Conservation Principles in AQUAL

We consider conservation of momentum in AQUAL, a field-theoretic extension to Modified Newtonian Dynamics (MOND). We show that while there is a sense in which momentum is conserved, it is only if momentum is attributed to the gravitational field, and thus Newton’s third law fails as usually understood. We contrast this situation with that of Newtonian gravitation on a field theoretic formulation. We then briefly discuss the situation in TeVeS, a relativistic theory that has AQUAL as a classical limit.