Anti-Newtonian dynamics

Consider a world in which Newton’s first and second laws hold, but where Newton’s third law takes the form that the forces between any two objects are equal in both magnitude and direction. We will refer to such a world as “antiNewtonian,” although that term has also been used to describe a general relativistic universe with a purely gravitomagnetic field. Violations of Newton’s third law are not uncommon and occur, for example, in the forces between moving charges when retardation effects are considered. An anti-Newtonian force pair is unusual, but it might approximate some biological processes such as a spatial predator-prey problem in which the fox is attracted to the rabbit, but the rabbit is repelled by the fox. It is useful to study such a model not only for its pedagogical value in understanding the role of Newton’s third law in classical mechanics but also because there may be situations outside of physics where such a model is sensible.