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Physics + MathPhysics & Math

Beautiful Losers: Kelvin's Vortex Atoms

ByFrank WilczekThe Nature of RealityThe Nature of Reality

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This essay is part of the series Beautiful Losers .

A tornado is just air in motion, but its ominous funnel gives an impression of autonomous existence. A tornado seems to be an object; its pattern of flux possesses an impressive degree of permanence. The Great Red Spot of Jupiter is a tornado writ large, and it has retained its size and shape for at least three hundred years. The powerful notion of vortices in fluids abstracts the mathematical essence of such objects, and led William Thomson, the 19th century physicist whose work earned him the title Lord Kelvin, to ask: Could atoms themselves be vortices in an ether that pervades space?

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Kelvin’s idea was inspired by the work of Hermann Helmholtz, who first realized that the core of a vortex—analogous to the eye of a hurricane—is a line-like filament that can become tangled up with other filaments in a knotted loop that cannot come undone. Helmoltz also demonstrated that vortices exert forces on one another, and those forces take a form reminiscent of the magnetic forces between wires carrying electric currents.

To Thomson, these results seemed wonderfully suggestive. At the time, evidence from chemistry and the theory of gases had persuaded most physicists that matter was indeed composed of atoms. But there was no physical model indicating how a few types of atoms, each existing in very large numbers of identical copies—as required by chemistry—could possibly arise.

In seemingly unrelated work, physicists were discovering that space-filling entities are an essential tool in Nature’s workshop. Today we accept those entities—known as electric and magnetic fields—on their own terms, as fundamental; but Thomson and his contemporaries believed them to be manifestations of an underlying fluid: an updated version of Aristotle’s Aether.

Thomson’s bold ambition, and instinct for unity, led him to a propose a synthesis: The theory of vortex atoms. The Ethereal fluid, being so fundamental, should be capable of supporting stable vortices, he reasoned. Those vortices, according to Helmholtz’ theorems, would fall into distinct species corresponding to different types of knots. Multiple knots might aggregate into a variety of quasi-stable “molecules.” All this remarkably fits the heart’s desire, in a theory of atoms: Naturally stable building-blocks, whose possibilities for combination seem sufficiently rich to do justice to chemistry.

Thomson himself, a restless intellect, moved on to gush other ideas, but his friend and colleague Peter Guthrie Tait, enthralled by the vortex atom theory, set to work. Thus inspired, he did pioneering work on the theory of knots, producing a systematic classification of knots with up to 10 crossings.

Beautiful Losers: Kelvin's Vortex Atoms-500px-knot_table.jpg

A table of knots. The ‘Unknot’ was thought to represent hydrogen; to its right, the knot thought to represent carbon. By Jkasd (Own work, Public domain), via Wikimedia Commons

Alas this beautiful and mathematically fruitful synthesis is, as a physical theory of atoms, a Beautiful Loser. Its failure was not so much due to internal contradictions—it was too vague and flexible for that!—but by a certain sterility. Above all, it was put out of business by more successful competitors. Eventually the mechanical Ether was discredited by Einstein’s relativity, and the triumphant Maxwell equations for electric and magnetic fields do not support vortices. The modern, successful quantum theory of atoms is based on entirely different ideas. And yet…

It’s easy to understand the appeal of vortex atoms, not only as fascinating mathematics, but as potential elements for world-building. When we turn from understanding the natural world to designing micro-worlds on our own, we might come to treasure their virtues. Vortices can have an impressive degree of stability; they can be knotted into topologically distinct forms, which are also quasi-stable; and their interactions are complex and intricate, yet reproducible.

Those attractive features can be embodied in artificial “atoms” specifically designed to be building blocks for quantum engineering. For quantum theory, though it made the vortex theory of natural atoms obsolete, provides us with a variety of far more reliable, and far more perfect, aethers than the old Aetherial fantasies. Classical fluids, whether they are real liquids or speculative substrates, are inherently imperfect. Any motion in them will stir up little waves that carry away energy, and eventually dissipate the flow. Quantum fluids, such as superfluid helium and a variety of superconductors, on the contrary, support flows that, in theory, will persist unchanged forever. And in practice, too—that’s why we call them “super”! The deep point is that in quantum mechanics energy comes packaged in discrete lumps (quanta). If you operate at low temperatures, where there’s very little energy available, it can become impossible to stir up those little waves that bedevil classical fluids at all. In quantum fluids, vortices really are forever.

There is lots of room for creativity in designing and constructing artificial aethers. Many materials become perfect (quantum) fluids at low temperature.

By choosing the right media, we can tailor our fluids to have useful properties. Physicists and engineers have become quite adept at designing useful fluids, such as the liquid crystals that enable computer monitors and LCD displays. In those examples the fluids have internal structure, which can be manipulated electrically to change their appearance. So far most of the effort has gone into classical fluids, but physicists are beginning to awaken to some promising new possibilities offered by quantum fluids. Though the details can be quite different—as I said, there’s lots of room for creativity here—the basic inspiration, to make fluids that we can manipulate externally to make them do something useful, is the same.

Designer quantum fluids can offer us a variety of vortex atoms, and the opportunity to design new chemistries that accomplish something we want done. Perhaps the most intriguing possibility is to embody, in real materials, the so-far theoretical concept of anyons. Anyons are particles that interact in a special, peculiarly quantum-mechanical way. Anyons don’t exert any forces upon one another, but when you wind one anyon around another, you make interesting, predictable changes in the wave function that describes your system. Quantum computers are, in principle, nothing but machines that process wave functions. (Since wave functions can simulate a tape, or more generally a collection of tapes, that encode data, operations on wave functions can be massively parallel operations on data.) On paper, at least, theorists have proposed ways whereby one might orchestrate the motion of anyons to construct a general-purpose quantum computer. The future will tell whether this beautiful idea blossoms into reality, or proves another seductive Beautiful Loser.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.