Relativity, Part 1

If you were asked, on the spur of the moment, to state a famous scientific equation–any old equation–the odds are you’d say “E=mc2.” Almost everyone has heard of it, and most people have also heard of Einstein and the theory of relativity.

Sooner or later, then, a science columnist like myself pretty well has to tackle the subject. I don’t know whether this is sooner or later (and, as we’re about to see, those terms don’t really mean much anyway), but here goes.

E=mc2 is only a small part of the theory of relativity–which, really, is two theories, the special theory and the general theory. Einstein set forth the special theory in 1905 (at the ripe old age of 26) and the general theory 10 years later.

Relativity relates to how physical laws and measurements change when considered by observers moving at different speeds and directions. All motion is relative–even though you may be sitting absolutely still relative to your house while you read this, relative to the sun you’re whirling through space, and relative to the centre of the galaxy the sun itself is far from stationary. Isaac Newton, whose view on these matters predominated until Einstein, believed that eventually you could find a point at “absolute” rest from which to measure everything else. Einstein said, “Nope!”

The special theory of relativity rests on two basic ideas. The first is that the laws of physics are the same in all non-accelerating frames of reference. That sounds pretty complicated, but it’s not: it just means that you can walk around and drink coffee in an airplane just as though it were stationary, even though it’s really travelling several hundred kilometres an hour.

The second idea is that the speed of light is independent of the velocity of its source. If, on that same plane, travelling at 800 kilometres an hour, a passenger walks from tail to cockpit at four kilometres an hour, she’s moving 804 kilometres an hour relative to a point on the ground–her speed plus the plane’s speed. But the beam from the landing light on the nose of the plane doesn’t travel at the speed of light (290,000 kilometres per second) plus 800 kilometres an hour–it stays at 290,000 kilometres per second.

Einstein knew this as a result of an experiment conducted in 1887 by U.S. scientists Albert Michelson and Edward Morley, who demonstrated that even the Earth’s own rapid journey through space had no effect on the speed of light–not at all the result the two scientists expected or hoped for, by the way.

The fact that the speed of light is constant results in some strange effects. For example, imagine that the Millennium Falcon is moving past the Enterprise at half the speed of light. Spock on the Enterprise scans the Millennium Falcon as it passes and raises one eyebrow.

“Fascinating,” he reports to Capt. Kirk. “The metre stick in Chewbacca’s workshop is now only 87 centimetres long, according to my instruments. In fact, the whole spaceship has shortened. And, Captain, its mass has increased. Han Solo used to mass 75 kilograms; he now masses 86 kilograms. As well, the Millennium Falcon‘s dashboard clock appears to be running slow.”

The increase in mass Spock noted is whereE=mc2 comes in. Einstein showed that the relative mass increase of an object at high speed is a measure of the energy imparted to it. If additional mass is a measure of energy, then, he argued, ALL mass must have an equivalent energy value–just to be fair. Hence the famous equation: E (energy) equals m (mass) time c2 (the speed of light squared). It was this equation that suggested the possibility of nuclear bombs, which convert mass into energy. Remember just how fast light moves? Note that in Einstein’s equation you multiply that already enormous number by itself. To quote the video game ad, “Now you’re playing with power!”

But all that was still 40 years in the future when Einstein published his theory, and even without nuclear bombs, there’s quite enough in there to boggle the mind. For one thing, the speed of light becomes a galactic speed limit that nothing except light can ever reach. This seems to violate common sense. Of course you can always go faster–why not?

Well, remember that mass increases and length decreases with speed. At the speed of light, an object would have infinite mass and no length. If that weren’t bad enough, there’s the problem of time running slower on the fast-moving ship. Someone travelling at close to the speed of light for what seemed to him only a few weeks would return to Earth to find that decades or even centuries had passed.

That seems particularly hard to grasp, but two U.S. physicists confirmed it with a 1971 experiment. Joseph Carl Hafele and Richard Keating flew around the world in opposite directions, each carrying four atomic clocks which were synchronized at the start of the trip with one in Washington, D.C. At the end of the trips the clocks that travelled eastward–faster than the spin of the Earth, and therefore faster than the clock in Washington–had lost 59 billionths of a second. Those that travelled west–against the Earth’s rotation–were effectively moving slower than the clocks in Washington, and therefore gained 273 billionths of a second. (Since airlines don’t schedule flights to within billionths of a second, this effect is probably nothing to fret over.)

Einstein’s special theory of relativity has born up well in experiment after experiment–even though it sounds pretty weird. But you ain’t seen nothing yet.

Next week, we’ll take a look at the general theory of relativity. Billiard balls and rubber sheets would come in handy…

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