Programming Planck Units from a Virtual (Black-Hole) Electron; a Simulation Hypothesis

Abstract

The Simulation Hypothesis proposes that all of reality is an artificial simulation, analogous to a computer simulation. This essay summaries a project to determine the feasibility of assigning geometrical objects to the Planck units such that the universe can be simulated using geometrical imperatives at the Planck scale instead of the dimensioned physical constants. This approach is suitable for coding a mathematical universe that can grow autonomously. If these geometrical objects cannot be distinguished from our physical Planck units then they can be used in Planck scale simulation hypothesis models. These objects are derived from an electron formula (a mathematical electron) that, although itself dimension-less, embeds geometrical objects for mass, length, time and charge. Consequently although the attributes of the electron (mass, charge, frequency, wavelength) derive from these embedded objects, this mathematical electron itself does not exist in any dimensioned sense. The sum particle universe (the simulation) is therefore dimension-less, but internally it has measurable parameters that could give the appearance of a physical reality to self-aware structures from within the simulation. The essay is divided into 4 sections; the Planck units and a magnetic monopole electron, a discretely expanding Planck unit black-hole scaffolding as the origin of the Planck units, relativity as the mathematics of perspective and gravitational orbits as the sum of particle-particle gravitational orbitals. There are only 2 dimension-less physical constants used; the fine structure constant alpha and Omega, however Omega can be further defined using mathematical constants, pi and ln(e) and so the information required to construct this Planck universe model could be embedded in the electron formula and the magnitude of alpha.