Programming Planck units from a virtual electron: a simulation hypothesis

Abstract

The simulation hypothesis proposes that all of reality is an artificial simulation. In this article I describe a simulation model that derives Planck level units as geometrical forms from a virtual (dimensionless) electron formula $f_{e}$ that is constructed from 2 unit-less mathematical constants; the fine structure constant $\alpha$ and $\Omega = 2.00713494 \ldots$ ( $ f_{e} = 4\pi^{2}r^{3}$ , $ r = 2^{6} 3 \pi^{2} \alpha \Omega^{5}$ ). The mass, space, time, charge units are embedded in $ f_{e}$ according to these ratios; $ M^{9}T^{11}/L^{15} = (AL)^{3}/T$ ( $ {\rm units} = 1$ ), giving mass $ M=1$ , time $T=2\pi$ , length $ L=2\pi^{2}\Omega^{2}$ , ampere $ A = (4\pi \Omega)^{3}/\alpha$ . We can thus, for example, create as much mass M as we wish but with the proviso that we create an equivalent space L and time T to balance the above. The 5 SI units kg, m, s, A, K are derived from a single unit $ u = \sqrt{({\rm velocity/mass})}$ that also defines the relationships between the SI units: $ {\rm kg}= u^{15}$ , $ {\rm m}= u^{-13}$ , $ {\rm s}= u^{-30}$ , $ {\rm A}= u^{3}$ , $ k_{B} = u^{29}$ . To convert MLTA from the above $ \alpha$ , $ \Omega$ geometries to their respective SI Planck unit numerical values (and thus solve the dimensioned physical constants G, h, e, c, me, kB) requires an additional 2-unit-dependent scalars. Results are consistent with CODATA 2014. The rationale for the virtual electron was derived using the sqrt of momentum P and a black-hole electron model as a function of magnetic-monopoles AL (ampere-meters) and time T.