# On the existence of exotic matter in classical Newtonian mechanics

## TL;DR

This paper explores the theoretical possibility of exotic matter with differing signs of inertial and gravitational masses within Newtonian mechanics, revealing diverse dynamics and conserved quantities in N-body simulations.

## Contribution

It introduces a generalized framework allowing particles with varying signs of mass and demonstrates the resulting complex dynamics and conservation laws.

## Key findings

- Diverse interaction classes for particles with different mass signs.
- Rich spectrum of dynamical behaviors observed in simulations.
- Conservation of energy and momentum under generalized definitions.

## Abstract

According to Newton's law of gravitation the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter all three of these are equal and positive. We consider here the more general case where these quantities are equal in magnitude for a given particle but can differ in sign. The resulting set of possible interactions allows each particle type to be assigned to one of precisely four different classes, and the results of N-body simulations show that the corresponding dynamics can give rise to a fairly rich spectrum of possible outcomes, some of which are familiar from nature at various scales. Total energy and momentum are conserved by all of these interactions if the definitions of momentum and kinetic and potential energy are suitably generalised.