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).

- Classically, that is, in our
*macroscopic world*, I could, in principle, measure the position and momentum of the object to infinite precision (more or less). There is really no question about a particle's position and momentum. - In the
*Quantum Mechanical world*, the idea that we can locate objects exactly breaks down. Let me state this idea more precisely. 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. There would be an*uncertainty*associated with each measurement that I could never get rid of, even in a perfect experiment!!! The size of the uncertainties are not independent; they are related asd *p*x d*x*> h / (2 x pi) = Planck's constant / (2 x pi)The preceding is a statement of the

*Heisenberg Uncertainty Principle*. A consequence of the*Uncertainty Principle*is that if an object's position*x*is defined precisely then the momentum of the object will be only weakly constrained, and*vice versa*. One cannot simultaneously find both the position and momentum of an object to arbitrary accuracy.

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 could predict the
path a particle will follow with 100 % certainty.

A consequence of the *Quantum 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 has interesting consequences for nuclear fusion in stars.