# I One way speed of light experiment proposal

1. May 18, 2017

### kkris1

Just recently I came up with a new idea to measure one way speed of light and/or synchronize distant clocks:

Let’s have two light sources at points A and B separated by distance d and sending constantly (perpendicular to AB) signals to clocks at A’ and B’
Let’s have an opaque rod of the length d (it can be measured against AB while at rest with AB, so accuracy can be high) traveling with constant speed v (non-relativistic) parallel (and very close to) the line AB from B towards A. Initially the light from B to B’ will be blocked and the light from A to A’ will be allowed to be transmitted. When front end of the rod will start cutting off the light from A to A’ the light from B will start to be transmitted to B’ . At this moment, we will have both clock at A’ and B’ synchronized.

Alternatively when front end of the rod will start cutting off the light from A to A’ we can start the clock at A and when the light from B will start to be transmitted to B’ we can also send the light from B to A .When the light from B arrives at A the clock at A will measure one way speed of light.
In this method only one clock is needed.
We can improve the accuracy of the measurement sending the rod from A to B with the same speed v and measure one way speed of light from A to B. The average 2 way speed of light from A to B and from B to A has to be c.

2. May 18, 2017

### Ibix

This is just Einstein synchronisation by another method. In fact, it's effectively the Einstein train thought experiment (with the clocks in the role of the ends of the platform and the rod in the role of the train), minus the central observers that would give away the lack of absolute simultaneity. In any frame other than the rest frame of the clocks the two "simultaneous" events are not simultaneous.

Last edited: May 18, 2017
3. May 18, 2017

### kkris1

In Einstein's thought experiment there were two lightning bolts supposedly simultaneously hitting both ends of the boxcar. How could one tell if they were simultaneous ? It was just assumption. And it had nothing to do with synchronization. (Please explain how would you synchronize the clocks using this thought experiment? would you be waiting for two lightning bolts to strike simultaneously both ends of the boxcar?) . Einstein's synchronization is to assume that one way speed of light is equal to 2 way speed of light. Then you emit a pulse of light from middle point C to points A and B and thus synchronize the clocks at A and B. This method would be perfectly ok if one way speed of light was equal to 2 way. Maybe it is, but how can you tell?
I'm my method there is no assumption that 2 flashes of light will occur simultaneously at both ends of the rods. There is no assumption that the one way speed of light is equal to 2 way. It is practically possible to carry out this experiment in even modestly equipped lab (you will need at least 2 good quality lasers, 2 photo sensors and at least one atomic clock with ability to measure the time with 100ps accuracy). If the rod's length is 10m, when the front of the rod is gliding past laser at A (with the speed let's say 10m/s, so the length contraction is really insignificant) , its rear end has to be exactly at point B, 10 m behind.

4. May 18, 2017

### Staff: Mentor

You are misunderstanding the point of the train experiment. If the light from two equidistant events arrives at our eyes at the same time, we know they happened at the same time: the distance traveled by the light was the same so the travel time for both light signals was the same; therefore they had to leave at the same time to reach our eyes at the same time. Einstein's point is that if two events are will not in general be simultaneous for observers moving relative to one another - if the light from equidistant events reaches one observer at the same time it will reach the other at different times.

The same principle would apply if the two events were not lightning strikes but rather clocks at each end of the train reading noon; if the train observer finds that they both read noon at the same time, the platform observer will find that they both read noon at different times.

5. May 18, 2017

### kkris1

There is assumption of one way speed of light same as 2 way speed of light. If for some reason speed of light was anisotropic, you could judge 2 events as simultaneous even if they were not.

6. May 18, 2017

### kkris1

And I do not understand how the train experiment is relevant to my proposal

7. May 18, 2017

### kkris1

"The same principle would apply if the two events were not lightning strikes but rather clocks at each end of the train reading noon; if the train observer finds that they both read noon at the same time, the platform observer will find that they both read noon at different times."

How could you tell two distant clocks are synchronized?
You have to again make assumption 1way speed of light=2way.

8. May 18, 2017

### Staff: Mentor

Of course we do. That's an essential postulate of special relativity.
It has to be assumed not proven, because we cannot measure the one-way speed of light to compare with the two-way speed. Any experiment that purports to measure the one-way speed of light (including yours in #1 of this thread) will, if carefully examined, turn out to assume somewhere that the one-way speed is equal to the two-way speed, so has to produce that result.

9. May 18, 2017

### Staff: Mentor

It's not all that obvious at first, but the relevance is there. I'll try stepping through the logic in a moment, but before I do.... I really strongly suggest that you get hold of a serious textbook that approaches relativity systematically; we can help you with focused questions and over hard spots, but there is no substitute for a systematic approach to the general principles. I personally am fond of Taylor and Wheeler's "Spacetime Physics" - it's challenging but not out of reach for someone who is starting I-level threads.

10. May 18, 2017

### Staff: Mentor

We can construct all sorts of clever and complicated experiments for measuring the one-way speed of light, but they all (yours too - bear with me for a moment) eventually have to come down to the same concept:
We have clocks at point A and point B, separated by a distance $d$. When the clock at A reads $T_0$ we send a light flash in the direction of point B; it arrives when the clock at point B reads $T_1$. Now, if one more crucial condition holds, we can say that the one-way speed of light is $d/(T_1-T_0)$. That last crucial condition is: the clocks are synchronized, meaning that at the same time that the clock at A reads $T_0$ the clock at B also reads $T_0$; we need that for $T_1-T_0$ to be the time that the light was in flight between A and B.

OK, so in our experimental design, how do we arrange for the clocks to be synchronized? A reliable way: We buy two identical clocks (identical meaning that they are observed to tick at the same rate when side by side at the clock factory) and place one of them at point A and one at point B. Our experimenter at point B notes that his clock reads $T_{b1}$ and sends a light signal to point A. When it arrives at point A, the experimenter there looks at his clock, sees that it reads $T_a$, and sends a light signal back to B: "Your light signal reached me when my clock read $T_a$". That light signal gets back to B at time $T_{b2}$; a bit of algebra tells B that when he received the reply A's clock read $T_a+(T_{b2}-T_{b1})/2$ so he sets his clock accordingly. The clocks are now synchronized and we can proceed with our one-way light speed measurement. This is Einstein clock synchronization.

But it's pretty obvious that this Einstein synchronization procedure is already assuming that the one-way speed is the same as the two-way speed so our "measurement" isn't proving anything about the one-way speed of light. It's just demonstrating that we've synchronized the clocks in such a way that $d/(T_1-T_0)$ has to come out equal to $c$.

So we need a different way of synchronizing the clocks, and that's what you're trying to do with your rigid rod. But there's a catch.
You've measured the rod at rest, but it's moving in your experimental design. There are two ways of dealing with that.
1) Ignore the length contraction completely; this may be what you mean when you said "non-relativistic". But if you do this, you will find that different values of $v$ yield different results for the one-way speed of light; but we're measuring the speed of light relative to A and B, not the rod, so clearly something is wrong with the experimental setup. There's no way that $T_1$, $T_0$, or $d$ should be affected by $v$.
2) Correct for the length contraction caused by the rod's motion relative to A, B, and the rest of your experimental apparatus. That will reliably give you $d/(T_1-T_0)=c$ every time. However, the length contraction formula itself is derived from (among other things) the assumption that the one-way speed of light is equal to the two-way speed of light; it's a consequence of requiring that $d/(T_1-T_0)=c$ regardless of $v$. Thus, it has the same problem as the simpler experiment using Einstein clock synchronization: It isn't proving anything about the one-way speed of light, it's proving that if you synchronize your clocks assuming that the one-way speed of light is equal to the two-way speed of light, then your clocks will agree with that assumption.

Bottom line: Yes, you can do your experiment. With sufficiently careful experimental design the result will be $c$ every time. But that result isn't the one-way speed of light; and if you were to get a result other than $c$ it would tell you only that you had messed up the calibration and synchronization of the clocks.

Last edited: May 18, 2017
11. May 18, 2017

### Mister T

And there's plenty of experimental evidence to support that assumption. If the speed of light in one direction were different from the speed of light in the opposite direction it would have been observed by the likes of Michaelson-Morley and many many others.

But as @Nugatory explained it is still an assumption. If the fact that the speed is the same in two opposite directions doesn't establish it for you, then consider the fact that every conclusion that follows from the assumption that has ever been tested has passed that test.

12. May 18, 2017

### Ibix

I'm not sure this is correct. Michelson-Morley would detect differences in the speed of light in the x and y direction. But it would be blind to differences in the +x and -x direction, as long as $2d/c=d/c_++d/c_-$, where d is the length of the interferometer arm, is invariant.

13. May 18, 2017

### Mister T

But suppose that after comparing the x and y directions we rotate the interferometer 90 degrees and then compare, say, y to -x. If the speeds in the x and y directions are the same, and the speeds in the y and -x directions are the same, then the speeds in the x and -x directions are the same.

You could probably design an apparatus like the interferometer that splits the beam more than once, and directly compares the speeds in the -x and x directions.

14. May 18, 2017

### Ibix

No - the interferometer compares round trip speeds because it's got mirrors at the end of the arms. That's the point Nugatory was making above. You have to compare a round-trip time if you don't want to get into clock synchronisation, so you cannot compare one-way speeds that way. And if you do some clock synchronisation then your answer is arbitrary.

15. May 18, 2017

### Mister T

Right. I should have stated that I was indeed referring to round trips. My point is that the round trip speed in one direction is the same as the round trip speed in any other direction, including the opposite direction. This doesn't demonstrate that the two-way speed is the same as the one-way speed, but it provides supporting evidence for that assumption. At least I think it does insofar as it demonstrates the speed is independent of the direction.

16. May 18, 2017

### Staff: Mentor

It demonstrates that an alternative to the one-way postulate must be some sort of very bizarre and implausible anisotropy - and of course we tend to choose postulates because they're plausible and the alternatives are less so.

Indeed, the one-way postulate is so plausible that we probably wouldn't spend much time on it if it were not the starting point for operational definitions of synchronization and simultaneity.

17. May 18, 2017

Staff Emeritus
The problem is very fundamental. You want to know three things: the one-way speed of light, the distance between the start and end points, and the difference in clock synchronization between the start and end points. You make two measurements: the distance between the start and end points, and the difference in clock readings when the light passes each point. You simply don't have enough measurements.

18. May 18, 2017

### Ibix

That's a very efficient way of putting it.

19. May 19, 2017

### kkris1

"
The problem is very fundamental. You want to know three things: the one-way speed of light, the distance between the start and end points, and the difference in clock synchronization between the start and end points. You make two measurements: the distance between the start and end points, and the difference in clock readings when the light passes each point. You simply don't have enough measurements"

The distance between start and endpoints is d , exactly the same as the length of the rod. If the rod is d=10m, can measure the length of the rod to at least 1mmaccuracy. More important is accurate alignment of the rod with the lasers We can align the lasers very accurately with both ends of the rod while the rod is stationary (at rest) with lasers.
The experiment is very simple:
You move the rod out and accelerate it to a constant speed v and let it glide without applying any force past our lasers. (the magnitude of speed is not that important )Then you start the clock at A when leading edge of the rod is passing point A.
The trailing edge will be exactly at point B ; length of the rod is exactly equal to the distance AB (we can disregard length contraction; for the speed of the rod v=10m/s and its length 10m it will be ~10^-14m) and the trailing edge will trigger the laser which will send the signal towards A. When the signal arrives at A, it will stop the clock .The will show the time of flight of the signal from B to A.
As you can see, one clock will be enough to do the measurement.
What other measurement do I need?

20. May 19, 2017

### Ibix

Not if the rod is moving. In that case the rod is length contracted.
Yes, it is important. If v approaches c it will become obvious that the rod is much shorter than the distance between the clocks, but the effect is present at all speeds. So you may either ignore this or correct for it. If you choose to ignore it you have an uncorrected systematic error that makes your one-way light speed measurement depend on v - i.e. the value you get is your choice. If you choose to correct for it then you need to measure the length of the rod while it's moving, which requires clock synchronisation of some type. Again the value you get is your choice.

@Nugatory put it at greater length in #10. Maybe worth a re-read.

Last edited: May 19, 2017