w00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000t! (Just in case that fails miserably, here's a big picture!)

__LOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOL__

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 as d

*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.
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 can 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 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.

Well, it's still not as wide as you.

*"HEHE"*

Seriously, Mr. Matt, you are the most random person *ever*.

Thats why he's an advanced member :p

Matt is randomness incarnate.

*RANDOM!!!*

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