Relativistic Perturbations and Ontological Implications: Exploring the Zitterbewegung and Laying the Groundwork for a Quantum Ontology

Saul Propp

2015

The effects of the Zitterbewegung on the wave functions of low-energy electrons and photons in cylindrically symmetric waveguides were compared, and the philosophical implications for existence of considering quantum entities like photons and electrons to be fundamental were explored. Using degenerate perturbation theory, the changes in the radial wave function ψ(ρ) due to the Zitterbewegung were approximated to first order for electrons and photons. These perturbed wave functions were used to calculate the perturbed expectation values and standard deviations of the radial coordinate ρ, which was compared to the unperturbed values. The validity of this perturbative approach was checked by comparing it to the results found via the method of finite differences, and perturbation theory found to be accurate for the low Δ, low n, high R regime. It was also found that the effect of the Zitterbewegung varies drastically between states with m = 0 and m ≠ 0, as well as varying gradually with subsequent nonzero values of m and subsequent values of n. It was found that despite the analytic forms of the first order corrections to the radial wave functions being different for the photon and electron, there exists a unified behavior in the high R limit, with the unification being stronger for low values of n. Violations of this unified behavior were tentatively observed in the low R regime, but it was impossible to be certain without better error estimates. If real, these violations were explained by the differences in how electrons and photons react to localization, and a physical analogy to the Zitterbewegung for m ≠ to 0 states was developed that connects intuition and data. Through this, a groundwork for a heuristic understanding of the Zitterbewegung was established.

The implication for the notion of "existence" due to the empirical fact that quantum mechanical entities like electrons and photons exist were explored conceptually by unpacking the notions of "entity" and "this universe". In the case of the former, a classical understanding of what it means to be a fundamental entity was contrasted with multiple quantum understandings and analyzed through the lenses of three interpretations of quantum mechanics: the Copenhagen interpretation, the Many Worlds interpretations, and the Bohmian interpretation. For each interpretation of quantum mechanics, a precise summary of what must be given up in the classical account was presented. Unpacking "this universe" required understanding the problems of observer and measurement in quantum theory, and understanding the division between undivided wholeness and perspective as embodied by differing interpretations of quantum mechanics. By analyzing the implications of various interpretations of quantum mechanics for these problems and focusing on the issues posed for a classical ontology by the quantum reality, the groundwork for a quantum ontology was established.