A 150-Year-Old Mathematical Theory has Now been Tested and it Seems it was Wrong

Suck, Lord Kelvin. You may be right about thermodynamics, fluid dynamics, electronics, countless breakthroughs in engineering, the evolution and life cycle of stars, asymptomatic analysis of functions, and kinetic energy, but when it comes to tiny duds revolving around water, you. In 1871, Lord Kelvin, whose real name was William Thompson, proposed the existence of a certain shape – an “isotropic helicopter” – which should rotate naturally when dropped into a liquid. He described what this shape should look like, and for 150 years his idea was retained as an elegant example of the power of symmetrical analysis.

In fact, the idea was so believable that, apparently, no one actually went ahead and tested it. Well, a lot of old Victorian mathematicians are really going to feel embarrassed. A team of physicists has finally tested Kelvin’s hypothesis – and he seems to have done it wrong. “Although the symmetry analysis indicates that the particle should start rotating as soon as it settles, we did not detect any translation-rotation additions in our experiments,” concludes the team’s research paper published in this month’s Physical Review Fluid. “This raises the question [whether Lord Kelvin’s original argument is flawed.”

Following Lord Kelvin’s instructions, Team 3D has printed five small isotropic helicopters spheres with “wings” strategically placed in a center circle at 90- and 45-degree angles to the surface. The key to the shape is that the feature looks the same from any angle – it’s the “isotropic” part of the “isotropic helicopter”. The team varied the size and shape of the fins for each of the five experiments, but they all produced the same results: nothing. According to Kelvin’s original hypothesis, what should have happened when the helical was dropped into the liquid was that it would start to rotate because the strange shape interacted with the dynamics of the liquid around it. And the deeper it sinks, the faster it falls.

What actually happened when the helical was dropped into the liquid – specifically, the silicone oil – was that it fell to the ground without any rotation at all. Indeed, researchers suspect that the anticlimactic nature of their experiments may be the reason we have not yet seen others try.

“In Kelvin’s manuscript, he explicitly describes how to build an isotropic helicoid, which contains the ingredients to use, which suggests that he made one,” Greg Voth, head of research, told Live Science. “I personally suspect that since Kelvin and others have built and observed isotropic helicopters, the measured translation-rotation coupling is determined by the quality limits of the forgery, and so they have not disclosed their measurements.”