Imagine that I am riding a bicycle toward you. As I approach an intersection I nearly collide, so it seems to me, with a horse-drawn cart. I swerve and barely avoid being run over. Now think of the event again, and imagine that the cart and the bicycle are both traveling close to the speed of light. If you are standing down the road, the cart is traveling at right angles to your line of sight. You see me, by reflected sunlight, traveling toward you. Would not my speed be added to the speed of light, so that my image would get to you considerably before the image of the cart? Should you not see me swerve before you see the cart arrive? Can the cart and I approach the intersection simultaneously from my point of view, but not from yours? Could I experience a near collision with the cart while you perhaps see me swerve around nothing and pedal cheerfully on toward the town of Vinci? These are curious and subtle questions. They challenge the obvious. There is a reason that no one thought of them before Einstein. From such elementary questions, Einstein produced a fundamental rethinking of the world, a revolution in physics.
If the world is to be understood, if we are to avoid such logical paradoxes when traveling at high speeds, there are some rules, commandments of Nature, that must be obeyed. Einstein codified these rules in the special theory of relativity. Light (reflected or emitted) from an object travels at the same velocity whether the object is moving or stationary: Thou shalt not add thy speed to the speed of light. Also, no material object may move faster than light: Thou shalt not travel at or beyond the speed of light. Nothing in physics prevents you from traveling as close to the speed of light as you like; 99.9 percent of the speed of light would be just fine. But no matter how hard you try, you can never gain that last decimal point. For the world to be logically consistent, there must be a cosmic speed limit. Otherwise, you could get to any speed you wanted by adding velocities on a moving platform.
Europeans around the turn of the century generally believed in privileged frames of reference: that German, or French, or British culture and political organization were better than those of other countries; that Europeans were superior to other peoples who were fortunate enough to be colonized. The social and political application of the ideas of Aristarchus and Copernicus was rejected or ignored. The young Einstein rebelled against the notion of privileged frames of reference in physics as much as he did in politics. In a universe filled with stars rushing helter-skelter in all directions, there was no place that was ‘at rest,’ no framework from which to view the universe that was superior to any other framework. This is what the word relativity means. The idea is very simple, despite its magical trappings: in viewing the universe, every place is as good as every other place. The laws of Nature must be identical no matter who is describing them. If this is to be true – and it would be stunning if there were something special about our insignificant location in the Cosmos – then it follows that no one may travel faster than light.
We hear the crack of a bullwhip because its tip is moving faster than the speed of sound, creating a shock wave, a small sonic boom. A thunderclap has a similar origin. It was once thought that airplanes could not travel faster than sound. Today supersonic flight is commonplace. But the light barrier is different from the sound barrier. It is not merely an engineering problem like the one the supersonic airplane solves. It is a fundamental law of Nature, as basic as gravity. And there are no phenomena in our experience – like the crack of the bullwhips or the clap of thunder for sound – to suggest the possibility of traveling in a vacuum faster than light. On the contrary, there is an extremely wide range of experience – with nuclear accelerators and atomic clocks, for example – in precise quantitative agreement with special relativity.
The problems of simultaneity do not apply to sound as they do to light because sound is propagated through some material medium, usually air. The sound wave that reaches you when a friend is talking is the motion of molecules in the air. Light, however, travels in a vacuum. There are restrictions on how molecules of air can move which do not apply to a vacuum. Light from the Sun reaches us across the intervening empty space, but no matter how carefully we listen, we do not hear the crackle of sunspots or the thunder of the solar flares. It was once thought, in the days before relativity, that light did propagate through a special medium that permeated all of space, called ‘the luminiferous aether.’ But the famous Michelson-Morley experiment demonstrated that such an aether does not exist.
We sometimes hear of things that can travel faster than light. Something called ‘the speed of thought’ is occasionally proffered. This is an exceptionally silly notion especially since the speed of impulses through the neurons in our brains is about the same as the speed of a donkey cart. That human beings have been clever enough to devise relativity shows that we think well, but I do not think we can boast about thinking fast. The electrical impulses in modern computers do, however, travel nearly at the speed of light.
Special relativity, fully worked out by Einstein in his middle twenties, is supported by every experiment performed to check it. Perhaps tomorrow someone will invent a theory consistent with everything else we know that circumvents paradoxes on such matters as simultaneity, avoids privileged reference frames and still permits travel faster than light. But I doubt it very much. Einstein’s prohibition against traveling faster than light may clash with our common sense. But on this question, why should we trust common sense? Why should our experience at 10 kilometers an hour constrain the laws of nature at 300,000 kilometers per second? Relativity does set limits on what humans can ultimately do. But the universe is not required to be in perfect harmony with human ambition. Special relativity removes from our grasp one way of reaching the stars, the ship that can go faster than light. Tantalizingly, it suggests another and quite unexpected method.
Following George Gamow, let us imagine a place where the speed of light is not its true value of 300,000 kilometers per second, but something very modest: 40 kilometers per hour, say – and strictly enforced. (There are no penalties for breaking laws of Nature, because there are no crimes: Nature is self-regulating and merely arranges things so that its prohibitions are impossible to transgress.) Imagine that you are approaching the speed of light on a motor scooter. (Relativity is rich in sentences beginning ‘Imagine . . .’ Einstein called such an exercise a Gedankenexperiment, a thought experiment.) As your speed increases, you begin to see around the corners of passing objects. While you are rigidly facing forward, things that are behind you appear within your forward field of vision. Close to the speed of light, from your point of view, the world looks very odd – ultimately everything is squeezed into a tiny circular window, which stays just ahead of you. From the standpoint of a stationary observer, light reflected off you is reddened as you depart and blued as you return. If you travel toward the observer at almost the speed of light, you will become enveloped in an eerie chromatic radiance: your usually invisible infrared emission will be shifted to the shorter visible wavelengths. You become compressed in the direction of motion, your mass increases, and time, as you experience it, slows down, a breathtaking consequence of traveling close to the speed of light called time dilation. But from the standpoint of an observer moving with you – perhaps the scooter has a second seat – none of these effects occur.
These peculiar and at first perplexing predictions of special relativity are true in the deepest sense that anything in science is true. They depend on your relative motion. But they are real, not optical illusions. They can be demonstrated by simple mathematics, mainly first-year algebra and therefore understandable to any educated person. They are also consistent with many experiments. Very accurate clocks carried in airplanes slow down a little compared to stationary clocks. Nuclear accelerators are designed to allow for the increase of mass with increasing speed; if they were not designed in this way, accelerated particles would all smash into the walls of the apparatus, and there would be little to do in experimental nuclear physics. A speed is a distance divided by a time. Since near the velocity of light we cannot simply add speeds, as we are used to doing in the workaday world, the familiar notions of absolute space and absolute time – independent of your relative motion – must give way. That is why you shrink. That is the reason for time dilation.