Skulls in the Stars

In Part 1 of What the heck is the “speed of light?”, we noted how light in matter can move much slower than the vacuum speed of light c, or even appear to move much faster than c, under the right circumstances. We even noted that, thanks to the phenomenon of dispersion, there are cases where a single number cannot adequately describe the speed of light of a pulse in matter, because the pulse may break up into multiple pieces, each traveling at its own speed.

All of this may be summarized by saying that a pulse of light is “squishy,” and not a rigid object like a car or a softball. To measure the speed of an object, we look at how long it takes some part of the object to travel the distance from point A to point B. For a car, we can use the front bumper; for a softball, we can use its center of mass. But a pulse of light, which can change shape or break into multiple parts, there isn’t in general a clear mark we can use to define its absolute speed.

This problem of “squishiness” even arises when we look at light propagating in vacuum, and it leads to more unexpected surprises. This is what we look at in this post: the speed of light can be tricky to define sometimes, even in vacuum!

Most of us have heard a statement similar to the one that follows: “The speed of light is constant.” That particular phrasing of the statement comes from none other than the American Museum of Natural History’s Einstein exhibit, so I think it is fair to say that most people have heard it phrased in this way at one time or another.

Most physicists would add one very important caveat to this statement to reduce confusion: “The speed of light is constant in vacuum.” It is in this sense that it forms part of the foundation of Einstein’s special theory of relativity: any observer measuring the speed of a light wave traveling in vacuum will measure exactly the same result, about 186,000 miles per second or 300,000,000 meters per second, usually labeled c in physics. Different observers moving relative to one another will agree that a given light wave is moving at c, even if one is moving towards the light source and one is moving away from the light source! This is in contradiction to our day-to-day intuition: if I am driving towards a car that is approaching me, it will move towards me faster than if I am driving away from it.

From Einstein’s special theory of relativity, and the observation that “the speed of light is constant in vacuum,” comes all sorts of non-intuitive phenomena, like length contraction and time dilation and the idea that, as far as we know, nothing can move faster than c! Apparently the “speed of light” is the speed limit of the universe.

The statement “the speed of light is constant” is therefore arguably more accurate than not, but leaves out a lot of subtlety in discussions of the speed of light! I recently started thinking about the speed of light from an optical science perspective due to a question from a Twitter friend, and I thought I would muse a bit on all the ways that the speed of light is harder to define than you might think, even without talking about objects in relative motion.