Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS

Understand

It has been shown that the orbits of motion for a wide class of nonrelativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual.

• This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system.
• We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence with another Hamiltonian with conformally modified metric.
• Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit.