## 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*, m_{e}, k_{B}) 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*.

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Macleod, M.J. Programming Planck units from a virtual electron: a simulation hypothesis.
*Eur. Phys. J. Plus* **133, **278 (2018). https://doi.org/10.1140/epjp/i2018-12094-x

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