Let's talk about quanta, baby.

Dear Integrands, you are in for a treat. I am thinking of a little series on the subject

Quantum Mechanics for Everyone

which you will enjoy.

Deep down inside, everybody has a part of themselves that wishes they understood more about basic modern physics. (I know I do, and we're all basically the same, right?) It is a noble wish--but for most of us it is only that. It is hard to learn these things on one's own. They make it hard.

There is Them, gentle Integrands, and there is me. I am here to indulge your deep, dark, frustrated desires. To whisper in your ear the equations you have longed for. Let's start off with an easy one!

Today's Topic: The Uncertainty Principle

I think you have heard of this before? It is a very deep fact that requires very little math. It is wonderful and mysterious. It looks like this:

If you inspect the formula carefully, you will be pleased to fail to discover any calculus, or matrices, or complex numbers, or really anything to put you in a distemper.

Let's read it in English, shall we?:

Delta-x times delta-p is greater than or equal to h-bar over 2.

Which means more or less this:

When you measure a quantum system, the amount of uncertainty about its position times the amount of uncertainty about its momentum must be greater than or equal to a certain number (the reduced Planck constant divided by two).

Huh?

Let's talk about this. Maybe you have questions? Good, I like answering questions.

1. A quantum system is an atom, or a subatomic particle (an electron or proton, for example). It may also be a collection of atoms or particles that are grouped together and interacting with each other. Quantum mechanics is all about the behavior of these little creatures.
2. The uncertainty of a measurement is just what it sounds like. It is the "amount of our unsureness" that our measurement was exactly right.
3. The position of a quantum system is another easy one. It is the point where the thing is located in three-dimensional space. We represent it with an ordered triple (x, y, z), which is a way to pick out a point on a 3-D graph.
4. The momentum of a quantum system is the direction it is headed, and the magnitude with which it is heading there. We represent it by a vector, which is an arrow of a certain length on a graph.
5. H-bar (the dashed 'h') is a number. It is a form of the number called "Planck's constant", which basically is the "size" of a quantum of energy.
   

Dear reader, you are on the doorstep of understanding. All that's left is to put these ideas together.



There you are, looking for your lost electron. Where could it be?, you ask. Where is it going? The uncertainty principle tells you--alas!--that you can't answer both questions very exactly at once. The product of your position-uncertainty and your momentum-uncertainty must be bigger than a certain fixed amount. If you are quite sure where your electron is, you cannot be very sure where it is going. In fact, there is no possible experiment, even with the most sensitive and exact equipment anyone could make, that can tell you both with complete accuracy at once.

Congratulations! Now you understand the Uncertainty Principle of quantum mechanics. Be sure to tell your friends!