Question: What is the wavefunction? Is it a sea of probability of where the particle could lie? If so, are particles always found at the most probabilistic location in terms of the wavefunction? Which particles are the most predictable?

Joel Goldstein answered on 24 Feb 2023: last edited 24 Feb 2023 5:35 pm

Simple (but infuriating answer): no-one knows what the wavefunction really is, and hence what quantum mechanics really means.

In classical physics we describe a physical system as a bunch of particles, with definite position and velocity at any given time. We intuitively know what “position” and “velocity” mean, and the laws of classical physics tell us how they evolve with time.

In quantum mechanics we describe a physical system by the wavefunction, and we have equations that tell us how it evolves in time. Unfortunately, the wavefunction does not seem to have an intuitive meaning. The most we can say is that when we square the value of the wavefunction we get the probability of a particular occurence. For example, if we prepare a large number of particles with a wavefunction that is 0.6x(spin up) + 0.8x(spin down) and then measure the spin of each particle, we would find that 36% of the time it is up and 64% it is down.

Figuring out what this tells us about the nature of the universe is something that has been hotly debated for a century by physicists, philosophers and Oscar-nominated films.