An equation developed to describe the motion of undulating animals and robots looks like the famous Schrödinger equation from quantum mechanics.
The motions of undulating animals and the states of quantum objects can be described using strikingly similar equations.
Alexander Cohen at the Massachusetts Institute of Technology and his colleagues have found an equation that describes the motion of worms, snakes, centipedes and undulating snake-like robots.
They began by looking at previously recorded laboratory footage of Caenorhabditis elegans worms, Western shovelnose snakes (Chionactis occipitalis), brown centipedes (Lithobius forficatus) and bio-inspired mechanical snake robots in motion. They identified specific movement patterns these undulating creatures perform, and then developed a simple way of classifying the motions, so that they could decompose any wiggle into a series of simpler building-block moves.
These building blocks are all solutions to an overall equation that the team says could describe the motion of any thin animal or robot that undulates. When the researchers landed upon the equation, they were struck by its familiarity – it looked a lot like the famous Schrödinger equation that describes how quantum objects behave.
Alasdair Hastewell, also at MIT and part of the team, says that some of the similarity stems from the geometry of the animals and robots that they considered. They have finite length and lots of symmetry, like some more abstract quantum states, he says.
This mathematical similarity doesn’t mean the animals experience quantum effects. But, it allowed the team to use mathematical tools previously developed by quantum physicists to analyse the animals. For instance, the team quantified how differently a snake-like robot and a C. elegans move and created a diagram that placed them on a spectrum of other undulating creatures.
“It’s nice to know that whole organisms can be modelled with math that comes from physics. That’s not obvious, because they’re so complicated,” says Greg Stephens at the Free University Amsterdam in the Netherlands.
Cohen and his colleagues want to go beyond classifying motions and investigate how the motions come about at all.
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