The Special Theory of Relativity

Is the Speed of Light Relative?

In 1905, Albert Einstein published a revolutionary new idea that would later be called the special theory of relativity, or simply special relativity. It’s called the special theory because it turns out to be a special case of Einstein’s general theory of relativity, which he proposed a decade later. (Einstein’s general theory holds true “in general,” even in cases where special relativity fails; but it implies that special relativity is true in certain “special” circumstances. We’ll get to that soon.)

Einstein wasn’t a professional scientist when he proposed his first theory. He worked as a clerk in a patent office. In his spare time, though, Einstein was a physics enthusiast. Intrigued by the mysterious nature of light, he thought long and hard about the elusive aether—that undiscovered substance through which light waves were supposed to travel. He was dissatisfied with Lorentz’s hypothesis and the bizarre coincidences it seemed to require.

The reason aether had not been detected in any experiments, Einstein suspected, was that aether doesn’t exist. Perhaps there simply is no substance through which light travels, he thought. Maybe light waves don’t require any medium at all. Unlike sound waves, water waves, and all other types of waves, light waves are self-sustaining: they don’t need any material substance to carry them along.

This suspicion, however, gave rise to a puzzling question. In which reference frame does light travel at the speed predicted by Maxwell’s equations? Remember, Maxwell’s equations imply that the speed of light is about three hundred million meters per second. Everyone (including Maxwell himself) had assumed this was the speed at which light travels relative to aether. But if there is no such thing as aether, then there is no privileged reference frame in which the speed of light is determined. How could that be?

Einstein’s answer was simple: the speed of light is the same in all frames of reference. In other words, the speed of light isn’t relative. Unlike the speed of any other object, the speed of light is an absolute quantity.

This idea may sound unremarkable at first, but upon reflection it has surprising implications about the nature of space and time. To see what the theory implies, imagine an alien spaceship zooming away from Earth at 200,000 km/s—about ⅔ the speed of light. (Perhaps the alien has abducted some cows and is making a fast getaway.) A farmer on Earth shines a powerful flashlight in the same direction, and the beam of light catches up and passes the spaceship. How fast is the beam of light traveling relative to the spaceship?

Common sense tells us that if the beam of light is moving 300,000 km/s relative to Earth, and the alien spacecraft is moving 200,000 km/s in that same direction, then the light must be moving only 100,000 km/s relative to the alien. But according to Einstein, common sense is wrong! The beam of light travels at the same speed in all reference frames, including the reference frame of an alien who regards her spaceship as being at rest. From the alien’s perspective, the beam of light goes past at exactly the speed of light—no slower, no faster. In her frame of reference (regarding the spaceship as being at rest) the light is still moving at 300,000 km/s—the same speed at which it is moving relative to Earth. How is that even possible?

It’s not possible, if time and space work the way we intuitively think they do. But according to Einstein, time and space don’t work the way we always assumed. If the speed of light is the same in all reference frames, he realized, then distances and times must be relative quantities. We’ll talk about that on the next page.