Relativity, Part 2

Welcome back (those who came back) for the promised look at Einstein’s general theory of relativity. I hope you remembered the billiard balls and rubber sheet…

Einstein’s special theory of relativity, which we looked at last week, states that nothing can travel faster than light. Isaac Newton’s laws of gravity, however, assumed that somehow gravitational forces act instantaneously all through space–faster than light, in other words. That conflict (plus the fact that Newton’s laws, while generally accurate, fail to account for certain movements of the planets in their orbits, among other things) led Einstein to take another look at gravity.

We’re familiar with three dimensions, height, width, and depth, but in 1907 a Russian mathematician, Hermann Minkowski, went a step farther, combining time with the three spatial dimensions and proposing that everything in the universe occurs in this four-dimensional “space-time.”

Einstein adopted that idea, then applied it to the problem of gravity that concerned him. He had the notion that this four-dimensional “space-time continuum” is curved by the presence of massive objects. He also said that all particles–and therefore all matter–travels from point to point along the shortest possible route–which, when space-time is curved, is not a straight line. The shortest route through curved space-time is also curved, which makes the particles move as if they were attracted by whatever is causing the curving.

Here’s where the rubber sheet and the billiard ball come in. Imagine a rubber sheet stretched taut. If you roll a necklace bead across the sheet, it will roll in a straight line.

Now put a billiard ball in the middle of the sheet, where it makes an indentation. If you roll the bead across the sheet again, its path will be curved by the indentation of the billiard ball. In fact, if the indentation is deep enough, and you roll the bead fast enough, the bead will circle the billiard ball until it runs out of energy and falls into the indentation.

If you think of the rubber sheet as the space-time continuum (i.e., everything), the billiard ball as the sun and the bead as the Earth, you see how Einstein’s general theory of relativity accounts for orbiting bodies.

That’s pretty easy to understand. It only gets hard to grasp when you try to get your mind around the idea of curved space-time. And there are a few other strangenesses…

For example, according to the general theory of relativity, even light is affected by gravity. Now, since in our experience light always travels in a straight line, that’s hard to fathom. Light has no weight–how can it be affected by gravity?

But in Einstein’s theory, remember, gravity is a curvature of space-time. Light passing through a strong gravitational field–a deep indentation in the rubber sheet–has to curve. And, in fact, it does. In 1919 British astronomer Arthur Eddington observed that the light from a star, passing by the sun during a total eclipse, was deflected by the sun’s gravitational force–just as Einstein had theorized.

If the gravitational force of an object is strong enough, even light falls into it, and you get a “black hole.” Since an object would have to travel faster than the speed of light to escape such a hole, and nothing can travel faster than light, nothing can ever escape from a black hole and we can never know anything about what’s happening inside a black hole. (Some people have minds very similar to that . . . )

Einstein’s theory also says that an inertial frame of reference in gravity can’t be distinguished from an accelerating frame. In other words, if you were shut in a locked, windowless cabin on a spaceship, you couldn’t tell if you were still on Earth or accelerating through space, because the force of acceleration is indistinguishable from gravity. So, vice versa, being inside a strong gravitational field is the equivalent of accelerating through space–and remember from last week, if you’re travelling faster than someone else, to that other person your clocks (and you yourself) will appear to be running slow.

Atomic clocks at high altitudes gain time over ground-based clocks because at high altitudes the pull of Earth’s gravity is slightly lessened. Since acceleration and gravity are equivalent, the clocks on the ground are accelerating relative to the airborne clocks, and therefore run slower.

Einstein’s theories are at the centre of much of modern physics, but as you can see, they can be a bit confusing. They’d probably be clearer if we all understood the mathematics involved, but most of us don’t. Instead we have to settle for words–and if a picture is worth a thousand words, an elegant equation is worth millions.

Einstein’s actual equation for general relativity, according to the encyclopaedia, “describes the curvature of space at and the energy or mass of any point in the space-time continuum” in terms of 10 functions, called “metric tensors,” that characterize the geometrical properties of space, and a second set of 10 functions (energy-stress tensors) that specify its material contents.

Not bad for a man who showed no promise in grammar school, skipped most of his classes in university (he borrowed a friend’s notes a lot), and started his career as a clerk in a Swiss patent office.

Let Einstein and his theory of relativity be an example to you: the next time you’re bored with your job, while away the hours by creating a new theory that will revolutionize physics and change the course of civilization.

It beats doodling.

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