SciFri 5.13.05: A century of relativity

Einstein revolutionized physics 100 years ago

By Deane Morrison

Published on May 13, 2005

Picture yourself on a train going 100 mph. You're playing catch with a friend, throwing the ball at 20 mph. How fast is the ball moving when you throw in the same direction as the train's motion?

Of course, there's no answer to a question like that because all motion is relative. You would answer 20 mph. An observer watching the train go by would say 120 mph, the ball's speed relative to stationary landmarks. An observer on the sun would see the ball going at the speed of Earth's orbit plus the speed of the train plus the speed of the pitch. No one is right, and everyone is right, because it depends on your frame of reference.

If the motion in question involves light, or objects moving close to the speed of light, things get trickier. In the late 19th century, ideas about how light moves were a study in motion themselves. Earlier in the century, Scottish physicist James Clerk Maxwell had shown that light travels as a wave. German-American physicist Albert A. Michelson had measured the speed of light: 186,000 miles per second or 300 million meters per second. But if light is a wave, it must propagate through something; that is, there had to be a medium to carry light waves, just as water carries ocean waves. Physicists postulated the existence of such a medium that carried light and called it "ether." But did it really exist?

If it did, then light traveling upstream through the ether as Earth moved around the sun should be slowed, just as a motorcyclist is slowed by a "headwind" when traveling through calm air. In 1887 Michelson and E.W. Morley performed an experiment to test this hypothesis by measuring the speed of light in the direction of Earth's motion and perpendicular to it. The two scientists expected to find evidence for the existence of ether, but instead, the Michelson-Morley experiment showed that light moved at the same speed in both directions and, in fact, in all directions. The entire physics community was thrown into confusion.

"As a friend of mine said, [relativity is] not about going crooked in a straight world, but going straight in a crooked world," says Janssen.

It wasn't until 1905 that light broke through the clouds in the form of a series of papers by a clerk in the Bern, Switzerland, patent office named Albert Einstein. Einstein, who held a doctorate in physics from the Federal Polytechnic University in Zurich, had not endeared himself to his teachers by his habit of cutting classes and working on his own. A friend helped him get the job in Bern, which turned out quite well for all concerned.

"Einstein said he enjoyed this situation--there was no 'publish or perish' pressure," says Michel Janssen, an assistant professor in the University's History of Science and Technology program and a world authority on Einstein. "He could consolidate his [patent office] work in the morning and do physics the rest of the day."

The centennial of Einstein's "miracle year" is being celebrated this year to mark the publication of five seminal papers by the most famous physicist since Isaac Newton. One dealt with special relativity, and one introduced what may be the only equation that's a household word: E=mc2.

Einstein set the framework for his theories with two postulates: 1. It doesn't matter whether you're in uniform motion or at rest; the laws of physics will be the same. For example, if you're in a plane moving at constant speed, you can sip coffee as comfortably as you can in your kitchen. It's only when the plane accelerates or encounters turbulence that the laws of motion change. 2. Drawing on Maxwell's work, Einstein said the velocity of light is independent of the velocity of its source. In other words, if a car is traveling at a high speed, its headlight and taillight beams will still move at the speed of light, neither faster nor slower, in every direction.

Special relativity explains laws of motion, showing how observers in different frames of reference (either at rest or in uniform motion) will disagree about the timing and even the order of events. Consider this example, adapted from http://web.wt.net/~cbenton/relativity.htm.

Suppose Mary is watching a train go by. On the train is John. Next to him is a "light clock": two horizontal mirrors, one on the train floor and one several feet above it. The mirrors are reflecting a beam of light back and forth. Every time light makes a round trip between the mirrors it counts as one tick of the clock. John's watch is synchronized with this clock. Similarly, Mary has a light clock next to her, and her watch is synchronized with it. As the train moves, John will see no change in the synchronization of his watch with the light clock. And why should he? The light will always move the same distance between the two mirrors, and since its speed is constant, the clock will tick at the same rate.

But Mary sees John's light clock differently. After the light leaves the lower mirror, it must travel a longer distance to the upper mirror because the upper mirror has moved forward with the train (this is, of course, assuming the clocks and watches are very accurate). Similarly, when light bounces back from the upper mirror, the lower mirror will move while the light is in transit, forcing it to travel a longer distance. Since light travels at a constant speed, Mary will conclude that the time it takes to make one round trip between the mirrors--one "tick" of the light clock--will be longer. And John's watch, which is synchronized to the mirrors, will also appear slower to Mary.

Such an effect, of course, is negligible for a real train because light travels so fast. But if John were on not a train but a spaceship going close to the speed of light, this relativistic effect could be significant. Mary would see time slow down for John. She might observe him to be gone for 20 years. But because she also sees time slowing down for him, he may appear to have aged only 10 years when he returns.

This effect has actually been observed, using highly accurate atomic clocks. When two such clocks were synchronized and one was flown on a high-speed airplane, the clock that flew came back to earth running behind its stationary partner.

The crucial factor is how close to the speed of light one is going. The equations of special relativity show that the faster you go, the stronger the effects on time. And no "ether" is needed; the concept has long been abandoned.

Another part of special relativity is Einstein's famous equation, E=mc2, which tells you how much energy would be released if all the mass of an object were converted to energy. In that equation, "E" is energy, "M" is the mass of an object, given in grams or kilograms, and "C" is the speed of light in a vacuum, 300 million meters per second, and its value is unchanging. It works like this: you take an object that, because it's an object, has mass. Perhaps it's a potato weighing 50 grams. You take that 50 grams and multiply it times the speed of light squared, and the answer you get--the "E"--is the amount of energy accounted for by the mass of the potato.

For example: Multiply just one gram of that potato by the speed of light squared. That would be 1 X 900 quintillion (900 followed by 18 zeros) centimeters squared per second squared, or 900 quintillion ergs. (Forty-two billion ergs equal one food calorie.) But exploding 1,000 tons of TNT would yield only one twentieth as much energy as converting a gram of potato to pure energy. Therefore, it's apparent that mass as we know it is a very compact form of energy.

General relativity is a different theory. The basic idea of general relativity is that mass and energy curve space and time. When a body approaches a huge mass, such as a star, the body follows a curved path as it falls into the star or passes around it. It's as if space were a flat sheet of cloth held taut, and you put a bowling ball in the middle. The ball would cause a depression in the sheet, and a marble would roll toward the ball--not because the ball attracts the marble, but because it curves the space around the marble. If we're talking about a star instead of a bowling ball, the star warps space in three dimensions, so that a body approaching the star from any direction would experience the curvature of space and change its course accordingly.

Even light is affected. This curved path is actually the shortest distance the body can follow; it's like traveling on the surface of the Earth. On Earth, the shortest distance between two points is a Great Circle, such as the equator, which divides the planet in half. One cannot go from point A to point B on a "straight" line because the surface is curved.

"As a friend of mine said, it's not about going crooked in a straight world, but going straight in a crooked world," says Janssen.

General relativity has survived several tests. In perhaps the most famous, light was observed to curve as it passed around the sun during a total solar eclipse. The effect is such that a star behind the sun's right hemisphere could become visible to the right of the sun, and vice versa for a star behind the sun's left hemisphere. In other words, the stars would appear farther apart than normal.

That is what happened in a test of general relativity. During a total solar eclipse, scientists observed stars on either side of the sun to appear farther apart than they really were.

General relativity also predicts the existence of gravity waves, which are generated whenever a massive body moves. Gravity waves, which would move at the speed of light, have not yet been directly detected.

A U of M note: Janssen says that in the 1930s, Einstein, who was notorious for revising and re-revising his theories, convinced himself that there are no gravitational waves. He sent a paper on the subject to the journal Physical Review, which was based in the U of M physics department. Editor John Tate (for whom the physics building, Tate Laboratory, is named) passed the paper to a referee, one H.P. Robertson. Robertson recommended that the paper be rejected. Evidently, its arguments against the existence of gravitational waves didn't pass muster.

"Later, Robertson talked to Einstein about this work, and Einstein didn't know he was talking to his referee," says Janssen. "Einstein changed his mind [about gravitational waves]." So if gravitational waves are ever detected, credit Tate and Robertson with helping set the master straight and keeping the idea alive.