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Sqrt Planck momentum

The sqrt of Planck momentum

The square root of momentum is used in the mathematical electron [1], a simulation hypothesis model, to link the mass constants with the charge constants. In SI unit terms the sqrt of Planck momentum denoted Q with units q;

Planck momentum = 2 π Q2, unit = kg.m/s = q2


mass constantsEdit

 

Planck mass : 

Planck energy : 

Planck length : 

Planck time : 

Planck force : 


charge constantsEdit

 

elementary charge : 

Planck temperature : 

Boltzmann constant : 

Magnetic field : 

Vacuum permittivity: 

Coulomb's constant : 

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.

 
 

Rewriting Planck length lp in terms of Q, c, α, μ0;

 


magnetic monopoleEdit

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). Proposed formula for a magnetic monopole; σe = 0.13708563 x10-6;

 
 

The Rydberg constant R, unit = 1/m.

 

This however now gives us 2 solutions for length m, if 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;

 
 

Electron mass as frequency of Planck mass:

 

Electron wavelength via Planck length:

 

Gravitation coupling constant:

 


Q15Edit

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; c, μ0, R, α;

 

From the formula for Q15 the least accurate dimensioned constants can be defined in terms of the most accurate constants; 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)
Constant Calculated from (R*, c, μ0, α*) CODATA 2014 [2]
Speed of light c* = 299 792 458, units = u17 c = 299 792 458 (exact)
Fine structure constant α* = 137.035 999 139 (mean) α = 137.035 999 139(31)
Rydberg constant R* = 10 973 731.568 508, units = u13 (mean) R = 10 973 731.568 508(65)
Vacuum permeability μ0* = 4π/10^7, units = u56 μ0 = 4π/10^7 (exact)
Planck constant h* = 6.626 069 134 e-34, units = u19 h = 6.626 070 040(81) e-34
Gravitational constant G* = 6.672 497 192 29 e11, units = u6 G = 6.674 08(31) e-11
Elementary charge e* = 1.602 176 511 30 e-19, units = u-19 e = 1.602 176 620 8(98) e-19
Boltzmann constant kB* = 1.379 510 147 52 e-23, units = u29 kB = 1.380 648 52(79) e-23
Electron mass me* = 9.109 382 312 56 e-31, units = u15 me = 9.109 383 56(11) e-31
Classical electron radius λe* = 2.426 310 2366 e-12, units = u-13 λe = 2.426 310 236 7(11) e-12
Planck mass mP* = .217 672 817 580 e-7, units = u15 mP = .217 647 0(51) e-7
Planck length lp* = .161 603 660 096 e-34, units = u-13 lp = .161 622 9(38) e-34
Von Klitzing constant RK* = 25812.807 455 59, units = u73 RK = 25812.807 455 5(59)
Gyromagnetic ratio γe/2π* = 28024.953 55, units = u-42 γe/2π = 28024.951 64(17)


AnalysisEdit

Sample standard formulas in terms of Q

 

 

 

 

 

 


where:


External linksEdit

ReferencesEdit

  1. Macleod, M.J. "Programming Planck units from a virtual electron; a Simulation Hypothesis". Eur. Phys. J. Plus 113: 278. 22 March 2018. doi:10.1103/10.1140/epjp/i2018-12094-x. 
  2. [1] | CODATA, The Committee on Data for Science and Technology | (2014)