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A Constant Source of Confusion

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Seven words we all know by heart: “The speed of light is a constant.”

It’s a sentence I learned long ago; since then, I have used this constant speed of light (299,792,458 metres per second) thousands of times in hundreds of different equations – but it is only recently that I have discovered what it really means. Unexamined, it’s just words. After a little thought, however, it explodes into something really remarkable and counterintuitive, rather like the old story of putting one grain of rice on the first square of a chessboard, two on the next, four on the next and eight on the next, and finding that by the end of the board (64 squares) you have rather more rice than you expected.*

The problem comes from having a speed that is constant. Because for something to be constant it must be constant for everybody ­– even people who are themselves moving.

The speed of light is c.

I have a friend, Alice, who is an astronaut. Her space ship’s top speed is half the speed of light ­– 0.5c. Alice’s space ship has headlights. When she is at top speed, she switches on her headlights and a beam of light leaves the front of her ship and travels ahead of her. How fast does the light move? It moves away from her at the speed of light, c. She can check this any way she likes, that is what she will find.

Space travel is not for me. I prefer to stay on Earth, but I do look out of the window and see Alice from time to time.

When Alice is moving away from me at half the speed of light, and switches on her headlights, we know how fast the light moves away from her: c. But how fast does the light move away from me? Surely it should be one and a half times c ­– the speed of light, plus Alice’s speed when she turned on the headlights.

But it’s not. The beam of light moves away from me at speed c, too, because the speed of light is constant, wherever you’re standing.

I would expect Alice to tell me she detected the light crawling away from her at a mere half-c, because that is what I see is the difference between her speed and the speed of light. But she insists she saw the beam move away at c as well.

Which of us is right?

Amazingly, we both are.

In order for the speed of light to remain constant, other things change instead – space and time. If Alice and I measured the distance between Earth and Alice’s destination, we would report different distances ­– and we would both be correct. We would disagree about how long things took to happen outside the space ship, and both be correct.

Space and time distort depending on how you are moving, all so that the speed of light doesn’t have to. It remains, for all observers, a constant.


An excellent introduction to relativity is Bertrand Russell’s “The ABCs of Relativity” (1925).

* 18,446,744,073,709,551,615 grains of rice, or about 9.2 cubic kilometres of rice, according to Wikipedia.

Written by The S I

August 5, 2011 at 8:30 pm