Index header
Intermediate Membranes

And if we were to put Quantum Mechanics and Relativity together ?

So, general relativity tells us that space and time may be curved, and that curvature causes what we see as gravity. And quantum mechanics tells us, among other things, that something may exist in an indefinite state, and that these uncertainties become very important when we try to precisely measure very small objects.

What then are space and time like on a very very tiny scale? Nobody knows for sure, but it seems fairly certain that a theory describing the nature of space-time on a small scale must have some of the important aspects of quantum mechanics. It might be that the exact shape of space and time is rather indefinite on some small scale. Just like we sometimes have to think of an electron as a cloud-like entity that exists everywhere that an electron particle might exist, perhaps we have to think of space and time on some small scale as existing in a fuzzy state that is a combination of all the possible ways that might be curved. Such a theory is called a theory of quantum gravity.

What does this mean? When we talked about the way large masses curve space and time, we used the analogy of a bowling ball sitting on a mattress. In studies of quantum gravity we often continue to use the analogy of a two dimensional universe. In this case the advantage is not just that its easier to envision, but also its easier to perform some of the calculations. We can still learn useful things, though.

Lets suppose we want to look very closely at the small scale structure of a two dimensional universe. From far away the universe may look pretty flat, like the surface of a mattress. Possibly there are dimples here and there where large masses are. Now suppose we can zoom in and look very closely at the surface. At this level the effects of quantum mechanics should be very important. The surface does not seem as crisp and well defined anymore, instead, it is a blur of a surface, a combination or superposition of all possible surfaces. Every way that one can imagine to distort a surface is represented in this blur. There is an almost infinite number of them. Some are wild jungles of undulations with tongues of the universe's `fabric' stretched and twisted far from what would be a smooth surface. Perhaps there are even some with loops of the surface pulled out like a handle or a stone arch one might see in the southwestern United States. A few are relatively flat. No one of them alone is space-time, but all of these surfaces together are.

Why do we know so little about quantum gravity? It is because of the incredibly small size of the fluctuations. It is expected that they are about

0.0000000000000000000000000000000001
of a meter in size. That's SMALL! This length is called the Planck Length. How small is that? Lets imagine we had a very special imaginary meter stick. On it we have marked not just centimeters and millimeters but in very, very, very tiny writing, much too small to see, are lines marking off one Planck Length, two Planck Lengths, etc. Now suppose we are able to stretch the whole stick proportionally, markings and all, so it is the size of the Milky Way galaxy (a distance that it takes light 100,000 years to travel.) Even after all this stretching the lines that separated the Planck Lengths are still about 1/100 the diameter of a hydrogen atom apart.

This is far too small to see with any microscope. In fact no one has come up with any type of experiment to test the nature of space on such a small scale So how can we study such a universe? One answer is by using computer simulations.

Studying Quantum Gravity with a Computer