(from University of Oregon physics.)

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). Now, let me say something strange about what happens when I try to measure its position and momentum.

• Classically, i.e., in our macroscopic world, I can measure these two quantities to infinite precision (more or less). There is really no question where something is and what its momentum is.
  
  
• In the Quantum Mechanical world, the idea that we can measure things exactly breaks down. Let me state this notion more precisely. Suppose a particle has momemtum p and a position x. In a Quantum Mechanical world, I would not be able to measure p and x precisely. There is an uncertainty associated with each measurement, e.g., there is some dp and dx, which I can never get rid of even in a perfect experiment! This is due to the fact that whenever I make a measurement, I must disturb the system. (In order for me to know something is there, I must bump into it.) The size of the uncertainties are not independent, they are related by
  
  
• dp × dx > h / (2 × pi) = Planck's constant / (2 × pi)
  
  

The preceding is a statement of The Heisenberg Uncertainty Principle. So, for example, if I measure x exactly, the uncertainty in p, dp, must be infinite in order to keep the product constant.

This uncertainty leads to many strange things. 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 say that an atom will be at some location with a 99% probability, but there will be a 1% probability it will be somewhere else (in fact, there will be a small but finite probabilty that it will 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 probably incomplete. That is, we do not know if the Universe actually behaves in a probabilistic manner (there are many possible paths a particle can follow and the observed path is chosen probabilistically) or if the Universe is deterministic in the sense that I can predict the path a particle will follow with 100% certainty.

A consequence of the Qunatum Mechanical nature of the world, is that particles can appear in places where they have no right to be (from an ordinary, common sense—classical—point of view)!

This notion has interesting consequences for nuclear fusion in stars, which we get to in our studies of the production of energy in the core of the Sun.