A non-relativistic theory of quantum mechanics with local modulus symmetry

We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and positive function called the quantum metric function is attached to the complex conjugate of the wave function to satisfy the local modulus symmetry requirement. In an expanding universe, these theoretical features produce new effects that deviate from predictions of conventional quantum mechanics and Newtonian gravity. The quantum metric function yields negligible change for microscopic objects but produces quantum pointer states for macroscopic objects, thus providing a solution to the quantum measurement problem. The time-reversal symmetry is broken in the new quantum kinematics, which has implications for the second law of thermodynamics. The modification of Newtonian gravity is negligible in smaller bound systems but can become significant at the galactic scales. Its potential association with the mass discrepancy problem in the galactic systems is discussed.