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Schrödinger equation: worms and quantum objects have more in common than expected

15.7.2023

Translation: machine translated

If we describe the locomotion of worms in mathematical terms, parallels to the world of the very smallest become apparent. So do the wriggling animals behave like quantum objects?

What do worms, eels, snakes and millipedes have in common? They move in an undulating manner. The pattern that runs through their bodies as they writhe across the ground is, to a certain extent, a reflection of the underlying biochemical and neuronal excitation pulses. But what is astonishing is that if the locomotion of the animals is represented mathematically, remarkable parallels emerge with the Schrödinger equation, which describes the behaviour of objects in the world of the very smallest. Alexander Cohen from the Massachusetts Institute of Technology and his colleagues report on this in the current issue of the scientific journal "Physical Review Letters".

The team analysed video recordings of nematodes of the species Caenorhabditis elegans, western shovel-nosed vole snakes (Chionactis occipitalis), common stonecats (Lithobius forficatus) and biologically inspired snake robots. They identified specific locomotion patterns and then developed a simple method for classifying movement so that they could break down each wriggle into a series of simpler building blocks. When the researchers finally put together the overall equation, they realised that it seemed surprisingly familiar: it looked very similar to the famous Schrödinger equation, which formulates the temporal change of the quantum mechanical state of a physical system.

"When characterising quantum objects, the eigenvalues of the Hamilton operator provide the associated energy spectrum," write the authors. "In our case, this provides an efficient classification of the locomotion dynamics of worms and snakes." This can be used to describe the movement of any thin animal that moves in waves. In other words, in the same way that the state of a quantum object emerges from the underlying eigenvalues, the movement of a wriggling animal emerges from the building blocks identified by Cohen's team.

Of course, the mathematical similarity of the equation systems does not mean that wriggling animals behave like quantum objects. Rather, part of the similarity is due to the geometry of the animals under consideration, said Alasdair Hastewell, mathematician and co-author to "New Scientist". "They have a finite length and a high degree of symmetry - just like some more abstract quantum states." The advantage of the finding is that one can now draw on the comprehensive toolbox of quantum physics to characterise and predict the locomotion of living animals. This could potentially facilitate the development of biomimetic robotic systems.

Spectrum of Science

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Cover image: Shutterstock / D. Kucharski K. Kucharska

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