Why do Planck units serve as limits of quantum mechanics?

Question

The Planck units are built so that they normalize several fundamental constants of physics to one. During high school, I always used to consider them mathematical toys without any obvious importance (the only two close enough to common values, the Planck mass and Planck charge, seems not to refer to anything actually important in the universe, and the other ones are far unreachable).

However, one is still hearing that quantum mechanics & general theory of relativity fail when faced with Planck length, time, temperature and the like. The ONLY reason I have ever heard is that measuring the Planck length would produce a micro black hole which would spoil it. Quite vague for me, moreover, as black holes are described by GTR and GTR is said not to work about Planck length, this is self-contradictory.

Could you please show me any further theoretical evidence of what's wrong with reaching these units?

Answer 1

The problem is that in general relativity, we assume that h-bar is so small, we don't have to worry about it (no quantum effects). In quantum mechanics (at least as far as the standard model goes), we assume that G is small, so we don't have to worry about gravity. We haven't figured out a good quantum gravity theory, though. We have a model of the quantum field theory of the graviton, and it reproduces the results of GR, but it's non-renormalizable. So it's only an effective theory that will break down at high energy. So physics as we currently know it is going to break down somewhere between the energy scales we have explored and the planck scale, where both h-bar and G are significant.



If you think that sounds somewhat vague, you're right. It is. Nobody really knows what would happen. That black hole talk is speculation. One of the great promises of string theory is that is might be able to reconcile GR with quantum field theory. We'll see.

Answer 2

I can tell you that the Planck length is beyond "the infamous boundary" and in quantum land where we cannot travel. We can't experience the quantum world in any way. Only when a particles gets kicked up to our level of reality, do we see RESULTS of quantum events. In the end, it is all speculation. The math is beautiful. So accurate in its predictions, Out to -- what 5? 6? decimal places -- but math does not tell us anything about WHY.



Look. The furthest :"down" we can see is when we use the smallest particles to create a signal when hitting what we want to "see", as in the electron scanning microscope. Electrons size allow us to see further into the microworld than photons sizes, if you'll allow the word "size" because they are smaller so there are more hits. Like white lint on a black shirt. The smallest lint is the most prevalent. This is about all I can say I hope I got you thinking you seem to be a very, very smart person.

Answer 3

It is explained in a non-technical way in this recent article:



http://arxiv.org/abs/0803.0749



You'll find the references to more rigorous arguments in this article.