On the Foundations of Quantum Mechanics

We consider three long-standing conceptual difficulties of quantum mechanics; the time variable, the quantum-classical divide, and gravitational fields. We investigate possible solutions by extending matrix mechanics from single points in time to continuous time in order to describe the absorption energy of a quantum system. Due to the conservation of energy absorption is equal to emission, as described by wave functions; which is an illustration of the classical-quantum divide. Hamilton’s principle of least action proves to be a natural fit for describing the resulting two-part quantum system and it specifies the true paths to be the ones with action equal to ћ. Energy absorption followed by discrete, four-dimensional changes in structure and energy emission is shown to be a pattern that is repeated countless times throughout nature by phase transitions and other phenomena. Experimental evidence is cited to show that the resultant mathematical model varies consistently with changes in gravitational potential. A universal physical interpretation is proposed.