# How to measure the one way speed of light.

It is often stated that the one way speed of light cannot be measured and that the isotropic speed of light is just an assumption based on two way measurements and clock synchronisation conventions.

Here is a proposal for measuring the one way speed of light. It is not entirely original as it is based on the method used by Ole Romer to make this measurement by observing eclipses of Jupiter's moon Io, but is slightly simplified and idealised for easy analysis.

First we require a radial arm of length r. One end of the arm is anchored to an axis and the other end is free. A single clock is placed at A on the circumference of the arms arc. The arm is rotated to a high velocity v. A signalling flash device is placed at B on the opposite side of the circle. Each time the arm passes B the flash is triggered. The tangential velocity of the free end of the arm is computed as 2*pi*r/T, where T is the time to complete one full circle as measured by the clock at A. When the arm is rotating at a steady high velocity, some reading are taken. Let's say when the arm passes A the time is t1. The time t2 of the flash when the arm passes B, as measured by the clock at A when it receives the signal, is (pi*r/v)+(2*r/c) which includes the light travel time.

The one way speed of light is obtained by solving for c which is c=2*r/(t2-t1-pi*r/v) or 2*r/(t2-t1-T/2).

Now because the one way speed of light is often disputed, there may be some hidden tautologies in the above thought experiment. Can anyone say what they think they are?

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Very intriguing. I can see no problems with it offhand. Even if the arm does not rotate rigidly, it should deform with a constant bend all the way around, and all we really need to know is where the end of the arm lies when it passes the clock and signalling device, which should also be constant, and can be measured easily all the way around while the arm is spinning to make sure it is following a circular path. So far it seems you have indeed found a method by which to measure the one way speed of light. Cool. I will have to do some intense thinking about this, though, because according to our definitions of speed as you have applied them to the apparatus, it should be right, but that would mean there is only one speed photons or any other particles emitted in a particular way while travelling at a lesser speed can be measured, meaning there is only one way that frames can be synchronized while still following the same definitions of speed.

That is actually something I have been searching for the last couple of years, a way to synchronize frames according to some absolute principle. I thought it might have to do with something like bouncing a ball against a wall so that it is measured at the same speed in every direction to the wall as back at any speed, but that would be a principle that would have to be applied in a similar way as the first postulate about the laws being the same in every frame, which makes it an assumption. What you have shown would be applied absolutely, being more than just a principle, having everything to do with the definition of speed itself. Hopefully no problems will be found, because that would be absolutely amazing. Okay yes, I think I see now. What you have done is found a much better and more natural way to synchronize frames than using light. If we have a clock at both A and B, then of course using light, we would set clock B to measure half the difference in the two way time for A when a pulse is emitted from A to B and reflected back to A. But by placing clocks A and B on opposite sides of the spinning arm, B would naturally have to be set such that it reads half the difference for a full rotation when the arm passes. I'm jealous, because that is what my bouncing ball thing was supposed to do, but not quite so neatly as what you have set up. The only potential problem I can see so far is verifying that the arm spins at a constant pace regardless of its frame, although there's no particular reason why it shouldn't.

K^2
First we require a radial arm of length r. One end of the arm is anchored to an axis and the other end is free. A single clock is placed at A on the circumference of the arms arc.
And this is where you end up having a problem. How do you synchronize clocks?

Saw
Gold Member
I wonder if there may be a problem with the time taken for the triggering mechanisms to do their respective jobs. When the arm passes by A, it has set to the clock in motion (a). When it passes by B, it has to release the flash (b). In both cases, that may be done through the arm moving a switch that sends and electric signal, which in turns activates a mechanism doing (a) or (b) as the case may be. If in (a) the electric signal travels, let us say, leftwards, then in (b) it must travel rightwards. Electricity does not travel at the speed of light, but it is subject to relativistic adjustments.

For example, in the display proposed by grav-universe where the arm is used for synchronizing clocks placed at A and B, another frame moving relative to the apparatus would argue that the clocks are not perfectly synchronized, precisely on the grounds that the time taken for the mechanisms to operate is different. In Galilean relativity, the velocity addition formula would guarantee that both signals would be simultaneous, since the forward one travels more distance but does it faster, while the backward one travels less distance but more slowly, one thing comepensating the other in exact terms, so that travel times are identical. But in SR the relativistic law for addition of velocities still provides for a difference of velocities as judged by a third frame, but one leading to a time difference between the two signals. (I know you know all that, but it write it to force myself to remember learnt concepts.)

It is not so clear to me, however, how this applies to the original display by yuiop. Do you see yourself a problem?

yuiop - taking the lazy way out here:
http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/p_roemer.html" [Broken]
http://arxiv.org/abs/1011.1318" [Broken]
http://arxiv.org/pdf/1003.4964v1"
Hope these help!

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And this is where you end up having a problem. How do you synchronize clocks?
The beauty of the thought experiment is that there is only one single clock that makes all the timing measurements, so there is no need to synchronise any clocks.

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K^2
Oh, I see. So instead of using light to carry information back, you are using a massive object. Id est, the rotating arm.

Well, then your problem is exactly the same. You have to assume that the arm takes the same amount of time to travel one way as the other. If you aren't ready to make that assumption for light, why should you make it for massive object?

Oh, I see. So instead of using light to carry information back, you are using a massive object. Id est, the rotating arm.

Well, then your problem is exactly the same. You have to assume that the arm takes the same amount of time to travel one way as the other. If you aren't ready to make that assumption for light, why should you make it for massive object?
Now that took me a few minutes to think about. But yes, I agree. I wonder if the same problem exists with the original roemer experiment? Can we know the diameter of earth's orbit to the degree of accuracy necessary for that version of the experiment?

Oh, I see. So instead of using light to carry information back, you are using a massive object. Id est, the rotating arm.

Well, then your problem is exactly the same. You have to assume that the arm takes the same amount of time to travel one way as the other. If you aren't ready to make that assumption for light, why should you make it for massive object?
This is a valid concern. One way to evaluate the significance of this is to assume that the one way speed of light is something other than the average of the two way speed of light and see if the experiment would detect this anomaly. Of course it is reasonable to require that physical objects (e.g. the arm) are constrained to move relative to the anisotropic speed of light in the direction they are moving. (We can't have massive objects overtaking photons.) For example the arm tip going Northwards at 0.8c is not the same as the arm tip going Southwards at 0.8c in the "big picture".

I propose this test case. Master clock A is at the South end of the circle and signalling device B is at the North end. We conjecture that the anisotropic speed of light is 1.5C going North and 0.75C going South and at C going East or West. (C is the average two way speed of light). What would the apparatus measure? Will the anisotropy of the speed of light be undetectable? I have reasons to think not. I will come back to this after more analysis.

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Oh, I see. So instead of using light to carry information back, you are using a massive object. Id est, the rotating arm.

Well, then your problem is exactly the same. You have to assume that the arm takes the same amount of time to travel one way as the other. If you aren't ready to make that assumption for light, why should you make it for massive object?
Oh, wait. That's the way I compared it too in regards to how the one way light speed is normally defined, but actually there's something a little more absolute about it, having to do with the symmetrical rigidity of the spinning apparatus. That is, with the arm, we can actually set both clocks at the same time, without regard to the rotational speed. Before spinning, the arm extends directly between points A and B. After spinning, whenever each end of the arm passes A and B, each clock ticks off one interval of time, in the same way as a light clock but with a single extended rigid object, and according to the symmetry principle of the frame, there should be no reason to assume that the ends of the arm do not reach each clock simultaneously, although we are also assuming the symmetry principle in the first place, so that frame considers clocks A and B to be synchronized, and of course other frames would claim that the apparatus is not rigid in the same way as they would not with the M-M apparatus, but viewing it while the arm is in motion.

K^2
You cannot use symmetry here. If it holds, then there is no need to measure one-way speed of light. If it doesn't, then matter will not really move the same way either, and what we think of as a straight line might not actually be a straight line.

You cannot use symmetry here. If it holds, then there is no need to measure one-way speed of light. If it doesn't, then matter will not really move the same way either, and what we think of as a straight line might not actually be a straight line.
We are not assuming the one way speed of light to conform to the symmetry principle. If it does, then we have the same synchronization by either method. If it doesn't, then we have to decide whether to synchronize using light or rotation, but again, not that there would be any reason both methods wouldn't conform, as well they should, but we can't assume that beforehand.

A straight line isn't a straight line anyway with SR. For instance, if the arm remains more or less rigid according to the frame of the apparatus, a frame moving relative to the apparatus, synchronized to light speed, will observe something close to the diagram below with the four colored lines at various alignments for the arm, although not drawn precisely.

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I propose this test case. Master clock A is at the South end of the circle and signalling device B is at the North end. We conjecture that the anisotropic speed of light is 1.5C going North and 0.75C going South and at C going East or West. (C is the average two way speed of light). What would the apparatus measure? Will the anisotropy of the speed of light be undetectable? I have reasons to think not. I will come back to this after more analysis.
After doing some rough sketches and calculations I have come to the conclusion (unfortunately) that any proposed anisotropy of light speed will be undetectable. It seems in the example above, that the arm going Northward going away from A arrives at B earlier than the isotropic case and gives time for the slow return light signal to arrive back at A at exactly the same time as the isotropic case.

If a long double arm is used, with a pivot at it centre so that it spans the full diameter of the circle and additional signalling devices are placed at the East edge (C) and the west edge (D), signals from C and D arrive back at A simultaneously with each other. This is despite the fact the arm bends due to differential speeds of the arm extremities on opposite sides of the circle. Additionally signals from C and D return to A at the same time as would be expected in the isotropic case. This is very unintuitive but seems to be the case on closer inspection.

It seems K^2 and MikeLizzi are correct in the concerns they raised. It also seems by implication that Ole Roemer only measured the two way speed of light in the eclipses of Io and not the one way speed of light as is sometimes suggested. Quite possibly, measuring the one way speed of light is tantamount to measuring absolute velocity, but that may be extrapolating too far.

I'm not sure what you mean with your last post. The spinning arm gives a different means by which to synchronize the clocks around the circumference, something other than using light signals. For instance, if the clocks are equally spaced around the circumference with the ends of separate arms originally directed at each one, then when the arms are spun at a steady pace and each reaches the next clock on the circumference, each of the clocks are set to T=0, at which point they are considered synchronized within the frame. Then the difference in times for light pulses to travel one way between any of the clocks can be measured using this synchronization of the clocks for the frame.

ghwellsjr
Gold Member
I'm glad that you have seen the light.

See this thread for another in depth discussion on this topic:

I don't quite understand your post either. If we were to synchronize clocks using light to begin with, then of course we couldn't determine the one way speed of light, sure, since if we were to use the Einstein synchronization method, for instance, then the one way speed would be as defined by the synchronization procedure itself. But we are not referring to light at all for the synchronization of clocks with the spinning arm. We can outline the points that the end of the arm passes to be sure it follows a perfect circle, as it should if we are not to determine any absolute motion, and it should do so at a steady pace through all points around the circle for the same reason. Since we know the length of the path the end of the arm follows and the time to complete a full rotation, we know its rotation speed, and all clocks around the circumference can be synchronized accordingly, and their synchronization will remain the same regardless of how the rotation speed is changed, so we have a natural almost absolute type of synchronization procedure. From this, between two of the clocks that are now synchronized in this manner or even with a single clock with the experiment yuiop set up, we can directly measure the one way speed of light. Most likely it would still be c, yes, but there is otherwise no connection between synchronization procedures that would tell us this beforehand, not without actually performing the experiment.

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yuiop - taking the lazy way out here:
http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/p_roemer.html" [Broken]
http://arxiv.org/abs/1011.1318" [Broken]
http://arxiv.org/pdf/1003.4964v1"
Hope these help!
Nice collection, especially the last one says it all. :-)

Regards,
Harald

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Nice collection, especially the last one says it all. :-)

Regards,
Harald
The last paper deals only with measuring the straight line path of light reflected off of a mirror. The synchronization of clocks along a straight line, however, is arbitrary. We can synchronize them to measure half the two way speed of light using the Einstein simultaneity convention or any number of a possible infinite number of synchronizations, as long as the clocks are set linearly. That is, we can add some amount of time to each clock per distance in a linear fashion and measure an anisotropic speed of light if we want to, it is completely arbitrary. The only rule governing this is that the clocks must be set such that if an object is travelling inertially, at a steady pace without any forces acting upon it, its speed should be measured to remain constant, so the difference in times measured for the object between clocks should be made proportional to the distance travelled by the object. Without this, our definition of speed becomes virtually meaningless, if we were to allow clocks to be set arbitrarily between themselves within a frame. Of course, likewise, they must run at the same rate as each other as well, which can be tested using inertial objects also, so that all must conform to these rules of speed to be useful.

Not just light, but massive objects travelling at less than c can have arbitrarily measured speeds along a straight line path in the same way, so no experiments that can be performed with bouncing light off of mirrors or massive objects off of walls will determine any differently. I know because I have spent the last couple of years trying, but the best I could come up with is relationships that include no absolute notions of motion or synchronization methods. Rotation, however, is absolute. I thought about using a rotating disk to find relations, but then I thought there would be additional complications with the clocks on the disk that might involve GR, so didn't get into it, but the experiment yuiop set up requires no clocks on the disk itself, only stationary clocks around the circumference.

So as the last paper claims, we cannot determine an absolute synchronization by which to set clocks along a straight line, so can't measure the one way speed of light along a straight either with clocks set arbitrarily along the same path, but it does not mention rotation. While we can add so much time to each clock per distance along a straight line indefinitely, we cannot do so around the circumference of a circle. When starting at clock A and working our way around the circumference, adding some time to each clock per arc, we would eventually reach A again, so there would be a discrepency there. All we could do is to set all the clocks ahead or behind by the same amount, but the overall synchronization would still be maintained. So beyond reforming our definition of speed upon which physics is based, and which can't really be redefined with without making a mess of things, rotation does seem to be an absolute method by which to synchronize frames. The first article where the one way speed of light is measured from Jupiter and Io by Roemer may be an extension of this, where the same basic principle is applied to orbits.

Dale
Mentor
A straight line isn't a straight line anyway with SR. For instance, if the arm remains more or less rigid according to the frame of the apparatus, a frame moving relative to the apparatus, synchronized to light speed, will observe something close to the diagram below with the four colored lines at various alignments for the arm, although not drawn precisely.
I think this is the key point. In the non-inertial reference frame the synchronization convention is defined such that the arm is bent. This bent arm means that the flash is triggered either earlier or later such that you get the value you would expect from a straight arm in an isotropic-c frame.

Thanks for this very interesting problem, yuiop!

The last paper deals only with measuring the straight line path of light reflected off of a mirror. [..]

So as the last paper claims, we cannot determine an absolute synchronization by which to set clocks along a straight line, so can't measure the one way speed of light along a straight either with clocks set arbitrarily along the same path, but it does not mention rotation. [..] The first article where the one way speed of light is measured from Jupiter and Io by Roemer may be an extension of this, where the same basic principle is applied to orbits.
The last paper not only mentions but even discusses rotation, in the form of an orbit! I copy-paste here the intro of that section: the "Romer Experiment, which measured the speed of light via changes in light transmission time from Jupiter and its moons [...] This effectively entails a time difference measured via a single clock on the Earth as this clock moves to different positions in the Earth’s orbit."

Cheers,
Harald

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In the non-inertial reference frame the synchronization convention is defined such that the arm is bent.
Did you mean the frame moving relative to the spinning arm?

The last paper not only mentions but even discusses rotation, in the form of an orbit! I copy-paste here the intro of that section: the "Romer Experiment, which measured the speed of light via changes in light transmission time from Jupiter and its moons [...] This effectively entails a time difference measured via a single clock on the Earth as this clock moves to different positions in the Earth’s orbit."

Cheers,
Harald
Okay yes, in appendix ll, right. It doesn't really discuss it, though, just simply stating it involves a single clock, and then goes on to say there is an on-going debate about slowly transporting clocks and about whether an absolute synchronization exists, the present consensus being that it does not. With yuiop's experiment, however, we can see that a single clock is all that is really necessary with rotation as well as apparently with orbits.

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Dale
Mentor
Did you mean the frame moving relative to the spinning arm?
No, I just meant that any frame where the one-way speed of light is not c is a non-inertial frame in the sense that the laws of physics don't take their "textbook" forms.