The Sqrt of Planck Momentum and the Mathematical Electron

3 Pages Posted: 22 May 2020

Date Written: December 24, 2019


The sqrt of Planck momentum, denoted here as Q, is attributed as a distinct Planck unit and is used to link the mass (gravity) constants with the charge (electric) constants. From these constants, formulas for a magnetic monopole and then an electron frequency in terms of magnetic monopoles and Planck time are derived. The electron frequency formula has units yet is unit-less suggesting that within the electron there is a ratio of units whereby they overlap and cancel (the electron is a mathematical object, units = 1). Consequently of the SI units (kg, m, s, A, K) only 2 are required as from these the rest may be derived. This then permits us to define the least precise constants $G, h, e, m_e, k_B$ in terms of the most precise $c, \mu_0$ (exact values), the fine structure constant $\alpha$ (10-11 digits) and the Rydberg constant $R$ (12-13 digits). Results are consistent with CODATA 2014.

Keywords: sqrt Planck momentum, Planck momentum, mathematical electron, magnetic monopole, monopole, Planck unit, simulation hypothesis, mathematical universe

JEL Classification: C60

Suggested Citation

Macleod, Malcolm, The Sqrt of Planck Momentum and the Mathematical Electron (December 24, 2019). Available at SSRN: or

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