Sunday, October 12, 2008

A Useful Antidote To Obvious Ideas And The Idea Of The Obvious

Even educated people commonly think that Einstein's theory of relativity is impossible to understand. This hasn't been helped by generations of explanations involving smoke and railway carriages, garbled versions of what started as a less than perfectly clear explanation by Einstein himself (to his credit, he tried mightily to make his theory comprehensible to non-physicists). I won't claim to have any reasonable grasp of the full "general theory" that Einstein ultimately derived. But after years of believing it was beyond my ken, I was stunned when I opened up Einstein's own 1916 book for the general reader to find just how dramatically simple the insight that motivated Einstein was, and how accessible the "special theory"--that's the one with e=mc2 is.

The version that most people get of the theory of relativity tends to stop when the eyes glaze over and before it gets to the interesting part, somewhere in the middle of a long explanation of relative motion. If the little Honda is heading toward the rickety old Eldorado with the drunk driver and both of them speedometers that reads 75 miles an hour, they're coming together at a total of 150 miles an hour. In a universe with nothing else, you can say the Honda's coming toward the Cadillac at 150 miles an hour. Or the Cadillac's coming toward the Honda at 150 miles an hour--it's the same no-fault relative kind of thing. Is there anybody who doesn't get this?

That is as far as folks get, because the only thing a longer version of this adds is confusion. The part that people don't get to is this: when the Cadillac turns on its headlights (too late, or the cars wouldn't be headed for a collision), the lights from the beams is heading away from the Cadillac at ... the speed of light. It's headed toward the Honda at the speed of light. The speed of light stays the same np matter how fast you're moving towards or away from it. If the driver of the Honda puts on the brakes, the light doesn't take any longer to get to him. All speed is relative, except that of light, which is always the same.

Obviously this is impossible, right? Or not. Up to Einstein, it seemed that way, and physicists worked hard to come up with fudge factors that would resolve the paradox and slow down or speed up light to avoid contradictions. Einstein's incredible insight was to say that instead of complicating things with additional special rules, you had to simplify. And the way to simplify things was to get rid of exactly the part that people were most certain of: the meaning of space and time. If motion is relative and the speed of light is constant, well, that meant that as you get closer to the speed of light what had to change was distance and time. And in that case, as Einstein puts it:

There is not the least incompatability between the principle of relativity and the law of propagation of light.

I think that the better you understand Einstein, the more inspiring his achievement appears. Many people could have come up with Einstein's theory before him. It is not that the math is so difficult (though that part of Einstein's book is not easy going). It is that no one could bear to accept that the constant speed of light had been proved experimentally while the most basic and immovable ideas about space and time had not. You can't get rid of the first, so you had to lose the second.

So Einstein's theory proceeds essentially not by adding a new idea, but getting rid of a very basic idea that every one up to him had taken for granted. All the rest follows from that. What Einstein does is discard the obvious in favor of the provable. In the history of intellectual life, Einstein's contribution is to demonstrate in a spectacular way not that "everything is relative" (a meaningless cliche) but that there is no idea--none--so intuitively obvious that it trumps experiment and observation.