If you’ve read or heard anything about quantum mechanics, you’ve heard the phrase “particle-wave duality.” The common wisdom is that this means that particles sometimes behave like waves and sometimes behave like particles. And although this is right, it’s a bit misleading. The truth is: Everything is always a wave. It’s just that waves can be made to behave like particles. To see what I mean, let’s actually show how one can make a set of waves behave like a particle. Specifically, let’s show how a set of light waves can be made to behave like a photon, a light particle.
Fourier
Mathematics / Physics / Quantum Mechanics / etc.
Resolution, Fourier Analysis, and The Heisenberg Uncertainty Principle
All the effects of nature are only mathematical results of a small number of immutable laws. ~Pierre-Simon Laplace In my discussion last time (corrections here), I discussed how there is a physical limit to how good a recording can sound, whether vinyl or digital. There is a more fundamental limit, however, that I glossed over—a limit that depends not on atoms or compression techniques, but on pure mathematics. This limit was partially discovered by Jean Baptiste Joseph Fourier, and the method we will discuss bears his name. The Superposition Principle Before we discuss Fourier’s discovery, let’s take a brief