Why Have We Never Measured The One-Way Speed Of Light?

How do we measure the speed of light? For a time, many – including influential philosopher and scientist René Descartes – believed the speed of light was infinite. 

While studying the eclipses of moon Io by its host Jupiter, Danish astronomer Ole Roemer noticed something odd. The moon has a short and consistent orbital period, making a complete trip around the gas giant once every 42.5 hours. Yet when Roemer measured the time between each eclipse, he noticed that the time varied depending on how close Earth was to Jupiter at the time. They would occur earlier than average when Jupiter was close, and later than average when Jupiter was its furthest away.

From this, he correctly deduced that the speed of light was not infinite, but took time to propagate. The moon wasn’t taking longer to orbit Jupiter when Earth was far from it, but the light was taking longer to arrive. Dutch scientist Christiaan Huygens attempted to calculate the speed of light using this information and came up with 210,824 kilometers per second (131,000 miles per second). The difference between that figure and what we now know to be the correct speed was down to Roemer’s maximum time delay estimate and the fact we hadn’t quite pinned down Earth’s orbit yet.

Since then, scientists have measured the speed of light using lasers and mirrors. In these setups, at first involving rotating mirrors, light is beamed out a known distance, and returns to its starting point where it is detected again. To get the speed, you then need to divide the distance by time, and our best measurements show a consistent 299,792,458 meters per second.

But in that setup, you are actually measuring the two-way speed of light: the time it took to go one way, and then return to its starting point. Though it seems pretty safe to assume that light travels the same speed in every direction – as Einstein did – it is still an assumption. It could be, as far as we have experimentally confirmed, that light travels in one direction at a higher speed and returns at a lower speed, averaging out to the speed that we measure.

So, why can’t we measure the one-way speed of light? That’s down to how we synchronize clocks. 

Say you want to measure the one-way speed of light. To do that, you need to know that your clock at the light emitter is exactly in sync with the clock at the detector. You cannot divide the distance by time to get speed without both clocks being in sync. 

This is where the problem arises, as in special relativity when you move the clocks away from each other, they begin to tick at different rates. While this sounds quite abstract, experimentation (and even the way GPS operates) shows that clocks really do tick at different rates for different observers depending on the relative velocity they are traveling at, or the strength of the gravitational field. So when you synchronize two clocks together and then move them apart to begin measuring the speed of light, they become unsynchronized in the process. Meanwhile, if you start the experiment with two clocks separately and then try to synchronize them, you are also left with a problem.

“This synchronization uses in turn light signals, creating a circular argument that so far has made this type of measurement invalid,” a preprint paper on the topic explains.

Einstein was aware of the problem, outlining it in his 1905 paper On the Electrodynamics of Moving Bodies.

“If there is a clock at point 𝐴 of space, then an observer located at 𝐴 can evaluate the time of the events in the immediate vicinity of 𝐴 by finding the clock-hand positions that are simultaneous with these events. If there is also a clock at point 𝐵—we should add, ‘a clock of exactly the same constitution as that at 𝐴’—then the time of the events in the immediate vicinity of 𝐵 can likewise be evaluated by an observer located at 𝐵,” a translation of Einstein’s paper explains.

“But it is not possible to compare the time of an event at 𝐴 with one at 𝐵 without a further stipulation; thus far we have only defined an ‘A-time’ and a ‘B-time’ but not a ‘time’ common to 𝐴 and 𝐵. The latter can now be determined by establishing by definition that the ‘time’ needed for the light to travel from 𝐴 to 𝐵 is equal to the ‘time’ it needs to travel from 𝐵 to 𝐴.”

“For, suppose a ray of light leaves from 𝐴 toward 𝐵 at ‘A-time’ 𝑡_𝐴, is reflected from 𝐵 toward 𝐴 at ‘B-time’ 𝑡_𝐵 , and arrives back at 𝐴 at ‘A-time’ 𝑡_𝐴′. The two clocks are synchronous by definition if 𝑡_𝐵−𝑡_𝐴 = 𝑡_𝐴′ − 𝑡_𝐵.”

In essence, Einstein made the assumption that the speed of light is the same in both directions, but acknowledged that this was an assumption, rather than experimentally verifiable. Since then, scientists have not come up with some clever trick to get around this problem, and have shown that the Roemer measurement took an average measurement rather than a one-way measurement. 

While it seems a reasonable assumption to make, it’s not ideal that our best ideas for how the universe works are based on an assumption. 

But given one-way measurement may be impossible, we may just have to get comfortable with it.

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