The sqrt of Planck momentum can potentially be used to link the mass constants and the charge constants [1] and so can be used to reduce the required number of SI units, this permits the least accurate physical constants, (G, h, e, me, kB ...) to be defined and solved using the 4 most precise constants (c, μ0, R, α). The electron is reduced to a construct of magnetic monopoles. In more general terms the sqrt of momentum is used to reference the dimensionless mathematical electron[2], a simulation hypothesis model.
As it has no assigned SI unit, it is denoted here as Q with units q whereby Planck momentum = 2 π Q2, unit = kg.m/s = q2. It can be argued that Q qualifies as an independent Planck unit.
The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to exactly 2.10^{-7} newton per meter of length.
A magnetic monopole is a hypothesized particle that is a magnet with only 1 pole. The unit for the magnetic monopole is the ampere-meter, the SI unit for pole strength (the product of charge and velocity) in a magnet (A m = e c). A proposed formula for a magnetic monopole σe;
The formula for an electron in terms of magnetic monopoles and Planck time
The Rydberg constant R∞, unit = 1/m (see Electron mass).
This however now gives us 2 solutions for length m, if we conjecture that they are both valid then there must be a ratio whereby the units q, s, kg overlap and cancel;
and so we can further reduce the number of units required, for example we can define s in terms of kg, q;
Replacing q with the more familiar m gives this ratio;
The Rydberg constant R∞ = 10973731.568508(65) has been measured to a 12 digit precision. The known precision of Planck momentum and so Q is low, however with the solution for the Rydberg we may re-write Q as Q15 in terms of the 4 most precise constants; c (exact), μ0 (CODATA 2014 exact), R (12 digits), α (11 digits);
From the above formula for Q15, the least accurate dimension-ed constants can now be defined in terms of c, μ0, R, α. The constants are first arranged until they include a Q15 term which can then be replaced by the above formula. Setting unit X as;
There is a solution for an r2 = q, it is the radiation density constant from the Stefan Boltzmann constant σ;
Physical constants; calculated vs experimental (CODATA)
Q is used in the context of SI units and so is related to the SI Planck momentum. The mathematical electron model uses geometrical objects for the Planck units and defines P as the sqrt of momentum with the unit u16. Although different sets of geometrical objects may be used in the mathematical electron model, so far only the following set can also translate to the Q related formulas and so Q places a limit on this model.
↑Macleod, M.J. "Programming Planck units from a virtual electron; a Simulation Hypothesis". Eur. Phys. J. Plus113: 278. 22 March 2018. doi:10.1103/10.1140/epjp/i2018-12094-x.
↑[1] | CODATA, The Committee on Data for Science and Technology | (2014)