c' + n/c'' = 2n/c (cables).

The time differential that Don measures on his oscilloscope:

(2) \Delta T = 1/c' + n/c'' - n/(2c') - n/(2c'') = 1/c' - n/(2c') + n/(2c'')

This correlates with the 2-way speed of light in vacuum only if n = 1; e.g. if n = 2, then \Delta T = 1/c''.

Or am I making a wrong assumption somewhere?

You're not making a "wrong" assumption but you are making assumptions that hide the fact that Don's method is measuring the two-way propagation of light for the last half of the trip and calling it the one-way propagation for the entire trip.

That is why I asked you to use cables that propagate an electrical signal the same as light in free space along a parallel path. This is something that can be measured without resorting to clock synchronization or identifying how long that propagation took or what the speed of the light or electrical signal are, just like we can measure that the propagation of light is independent of the speed of the source. See the section called "Experiments that can be done on the one-way speed of light" in the wikipedia article on the one-way speed of light that I referred you to in post #2.

That is also why I asked you to not attempt to identify the length of the cables or the distance between the source and the target. All we care about is that the observer is at the midpoint and that the two cables add up to that distance.

That is also why I asked you not to attempt to identify the speed of the round trip for light or the electrical signals. Instead, I asked you to only make a measurement of a time interval by a single timing device located at a single position with identifiable stimuli, namely when the observer sees the light and electrical signals after they propagate from the source and when the observer sees the light and electrical signals after they propagate from the target.

All I'm trying to get you to recognize, which you already agreed to, is that there is no difference between making the timing measurement with light or with cables. And you already agreed that with light, it is a two-way measurement of the last half of the distance.

Now if you want to understand the problem taking advantage of a hundred years of experience with physics then I suggest a different approach. Set up the problem in a single Inertial Reference Frame and establish the coordinate times for each event: the emission of the light at the source, the arrival of the light at the observer when he starts his timer, the arrival of the light at the target when the reflection and return starts, and the arrival of the reflected light back at the observer when he stops his timer. In this IRF, the propagation of light is defined to be c.

Now transform the scenario into another IRF moving at some high speed with respect to the first IRF. You will see that the new time coordinates for the same events do not show equal time intervals for each direction.

For example, let's say that the source and start of the experiment are at the origin of the IRF's and the observer is located at x=0.5 and the target is at x=1 in the first IRF. Here are the coordinates of the events for the first IRF:

Start of light: x=0 t=0
Light reaches observer: x=0.5 t=0.5
Light reaches target: x=1 t=1
Reflected light reaches observer: x=0.5 t=1.5

Now transform the time coordinates of these events into an IRF traveling at 0.6c with respect to the first IRF:

Start of light: t=0
Light reaches observer: t=0.25
Light reaches target: t=0.5
Reflected light reaches observer: t=1.5

The difference between the time coordinates of the light reaching the observer and the reflected light reaching the observer is 1.25. This is partitioned into 0.25 for the light to get from the observer to the target and 1.0 for the reflected light to get from the target back to the observer.

Now when traveling at 0.6c, gamma is 1.25, so the observer's clock is time dilated by that factor so that when he measures the time for the light to make its trip from him to the target and back, his clock will advance by 1 unit, just like it did in the first IRF. He cannot tell that the light got to the target in one quarter of the time that the light took to get back from the target to himself.

Now if you understand this explanation, you can go ahead and repeat it for cables that propagate signals identically to light or at some reduced rate.

[George: prepare yourself for the barrage of criticism that you are mixing coordinates from two different IRF's.] Ok, I'm prepared.

 

[Jorrie]

Now if you understand this explanation, you can go ahead and repeat it for cables that propagate signals identically to light or at some reduced rate.

[George: prepare yourself for the barrage of criticism that you are mixing coordinates from two different IRF's.] Ok, I'm prepared.

I understand what you said and it is very clear when using only light, because then Don Lincoln's setup becomes exactly equivalent to your setup. It is not so clear in Don's actual setup, because I have shown in #42 that his result could depend on any anisotropy of light propagation:

The time differential that Don measures on his oscilloscope:

(2) ΔT=1/c′+n/c′′−n/(2c′)−n/(2c′′)=1/c′−n/(2c′)+n/(2c′′)

I agree that Don cannot claim to have measured the one-way speed of light, because components of light propagation in both directions (c' and c'') are present in this result. Which is essentially what this thread has cleared up now.

Thanks for your patience.

 

[ghwellsjr]

Thanks for your patience.

You're welcome--and thanks for the feedback.

Now, are you going to have another discussion with Don Lincoln? If you do, I would hold out the possibility that he is already well aware that his test is not really measuring the one-way speed of light independent of a synchronization convention but it is an excellent and practical way to follow Einstein's convention to measure the propagation of light in the lab, something that he and his co-workers are probably doing all the time at Fermi-Lab.

 

[Jorrie]

The time differential that Don measures on his oscilloscope:

(2) \Delta T = 1/c' + n/c'' - n/(2c') - n/(2c'') = 1/c' - n/(2c') + n/(2c'')

Don Lincoln has made one remark that I still need to consider: if the \Delta T that he measured correlates with c for the specific length of the cables, then for his lab he has established that c' = c'' =c, within experimental error. How else?

This shows that it is equivalent to having a synchronized clock at each end of the cable; but still, he needed only one clock, the oscilloscope. One clock, two clocks? Probably a moot point.

 

[ghwellsjr]

Don Lincoln has made one remark that I still need to consider: if the \Delta T that he measured correlates with c for the specific length of the cables, then for his lab he has established that c' = c'' =c, within experimental error. How else?

"Established"--now that's a very interesting word. It can mean to make or bring into existence or it can mean to determine the truth of something. So which do you mean? I hope you mean the first meanings because that is what he's doing.

And now I see that Don Lincoln used that same word in his description of the test setup.

This shows that it is equivalent to having a synchronized clock at each end of the cable; but still, he needed only one clock, the oscilloscope. One clock, two clocks? Probably a moot point.

How 'bout three clocks? Two synchronized cables and the scope.

 

[Jorrie]

"Established"--now that's a very interesting word. It can mean to make or bring into existence or it can mean to determine the truth of something. So which do you mean? I hope you mean the first meanings because that is what he's doing.

Yes, he first establishes simultaneity and then determines the one-way speed of light for the lab - which is then a given...