Quantum Theory Cannot Hurt You_ A Guide to the Universe - Marcus Chown [62]
Eddington’s observations made Einstein’s reputation as “the man who proved Newton wrong.” But it was not the end of general relativity’s successful predictions. Newton had demonstrated theoretically that the planets orbited the Sun not in circles but in ellipses—squashed circles. He proved that this was a direct consequence of the fact that the force of gravity drops off in strength with a so-called inverse-square law. In other words, when you are twice as far away from the Sun, the force of gravity is four times as weak; three times as far away, it is nine times as weak; and so on.
Relativity changes everything. For a start, all forms of energy, not just mass-energy, generate gravity. Now gravity itself is a form of energy. Think of a warped trampoline and how much elastic energy that contains. Since gravity is a form of energy, the gravity of the Sun itself creates gravity! It’s a tiny effect and most of the Sun’s gravity still comes from its mass. Nevertheless, close in to the Sun, where gravity is strong, there is a small extra contribution from gravity itself. Consequently, any body orbiting there feels a gravitational tug greater than expected from the inverse square law.
Now—and this is the point—planets follow elliptical orbits only if they are being tugged by a force obeying an inverse-square law of force. This was Newton’s discovery. Relativity predicts that the force does not obey an inverse-square law. In fact, there are other effects that also cause a departure from Newtonian gravity, like the fact that gravity takes time to travel across space. The gravity that a moving planet feels at any moment therefore depends on its position at an earlier time and, because of this, is not directed towards the dead centre of the Sun. The upshot is that planets do not follow elliptical paths that repeat but rather elliptical paths which gradually change their orientation in space, tracing out a rosette-like pattern. This is not noticeable far from the Sun. The biggest effect is close in, where gravity is strongest.
Sure enough, there is something odd about the orbit of the innermost planet, Mercury. For some time before Einstein published his theory of gravity in 1915, astronomers had been puzzled by the fact that Mercury’s orbit gradually traces out a rosette pattern in space. Most of this effect is due to the gravitational pull of Venus and Jupiter. The odd thing, however, is that Mercury’s orbit would still be tracing out a rosette pattern even if Venus and Jupiter were not there. It is a tiny effect. Although Mercury orbits the Sun once every 88 days, a rosette is traced out only once every 3 million years. Remarkably, this is exactly what Einstein’s theory predicted. Using general relativity, he could explain every last detail of Mercury’s orbit. With yet another successful prediction under its belt, there could be no doubt that Einstein had discovered the correct theory of gravity.
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THE PECULIARITIES OF GENERAL RELATIVITY
General relativity is a fantastically elegant theory. Nevertheless, it is tremendously difficult to apply to real situations—for instance, to find the warpage of space-time caused by a given distribution of mass. The reason is that the theory is rather circular. Matter tells space-time how to warp. Then warped space-time tells matter how to move. The matter, which has just moved, tells space-time how to change its warpage. And so on, ad infinitum. There’s a kind of chicken-and-egg paradox at the heart of the theory. Physicists call it nonlinearity, and nonlinearity is a tough nut for theorists to crack.
One manifestation of nonlinearity already mentioned is the fact that gravity is a source of gravity. Well, if gravity can make more gravity, that extra