One way speed of light experiment proposal

[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.

 

[Ibix]

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.

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.

 

[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.

 

[Nugatory]

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.

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.

 

[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.

 

[kkris1]

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

 

[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.

 

[Nugatory]

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

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.

 

[Nugatory]

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

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.

 

[Nugatory]

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.

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) ...

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.

 

[Herman Trivilino]

There is assumption of one way speed of light same as 2 way speed of light.

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.

 

[Ibix]

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.

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.

 

[Herman Trivilino]

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.

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.

 

[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.

 

[Herman Trivilino]

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.

 

[Nugatory]

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.

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.

 

[Vanadium 50]

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.

 

[Ibix]

You simply don't have enough measurements.

That's a very efficient way of putting it.

 

[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?

 

[Ibix]

The distance between start and endpoints is d , exactly the same as the length of the rod.

Not if the rod is moving. In that case the rod is length contracted.

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 )

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.

 

[kkris1]

"The distance between start and endpoints is d , exactly the same as the length of the rod. Not if the rod is moving. In that case the rod is length contracted."

I'm talking about practical experiment; I expect v to be between ~10-100m/s. For this speeds length contraction (between (10^-15)m---(10^-12)m) is below our accuracy to align the lasers with the rod (I think we can do it with ~(10^-9)m---(10^-10)m accuracy).
As you can see for any practical speeds we can ignore length contractions and still our inaccuracy because of it will be less then 1%.

 

[Ibix]

If your experiment is not precise enough to detect relativistic effects then it will not detect relativistic effects, that's true. It doesn't change the fact that they are there. It doesn't change the fact that there is an arbitrary systematic offset that you aren't correcting for. And it doesn't change the fact that you are literally running Einstein's train experiment and simply removing the central observers to try to avoid the implications.

 

[kkris1]

"If your experiment is not precise enough to detect relativistic effects then it will not detect relativistic effects, that's true. It doesn't change the fact that there is an arbitrary systematic offset that you aren't correcting for. It also doesn't change the fact that you are literally running Einstein's train experiment and simply removing the central observers to try to avoid the implications."

How is it the same as Einstein's train experiment?
You could not measure one way speed of light using that experiment. You just had to assume one way speed of light equals 2 way.

In my experiment there are no such assumptions. You just do measurements and if you manage to them with high enough accuracy, you can measure time of flight of light in one direction.
I believe that using modern technology my experiment can be carried out and accuracy can better than1%

 

[Vanadium 50]

What other measurement do I need?

Exactly what I said in my post: the synchronization convention. How do you know the light start time at B is the same as the start time at A?

To be honest, this wasn't really an attempt to convince you. Like those who have come up with ways to square the circle or trisect an angle I don't think any argument whatsoever will convince you. It's an attempt to get a simple bulletproof argument into this thread before it's locked.

 

[kkris1]

"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 vv 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 T1T1, T0T0, or dd should be affected by vv. 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/(T1−T0)=cd/(T1−T0)=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/(T1−T0)=cd/(T1−T0)=c regardless of vv. 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 cc every time. But that result isn't the one-way speed of light; and if you were to get a result other than cc it would tell you only that you had messed up the calibration and synchronization of the clocks."

Because it is constant speed, we can say that the rod is at rest and "embankment" AB is moving with the speed -v, so it should contract by the same amount.
Therefore I would prefer to use the speed when ignoring it completely does not introduce any substantial error.
Different value of v won't give you different value for the speed of light; it merely will give you different accuracy, which is not the same.

The experiment has been designed in such a way that it should be possible to carry it out in even modest lab. Most crucial part is positioning the lasers against the rod (the experiment could be modified with 2 narrow slots cut in the rod so both lasers could shine through only if they are perfectly aligned) and the clocks which should measure the time to at least 100ps precision.( As I have mentioned before, we could modify the experiment that only one clock would be required) The length of the rod doesn't need to be measured extremely precise; accuracy to 1mm will do. Now let's do some calculations:
time for the light to cover 10m is d/c=10m/3x10^8=~33ns.
The length contraction of the rod of length d=10 for v=100m/s will be dx((v^2)/(c^2)=10mx((10^4)/9x10^16)=~(10^-12)m.
If we can position the lasers against the rod with 1nm accuracy, the length contraction will be 1000 time smaller then our uncertainity in positioning the lasers..
For 1nm accuracy in positioning the lasers there will be uncertainty in synchronizing the clocks:
delta t= 1nm/100m/s=~10^-11s, which still will allow us to measure one way speed of light with 0.5% accuracy.
I think it could be possible to carry out such experiment without spending exuberant amount of money on necessary equipment.

 

[kkris1]

"Exactly what I said in my post: the synchronization convention. How do you know the light start time at B is the same as the start time at A?"

Because length of rod is exactly the same as the distance AB. So if the leading edge is at point A, the trailing edge has to be at point B

 

[Dale]

we can disregard length contraction

If you do then you will find that the one way speed of light depends on v.

Different value of v won't give you different value for the speed of light;

This is false, please post your math.

 

[DanMP]

Just recently I came up with a new idea to measure one way speed of light [...]

Let’s have two light sources at points A and B separated by distance d [...]

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)

...

The idea is interesting, but not enough, as discussed until now.

Still, from it (the elements quoted above) the measurement can be done if the rod is rigid, equipped with toothed wheels at the ends (A and B) and rotates. The light sent from B through one notch gets to A through the next notch of the other wheel, somehow similar to Armand H. L. Fizeau experiment:

(the image is taken from http://www.chegg.com/homework-help/questions-and-answers/experiment-measure-speed-light-using-apparatus-armand-h-l-fizeau-see-figure-distance-light-q2735778).

In this scenario, length contraction is not a problem if we want to compare the one way speed of light from A to B with the one from B to A. The problem is the distance (too short) and the perfect "synchronization" of the wheels, but although the results would not be perfect, it may appear a difference ...

 

[Nugatory]

In this scenario, length contraction is not a problem...

This is a measurement of the round-trip speed of light, not a one-way measurement. There's no problem with the conclusion that the round-trip time is equal the the time it takes for one tooth to move by, but that tells us nothing about the one-way speed; you just have to assume that the time the light spends moving towards the mirror is equal to the time it spends on the return and is half the total.

For all practical purposes the toothed wheel is a clock (pick a tooth and call it a "sweep second hand"). I's the only clock in the experiment so this is a one-clock experiment, which avoids the need ofr clock synchronization but cannot provide a one-way measurement.

 

[DanMP]

This is a measurement of the round-trip speed of light, not a one-way measurement...

Sorry, the experiment I suggested is not the one in the picture. It is just "somehow similar" to it. Read again.