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 (it can also be thought of in terms of energy and time).

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 its velocity (more precisely, its 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. Consequently, I can tell with infinite precision where that
particle will at the next instant in time.

In the Quantum Mechanical world,
the idea that we can know things exactly breaks down. More precisely, suppose a
particle has momemtum p and a position x. In a Quantum Mechanical world, I
would not be able simultaneously to measure both p and x precisely. There is an
uncertainty associated with this pair of measurements, e.g., there is some dp
and dx, which I can never get rid of even in a perfect experiment!!!.