The Speed of Light

How Do We Know the Speed of Light?

Until the 17th century it was assumed that light traveled instantly. Galileo tried to measure the speed of light in 1638 by having a series of people holding lanterns on distant hills relay a signal. He found that it seemed instantaneous or at least extraordinarily fast. He estimated that it was at least 10 times faster than the speed of sound.

The first indication that light wasn't instantaneous was observed in the 1670's when observations of the moons of Jupiter showed unexpected discrepancies. This was seen while trying to solve one of the great problems of the time: The determination of longitude. This could be solved with a very accurate clock. Giovanni Domenico Cassini, following a suggestion by Galileo, tried to use the eclipses of the moons of Jupiter as such a clock. But the eclipses were seen sooner when Jupiter was near the Earth and later when it was farther away. Cassini realized that this was due to the time it took light, at a finite speed, to cross the Earth's orbit. To see why this is the explanation take a look at these two diagrams. In each the inner circle is the Earth's orbit and the outer one is Jupiter's.

The figure on the left shows the situation where Jupiter and the Earth are nearest to each other, while the one on the right shows them at their most distant. Let's be specific. Jupiter's moon Io orbits Jupiter once every 1.77 days and is eclipsed by Jupiter's shadow once every orbit. These eclipses are usually quite easy to see and naively you would expect them to occur every 1.77 days. But they don't. Let's say you start observing when Jupiter is nearest the Earth and you make a prediction of the time of every eclipse for the next year. The eclipses are seen to occur right on schedule at first but eventually they will be seen later and later until, when Jupiter is as far from Earth as it gets, they are seen a bit over 16 minutes later than predicted. At this point the discrepancy shrinks until, when Jupiter is again near the Earth they are right on time. Of course the eclipses happened at regular intervals but they appeared to happen at different times when the planets were at different distances because light takes time to travel. We can see that the difference between the paths that light takes in these situations is the diameter of the Earth's orbit.

This was followed up by Ole Roemer who made more observations and determined the time it took for light to cross the Earth's orbit. At the time the sizes of orbits in our solar system weren't that well known so he was unable to confidently estimate the speed of light but determined that light traveled at a finite speed.

This was confirmed via the discovery, in 1728, of the aberration of starlight which is discussed in another entry on this website; How do we know the Earth revolves? The finite speed of light causes the apparent location of stars to shift, very slightly, throughout the year. This indicates that the speed of light is about 10,000 times faster than the speed of the Earth around its orbit.

The fact that the speed of light was finite was then widely accepted but it's value wasn't accurately determined. The first measurement was done in 1849 by Hippolyte Fizeau using a simple but ingenious device. He reflected a beam of light off a mirror 8 kilometers away and had the beam pass through the gaps in a rapidly rotating slotted disk twice, once on the way to the mirror and once after it returned. By changing the speed of the disk he could determine the length of time between the two trips through the disk. He got an answer of 313,300 kilometers/second, within 5% of the current value.

Leon Foucault improved this by replacing the disk with a rotating mirror in 1862 and got an answer of 299,796 kilometers/second. This technique can be seen in action in this video.

But there is more to the story than this. Einstein's Special Theory of Relativity is based on a very strange property of light. Any time that the speed of light (in a vacuum) is measured, the result will be the same. This doesn't sound surprising until we point out that the relative speeds of the source and the detector don't matter. Special Relativity predicts many strange things happen at high relative speeds and all of them have been demonstrated in experiments. Taking advantage of this, and the ease of measuring the speed of light, the question was turned around and now the speed of light is used to define the meter. Effectively the speed of light is DEFINED to be 299,792,458 meters/second.