Researchers have developed a new theoretical framework that allows accurate simulations of systems like bird flocks, which appear to violate Newton's third law of motion. The approach introduces fictitious partners to transform non-reciprocal interactions into reciprocal ones that existing methods can handle.
Birds in flocks align only with neighbors ahead or beside them, creating interactions that seem to break the action-reaction principle central to classical physics for over 300 years. Similar patterns appear in bacterial swarms and cell groups, where traditional models fall short.
A team led by Marín Bukov at Technische Universität Dresden, working with Roderich Moessner and Ricard Alert, introduced auxiliary mathematical variables representing imaginary partners. For each bird, they place a fictitious counterpart in the opposite direction to restore balance in the equations.
"The trick behind the new theory is that it constructs a partner for each component of the system -- a fictitious partner that doesn't exist in nature," Alert explained. The method enables precise simulations using established many-body physics tools.
The findings, published in Nature Physics, open possibilities for studying collective behavior in both biological and quantum systems. Moessner noted the potential for discovering new forms of quantum matter arising from such non-reciprocal dynamics.
