Kelvin’s Brilliant Vortex Atoms

Houssem Kasbaoui
6 min readSep 6, 2016


A smoke vortex ring. Watch in slow-mo:

Before it was firmly accepted that atoms are made of electrons orbiting a nucleus, Sir Walter Thomson, a British scientist famously known after his lordship title 1st Baron Kelvin, noted in an 1867 paper titled “On Vortex Atoms”, the following:

“Helmhotlz’s admirable discovery of the law of vortex motion […] inevitably suggests that Helmholt’z rings are the only true atoms. Helmholtz has provided an absolutely inalterable quality in the motion of any portion of a perfect fluid in which the peculiar motion which he calls ‘Wirbelbewegung’(i.e., voriticty) has once been created. Thus any portion of a perfect fluid which has ‘Wirbelbewegung’ has one of recommendation of Lucretius’s atoms — infinitely perennial specific quality”

Lord Kelvin by Hubert von Herkomer

Lord Kelvin is among the most revered scientist of the late 19th century famous for his seminal work in thermodynamics, discovering the absolute zero temperature and popularizing kinematics. For over 50 years, he was Professor of Natural Philosophy at the University of Glasgow where he left an indelible impact in our understanding of the motion of fluids. At the core of his craft is a very strong hold on mathematics and an incredible talent for modeling physical phenomena.

To understand how Lord Kelvin came to think that vortices are the elemental constituents of matter, one needs to put things in context. In the second half of the 19th century, a series of experiments by English chemist John Dalton made it clear to scientists that matter is made of discrete elements, called atoms, constituting the fundamental building blocks of the universe. While direct observation with the naked eye, or any other device, was impossible at the time, researchers were looking for mathematical objects that would exhibit the properties they thought fundamental quanta of matter should have. It was the race for atom models.

Models feed on ideas and intuitions and Lucretius’s double millennial old yet visionary ideas were critical in shaping the mainstream conception of the atom. In an awe-inspiring and surprisingly relevant to present-days philosophical poem from the first century BC, he theorized that:

1. Matter is constituted of indivisible portion
He calls them bodies or seeds, atoms combine to form complex structures

“All nature, then, as self-sustained, consists,
Of twain of things: of bodies and of void[…]
And by their combinations more condensed,
All objects can be tightly knit and bound
And made to show unconquerable strength.”

2. Atoms are perpetual objects.

“Thus if first bodies be, as I have taught,
Solid, without a void, they must be then
Eternal; and, if matter ne’er had been
Eternal, long ere now had all things gone
Back into nothing utterly, and all
We see around from nothing had been born”

3. Atoms are in constant motion at great speed, bouncing and deflecting off each other.
Complex matter consists of a stable equilibrium of an inflow and outflow of atoms.

“For truly matter coheres not, crowds not tight,
Since we behold each thing to wane away,
And we observe how all flows on and off, […]
Albeit the sum is seen to bide the same,
Unharmed, because these motes that leave each thing
Diminish what they part from, but endow
With increase those to which in turn they come”

4. Atoms posses a nondeterministic swerving motion.
This is maybe Lucretius’s most celebrated idea. In modern physics, it could relate to the brownian motion of nano-particles or the quantum uncertainty postulate.

“For thou wilt mark here many a speck, impelled
By viewless blows, to change its little course,
And beaten backwards to return again,
Hither and thither in all directions round.”

When Helmholtz showed in his 1858 paper “On Integrals of the Hydrodynamical Equations, which Express Vortex-motion”, that vortices in a perfect fluid (i.e., destitute of viscosity) are stable objects that exert long range (hydrodynamic-)forces according to the Biot-Savart law, the very same law describing the magnetic force created by conducting wires, Lord Kelvin had the intuition that vortices might be the “perennial” elemental matter described by Lucretius. Furthermore, it would be a plausible explanation for the origin of magnetism.

At that time, the idea that space was filled with a hypothetical perfect fluid called Ether was not particularly controversial (although in contradiction to Lucretius’s void), and atoms as vortices in this fluid was a reasonable concept that was eventually endorsed by a large part of the scientific community including distinguished Scottish mathematician Peter G. Tait and German physicist Gustav Kirchhoff. In his paper, Lord Kelvin speculated that knotted and linked vortex rings could combine in ways that “the infinite variety of which is more than sufficient to explain the allotropies and affinities of all known matter”, i.e., atom species. After he witnessed P. G. Tait’s experiments with smoke vortex rings. it struck him that the oscillations of the rings might relate to the recent discovery of spectral emissions. He says

“It is probable that the vibrations which constitute the incandescence of sodium-vapour are analogous to those which the smoke-rings had exhibited”.

A dolphin creates a vortex ring in water. See how it oscillates!
Rutherford’s atom

The similarity with Rutherford’s atom, the mainstream model generally accepted as true, is striking. The atom being an ensemble of a nucleus and electrons, light is emitted when an electron jumps from one electronic configuration to another. The latter is also represented by three integers usually noted as |n,l,m>. Physically speaking, the first integer (n), measures the distance between the nucleus and the electron while the two others (l and m) determine the orbit.

Meanwhile, Tait began work on ring knots in three dimensions with the goal to establish a one-to-one link between known atoms and possible knots. The pair of Thomson and Tait became known as T&T’.

In Thomson and Tait’s (T&T’) theory, different knots correspond to different atoms. Hydrogen: unknot, Carbon: 3_1 , Oxygen: 4_1.

The vortex atom was off to a good start. For two decades, it was immensely popular due to three solid features that no other model combined: perennial, magnetism and discrete emissions. Unfortunately, its success came shuttering with the discovery of the electron by J. J. Thomson in the 1890s. The scientific community gradually moved away from Kelvin’s vortex atom. Later on, Rutherford’s atom became the most popular and survives to nowadays. Additionally, the analogy with the magnetic field stopped short after Maxwell came up with his equations, a generalization to the Biot-Savart law. At first glance, the magnetic field and the vorticity seem to obey the same equations, suggesting that they are indeed the same thing:

The equations dictating the evolution of vorticity and magnetic field appear to be identical, suggesting the two quantities might actually be the same.

where B is the magnetic field, ω is the vorticity, η and ν are respectively the resistivity and viscosity. But these equations are not complete, and come with additional constraints. The critical difference comes from the origin of vorticity. Whereas, the vorticity ω is curl of the velocity u, B has no such links with the charges velocity v.

Kelvin’s vortex atom was a formidable mathematical object. Unfortunately, like many theories, it didn’t survive the brutal test of experiments, and the vortex atom went out of fashion.

But this is not the end of it. In recent experiments, scientists observed the Kelvin vortex over a century after its theorization by Kelvin and Helmholtz. The supporting fluid was cooled down to near absolute zero temperature to inhibit viscous effects, creating what is known as a super fluid. An ether of some sort one might say.

Kelvin waves, i.e., the vibrations of the vortex tubes, were first observed in 2012 in a superfluid, an inviscid fluid at near zero temperatures! See here for full video:

And it seems that scientists would not let go of the Vortex Atom. At least the mathematical description behind it. Today’s most obscure and fascinating theory, String Theory, recycles elements of T&T’s work.

Based on the same idea of classifying stuff as knitted and knotted rings and tubes, string theory adds a new quantum flavor and aims to succeed where “classic” quantum mechanics falls short: describing the graviton, one of the most hyped quantum mechanical particles that could be the source of gravity. In string theory, the graviton is a vibrational mode of a closed string. Sounds familiar?



Houssem Kasbaoui

Rocket scientist & applied mathematician. Trying to understand the universe one equation at a time.