Programming Planck units via a virtual electron; a Simulation Hypothesis

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. In this essay I describe a method for programming units of mass, space, time and charge as geometrical objects from a virtual electron. As objects they are independent of any set of units and also of any numbering system. The virtual electron is a mathematical formula $f_e = 4\pi^2r^3$ ($r = 2^6 3 \pi^2 \alpha \Omega^5$) that is a construct of 2 unit-less constants; the fine structure constant $\alpha$ = 137.03599... and $\Omega$ = 2.00713494... thus $r$ is also unit-less. The units mass, time, length, ampere (MTLA) are not independent units but overlap and cancel (units = 1 ) in these ratio M$^9$T$^{11}$/L$^{15}$ and (AL)$^3$/T. These ratio are embedded within $f_e$ giving geometries M = (1), T = ($2\pi$), L = ($2\pi^2\Omega^2$), A = ($4\pi \Omega)^3/\alpha$. These units are formalized in an array structure $u$ that assigns relationships between them; mass = $u^{15}$, length = $u^{-13}$, time = $u^{-30}$, ampere = $u^{3}$. Velocity V would then become V = 2L/T = ($2\pi\Omega^2, u^{17}$). To translate MLTA from the above unit-less ($\alpha, \Omega$) geometries to their respective SI (or imperial) Planck unit values requires an additional 2 unit-dependent scalars. We may thereby derive the physical constants ($G, h, e, c, m_e, k_B$) via 2 (fixed) mathematical constants, 2 (variable) unit scalars and the reference unit $u$. Results are consistent with CODATA 2014.
Keywords black hole electron  Mathematical Universe  fine structure constant alpha  Planck units  Simulation Hypothesis  Simulated Universe  Planck momentum  magnetic monopole  Virtual Universe  Virtual electron
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