You want to understand the theory of relativity? Simple. Nothing to it.
So we were told.
Forget all those legends about how only 12 people in the world understand Einstein. Today, relativity is routinely taught to college freshmen. It is thoroughly in the mainstream of physics.
After all, the man thought it up in 1905, the special theory, that is, and the general theory in 1915, which is still years before most of us were born.
We attended a recent Smithsonian Associates lecture on the subject by James Trefil, a professor of physics and the philosophy of science who came to us by way of Oxford, Stanford and George Mason University.
There were 145 of us packed into a room three stories underground in the new Smithsonian building. Mostly between 30 and 60, about even for men and women. Everybody had note pads.
"Relativity is as well verified as any other theory. But," Trefil warned, "it violates your intuition."
With that, he set the stage: Newton's clocklike universe, which explained nearly all, but not all, the visible phenomena of the solar system, had come into conflict with the 19th-century ideas of James Clerk Maxwell on magnetism. Magnets, for a starter, defied gravity. With a magnet you could pull a chunk of iron up off the ground and hold it in the air forever, if it was important to you.
Maxwell's four laws attempted to explain electricity and magnetism, showing that all the various waves in the electromagnetic spectrum -- X-rays, radio waves and such -- travel at the speed of light. And it was over what happens at the speed of light that the trouble came.
"Newton's mechanics say that the laws of nature are independent of the observer, of any frame of reference," Trefil said. Thus, if you drop a ball inside a moving car, you see it fall straight down, but someone standing on the sidewalk sees it fall in a curve. Yet you both agree on how long the ball took to fall, so it doesn't matter how you saw it. Newton's laws of compound motion are still being obeyed.
(Furthermore, we are all so accustomed to that visual discrepancy that we tend to subconsciously place ourselves in the position of the one in the car and don't really admit to ourselves that it seemed to curve. It's common sense at work. But as Einstein once observed, common sense is nothing but a bunch of prejudices learned from childhood.)
Another point: If you stand on a moving truck and throw a ball forward, the ball goes at the speed of the truck plus the velocity you gave it. And if you throw the ball out the back, its net speed is the velocity you gave it minus the truck's speed. According to Newton.
The difficulty comes when one includes the speed of light as a factor. For Maxwell's laws showed that the speed of light is always the same. That is, if you shoot a beam of light forward from a truck or even a very fast rocket, its speed is not speed-of-light plus speed-of-rocket. Light beamed out the rear of the rocket would travel just as fast.
Einstein's greatness, in part, was that he realized that this conflict was not just a minor inconsistency, but something basic.
Some other theorists assumed it was simply a matter of inadequate measurement, that the speed of light changed with your velocity but too little to be perceived.
Wrong. Astronomers found a double star, two stars revolving around each other horizontally in relation to the Earth, and measured the speed of the light given off one of them as it approached and again as it receded. It was the same.
Some thought the hypothetical ether believed to inhabit space must have an effect. But the famous Michelson-Morley experiment of 1881 indicated, at the very least, that ether couldn't be measured. To Einstein it indicated something far more important: that ether didn't exist.
Our evening lecture ended there. The rest of the explanation would take up the entire next day.
And a good deal of that went into our discussion of the light-clock experiment. If we could grasp that truly, Trefil said, we were halfway home. With amazing patience, he took questions on it for two hours.
Here is the experiment: The light-clock consists of a flashbulb, a photoelectric cell set next to it, and a mirror placed a measured distance directly above. The flash travels to the mirror and back and sets off the photoelectric cell, which records the time elapsed.
Incidentally, modern techniques permit measurement of light over astonishingly small distances. It travels 186,284 miles in one second, which is just a few feet in a nanosecond. And we can measure the nanosecond, a billionth of a second.
Now suppose you have two photoelectric cells, one stationary, one moving away from it horizontally. The light beam goes up to the mirror and back to the first cell as usual. The same beam is recorded by the second cell too. But it has to go slightly farther, on a diagonal (describing an inverted V), since the second cell has moved. Thus the second clock appears to get the signal slightly later.
To you, that is, standing beside the first clock. To someone moving along with the second clock, the first clock appears to be a hair faster.
"And all descriptions," Trefil said slowly, "are equally valid."
The questions began. How far does the light really travel? Which is the real clock? Reality, he replied, is nothing more than what the observer observes, so both are right. People seemed to have trouble reconciling the fact that the speed of light is absolute -- that nothing can go faster -- and yet is a measurable quantity.
Trefil summed up: "It's not events that you see; it's the laws you deduce from events. We all exist in a frame of reference, and we tend to assume the Earth's frame of reference as 'real.' "
As Lincoln Barnett put it in his wonderfully readable classic "The Universe and Dr. Einstein," this sort of experiment demonstrates "one of the subtlest and most difficult concepts in Einstein's philosophy: the relativity of simultaneity. It shows that man cannot assume that his subjective sense of 'now' applies to all parts of the universe.
"For, Einstein points out, 'every reference body (or coordinate system) has its own particular time; unless we are told the reference body to which the statement of time refers, there is no meaning in a statement of the time of an event.' The fallacy in the old principle of the addition of velocities lies therefore in its tacit assumption that the duration of an event is independent of the state of motion of the system of reference."
Interestingly, Trefil pointed out, the Einstein theory was published about the time that Sigmund Freud was developing psychoanalysis. Publicity and misinformation about both disciplines gave rise to popular notions that "everything is relative," possibly even contributing to the hedonism of the '20s.
He told of Einstein's initial inspiration about relativity as he rode a streetcar in Bern, Switzerland: Approaching a street clock, he reasoned that if he were to approach it at the speed of light, the clock would seem to stop.
And Trefil reminded us that this is no mere hypothetical philosophy conundrum like Plato's Cave. It really happens. In 1971 some scientists took a set of extremely accurate atomic clocks around the world on jet airliners (Pan Am, if you must know). They compared the traveling clocks with others that had stayed at home -- and found them slow by exactly the amount predicted.
Science fiction fans quickly make the jump from this modest discrepancy to a spaceship pilot who comes home from rushing about at near the speed of light to find everyone he knew on Earth doddering with age.
In fact, Trefil said, if you rushed about at 60 miles an hour for the lifetime of the universe, your life would be slowed one second. "This is why," he added, "it took us so long to find."
Of course, with space travel in the neighborhood of 25,000 miles per hour, the effects would be far more noticeable.
The Dutch physicist Hendrik Lorentz worked out the Lorentz Transformation, formulas that "preserve the velocity of light as a universal constant, but modify all measurements of time and distance according to the velocity of each system of reference," as Barnett wrote. Trefil scribbled the fairly simple formulas on the board for us only after much reassurance that he didn't intend to frighten us. It was clear that he could easily have covered the whole wall with further figuring, and we could see why they say mathematical formulas are the natural language of physics.
From this simple proposition, the other wild-sounding conclusions that to this day make relativity a conversation stopper can be projected: As an object approaches the speed of light, not only does time on it go more slowly, but also it gets heavier, and it shrinks in the direction of travel, seeming to telescope into its front end.
As Trefil put it, "Length shrinks, time expands, mass gets heavier." No wonder it upset people. No wonder Stalin banned it in the Soviet Union.
Ironically, Einstein originally called the theory "invariance," because the speed of light is invariant no matter what the frame of reference.
We were shown a 1962 film in which physicists James Smith and David Frisch demonstrate the dilation of time by measuring the speed of mu-meson particles hurtling to Earth, from the reference point of Earth. It was intellectually convincing, yet it seemed to leave many of us with a vaguely unreal feeling: Seeing is not necessarily believing. As Trefil had warned, the instincts of our senses were being violated. We had to remind ourselves that objects moving at the speed of light are not within our normal everyday experience.
All this, Trefil said, was the special theory of relativity. Now we would consider the general theory, which is concerned with the phenomenon of acceleration.
Imagine you are standing on the equator, he said, and your partner throws a ball to you from the North Pole. While the ball is in the air, the Earth turns, so you see the ball swerve to the west of you in a great curve. You think: Ah, the Coriolis Effect, which results from the Earth's turning, rather similar to centrifugal force. But to a witness on a hovering spaceship, the ball appears to fly due south, perfectly straight.
In the same way, when a speeding car misses a sharp turn on a mountain road, just before flying off on a tangent the driver will feel centrifugal force, but the airborne witness will just see the car run straight off the edge and will not perceive any force at work.
We are talking about "fictitious forces," so called, Trefil said, because their perception depends entirely on one's point of view.
The main thrust of the general theory is that gravity itself is a fictitious force.
"Einstein says that mass warps space, making the effect of gravity." Gravity, Trefil speculated, may be just a form of acceleration. If you stand on a spaceship, weightless in space, and the ship then accelerates upward, the downward pull will feel exactly like the pull of gravity, but it will be simply the acceleration.
Somebody took him up on "space warps," a term dear to science fiction, and he was ready with a cocktail napkin, upon which he drew two separate spots. In a two-dimensional world, he said, you get from one spot to the other by traveling across the napkin surface.
But look. You can fold the napkin to make the spots overlap, so your traveler gets from here to there instantaneously. Space warp.
From there it was easy to move on to a picture of space as a curved surface, like the outside of a balloon, and the stars as indentations. Imagine a baseball thrown at a gently curving badminton net, and think of the indentation it makes in the grid of strings that forms the net. It is, he said, a geometric rather than a dynamic concept of space-time. Comets, for instance: Newton talked of the forces that moved comets; Einstein said no, it wasn't force but geometric warping.
By this time relevant questions had all but ceased, as the information soared beyond our perceptions and pushed at the outer edges of our imaginations.
"There are only three kinds of tests so far of general relativity," Trefil said, and Einstein devised them all. "The big one was bending light."
He told the famous story of how Einstein predicted that light from a star would bend a specified amount as it passed through the sun's gravitational field. (Except that he didn't say it was bent by gravity but that it followed the indentation the sun makes in the space-time grid.) When he was proved bang-on accurate during a 1919 eclipse, he was suddenly a world celebrity.
The cute-little-physicist with his wild white hair and twinkly eyes was to captivate the public, who idolized and patronized him and joked about how nobody understood him for almost a generation -- until Aug. 6, 1945, to be exact. Once, during a hysterical reception in Hollywood, when cheering throngs surrounded him and starlets kissed him and cameramen made movies of him, Einstein turned to Charlie Chaplin and asked, "What does it mean?"
Chaplin replied quietly, "Nothing."
Someone asked Trefil about E=MC . He had forgotten to mention it. It belongs in the special theory, of course, and its assertion that energy (E) and mass (M) are interchangeable at the speed of light (C) squared is confirmed daily in laboratories where particles are routinely produced from enormous electric charges.
Max Planck and the quantum theory were never mentioned at all. Perhaps it was just as well.
We moved on through other tests for the general theory and discussed competing concepts of the cosmos, neutron stars and black holes, which can only be explained with something like Einstein's theories. We touched on the new thinking that has gone far, but not all that far, beyond the old master, even to the Theory of Everything, which seeks to explain all phenomena with a single equation.
At the end, Trefil got a big hand. We thought we had a handle on it now, especially while we were listening to him and he was putting things on the blackboard. As soon as we had walked out of the place, it all began to get a little fuzzy.
But for a few minutes there we really did understand relativity, kind of.