Wonders of the Universe - Brian Cox [79]
The complicated bit about Einstein’s Theory of General Relativity is that the surface we need to think about, spacetime, is not two-dimensional but four-dimensional. It is a mixture of the familiar three dimensions of space, plus an additional dimension of time mixed in. It will take us too far from our story to explore spacetime in detail, but it was found to be necessary by Einstein and others at the turn of the twentieth century to explain, in particular, the behaviour of light and the form of Maxwell’s equations that we met in Chapter 1. Suffice to say that the surface of our universe, on which we all live our lives, is four-dimensional. What Einstein showed is that the presence of matter and energy – in the form of stars, planets and moons– curves the surface of spacetime, distorting it into hills and valleys. His equations describe exactly what shape spacetime should be around any particular object, such as the Sun, for example, and they also describe how things move over the curved surface. And here is the key point: just like our two-dimensional friends, things move in straight lines; but just like our two-dimensional friends, this isn’t what it looks like if you don’t know that spacetime is curved. When you’re moving across the curved surface, it appears that a force is acting on you, distorting your path. One of the first things Einstein did with his new, geometric theory of gravity was to calculate what Mercury’s straight-line path through the curved spacetime around the Sun would look like to us, trapped on the surface of spacetime. To his delight, he found that Mercury would orbit the Sun, and in precisely the way that had been observed over the centuries of transit observations. Where Newton failed, Einstein succeeded.
Einstein had found a completely geometrical way of describing the force of gravity, and it is quite wonderfully elegant. Not only does it predict the orbit of Mercury, but it also provides a very appealing explanation for the equivalence principle. Why do all objects fall at the same rate in a gravitational field, irrespective of their mass or composition? Because the path they take has nothing to do with them at all – they are simply following straight-line paths through the curved spacetime.
Perhaps the most startling demonstration of this is the bending of light by gravity. Light has no mass, and so in Newton’s theory it shouldn’t be affected by gravity at all. However, according to Einstein’s theory, it doesn’t matter that it has no mass, it will still be following a straight line through the curved spacetime, so it will appear to follow exactly the same path as everything else. Let’s do a thought experiment to see how strange this is. Stand on the ground (on a very, very big planet – I’ll explain why I said this in a moment!) with a rock in one hand and a laser beam in the other. Point the laser beam horizontally, drop the rock and fire the laser. Which one hits the ground first? The answer is that they both hit the ground at the same time, because they both move through the same curved space. Light falls at the same rate in a gravitational field as everything else. Now, there is a caveat here. Why did I say a very very big planet? Because light travels at almost 300,000 kilometres per second, so if the rock takes a second to hit the ground, so will the light. But it will have flown 300,000 kilometres in the horizontal direction by the time it reaches the ground, and on Earth that would mean the surface of the planet had long since curved away! However, the principle still holds.
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In the language of General Relativity, we might say that the presence of Earth bends spacetime near it such that time passes more slowly than it does far away.
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As an interesting aside, what would happen if you fired the laser beam directly at the ground? Light must always travel at the same speed, it can’t speed up, so it will travel towards the ground at