Ken G

2006-Aug-13, 09:43 PM

I'm posting this in Q&A because there seem to be a lot of questions about it, and there are some oft-repeated answers that don't really hit the mark, which may contribute to why the questions are heard so often! The usual statement is that macro particles, like cannon balls, obey particle mechanics, which is basically Newton's laws applied to trajectories, while micro particles, like electrons, sometimes do this, and sometimes obey wave mechanics. Hence the latter are said to exhibit "wave/particle duality".

This is a very confusing pedagogy, because it seems to arbitrarily insert different behaviors for different objects, based on their masses. But what about a particle the size of an atom with the mass of a cannon ball? Is that going to exhibit "duality"?

I feel the best answer to this can be seen using a mathematical analogy. Have you ever heard of "calculus/arithmetic duality"? Probably not, it wouldn't have the same mystique as "wave/particle duality". But it's the same thing. Here's what I mean. Let's say I told you that I travel at 50 miles per hour in a straight line, for an hour. How far did I go? As a calculus problem, this goes: the distance is the integral of v*dt over an hour of time. Since v=50 is constant, it comes out of the integral, dt integrates to t, and we get distance=50*t. Now I'll bet you were way ahead of me-- you used arithmetic to accomplish the same result. You see, that's "calculus/arithmetic duality". It was "really" a calculus problem, but you were able to solve it using arithmetic instead. Get it? So it is with wave/particle duality-- all things obey wave mechanics, you just don't always need to know this. It's not so mysterious when you look at it this way, which makes it a better pedagogy, I claim.

This is a very confusing pedagogy, because it seems to arbitrarily insert different behaviors for different objects, based on their masses. But what about a particle the size of an atom with the mass of a cannon ball? Is that going to exhibit "duality"?

I feel the best answer to this can be seen using a mathematical analogy. Have you ever heard of "calculus/arithmetic duality"? Probably not, it wouldn't have the same mystique as "wave/particle duality". But it's the same thing. Here's what I mean. Let's say I told you that I travel at 50 miles per hour in a straight line, for an hour. How far did I go? As a calculus problem, this goes: the distance is the integral of v*dt over an hour of time. Since v=50 is constant, it comes out of the integral, dt integrates to t, and we get distance=50*t. Now I'll bet you were way ahead of me-- you used arithmetic to accomplish the same result. You see, that's "calculus/arithmetic duality". It was "really" a calculus problem, but you were able to solve it using arithmetic instead. Get it? So it is with wave/particle duality-- all things obey wave mechanics, you just don't always need to know this. It's not so mysterious when you look at it this way, which makes it a better pedagogy, I claim.