How Do We Measure the Speed of Light?

From a lecture series presented by The Great Courses

Before Einstein introduced his theory of special relativity, the science community was perplexed about how to measure the speed of light. Einstein proposed that light waves did not behave like sound or water, and he was right. Discover how he came up with a solution to this puzzling phenomenon.

The universe within. Silhouette of a man inside the universe, physical and mathematical formulas.

Examining the Mysteries in Our Solar System

For years, scientists struggled to find an explanation for why sound waves and water waves moved at a speed relative to the medium they were traveling through, but light waves did not seem to behave in the same way. In fact, light did not appear to move through any medium at all.

Physicists argued that light did move through a medium that they called the luminiferous aether, or just the aether for short.

In order for this hypothetical aether to make sense, it had to have some rather strange properties. For one thing, astronomers had long known that the planets in our solar system weren’t appreciably slowing down over time.

If our solar system was filled with any kind of ordinary material, like a gas or something similar, that material would act like a form of wind resistance to the planets, inducing a drag force and causing them to gradually slow down.

This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

Whatever the aether was, it had to fill all of space, but not be felt by the objects moving through it. The aether had to be a very exotic substance indeed, and the physicists of the late 19th century clamored to be the first to detect and study it.

Physicists knew that, if the aether existed, there would be ways to detect it—at least, indirectly. At different points in time, and at different times of the year, the Earth would be moving at different speeds relative to the rest frame of the aether.

At some times, the light from a given direction would be moving along with the motion of the aether. And at these times, we would expect to measure the speed of this light to be a little faster than normal.

And at other times, light from the same direction would be moving against the motion of the aether. And in these cases, we should measure the speed of that light to be a little slower.

New Discoveries about the Speed of Light

In experiments conducted in the 1880s, the American physicists Albert Michelson and Edward Morley were able to measure the speed of light with enough sensitivity that they should have been able to detect the variations induced by the aether.

Photo of Albert Abraham Michelson.
American physicist Albert Michelson

But over and over again, their experiments measured the same value for the speed of the light. Light—measured at different times, and from different directions—always seemed to reach their experiment moving at precisely the same speed.

At the time, this was a very unexpected result. And it seemed to be incompatible with the hypothesis that light moved through some sort of medium like an aether.

Some physicists tried to save the idea of the aether by suggesting that perhaps the Earth dragged a cloud of aether along with it as it moved along its orbit. This would have had the effect of making the speeds of the incoming light more uniform.

But these aether-dragging scenarios also had their problems. In reality, these experiments were telling us that the light did not behave like other kinds of waves. In fact, there is no such thing as luminiferous aether.

Learn more about the special theory of relativity

Einstein Proposes Theory about Light Speed

When Einstein was approaching this problem, he took as a starting point—as an axiom if you will—the idea that light always travels through empty space at exactly the same speed. He suspected this might be true for a number of different reasons.

First of all, Einstein knew that Maxwell’s equations predicted a specific value for the speed of light. And in doing so, these equations don’t specify any particular frame of reference. This made Einstein think that the speed of light is a universal quantity—one that is the same in all frames of reference.

Furthermore, these equations don’t seem to require or make any reference to the aether. Unlike other kinds of waves, light can just move through space itself.

Among other things, Einstein’s hunch that the speed of light was a universal constant could explain why Michelson and Morley, and other experimental physicists, hadn’t been able to measure any variations in the speed of light.

To Einstein’s way of thinking, light always traveled at the same speed, and any experiment you did—regardless of the time or direction—would measure the same value for this quantity.

Learn more about Einstein’s rejection of black holes

Complications in Einstein’s Light Speed Theory

So, in some ways, Einstein’s premise of a universal speed of light seemed to solve some problems. But in other ways, it seemed to be very problematic. To see why, imagine the following scenario. Picture a spaceship that is moving through space at a speed equal to half of the speed of light.

As the spaceship approaches a space station, the pilot of the spaceship turns on its headlights. To someone who’s standing on the space station, you should ask yourself, how fast the speed of the approaching light beam is?

Since the spaceship is moving at half of the speed of light, and the light itself is, of course, moving at the speed of light, the incoming light should be moving at 1.5 times the speed of light. But this, of course, is in contradiction with Einstein’s starting assumption that light always moves at the same speed.

To Einstein, no one should ever measure a speed of light that is moving at 1.5 times the speed of light, or at any other speed other than exactly the speed of light. So, at least, at first glance, it would seem that Einstein’s axiom of a universal speed of light leads to paradoxical nonsense.

In thinking through this example, we used something that physicists call a “Galilean transformation.” In a Galilean transformation, velocities simply get added together.

In the previous case, for example, we said that half of the speed of light, plus the speed of light, equals 1.5 times the speed of light. Our intuition and our experience strongly supports this kind of reasoning.

It just works very well in any number of situations. In fact, this kind of reasoning is so intuitive that it can be hard to imagine the world might work in any other way.

But according to Einstein, the Galilean transformation is only accurate in those situations in which everything is moving at a speed that is much slower than the speed of light. In other situations—those in which something is moving at a speed comparable to the speed of light—the Galilean transformation breaks down and fails.

The Lorentz Transformation

In place of the Galilean transformation, Einstein instead adopted an alternative known as the “Lorentz transformation.” For slow-moving objects, the Lorentz transformation is nearly identical to the ordinary Galilean transformation.

For example, according to these equations, two small velocities add up together normally: one mile per hour, plus two miles per hour, equals three miles per hour.

Derivation of the Lorentz Transformation. Author: Stigmatella aurantiaca [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Derivation of the Lorentz transformation, used by Einstein to show that light travels at a fixed and constant speed

In other words, our intuition works perfectly well, so long as everything in the problem is moving at a speed much slower than the speed of light. But for objects that are moving at speeds close to the speed of light, the Lorentz transformations behave very differently.

For one thing, combinations of velocities never exceed the speed of light. For example, half of the speed of light plus the speed of light works out to be equal to the speed of light according to these equations. Using the Lorentz transformation, light always travels at the same speed—just as Einstein had adopted as his starting point.

On June 30, 1905, Einstein submitted a paper titled “On the Electrodynamics of Moving Bodies” to the prestigious German journal, the Annals of Physics. In this paper, he introduced the theory that we now call special relativity.

In this theory, Einstein replaced the more intuitive Galilean transformations with Lorentz transformations, ensuring that light always travels at a fixed and constant speed.

From the lecture series What Einstein Got Wrong, taught by Professor Dan Hooper

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Derivation of the Lorentz Transformation. Author: Stigmatella aurantiaca [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons