Analogies for the Behavior of the Wave Function

Question

In an overview of Quantum Field Theory, I recently heard the behavior of an elementary particle compared to that of a plucked (bowed) string. Although the stable states of excitation of the string are limited (quantized) by its boundary conditions, the final waveform is actually quite complicated, representing as it does a superposition of each state, with their respective contributions determined by amplitude (i.e., fundamental and harmonics). Likewise in this view, the final behavior of the particle is informed by all the potential measurement results.

This differs from conventional descriptions of quantum events involving the realization of a single alternative and a corresponding collapse of the wave function. Unless you consider the trivial case of the outcome as a superposition of alternatives with all but one of them assigned a probability of 0 – in a sense a fundamental with multiple zero-amplitude harmonics. Are these two descriptions reconcilable? Or is the plucked string analogy simply inappropriate?

Answer 1

The plucked string is an oversimplified analogy to describe how what we perceive as particles are actually excitations of respective particle fields. The fields exist everywhere, and don't need to be in an excited state across all space, so in a specified space, if we were to "pluck" (excite) a particle field, it would result in what we observe as a particle.

An electron in a 1D quantum well would, by QFT, be an excitation in the electron field, with wavefunction $\Psi$ dependent on the boundaries of the well.

Take the Higgs Field as an example. Within a particle accelerator, a particle collided resulting in enough energy to excite the Higgs Field, which we observed as a Higgs Boson particle.

The plucked string is more a way to describe the existence of what we observe as a particle, and the behavior of a particle field. Not so much the resulting waveform of the particle itself. In other words, the analogy serves a purpose, but not one as deep as you are interpreting it.