A Simulation-Based Approach to Bekenstein's Model of a Varying Fine Structure Constant

Some evidence from quasars suggests that the fine structure constant α is actually not constant and instead varies over time. We examine Jacob Bekenstein's model of a varying α. We first simulate the early universe at a redshift of 1100 using a particle-in-cell plasma simulation in Python in order to model the strength of magnetic and electric fields generated by interactions between protons and electrons. We then use this simulation to determine the magnitude of a parameter ς originally conceived by Bekenstein that could provide the source of temporal variations of α. Using this simulation, we estimate that ς ≈ 10^-12, which is 8 orders of magnitude less than the value most other authors use, 10^-4. Additionally, we adapt our simulation to test Bekenstein's "Cancellation Theorem," which claims that Coulombic contributions from nucleons to ς are negligible because two terms cancel in the equation of motion for a scalar field that provides the source of α variation. Our simulation disagrees with this result, showing instead that the two terms differ by 5 orders of magnitude and thus do not cancel. Additional work is needed to investigate other possible contributions to ς, e.g nuclear magnetic contributions.