nLab On Vortex Atoms



Knot theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

The text

  • Lord Kelvin,

    On Vortex Atoms

    Proceedings of the Royal Society of Edinburgh, Vol. VI, pp. 94-105.



presented the hypothesis that atoms (elementary particles) are fundamentally vortices in some spacetime-filling substance (the “aether”).

Review and discussion:

Discussion in comparison to knotted states in superconductors:

  • Filipp N. Rybakov, Julien Garaud, Egor Babaev, Kelvin knots in superconducting state, Phys. Rev. B 100, 094515 (2019) (arXiv:1807.02509)

Discussion in relation to skyrmions:

  • Antonio Ranada, J. Trueba, Force Lines, Vortex Atoms, Topology, and Physics, Section I.A In: Topological Electromagnetism with hidden nonlinearlity in: Myron Evans (ed.) Modern Nonlinear Optics – Part 3, Wiley 2001 (doi:10.1002/0471231495.ch2)



As a literal theory of physics the vortex atom hypothesis lasted no more than 30 years, even Thomson himself giving up on it by 1890 (Krage 02, p. 34), but it did make Peter Tait start thinking about classification of knots, which eventually led to modern knot theory in mathematics. Moreover, faint shadows of Kelvin’s original idea have been argued to be visible in string theory – and the failure of the vortex atom theory has been used to warn of too much hope into string theory.

Similarity with Descartes’ thoughts

According to the Routledge encyclopedia of Philosophy here:

Descartes also rejected atoms and the void, the two central doctrines of the atomists, an ancient school of philosophy whose revival by Gassendi and others constituted a major rival among contemporary mechanists. Because there can be no extension without an extended substance, namely body, there can be no space without body, Descartes argued. His world was a plenum, and all motion must ultimately be circular, since one body must give way to another in order for there to be a place for it to enter ( Principles II: §§2–19, 33). Against atoms, he argued that extension is by its nature indefinitely divisible: no piece of matter in its nature indivisible ( Principles II: §20). Yet he agreed that, since bodies are simply matter, the apparent diversity between them must be explicable in terms of the size, shape and motion of the small parts that make them ( Principles II: §§23, 64) (see G. W. Leibniz §4 ).

However, according to (Krage 02, p. 33):

In spite of the similarities, there are marked differences between the Victorian theory and Descartes’s conception of matter. Thus, although Descartes’s plenum was indefinitely divisible, his ethereal vortices nonetheless consisted of tiny particles in whirling motion. It was non-atomistic, yet particulate. Moreover, the French philosopher assumed three different species of matter, corresponding to emission, transmission, and reflection of light (luminous, “subtle”, and material particles). The vortex theory, on the other hand, was strictly a unitary continuum theory.

Similarity to concepts of modern particle physics


It is however striking that the modern concept of baryogenesis via the chiral anomaly and its sensitivity to instantons is not too far away from Kelvin’s intuition.

To play this out in the most pronounced scenario, consider, for the sake of it, a Hartle-Hawking no-boundary spacetime carrying NN Yang-Mills instantons. Notice that an instanton is in a precise sense the modern higher dimensional and gauge theoretic version of what Kelvin knew as a fluid vortex.

Then the non-conservation law of the baryon conserved current due to the chiral anomaly says precisely the following: the net baryon number in the early universe is a steadily increasing number – this is the modern mechanism of baryogenesis – such that as one approaches the asymptotically late time after the “Big Bang” this number converges onto the integer NN, the number of instantons.

Hence while in the modern picture of baryogenesis via gauge anomaly an elementary particle is not literally identified with an instanton, nevertheless each instanton induces precisely one net baryon.

(If one doesn’t want to consider a Hartle-Hawking-type Euclidean no-boundary spacetime but instead a globally hyperbolic spacetime then the conclusion still holds, just not relative to vanishing baryon number at the “south pole” of the cosmic 4-sphere, but relative to the net baryon number at any chosen spatial reference slice. )

For more on this see at baryogenesis – Exposition.


Skyrmions realize baryons and atomic nuclei as “knotted states” (in fact as cohomotopy classes) of a meson-field.

According to Ranada-Trueba 01, p. 200:

Skyrme had studied with attention Kelvin’s ideas on vortex atoms.

category: reference

Last revised on September 18, 2021 at 13:41:32. See the history of this page for a list of all contributions to it.