## Is Quantum Mechanics Just a Special Case of Classical Mechanics?

The bouncing is antiphase in (a) and (c) and in-phase in (b) and (d). From “Why bouncing droplets are a pretty good model of quantum mechanics.”

If you enjoyed my post from about three months ago on Hydrodynamic Quantum Analogs, or perhaps even if you didn’t, you will likely enjoy this new paper by Robert Brady and Ross Anderson at the University of Cambridge: “Why bouncing droplets are a pretty good model of quantum mechanics“.

They discuss the recent experimental work with silicon oil droplets bouncing on vibrating trays and the behaviors exhibited by these systems; behaviors normally associated with quantum mechanical systems.  They quantify the effective forces between the droplets and their environment.  Then, they go on to show how the classical physical and mathematical description is equivalent to the Schrodinger equation, with the substitution of a surrogate parameter for Planck’s constant.  See “Droplets moving on a fluid surface: interference pattern from two slits” for a similar discussion.

## Quantum Mechanics and Spin Statistics

What is perhaps most intriguing about this new paper is the demonstration of how spin-half behavior can arise in these classical systems.  One of the central characteristics of quantum physics, and indeed an essential feature of our Universe, is the difference between fermions (particles with half-integral spin; electrons, neutrinos, protons, etc.) and bosons (particles with integer spin; photons, W and Z bosons, etc.).  This feature results in these two classes of particles having completely different statistical properties; Fermi-Dirac statistics for fermions, and Bose-Einstein statistics for bosons.  It is what leads to the Pauli exclusion principle and the stability of atoms.  The overall wavefunction for a boson is an even function and the overall wavefunction for a fermion is an odd function.

A peculiar feature of fermions that is reproduced in the hydrodynamic wave field is the fact that, if the direction of a fermion’s angular momentum is rotated through 360 degrees, its wavefunction changes sign.  This has typically been assumed to be an exclusive behavior of the quantum realm.  But here it is, in a table-top, classical experiment.

## Is Quantum Mechanics Just a Special Case of Classical Mechanics?

These experiments continue to provide tantalizing and provocative insights into the quantum world, challenging our notions and assumptions.  Some of the questions that come to mind as I ponder the implications for interpretations of quantum mechanics in general, and de Broglie-Bohm pilot wave theory in particular, include:

Is Quantum mechanics just a special case of classical mechanics?  Is quantum physics simply a subclass of events where we recognize certain behaviors over other noise and interference?

What are the quantum parallels for the effective external forces in these hydrodynamic quantum analogs, i.e. gravity and the vibrations of the table?  Not all particles carry electric charge, or weak or color charge.  But they are all effected by gravity.  Is their a connection here to gravity? Quantum gravity?

In addition to helping us understand quantum mechanics, can these or similar experiments help us understand general relativity as an effective force?

What are the technical challenges to doing these experiments in a microgravity environment, like the International Space Station?  What about somehow curving or warping the oil surface?

Why does the quantum world seem to have no energy (or frequency or wavelength) dependence for the limiting speed c (contrary to hydrodynamic quantum analogs)?

Until next time, have fun pondering!