Theory of Particles with Variable Mass. I. Formalism

The equivalence principle (through the mechanism of the gravitational red shift) allows one to set up a classical formalism with the proper time as an extra degree of freedom, independent of the coordinate time, and with an immediate physical interpretation. Then proper time and mass occur as conjugate variables in a canonical formalism, leading to a gravitational theory of particles with variable mass. The nonrelativistic theory and a relativistic vector theory of gravity are described as models. The theory is capable of providing a dynamical framework for cosmological models with the creation of matter. Some simple examples are discussed, including the steady-state universe with continuous creation, where the correct relation between the density of matter and the Hubble constant appears automatically, with no free parameters.