Programming Physical Planck Units From a Mathematical Electron; a Simulation Hypothesis (Summary)

7 Pages Posted: 1 Jul 2017 Last revised: 2 Oct 2019

Date Written: November 24, 2014


The Simulation Hypothesis proposes that all of reality, including the earth and the universe, is in fact an artificial simulation, analogous to a computer simulation, and as such our reality is an illusion. Here is summarized a method for programming mass, length, time and charge (MLTA) units as mathematical (geometrical) objects that are indistinguishable from their corresponding physical structures (the Planck units). A dimensionless formula for a mathematical electron is proposed; f_e = 4π^2r^3 (r = 2^6 3 π^2 α Ω^5) where the fine structure constant α = 137.03599... and Ω = 2.00713494... are mathematical constants. From this formula the MLTA geometries can be derived as; M = (1), T = (2π), L = (2π^2Ω^2), A = (64π Ω)^3/α. As geometrical objects they are independent of any set of units and also of any numbering system. As they are a function of f_e they are not independent and so we can replace designations such as the SI units (kg, m, s, A) with a rule set that defines their respective relationships; mass = u^{15}, length = u^{-13}, time = u^{-30}, ampere = u^{3}. As f_e is unit-less (u^0) we find these objects recombine in the following unit ratios; units (M^9T^{11}/L^{15}) = (AL)^3/T ... = 1. To translate MLTA from geometrical objects to corresponding Planck unit equivalents requires an additional 2 system-dependent scalars. The CODATA 2014 physical constants may thus be derived via the 2 (fixed) mathematical constants (α, Ω) and the 2 scalars according to the rule set u. As all the constants can thus be defined as overlapping geometrical objects, the least precise constants (G, h, e, m_e, k_B...) can be solved via the 4 most precise (c, mu_0, R, α), numerical precision then limited by the precision of the fine structure constant α.

Keywords: mathematical universe, simulation hypothesis, mathematical electron, Planck unit, magnetic-monopole, fine structure constant alpha, Omega, black-hole electron, sqrt, Planck momentum, Matrix, source code, program, Platonism, mathematical realism

JEL Classification: C00

Suggested Citation

Macleod, Malcolm, Programming Physical Planck Units From a Mathematical Electron; a Simulation Hypothesis (Summary) (November 24, 2014). Available at SSRN: or

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