Motion | Pages 22-23 | See Linked Version

Einstein asserted that the speed of light--186,282 miles per second--remains constant and can never be exceeded.

This theory has peculiar consequences. For example, if that unicyclist could pedal past you at 87 percent the speed of light, you would see him and his unicycle shrink to half their usual lengths. You would see his clock run at half the speed as your own. Further, his mass would be twice as large as when he stands still next to you. These bizarre relativistic effects are important in particle colliders, where physicists boost electrons and protons near the speed of light. They also dictate the behaviors of quasars and other superenergetic objects in the universe, which can expel matter at extremely high speeds.

On Earth special relativity rarely comes into play. Newton's laws suffice for most of our day-to-day activities. Among the exceptions are satellites that use exquisitely accurate clocks, such as those in the Global Positioning System. These satellites orbit the planet at thousands of miles per hour. Their clocks slow down a tiny bit relative to those on the ground, just enough to ruin the precision of their measurements if we ignore the effect.

The constant speed of light has another profound implication for our studies of the universe. On Earth we don't notice a delay as light travels from an object to our eyes. After all, a light beam can dash around the globe nearly eight times a second. But light's fixed speed begins to matter away from our planet. Light from the Sun takes about eight minutes to get here. We never see the Sun as it is now, only as it was eight minutes ago. Similarly, we see the next nearest star, Proxima Centauri, as it was 4.1 years ago--the amount of time its light takes to reach us. We see the nearest big galaxy, Andromeda, as it existed more than 2 million years ago. The light from ever more distant galaxies takes billions of years to reach us, from a time when the universe itself was still young. Indeed, our giant telescopes are the time machines into the past that Jules Verne dreamed about--with the disappointing exception that we cannot physically travel through those portals.

Newton's laws also cease to operate reliably at submicroscopic scales. In the world of Galileo and Newton, one object orbiting another behaves much like a cat on a ramp. It can walk up or down the ramp, pausing at any level it likes. But when physicists early in this century scrutinized the behaviors of atoms, they realized that only certain motions and energies are allowed. All others are forbidden. In this world, an electron orbiting the nucleus of an atom behaves more like a kangaroo on a (continued)

The Relativity of Time, Mass, and Length

Most aspects of the physical world can be described in terms of three quantities that we would normally consider easily measured: time, distance, and mass. According to Einstein's relativity theory, however, most measurements are not absolute. Contrary to ordinary experience, they depend on the frame of reference of whoever is doing the measuring--that is, on the location and motions of the observer. This is especially true at speeds approaching the speed of light.

The first assumption of special relativity theory is that observers inside a uniformly moving frame of reference will perceive physical events within their frame to be unaffected by its motion. But when observers look outside their own frame, its motion will affect what they see. This is the direct result of the theory's second assumption: that the speed of light is constant for all observers in uniform motion.

Observers moving at different speeds relative to a light source thus will receive the light at different times and will be unable to agree that given events occur simultaneously. Without simultaneity we can make no comparison against a standard, such as determining the accuracy of clocks or matching both ends of a train to a length of track.


An observer aboard a train with a tall clocklike device that sends pulses of light from the top to the bottom of the clock face sees the light pulse at the same rate whether the train is moving or not (right,top). But to an observer standing at the station, the moving train's light clock runs slow. Movement causes each light pulse to travel in the direction of motion as well as from top to bottom, resulting in a long diagonal path (right, bottom). Since the speed of light is fixed, the light pulse takes longer to reach the end of its path. The faster the train, the longer the path and slower the clock.


According to relativity theory, an object's mass (indicated here by degree of opacity) increases with its velocity, a phenomenon that has been verified in particle accelerators. The mass of a vehicle traveling at half the speed of light--nearly 20,000 times the normal orbiting velocity of the Space Shuttle--increases only 15 percent. (For simplicity, other relativistic effects are not shown here.) At 70 percent of the speed of light, the mass increases 40 percent. But at the speed of light an object's mass would be infinite.