A 19th-century theory of matter, long dismissed as a scientific curiosity, is being re-examined by physicists as a potential key to one of the universe’s most profound mysteries: its own existence. The original idea, proposed by Lord Kelvin in 1867, envisioned atoms as intricate knots tied in a hypothetical medium called the aether. Though disproven by the discovery of subatomic particles and the absence of an aether, the underlying mathematical framework of knot theory has found an unexpected and powerful new application in the physics of the early universe.
Researchers in Japan now propose that while atoms are not knots, knotted fields of energy may have briefly dominated the cosmos moments after the Big Bang. This “knot-dominated era” could have tipped the delicate balance between matter and antimatter, ensuring that matter survived the initial annihilation to form the stars, galaxies, and life we see today. This novel approach connects a Victorian-era concept to modern particle physics, suggesting that the decay of these primordial knots could have left behind a faint gravitational wave signal that future observatories might detect.
A Victorian Idea of Matter
The original concept of vortex atoms emerged from the mind of William Thomson, later known as Lord Kelvin, after he observed experiments with smoke rings in 1867. He was captivated by their stability and complex interactions, leading him to hypothesize that atoms were not tiny, hard spheres but rather knotted vortices in the luminiferous aether, a medium then believed to permeate all of space. The theory was appealing because the endless variety of possible mathematical knots seemed to mirror the diversity of the chemical elements. A simple knot could represent hydrogen, while a more complex one could be oxygen.
Inspired by this vision, Scottish physicist Peter Guthrie Tait embarked on a massive project to classify and tabulate all possible knots, hoping to create a mathematical equivalent of the periodic table of elements. He, along with others, meticulously cataloged knots with up to 10 crossings. However, the vortex-atom theory began to unravel by the late 1880s. The discovery of the electron and the atomic nucleus revealed a completely different structure for the atom, and experiments like the Michelson-Morley experiment failed to detect the aether. The idea was abandoned, and knot theory transitioned from a potential theory of everything into a branch of pure mathematics.
A Modern Twist on Cosmic Knots
More than a century later, the concept of cosmic knots has been revived, not as a theory of atoms, but as a mechanism to explain the origin of matter itself. A team of researchers, including Muneto Nitta and Minoru Eto from Hiroshima University’s International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2) and Yu Hamada from the German research center Deutsches Elektronen-Synchrotron, have shown how such knots could realistically form within the framework of modern particle physics. Their work suggests these knots are not made of aether but are tangled configurations of fundamental energy fields that existed in the universe’s turbulent infancy.
According to their model, these knots would have formed naturally and rapidly, their energy density quickly surpassing that of radiation to rule the cosmos. This “knot-dominated era” was a crucial, albeit fleeting, period. The stability that made knots so appealing to Lord Kelvin allowed them to persist long enough to influence cosmic evolution before ultimately decaying through a quantum mechanical process. It is in this decay that the physicists believe the solution to the universe’s matter imbalance lies.
Solving the Matter-Antimatter Mystery
One of the most significant challenges in cosmology is explaining the observed asymmetry between matter and antimatter. The Standard Model of particle physics predicts that the Big Bang should have produced matter and its mirror-image, antimatter, in exactly equal quantities. If that had been the case, they would have annihilated each other upon contact, leaving behind a universe filled with only light and no substance. The fact that matter exists at all indicates that some process in the early universe created a slight surplus of matter over antimatter—about one extra particle of matter for every billion matter-antimatter pairs.
The new theory provides a mechanism for generating this surplus, a process known as baryogenesis. The researchers propose that the cosmic knots, once dominant, did not last forever. They eventually untangled themselves through a phenomenon called quantum tunneling, where particles can pass through energy barriers that would normally be insurmountable. This collapse generated massive, ghostly particles known as heavy right-handed neutrinos. As these neutrinos then decayed into lighter, more familiar particles, their breakdown was not perfectly symmetrical. It had a faint but crucial bias that produced slightly more matter than antimatter, seeding the universe with the building blocks of everything we know.
The Underlying Physics Framework
This knot-based theory is not merely a conceptual story; it is grounded in a realistic extension of the Standard Model. Nitta and his colleagues achieved their breakthrough by combining two advanced symmetry concepts that had not been studied together in this context before. The first is the Baryon Number Minus Lepton Number (B-L) symmetry, which is invoked to explain why neutrinos have mass. The second is the Peccei-Quinn symmetry, which was proposed to solve a lingering puzzle in the theory of the strong nuclear force known as the strong CP problem and also introduces axions, a leading candidate for dark matter.
By weaving these two frameworks together, the team discovered that stable knots could naturally form in the early universe’s fundamental fields. “Nobody had studied these two symmetries at the same time,” explained Nitta. “Putting them together revealed a stable knot.” Their calculations also showed that the energy released when the knots collapsed would have reheated the universe to a temperature of about 100 giga-electron volts (GeV). This is precisely the threshold required for the matter-producing decay of the heavy neutrinos to be effective and cement the matter-antimatter asymmetry permanently.
Searching for Echoes of Knots
A compelling feature of this new theory is that it offers a testable prediction, a rarity for ideas concerning the universe’s first moments. The violent collapse of the cosmic knot network would not have been silent. This event would have sent ripples through the fabric of spacetime, generating a unique gravitational-wave signal with a distinctive frequency. This ancient hum would still be propagating across the cosmos today.
While the signal would be far too faint for current detectors to pick up, future, more sensitive gravitational-wave observatories may have the ability to listen for this specific echo from the knot-dominated era. Finding such a signal would provide powerful evidence for the theory and open an unprecedented window into the physics that governed the birth of the universe. The research provides a clear path forward, allowing scientists to refine their models to better predict the signatures of these ancient knots and guide the search for these elusive cosmic messengers.