DarwinX wrote:You can't curve space because space is 3 dimensional.
Yes, you can curve space. But such curving is extremely difficult to convey in a 2 or 3 dimensional image. We humans like to picture concepts in our minds using things with which we are familiar, and we are unfamiliar, and thus unable to conceive of, what a curved 3 dimensional space looks like.
But perhaps it's easier to envision if you think of it in a slightly different way. Richard Feynman gave a very simple explanation as to why light is seen to travel in a straight line. If you envision light as traveling as waves, (
these can be waves in a quantum field of some type, or purely mathematical constructs, if you like). But a peculiar aspect of waves is that they interfere, either constructively, or destructively with each other. Feynman explained that if you plot all the paths that a photon (
a wave) can take to get from point A to point B, and you sum them all up, such that some waves constructively interfere and some waves destructively interfere, then the only paths that will avoid destructive interference are the waves that travel in a straight line. A simple way to think of this is, that for every path that strays either to the left or to the right, there is a mirror image of that path that will cancel it out. This is true for every path, except for the straight one. For the straight path, there is no other path that can cancel it out. Thus when you sum up all the possible paths, the only ones that survive are the straight ones. And that's why you always see light traveling in a straight line.
However, this isn't always true, or at least it doesn't appear to be. If you have ever experienced a heat mirage, a phenomena where a road on a hot day will give the illusion of water. This is caused by the fact that the air close to the road is hotter than the air above, and waves travel faster through hot air than they do through cool air. So light from just the right angle will find that the quickest path from point A to point B is to bend slightly, and travel through the hot air, rather than through the denser cool air. Thus what you're actually seeing is the reflection of the sky, caused by the bending of the light as it travels through warmer and cooler air. But why does this happen if light always travels in a straight line? It happens because the shortest path isn't just a matter of space, but also a matter of time. Generally the straight path through space will also be the quickest path through time, but not always, and as it turns out, the key to avoiding destructive interference is to take the shortest path, not just through space, but also through time. The shortest path through spacetime isn't always the straight one. It there are variations in the space between point A and point B, then the "shortest" path may indeed be the curved one. With a heat mirage, the path of the light curves, because light travels faster through hot air, than it does through cool air. But it gives us a simple proof, that the path of a light wave can curve if there are variations in the possible paths.
Okay, so the heat mirage example shows us that light waves can travel in a curved line. But what does this have to do with why Einstein described gravity as a curvature in 3 dimensional space? For one simple reason....the speed of light is constant. Thus if light traveling through a vacuum takes a curved path, it can't be because it travels faster along one path than the other, as the light in the heat mirage does. In the example of a heat mirage the path of the light curves because the light travels faster through hot air, than it does through cool air. But in space, both paths are traveling through a vacuum, so the light must travel at the same speed along both paths. But if it's not the rate of speed that makes light take a curved path, then what does? The only other explanation is, that space itself is curved, such that the curved path, is the shorter path. The space around massive objects must be curved if we are to explain why the path of light in a vacuum, bends. You can alter the path of a wave by either altering the difference in space between two paths, or altering the the difference in time. In the heat mirage we alter the difference in time, but in the example of light traveling through a vacuum, we have no choice but to alter the difference in space.
If you stick strictly to QM, then the curvature in space distorts the wave function, such that one side of the wave is no longer a mirror image of the other side, then when you sum up the possible paths, the only remaining path will be a curved one, not a straight one as Feynman described. An object, say an asteroid, passing through a planet's gravitational field will experience a slightly greater distortion on the side nearer the planet, than on the side further away, and this slight difference in distortion will cause the asteroid's path to curve. In essence gravity is not really a force at all, it's merely a distortion of the space through which an object passes. An object's path curves because the probability wave defining its possible paths is distorted, making the curved path, the only possible path.
However it ends up being defined, gravity is a distortion in the wave function describing the path of an object. The cause, or mechanism of this distortion is yet to be determined.
