Heisenberg Uncertainty Principle

An odd aspect of Quantum Mechanics is contained in the Heisenberg Uncertainty Principle (HUP). The HUP can be stated in different ways, let me first talk in terms of momentum and position.

If there is a particle, such as an electron, moving through space, I can characterize its motion by telling you where it is (its position) and what its velocity is (more precisely, its momentum).

• In the Classical World, that is, in the macroscopic world, I could, in principle, measure the position and momentum of the object to infinite precision. There really is no question about a particle's position and momentum.

• In the Quantum Mechanical world, the idea that we can both locate and how objects move simultaneously breaks down.
  

  Suppose a particle has momemtum p and position x. In a Quantum Mechanical world, I would not be able to measure p and x precisely at the same instant. There would always be an uncertainty associated with the position and momentum that I could never get rid of, even in a perfect experiment!!! The size of the uncertainties are not independent; they are related as

  

  where the first factor in the term on the left is the uncertainty in the momentum and the second factor is the uncertainty in the position, and the little h on the right hand side is the known as the Planck constant. The above is the statement of the Heisenberg Uncertainty Principle (HUP). A consequence of the HUP is that if an object's position x is defined precisely then the momentum of the object is completely unknowable, and vice versa because the product of the two uncertainties must always produce a number greater than 0.

This uncertainty leads to some strange effects. For example, in a Quantum Mechanical world, I cannot predict where a particle will be with 100 % certainty. I can only speak in terms of probabilities. For example, I can only say that an atom will be at some location with a 99 % probability, and that there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probabilty that it may even be found across the Universe). This is strange.

We do not know if this indeterminism is actually the way the Universe works because the theory of Quantum Mechanics is incomplete. That is, we do not know:

if the Universe actually behaves in this probabilistic manner
or
if the Universe is deterministic in the sense that I could predict the path a particle follows with 100 % certainty.

A consequence of the Quantum Mechanical nature of the Universe is that particles can appear in places where they have no right to be (from ordinary, common sense [classical] points of view)! This has interesting consequences for nuclear fusion in stars.