Saturday, October 15, 2011
There is nice an argument that combines general relativity and quantum mechanics to show that our ideas of space and time start to break apart at the Planck scale (1E-35 meter). Imagine I try to constrain anything (say an elementary particle) inside a box of size 1E-35m x 1E-35m x 1E-35m (a *very* small box I will call a Planck box).
According to quantum mechanics, if we want to contain anything inside a very tiny region of space, then its momentum (mass x velocity) becomes highly uncertain. The more we try to constrain space the more uncertain the momentum becomes (the Heisenberg uncertainty principle). This means that if I would actually measure the momentum, then the outcome could be extremely large. Since momentum carries energy the energy could become so large that, just like stars, they can form black holes. This happens exactly when the box is a Planck box.
What does this say? To me it seems a really nice argument to show that at this scale the concept of space starts to break down. We can simply not contain anything inside a Planck box, for if we do, nature closes the box and we will not be able to peek inside it! A black hole is in a real sense the boundary of the universe, so if we try to look at scales smaller than the Planck scale we will be looking at the end of the universe. (As a kid I always tried to imagine how the end of the universe looked like -- maybe its all around us).
Roger Penrose has introduced a name for this trick that nature plays with us: "cosmic censorship". This principle says that anywhere where there are singularities in our theories a horizon will form around it so that we may not see it! Maybe mother nature doesn't want us to see something :-)