This analysis explores the dynamics of Dirac fermions and their implications in quantum mechanics and gravity.
In quantum mechanics (QM), the electron of spin-charge in probabilistic distribution about a nucleus of a hydrogen atom is described by non-relativistic Schrödinger’s wave equation. Its transformation to Dirac fermion of a complex four-component spinor is incorporated into relativistic quantum field theory (QFT). The quantum system in both cases is represented by a wave function but how it collapses to a point at observation omits out both the hidden variables of the spinor and their evolutionary paths into space-time. This presents an ontological dilemma that cannot be satisfactorily explained by conventional theories either driven by experiments or vice versa. In this study, the ontology of Dirac fermion within a proposed MP model of 4D quantum space-time of hydrogen atom type is examined. The electron of a point-particle and its transformation to Dirac fermion appears consistent with Dirac belt trick (DBT) for the generation of superposition states of spin-charge and their antimatter. Center of mass reference frame owed to DBT offers an alternative version of Newtonian gravity and this is assigned to a specific spherical point-boundary of the model as an emergent geometry. This offers an intricate dynamic tool compatible with basic aspects of both QM and QFT. Some of these are explored for non-relativistic wave function and its collapse, quantized Hamiltonian, Dirac spinors, Standard Model and Lorentz transformation. The space-time geometry of the MP model is presented in the last section and a multiverse of the models at a hierarchy of scales is suggested for a planet in orbit of the sun. These outcomes offer a dynamic intuitive tool that can be modelled and tested for the hydrogen atom in order to probe the fundamentals of physics.
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Samuel Yuguru (2025) studied this question.
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