Mathematical modelling of particle-wave mechanical systems

Date: Thursday 29th Feb 2024

Abstract

Despite successes of modern physics, the existence of dark energy and matter is indicative that conventional mechanical accounting is lacking. The most basic of all mechanical principles is Newton’s second law, and conventionally, energy is just energy whether particle or wave energy. In this talk, Louis de Broglie’s idea of simultaneous existence of both particle and associated wave is developed, with a novel proposal to account for mass and energy through a combined particle-wave theory. Newton’s second law of motion is replaced by a fully Lorentz invariant reformulation inclusive of both particles and waves and involving a new term which takes into account the overall observed expansion of the universe.

The model springs from continuum mechanics and forms a natural extension of special relativistic mechanics. It involves the notion of “force in the direction of time” and every particle has both particle and wave energies, arising as characteristics of space and time respectively. Dark matter and energy then emerge as special or privileged states occurring for alignments of spatial forces with the force in the direction of time. Dark matter is essentially a backward wave and dark energy a forward wave, both propagating at the speed of light. The model includes special relativistic mechanics and Schrödinger’s quantum mechanics, and therefore the major achievements of mechanics and quantum physics.