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From our star鈥檚 excess heat to the complexities of fluid turbulence, many a mystery might be unravelled by the bane of the headphone wearer 鈥� knots

PERHAPS it was the foul stench that inspired to one of his oddest ideas. In 1867, the physicist, now better known as Lord Kelvin, was observing his colleague producing smoke rings from ammonia, sulphuric acid and salt in his Edinburgh laboratory. As the rings glided across the room with elegant stability, a thought struck Thomson: ?

What if atoms weren鈥檛 solid spheres, as most gentleman scientists then believed, but looped vortices tied in the field of the lumeniferous aether, the medium then thought to carry light waves? That might explain why atoms absorb light. And as for the different chemical elements 鈥� why, they would just be ever more complex sorts of knots.

Thinking they were constructing a table of the elements, Tait and others went on to busy themselves classifying all the different sorts of knots by their number of loops and crossings, thus founding the modern mathematical discipline of knot theory. Sadly, though, the underlying idea was soon undone: apart from anything else, experiments two decades later showed the lumeniferous aether didn鈥檛 exist.

But the basis of Thomson鈥檚 ruminations has been bugging some physicists ever since. Can you actually tie a knot in anything so ethereal as a field 鈥� be it light, gravity or anything else? It has taken a century and a half, but now it seems we have an answer.

Knots are possible not just in shoelaces and headphone cords, but more slippery contexts such as water flows (PM Images/Getty Images)

The attraction of knots for physicists is apparent to anyone who has fought with entangled earphone cords. Knots are extraordinarily stable, needing considerable investment of time or energy to untie. 鈥淥nce you have a knotted structure, it鈥檚 persistent, it鈥檚 stuck,鈥� says theoretical physicist of the University of Pennsylvania in Philadelphia.

That鈥檚 one reason why knotted fields have become the mainstay of many a physical theory since Thomson鈥檚 day. In the late 1960s, theorists found that knots in the fields that map out fluid flows could help to explain turbulence, itself one of physics鈥檚 knottiest problems 鈥� or at least, they might do in a hypothetical, perfectly flowing fluid.

鈥淜notted fields pop up in all sorts of theories 鈥� but can you make one in practice?鈥�

The quantum field theories that underlie the standard model of particle physics, too, suggest that Thomson wasn鈥檛 so far from the truth after all. The building blocks of matter might come not just in the form of the point-like elementary particles already known, but also as knotted 鈥渢opological鈥� particles with exotic names such as glueballs and magnetic monopoles. These particles could play a big part in the universe, most notably in its earliest moments.

Closer to home, theories first developed in the 1980s suggest the tying and untying of braids in the magnetic fields of the sun鈥檚 outer layers might release energy. That would explain why these layers are so much hotter than our most basic models allow.

All this leaves a rather large loose end dangling: can you actually make a knotted field in practice?

It is certainly no easy task. Fields map quantities that fill all of space, so to tie a knot in one bit of one, you must distort it in all the surrounding space, too. at the University of Chicago can fill books with his failed attempts to pull that off. One idea of his was to distort a flow field in water to create tiny doughnut-shaped vortices rather like Tait鈥檚 smoke rings, and shoot two of them at each other in the hope they would link up into a simple trefoil knot. In vain. 鈥淲e learned afterwards that this is what Kelvin himself had tried, and many people since,鈥� he says.

New twists

The French physicist Yves Bouligand got the closest four decades ago when investigating liquid crystals. These materials, commonly used in display screens, consist of rods that all have the same orientation, as in a solid crystal, but are otherwise free to move around, as in a liquid. The orientation of the rods maps out a 鈥渘ematic鈥� field, whose alignment can be changed from parallel to twisted by applying an electric field. In 1974, Bouligand saw a in one twisted alignment 鈥� but the experimental tools at his disposal didn鈥檛 allow him enough control over the liquid crystals to confirm it.

It was left to at the University of Bristol, UK, to make a breakthrough in 2010. His team used the fields of a liquid crystal to imprint patterns in the field of a laser beam. The contrast between light and dark regions created was too faint to observe anything directly, but when digitally enhanced, the lines of complete darkness .

Just recently, though, evidence of knotty fields has been multiplying faster than the twists in a telephone cord. Using a 3D printer, Irvine and his colleague Dustin Kleckner last year made tiny knot-shaped plastic wings that created eddies off their edges when accelerated under water. Injecting these eddies with air bubbles to make them visible exposed .

at Ljubljana University in Slovenia and his team have recently achieved something similar in a nematic field. Differently shaped 3D-printed nanoscale knots coaxed the rods of the liquid crystal to align, . These had different numbers of loops and crossings that could be made out using advanced microscopic techniques.

And there鈥檚 also been tentative evidence that knots are indeed the explanation for some of nature鈥檚 conundrums. Last year solar physicists using NASA鈥檚 (Hi-C) instrument claimed to have observed just the signature of knotty energy release in the sun predicted by theory.

The aim now is to refine techniques to make knotty fields in the lab, and so explore natural knot dynamics in the sun as well as in other situations in which they are proposed to arise. 鈥淭he next step is taking one of the knots and looking at what it does after it鈥檚 produced,鈥� says Irvine.

There are more down-to-earth goals, too. The stability of knots makes them promising candidates for creating a long-term, durable way of storing information. In this vision, a high-intensity knotted light field would be used to encode knots in a liquid crystal, say, with lower intensity knotted light used to read it out. 鈥淭he holy grail would be to be able to use knotted light fields to put knots into liquid crystals,鈥� says Kamien.

That鈥檚 still a way off 鈥� but a century and a half on, it seems there might have been something in Kelvin鈥檚 vision after all.

This article appeared in print under the headline 鈥淕et knotted鈥�