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Measuring the speed of light #### December 3, 2020

299,792,458 metres per second. That is the speed of light as we concluded ourselves. Even the definition of a metre is based on this. One metre namely is equal to the distance light travels in 1/ 299,792,458 of a second. Even though this sounds like a joke, as it is so straightforward, it is actually true. It shows that we are really sure about the speed at which light travels. However, should we be so sure that this number is correct?

The answer should be no, as we actually do not know the “one-way” speed of light. The “one-way” speed is the speed it has when we measure it going from one point to another.  The speed physicians measured, and the speed we know, is the average speed at which light travels from one point to another and back. This is called the “two-way” speed of light. In fact, it is not even possible to measure the “one-way” speed of light. So the value we give to the speed of light is nothing more than a convention. To try and understand why we can’t measure the “one-way” speed of light, let’s create a hypothetical test.

Suppose we let light travel from a starting point A to an end point B. We use a timer at point A, which starts the instant that light leaves point A and stops when the light reaches point B. This sounds really simple, but how do we exactly know when the light reaches point B? Of course we are not able to see the light reach point B. Suppose there is also someone with a timer at point B. This timer would stop the instant the light reaches point B. To make this work, the two timers would need to be synchronized to assure us that we obtain valid results.

For example, let’s use a wire connected to both timers to synchronize them, as in scenario 1 of the figure. However, then the problem arises that the impulses sent via the wire also need travel time, which creates a time delay between the timers at exactly the speed of light multiplied by the distance it covers.

Alternatively, let both timers be synchronized at point A and then one of the timers is brought to point B, as in scenario 2 of the figure. This also does not work, as a result of special relativity: since one of the timers is moving with respect to the stationary one, it perceives time slower relative to stationary observers, resulting in the fact that the timers are no longer synchronized when the moving timer reaches point B.

This use of a second timer isn’t working as it is impossible to make sure that they are synchronized. The only way to successfully measure the speed of light is to use one timer and to place a mirror at point B, so the light comes back to the starting point. As you might already recognize, this means that we have measured the “two-way” speed of light and not the “one-way” speed. It seems like the “one-way” speed cannot be measured.

Now comes the tricky part, as this implies that it is possible that light travels faster in one direction than in the other. In the most extreme scenario, light could travel at half the speed we know in one direction, while it would travel instantaneously in the other direction. The fact that the speed could differ in opposite directions, does not mean that it will be different, but we are simply not able to rule out the possibility.

If the speed were different, an interesting consequence of this would be that we are possibly seeing stars as they are right now, real-time. It wouldn’t take light-years for us to get the information of other galaxies as they were light-years ago. Even the definition of a light-year would be questionable.

But maybe we jumped too quickly to a conclusion for the test, so let’s go back. Perhaps you thought of another idea where you could be able to eliminate the special relativity problem, so the two timers would be synchronized.  Suppose both timers start at exactly the middle point between point A and B, as in scenario 3 of the figure. We could synchronize them and then they would be moved to point A and B. Both timers would then experience the same special relativity effects and they would still be synchronized at point A and B.

Or would they? If light would travel faster in one direction, this would also have an effect on the special relativity theory. The speed in the direction in which you are moving would then also play a role in the effects. This implies that one timer might perceive time even slower relative to stationary observers than the other timer when moving. Therefore they would still not be synchronized. The remarkable part is that if you would then perform the test, your outcome would still be the conventional speed of light. You wouldn’t even know that the speed was different in opposite directions. The reason for this is that one of the timers would be ahead of the other by just the right amount of time that we would still get the conventional speed as the outcome.

It is impossible to measure the speed of light with the certainty that you are actually measuring the “one-way” speed. We need synchronized timers to measure the speed of light, but we also need the speed of light to be able to synchronize the timers.

The actual speed of light could remain a secret of the universe for eternity, but the idea that we could possibly admire the universe as it is right now is mind-boggling. It sure makes gazing at the stars even better.