Warped imagination

29th December 2000 at 00:00
Is Einstein's theory of general relativity too hard for school? David Bodanis says the fundamental ideas can easily be illustrated in the classroom

When Albert Einstein was an old man, world-famous and living in Princeton, he was asked why he had been so successful: what was it that had allowed him to see so much further than anyone else? He replied that it was the attitudes he had carried over from childhood. Most schoolchildren ask questions about why things fall, or what time means, but after a while they see these as childish topics and turn away from them, entering the whirl of exams and going out and other ordinary concerns.

Einstein was different. As a young man he was romantically handsome, so social life was easy; although he could be lazy as a student, when he wished to concentrate he could do well, so exams were not a problem either. This meant he could carry on with the ordinary concerns of his peers, yet still, privately, keep on concentrating, for year after year, on the fundamental questions that perplexed him so much.

For a long time most people were convinced he would be a failure - there was the famous case of his secondary school Greek teacher, Joseph Degenhart, who declared to Einstein that "nothing will ever become of you". In his early twenties, even his own family began to question whether he would get anywhere. His university classmates were beginning to publish research papers. But Einstein? He was still just thinking; still trying to work it all out.

And then, in 1905 - when he was 26 years old - it all finally began to come together. Einstein began a 20-year period of creativity which is perhaps comparable only to the key creative periods of Shakespeare or Da Vinci. Of his great works, the finest is the theory of general relativity, which he first published in its entirety in 1915. It is a theory that explains how the universe is put together, and gives us powerful predictions about what will happen in our future.

The fundamental idea of general relativity can be illustrated by asking students to imagine a very taut bed sheet. If you place a small coin at one point on the sheet, it will bend downwards slightly. If you place a heavy paperweight at some other point on the sheet, it will sag down even more. To Einstein, that was how the gravitational effects around the planets in our solar system were built up. The Sun is a huge and massive object, and so bends or curves the space around it a lot - it is like the heavy paperweight on the taut sheet. The Earth is a much less massive object, and so only curves the space around it a little - it is like the small coin on the sheet. (See Figure 1.) Think what that means to a comet, spaceship or other object whirling into our solar system. If it passes very close to the Earth it will start spiralling down the indent our planet makes and eventually hit us - that is what happened with the asteroid or comet that wiped out the dinosaurs. But if an incoming object is further away it will not be affected by the Earth's gravitational pull - because our planet is so small there is no great bending of space around us.

The Sun, by contrast, is far more massive, and a great many comets and other free-floting debris are constantly pulled in. The Earth itself skims along the rim of the indent which the Sun makes in space - that is why we orbit around it. The more massive and dense an object is, the more powerfully it will twist or "warp" the space around it. That is why huge objects have huge gravitational effects. But Einstein went even further. It was not accurate merely to say that the Sun made space bend around it. Rather, Einstein realised, any object makes both space and time bend around it. This sounds preposterous - how can ordinary time become "bent"?

It is hard to make sense of this in ordinary language, but just take it on trust at this point: imagine that instead of time being a smooth flowing thing, it can operate in a "denser" or "thinner" manner. Near a huge heavy object that gives a huge warp or bend to everything around it, time really will appear "dense", and objects will seem to be in slow motion as they travel near it. Near a lighter object, time will be less disturbed, and there will be much less slowing down. One of the densest places in our universe is near the edge of a black hole. A black hole is where a star has collapsed in on itself, leaving a huge gravitational "warp" of the space and time around it. In the centre of our galaxy there is a huge black hole, and it is growing steadily larger as it slowly absorbs - or "eats" - the stars nearest to it.

In about five billion years, our Sun will have used up so much fuel that it will be much less massive, and so the warp or bend it produces in the space around it will be less. The "dip" which the Earth currently glides along in orbit will become less, and as a result our planet will fly free, heading off into the blackness of space.

It seems likely that in time we will get closer and closer to the waiting black hole. But for any beings still alive on our planet there will no sudden sensation of being sucked in because it is not just space that gets bent around a dense object - it is time as well. As the Earth gets close to that black hole, time will begin to go slower and slower for us. The moment we spend perched on its edge will seem to take forever.

Again, this truly sounds like science fiction, but there is proof. Above us there is a system of gliding satellites which send signals down to our planet. It is part of the Global Positioning System and everyone from air traffic controllers to hikers and ordinary London taxicabs use it for navigation. But without taking into account the way time slows down around massive objects those GPS signals would gradually go out of sync. Instead, circuits inside all our handheld or car-mounted GPS receivers constantly correct for the way even the Earth's slight gravitation warps time around our planet.

Those corrections are in exact accord with the equations Einstein worked out in 1915 - which means that when you hold a GPS receiver, you are actually holding a device that follows the same logical processes which once operated in Einstein's brain.

David Bodanis ithe author of'E=mc2: A Biography of the World's Most Famous Equation'. (Macmillan, pound;14.99).He has addressed students and teachers at many schools. Contact: DavidBodanis@compuserve.com

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