Waves & Whirlpools: on Energy, Structure, Matter, & Antimatter (Part III)

This post is part of a series, (read Part I and Part II) introducing a heuristic method for thinking about spacetime and charge that I like to call “the pond”. Electromagnetic waves are often described as being similar to waves on water, and it turns out the analogy can be extended—if photons are waves, charged particles are like whirlpools: excitations with a little bit of angular momentum to them which allows them to persist.

So far, we’ve established that vortices (or eddies, if you prefer) on the surface of a pond are an intriguing analogy for charged particles. They allow energy to be expressed as a disturbance from the water’s flat equilibrium, but in a more stationary way than transient waves. Just as similar electric charges repel, two eddies spinning the same direction will repel one another, while eddies with opposite spins attract. Remarkably, if these counter-rotating vortices meet, they “annihilate”—the angular momentum of one neutralizing that of the other—and the energy they contained radiates away as waves, closely mimicking the dynamics of matter and antimatter.

The analogy isn’t perfect, but the surface of the pond manifests a surprising number of familiarly particle-like phenomena.

Stability in Balance
There’s one circumstance where two counter-spinning vortices won’t attract and annihilate one another—a curious phenomenon known as a “Falaco soliton”.

If you’ve ever been canoeing, you’ve likely created individual eddies on the surface of the water. As you pull your paddle back and create a small void, water rushes in from the sides to fill that void and return the pond to equilibrium, where the entire surface is at the same height. When a current of this water catches its tail, a persistent dimple forms. Before too long, though, the viscosity of the water saps away its angular momentum, and the vortex dissipates.

But imagine we use a plate, rather than a paddle, so that the water rushes in from both sides symmetrically. Done at just the right speed, this process can create a pair of counter-spinning vortices. Unlike vortices created independently, though, these ones won’t annihilate each other, thanks to a special difference: they’re linked, joined by a “string” of current through the water—the eddies are two ends of a single “topological defect”. This is a Falaco soliton.

If you could lift the “defect” out of the water and straighten it out, you’d see it as a rotating cylinder.
If you linked the two “mouths”,  you’d have created a vortex ring—like a smoke ring.

For more on Falaco solitons, (including a discussion of what the term means), check out our prior post, Particles at the Pool.

The remarkable thing about these paired vortices is that they are extraordinarily stable compared to individual ones; they can persist for minutes at a time, rather than the seconds that a vortex usually lasts. But disrupt the string that joins them, and they’ll dissipate almost instantly.

While two counter-spinning eddies created individually behave like matter and antimatter, the Falaco soliton lets us see opposite “charges” interacting in a way that more closely resembles the behavior of neutrons, or of protons and electrons. Here, they balance out and prevent one another from interacting as strongly with the environment. They create a “vorticity-neutral” system on the surface, the same way a neutron or a hydrogen atom is charge-neutral.

But if charge is analogous to angular momentum here, it raises some questions: why is the proton so much more massive than the electron? (The technical answer to this question—that one is a baryon made of quarks and the other is a fermion, is boring and intuitively unhelpful in my opinion.)

We’d expect the amount of energy in a particle—and therefore its mass—to correspond to something like the amount of water it displaces in the pond. The fact that particles with vastly different energies carry the same quantity of charge suggests that there’s an asymmetry, a bias in the pond that makes  spinning one way preferential to the other. Perhaps we can imagine larger-scale flows that might allow for a Falaco soliton that is asymmetrical in terms of the water displaced, but still balanced rotationally; how would one formed in the vicinity of a larger whirlpool behave?

Pictured: a larger whirlpool.
Image Credit: ESA & NASA (CC BY 3.0)

I’m mostly joking with that suggestion; if the charge-to-mass ratio of elementary particles depended on things like the galaxy’s angular momentum, we’d see unusual features in starlight from other galaxies, unless other physical constants also varied proportionately.

But even if we imagine a larger, symmetry-breaking flow that envelops our entire universe, this still leaves plenty of mysteries—what’s the difference between a proton and a positron, if they’re both “spinning” the same way? Perhaps this is a sign that we’re stretching the analogy too far, but then again perhaps not—Russian physicist Grigory Volovik has famously said that every fundamental particle can be modeled as a topological defect in superfluid helium.

Bridging the Quantum and the Continuum
This whole line of thinking is rooted in a kind of optimism—a hope that the quantum numbers and gauge fields and wave functions that comprise modern physics reflect something about the universe that we can understand in familiar, physical terms. Unfortunately, this kind of optimistic view has been scoffed at for years in the physics community, even when professed by one of its greatest minds.

Einstein was a firm believer in deterministic models of reality, where every moment is determined completely by the previous one, a view expressed in his assertion that “God does not play dice”. The famous riposte to this, spoken by quantum physicist Niels Bohr, was “Don’t tell God what to do.” The line reflects a kind of intellectual resignation popular among early pioneers of quantum theory: when it became apparent that even the most fundamental particles exhibit weird, wavelike behavior, many of our finest minds threw up their hands and gave up on the prospect that the universe is a place that should make intuitive sense.

Looking at the results of something like the electron double-slit experiment, where a single particle behaves as though it’s traveled along two separate paths, it’s hard to blame them—philosophically, there’s no reason why the universe should behave in an intuitively friendly manner. And so, the “Copenahgen interpretation”, which teaches that particles do not have definite properties until they’re measured, has become the standard across the world. But although it’s the most popular, this is not the only way to make sense of the bizarre behavior in quantum systems; a contemporary theory, in which particles are guided by “pilot waves”, can explain the experiment’s results equally well, and without letting go of the notion that our universe is a place where a single particle remains a single particle.

It’s interesting to note that, although the demonstration here used droplets on the surface of the fluid, it ought to work similarly if inverted—a bubble trapped underneath the surface might be expected to bounce along in precisely the same way. Consider, too, the way a vortex in a glass of water can trap bubbles beneath it, preventing them from rejoining with the surface overall, just like the waves we see here.

So is all this talk of waves and whirlpools simply a friendly analogy, or is it an insight into the true nature of things? Do electrons merely behave like eddies, or are they actually—as Volovik argues—structured excitations of the vacuum of spacetime?

Next time, to try and answer these questions, we’ll take a step out of the universe as we know it—and into the fifth dimension.

—Stephen Skolnick

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