A non-relativistic theory of quantum mechanics and gravity and its application to the quantum measurement problem

Drawing analogies with general relativity and quantum electrodynamics, we construct a non-relativistic theory of quantum mechanics and gravity that also contains two universal constants and a local symmetry. We postulate that quantum system remains invariant to local modulus transformation, which introduces a purely imaginary connection field that is identified as the gravitational escape velocity, and 3 new scalar functions that need to be attached to particle probability density. These scalar functions also serve a role similar to the metric tensor in general relativity, with gravitational information encoded in them. A modified equivalence principle enables us to relate the new escape velocity vector field with these three so-called quantum metric functions. There are two parts in the escape velocity, one is invariant to local modulus transformation and has the same magnitude as the Newtonian escape velocity. The other, in an expanding universe, is proportional to the Hubble constant. This later part also results in quantum metric functions that kinematically modify macroscopic object’s wave function into essentially delta function in real space. The wave function of object with microscopic mass is changed by a negligibly small amount. The Hubble constant thus decides the macro/micro boundary. We also find that time reversal symmetry is fundamentally broken in an expanding universe in our theory. Whether it can serve as the basis of the 2^nd law of thermodynamics awaits further investigations.