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As with almost every question on this topic, this question is also inspired by the Vertiasium video Why No One Has Measured The Speed Of Light.

This experiment tries to measure the one way speed of light between two points, by exploiting the possibility of using objects, to communicate, which are moving at comparatively low speed than light, thereby avoiding relativistic effects and possibility of difference in light’s speed in various directions affecting the outcome of the experiment.

EXPERIMENT

SETUP: Let’s say there are two points A and B and we want to measure the speed of light from A to B and the distance between A and B is d. So we station our apparatus which can send a light signal on A and another one, which can receive a light signal on B. A and B is equipped with identical apparatus which can shoot a ball at the same speed. There is another point C which is equidistant from both A and B. C is equipped to measure the time interval between the consecutive arrival of balls from A and B.

Note: There are no clocks on either A or B. The points A, B and C are in rest with respect to each other.

enter image description here

Now, A shoots ball-A towards C and simultaneously sends a light signal to B, and the moment B receives the light signal from A, B shoots ball-B towards C. Now both balls ball-A and ball-B head towards C and reach C. The time difference ?t, between the arrival of ball-A and ball-B is expected to be same as the time taken for light to travel from A to B.

$$c_{AB} = \frac{d}{\Delta t}$$

There are no relativistic effects involved as the balls are traveling at relatively small speed than light. And A, B and C are all at rest with respect to each other. By using balls, to signal to a third point C, instead of B using light to try to communicate back with A, this experimental setup solves the need to synchronize clocks between A and B and also avoids the circular trip of light.

Note: I'm aware of the opinion that

The bottom line is that it is not a matter of clever experimental design. There is fundamentally no possible way to measure the one-way speed of light independently of the synchronization convention, because the one-way speed of light is defined based on the synchronization convention.

Reference: https://www.physicsforums.com/threads/one-way-speed-of-light-measurement.1003212/

This seems like an unnecessarily circular definition, which forces one two use two synchronizing clocks and assumes that this is the only way to measure the time taken by light to travel between two points. Which is not true as shown in the experiment.

The experiments designed until now mainly falls into two categories

  1. Either uses two synchronized clocks

  2. Or makes use of round trip of light

And the proofs offered for the impossibility of measuring speed of light assumes one of the above and the one way speed of light is considered more of a convention than an objective fact. Which is not necessarily true as pointed out by this experiment. This experiment has no clock synchronization problem, avoids round trip of light and uses objects moving at a relatively slow speed than light and thereby avoids the relativistic effects to affect the outcome of the experiment.

Does this experiment solve the problem? If not, why exactly does it fail to measure one way speed of light.

Edit: Response to this answer which claims that

  1. It is possible, because light can travel at different speed in different directions, the balls will be shot at different speeds

  2. Hence the difference in the velocity of balls affects the final measurement at C and makes it impossible to measure the speed of light.

My response:

  1. Yes, it is true that if light moves in different speeds in different directions then it impacts the speed of balls launched in two opposite directions.

  2. I anticipated this response, so in Abstract it self I did try to answer this when I said

using objects, to communicate, which are moving at comparatively low speed than light, thereby avoiding relativistic effects and possibility of difference in light’s speed in various directions affecting the outcome of the experiment

But many people didn't get this and they have claimed that the difference is big enough between the velocities of the two balls in order to make it impossible for measuring the speed of light in one direction. Which is false as the difference between the velocities of the balls has an upper limit because of relativistic effects. Let me work it out with a numerical example, so people can point exactly what is wrong

There are two extreme scenarios

  1. Light moves at the same speed 299,792,458 $m/s$ in all directions

  2. Light moves at $c/2$ or 149,896,229 $m/s$ in one direction and at infinite speed in another direction.

  3. The weight of balls is 1 $kg$

All other scenarios lie in between these two extremes as we know the round trip averages to $c$.

Let's assume the extreme scenario of light travelling in c/2 in one direction and at infinite speed in another direction.

Consider this,

  1. Let AB be 299,792,458 $m$

  2. CA and CB be 200,000,000 $m$

  3. And the ball from A be launched at 1000 $m/s$

If light travels at infinite speed from A to B, and A launches the ball at 1000 $m/s$ it takes 200,000 seconds for ball to reach to C from A. And as light reaches instantaneously from A to B, B will also launch the ball simultaneously. Now for this to be useless the ball from B must take 200,001 seconds to reach C, so that time difference is still one second for distance of 299,792,458 $m$. So the total distance travelled by ball_B is 200,000,000 $m$ in 200,001 seconds, so its velocity for this experiment to be useless is 999.995000025 m/s

Now note that A and B are in rest with respect to each other. They both are designed to use 500,000 Joules to accelerate the balls. The energy is same for both A and B as they are in rest with respect to each other. Newtonian speed of 1000 m/s is achieved by ball_A as light travels at infinite speed in the direction of AB. Assuming the speed of light from B to A would be $c/2$ which is 149,896,229 $m/s$. So when B uses 500,000 Joules. Relativistic resultant velocity can be calculated for this using the formula

$$v=c/2\sqrt{1-\frac{1}{\left(1+\frac{K_e}{m(c/2)^2}\right)^2}}$$

So,

$$149896229\sqrt{1-\frac{1}{\left(1+\frac{500000}{(149896229)^2}\right)^2}} = 999.99999998$$

So the time ball_B takes to reach C is

$$\frac{200000000}{999.99999998} = 200000.000004$$

enter image description here

So the difference between the arrival of ball_A and ball_B is

$$200000.000004 - 200000 = 0.000004$$

So this experiment, if done in the direction in which light trvels at an infinite speed will give us

$$c_{AB} = \frac{d}{\Delta t}$$

So,

$$c_{AB} = \frac{299792458}{0.000004} = 7.49e+13 $$

One can clearly see this is way greater than the value of c.

And if we do the same experiment in the opposite direction the time difference would be

$$200002.000004 - 200000 = 2.000004$$

Which would give us a speed of

$$c_{AB} = \frac{299792458}{2.000004} = 149895929.208 m/s $$

Which is quiet close to c/2 which is $149896229 m/s$

And only if light travelled at c, in both the directions, then we would get a value of c.

Link to the original paper: A Proposal Of a Novel Experiment To Measure One Way Speed Of Light

Qmechanic
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Srinivas N Rao
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2 Answers2

5

No.

"identical apparatus which can shoot a ball at the same speed [in opposite directions]"

The same what now? The same speed in two directions? Sure, the apparatus looks like it works the same in both directions, but looks are just measurements that we make with the speed of light, and touches aren't any better, since we "touch" with interactions of c-propagating force fields. Are you sure it fires the ball at the same speed in both directions? You'd better test it to be sure. You're going to need your laser and a clock and the assumption that the speed of light is the same in all directions, or a laser, two clocks, and a clock synchronization convention...

Your quote from physicsforums is true but it doesn't go far enough. The one-way speed of light is not something that is hard to measure, and it's not something that's impossible to measure, it is arbitrary. You define it however you want to make the math easy, like the geometry of your coordinate space.

g s
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4

Edited to add: The first four paragraphs below constitute my original answer. Below that is a new and better answer.

Original Answer:

Suppose the distance from A to C (and from B to C) is $s$. Suppose the ball from $B$ arrives at $C$ 1 second later than the ball from $A$.

Your conclusion: The ball from $B$ was fired 1 second later than the ball from $A$. Therefore light takes 1 second to get from $A$ to $B$. Therefore the rightward velocity of light is $1/s$.

My conclusion: The two balls were fired at exactly the same time (call it time zero). Therefore light takes 0 seconds to get from $A$ to $B$ and the rightward velocity of light is infinite. However, your cannons fire balls at some velocity $v$ in the rightward direction and at velocity $v'=sv/(s+v)$ in the leftward direction. This explains why the rightbound ball arrived at time $t=s/v$ and the leftbound ball arrived at time $s/v'=t+1$.

What basis do you have for asserting that one conclusion is better than the other? You seem to be saying that you will do an experiment with one cannon, measuring the speeds at which it shoots balls over short distances. But how are you going to measure those speeds without assuming that the speed of light is the same in both directions?

New Answer:

Your experiment reveals nothing at all about the one-way speed of light, but it does reveal something interesting, which I will get to in the coda.

Throughout, I will take the two-way speed of light to be $1$.

Step I. First, I need to know the velocities of the cannonballs, so I do a pre-experiment.
I shoot a cannonball at an identical cannon which, immediately upon being hit, shoots an identical cannonball back at me. I know the distance to the other cannon, so by timing this trip I can measure the average velocity of the cannonballs. Call it $v$.

To infer the leftbound and rightbound velocities $v_L$ and $v_R$, I choose two constants $s_L$ and $s_R$ and set $v_L=s_Lv$ and $v_R=s_Rv$. In order to get the right value for the measured average velocity $v$, I have to choose these constants so that

$$1/s_L+1/s_R=2$$

One way to do this (and in fact the only sensible way, for reasons I will comment on at the end) is to choose a single constant $A$ with $-1<A<1$ and then set $$s_L=1/(1+Av)\qquad s_R=1/(1-Av)$$

So that's what I do.

Step II. I do your experiment, taking the distance from $A$ to $B$ to be 2 and the distance from either to $C$ to be 1.

At time $0$, I send a light beam from $A$ to $B$ and a cannonball from $A$ to $C$. When the light beam arrives at $B$, a cannonball is sent to $C$. The difference between the two arrival times at $C$ is $$T=2/c_R+1/v_L-1/v_R$$ where $c_R$ is the rightbound speed of light.

Because you've already got values for $v_L$ and $v_R$, and because you've observed the value of $T$, you can now calculate $c_R$. This gives

$$c_R= {2\over T-2A}$$

Step III. I define "your theory" to be that $s_L=s_R=c_R=1$ (that is, the leftbound and rightbound velocities of a cannonball are equal, and likewise for light). Your theory implies that $T=2$.

I will assume that the experimental results are consistent with your theory. Therefore $T=2$ and I will plug this into the expression for $c_R$ above to get

$$c_R={1\over 1-A}$$

Step IV. Now we've done the experiment, and we've assumed that the results are consistent with your theory that $c_R=1$ (because it's possible that $A=0$). But we've discovered that then they must also be consistent with any theory in which the equation at the end of Step III holds.

As $A$ can take any value between $-1$ and $1$, $c_R$ can take any value between $1/2$ and $\infty$.

Conclusion. Your experiment reveals nothing about the one-way speed of light beyond what we already know for trivial reasons.

Coda. But your experiment DOES in fact reveal something valuable, namely this:

In Step I, I had to choose $s_L$ and $s_R$. I ended up choosing them via the formulas $s_L=1/(1+Av)$ and $s_L=1/(1-Av)$ for some parameter $A$. I can prove (though I am omitting the proof here) the following:

If $s_L$ and $s_R$ are chosen in any way other than the above, then either $c_R=1$ or your experiment will reveal a value for $c_R$ that depends on $v$.

To have $c_R$ depend on $v$ is crazy, because we could then repeat the experiment with other cannonballs having a different average velocity, causing calculated value of $c_R$ to change, which makes no sense. Thus your experiment does reveal the need to choose $s_L$ and $s_R$ in a very specific way.

(Summary of proof: Write down the expression for $c_R$ in terms of $s_L$ and $v$, note that this has to be independent of $v$, so take $s_L$ as a function of $v$, differentiate and set to zero; this gives a differential equation for $s_L$ that solves to $s_L=1/(1-Av)$.)

WillO
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