# Physical constant (anomaly)

Physical constant anomalies as evidence for a simulation universe

The mksa system of units is a physical system of measurement that uses the kilogram, meter, second and ampere (m, kg, s, A). These form the SI base units.

A physical constant, sometimes fundamental physical constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. Common examples being the speed of light c, the gravitational constant G, the Planck constant h and the elementary charge e. These constants can be divided into dimensioned constants which are measured in terms of the units (kg, m, s, A), and dimensionless constants such as the fine structure constant alpha which are unit-less (units = 1), and so independent of any numbering system or system of units.

Although the units (kg, m, s, A) are considered to be independent of each other, we do not measure distance using amperes and mass for example, there are anomalies which occur in certain combinations of the dimensioned physical constants which suggest a mathematical (unit number) relationship[1]; (kg = 15, m = -13, s = -30, A = 3, K = 20). This questions the independence of these units and so also the fundamental nature of the dimensioned physical constants, for if the units may be interchangeable, then so too these constants.

Furthermore, analysis of these anomalies suggest mathematical structures that we may associate with the simulation hypothesis. This is because the simulation hypothesis requires that these units can overlap and cancel, for the universe does not exist outside of the 'Computer' (the Programmer God hypothesis). Evidence these mksa units do cancel according to this unit number relationship[2] can therefore be construed as evidence we are in a simulation. The electron itself, being unit-less (units = 1), is an example of a mathematical particle.

## Anomalies

### Calculated (from R, c, μ0, α)

If we assign a unit number u to each of the SI units (kg = 15, m = -13, s = -30, A = 3, K = 20), then by matching the unit numbers we can numerically solve the least precise (CODATA 2014) dimensioned physical constants (G, h, e, me, kB ...) using the 3 most precise; speed of light c (exact value), vacuum permeability μ0 (exact value), Rydberg constant R (12-13 digits) and the dimensionless fine structure constant 'α'. The SI units themselves do not match and so officially the results must be simply coincidence, but the precision cannot be easily dismissed. The rationale for these results is explained with the introduction of scalars (below).

Table 1. R=10973731.568508 (u=13) ... c=299792458 (u=17) ... μ0=4π/107 (u=56) ... α=137.035999139 (u=0) ... (CODATA 2014)
Constant Formula* Units* Calculated* (from R, c, μ0, α) CODATA 2014 [3] Units
Planck constant ${\displaystyle {(h^{*})}^{3}={\frac {2\pi ^{10}{\mu _{0}}^{3}}{3^{6}{c}^{5}\alpha ^{13}{R}^{2}}}}$ ${\displaystyle {\frac {kg^{3}}{A^{6}s}}}$, u = 15*3-3*6+30 = 57 h* = 6.626 069 134 e-34 h = 6.626 070 040(81) e-34 ${\displaystyle {\frac {kg\;m^{2}}{s}}}$, u = 15-13*2+30 = 19
Gravitational constant ${\displaystyle {(G^{*})}^{5}={\frac {\pi ^{3}{\mu _{0}}}{2^{20}3^{6}\alpha ^{11}{R}^{2}}}}$ ${\displaystyle {\frac {kg\;m^{3}}{A^{2}s^{2}}}}$, u = 15-13*3-3*2+30*2 = 30 G* = 6.672 497 192 29 e11 G = 6.674 08(31) e-11 ${\displaystyle {\frac {m^{3}}{kg\;s^{2}}}}$, u = -13*3-15+30*2 = 6
Elementary charge ${\displaystyle {(e^{*})}^{3}={\frac {4\pi ^{5}}{3^{3}{c}^{4}\alpha ^{8}{R}}}}$ ${\displaystyle {\frac {s^{3}}{m^{3}}}}$, u = -30*4+13*3 = -81 e* = 1.602 176 511 30 e-19 e = 1.602 176 620 8(98) e-19 ${\displaystyle As}$, u = 3-30 = -27
Boltzmann constant ${\displaystyle {(k_{B}^{*})}^{3}={\frac {\pi ^{5}{\mu _{0}}^{3}}{3^{3}2{c}^{4}\alpha ^{5}{R}}}}$ ${\displaystyle {\frac {kg^{3}}{s^{2}A^{6}}}}$, u = 15*3+30*2-3*6 = 87 kB* = 1.379 510 147 52 e-23 kB = 1.380 648 52(79) e-23 ${\displaystyle {\frac {kg\;m^{2}}{s^{2}\;K}}}$, u = 15-26+60-20 = 29
${\displaystyle x={\frac {(k_{B}^{*})(e^{*})c}{(h^{*})}}}$ ${\displaystyle {\frac {m\;A}{s\;K}}}$, u = -13+3+30-20 = 0 x = 1.0 kBec/h = 1.000 825 132 ${\displaystyle {\frac {m\;A}{s\;K}}}$, u = 0
Electron mass ${\displaystyle {(m_{e}^{*})}^{3}={\frac {16\pi ^{10}{R}{\mu _{0}}^{3}}{3^{6}{c}^{8}\alpha ^{7}}}}$ ${\displaystyle {\frac {kg^{3}s^{2}}{m^{6}A^{6}}}}$, u = 15*3-30*2+13*6-3*6 = 45 me* = 9.109 382 312 56 e-31, u = 15 me = 9.109 383 56(11) e-31 ${\displaystyle kg}$, u = 15
${\displaystyle x={\frac {2^{3}\pi ^{5}({k_{B}}^{*})}{3^{3}\alpha ^{6}({e^{*}})^{2}({m_{e}}^{*})c^{4}}}}$ ${\displaystyle {\frac {1}{m^{2}A^{2}K}}}$, u = 13*2-3*2-20 = 0 x = 1.0 5kB/(27α6e2mec4) = 1.000 825 ${\displaystyle {\frac {1}{m^{2}A^{2}K}}}$, u = 0
Gyromagnetic ratio ${\displaystyle ({(\gamma _{e}^{*})/2\pi })^{3}={\frac {g_{e}^{3}3^{3}c^{4}}{2^{8}\pi ^{8}\alpha \mu _{0}^{3}R_{\infty }^{2}}}}$ ${\displaystyle {\frac {m^{3}s^{2}A^{6}}{kg^{3}}}}$, u = -13*3-30*2+3*6-15*3 = -126 e*/2π) = 28024.953 55 γe/2π = 28024.951 64(17) ${\displaystyle {\frac {A\;s}{kg}}}$, u = -42
Planck mass ${\displaystyle ({m_{P}^{*}})^{15}={\frac {2^{25}\pi ^{13}{\mu _{0}}^{6}}{3^{6}c^{5}\alpha ^{16}R^{2}}}}$ u = ${\displaystyle {\frac {kg^{6}m^{3}}{s^{7}A^{12}}}}$, u = 15*6-13*3+30*7-3*12 = 225 mP* = 0.217 672 817 580 e-7 mP = 0.217 647 0(51) e-7 ${\displaystyle kg}$, u = 15
Planck length ${\displaystyle ({l_{p}^{*}})^{15}={\frac {\pi ^{22}{\mu _{0}}^{9}}{2^{35}3^{24}\alpha ^{49}c^{35}R^{8}}}}$ ${\displaystyle {\frac {kg^{9}s^{17}}{m^{18}A^{18}}}}$, u = 15*9-30*17+13*18-3*18 = -195 lp* = 0.161 603 660 096 e-34 lp = 0.161 622 9(38) e-34 ${\displaystyle m}$, u = -13
${\displaystyle x={\frac {2^{11}\pi ^{3}(G^{*})^{2}(k_{B}^{*})}{\alpha ^{2}(h^{*})(c^{*})^{2}(e^{*})(m_{P}^{*})}}}$ ${\displaystyle {\frac {m^{4}}{kg^{3}s^{4}A\;K}}}$, u = -13*4-15*3+30*4-3-20 = 0 x = 1.0 211π3G2kB/(α2hc2emP) = 1.001 418 ${\displaystyle {\frac {m^{4}}{kg^{3}s^{4}A\;K}}}$, u = 0

### Natural Planck units*

From the above we can extrapolate to this set of (Planck scale) objects MLTVA as the geometry of 2 dimensionless constants; alpha and Omega,[4].

...ihre Bedeutung für alle Zeiten und für alle, auch außerirdische und außermenschliche Kulturen notwendig behalten und welche daher als »natürliche Maßeinheiten« bezeichnet werden können...

...These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as "natural units"... -Max Planck [5][6]
Table 2. Geometrical units
Attribute Geometrical object Unit number
mass ${\displaystyle M=(1)}$ ${\displaystyle 15}$
time ${\displaystyle T=(\pi )}$ ${\displaystyle -30}$
velocity ${\displaystyle V=(2\pi \Omega ^{2})}$ ${\displaystyle 17}$
length ${\displaystyle L=(2\pi ^{2}\Omega ^{2})}$ ${\displaystyle -13}$
ampere ${\displaystyle A=({\frac {2^{7}\pi ^{3}\Omega ^{3}}{\alpha }})}$ ${\displaystyle 3}$

(inverse) fine structure constant α = 137.035999139, Omega = 2.0071349496

#### Natural constants*

Table 3. Natural constants*
SI constant Natural constant* unit number
Speed of light c* = V 17
Planck constant ${\displaystyle h^{*}=2\pi MVL}$ 15+17-13=19
Gravitational constant ${\displaystyle G^{*}={\frac {V^{2}L}{M}}}$ 34-13-15=6
Elementary charge ${\displaystyle e^{*}=AT}$ 3-30=-27
Boltzmann constant ${\displaystyle k_{B}^{*}={\frac {2\pi VM}{A}}}$ 17+15-3=29
Vacuum permeability ${\displaystyle \mu _{0}^{*}={\frac {4\pi V^{2}M}{\alpha LA^{2}}}}$ 34+15+13-6=56

### Calculated (from α, Ω, scalars v, r)

As alpha and Omega can have numerical values (alpha = 137.035999139, Omega = 2.0071349496), the MLTVA objects can have numerical values (i.e.: V = 2πΩ2 = 25.3123819), and so we can use dimensioned numerical scalars to convert from the MLTVA objects to SI constants.

Although we may assign scalars to each of the MLTVA objects, via the unit number relationship we find that we need only 2 scalars to define the rest (by assigning values to any 2 scalars, the other scalars are then defined by default, consequently the CODATA 2014 values are used as only 2 constants (c, μ0) are assigned exact values, following the 2019 redefinition of SI base units , 4 constants have been independently assigned exact values which is problematic in terms of this model).

Here we use scalars (v, u = 17) and (r, u = 8):

scalar v = 11843707.905 m/s gives c = V*v = 25.3123819*11843707.905 m/s = 299792458 m/s (SI units)
scalar v = 7359.3232155 miles/s gives c = V*v = 186282 miles/s (imperial units)
scalar r = 0.712562514304, units = ${\displaystyle ({\frac {kg\;m}{s}})^{1/4}}$

Table 4. SI physical constants calculated from α, Ω, v (u = 17), r (u = 8)
CODATA 2014 [7] SI unit Natural constant* unit number
c = 299792458 ${\displaystyle {\frac {m}{s}}}$ (u=17) c* = V = 25.3123819329 * ${\displaystyle v}$ = 299792458 -13+30=17
h = 6.626 070 040(81) e-34 ${\displaystyle {\frac {kg\;m^{2}}{s}}}$ (u=15-26+30=19) h* = ${\displaystyle 2\pi MVL}$ = 12647.240312 * ${\displaystyle {\frac {r^{13}}{v^{5}}}}$ = 6.626 069 134 e-34 13*8-17*5=19
G = 6.674 08(31) e-11 ${\displaystyle {\frac {m^{3}}{kg\;s^{2}}}}$ (u=-39-15+60=6) G* = ${\displaystyle {\frac {V^{2}L}{M}}}$ = 50950.554778 * ${\displaystyle {\frac {r^{5}}{v^{2}}}}$ = 6.672 497 192 29 e11 5*8-2*17=6
e = 1.602 176 620 8(98) e-19 ${\displaystyle C=As}$ (u=3-30=-27) e* = ${\displaystyle AT}$ = 735.706358485 * ${\displaystyle {\frac {r^{3}}{v^{3}}}}$ = 1.602 176 511 30 e-19 3*8-3*17=-27
kB = 1.380 648 52(79) e-23 ${\displaystyle {\frac {kg\;m^{2}}{s^{2}\;K}}}$ (u=15-26+60-20=29) kB* = ${\displaystyle {\frac {2\pi VM}{A}}}$ = 0.679138336 * ${\displaystyle {\frac {r^{10}}{v^{3}}}}$ = 1.379 510 147 52 e-23 10*8-3*17=29

This also gives the rationale for why the constants can be derived in terms of (R, c, μ0) as was demonstrated above;

${\displaystyle {(h^{*})}^{3}=(2^{3}\pi ^{4}\Omega ^{4}{\frac {r^{13}u^{19}}{v^{5}}})^{3}={\frac {3^{19}\pi ^{12}\Omega ^{12}r^{39}}{v^{15}}},\;u=57}$ ... and ... ${\displaystyle {\frac {2\pi ^{10}{(\mu _{0}^{*})}^{3}}{3^{6}{(c^{*})}^{5}\alpha ^{13}{(R^{*})}^{2}}}={\frac {3^{19}\pi ^{12}\Omega ^{12}r^{39}}{v^{15}}},\;u=57}$

Rydberg constant ${\displaystyle R=({\frac {m_{e}}{4\pi L\alpha ^{2}M}})}$

### Calculated (scalars = 1)

We can find combinations of the physical constants where the unit numbers and scalars cancel, these combinations, which are unit-less (units = 1, scalars = 1), will then return the same numerical value as the (Planck) MLTVA objects. CODATA 2014 mean values are used.

If the scalars have cancelled, and as the scalars embed the numerical values as well as the units, then these combinations are defaulting to the underlying MLTVA objects. As the numerical values and units have both cancelled, this should apply to any set of units, even extraterrestrial and non-human ones, suggesting that these MLTVA objects are 'natural' units.

Note: the geometry ${\displaystyle \color {red}(\Omega ^{15})^{n}\color {black}}$ (integer n ≥ 0) is common to all ratios where units = scalars = 1.


Table 5. Dimension-less physical constant combinations (units = scalars = 1)
CODATA 2014 natural constant* units scalars
${\displaystyle {\frac {k_{B}ec}{h}}=}$ 1.000 8254 ${\displaystyle {\frac {(k_{B}^{*})(e^{*})(c^{*})}{(h^{*})}}}$ = 1.0 ${\displaystyle {\frac {(u^{29})(u^{-27})(u^{17})}{(u^{19})}}=1}$ ${\displaystyle ({\frac {r^{10}}{v^{3}}})({\frac {r^{3}}{v^{3}}})(v)/({\frac {r^{13}}{v^{5}}})=1}$
${\displaystyle {\frac {h^{3}}{e^{13}c^{24}}}=}$ 0.228 473 639... 10-58 ${\displaystyle {\frac {(h^{*})^{3}}{(e^{*})^{13}(c^{*})^{24}}}={\frac {\alpha ^{13}}{2^{106}\pi ^{64}(\color {red}\Omega ^{15})^{5}\color {black}}}=}$ 0.228 473 759... 10-58 ${\displaystyle {\frac {(u^{19})^{3}}{(u^{-27})^{13}(u^{17})^{24}}}=1}$ ${\displaystyle ({\frac {r^{13}}{v^{5}}})^{3}/({\frac {r^{3}}{v^{3}}})^{13}(v^{24})=1}$
${\displaystyle {\frac {c^{35}}{\mu _{0}^{9}R^{7}}}=}$ 0.326 103 528 6170... 10301 ${\displaystyle {\frac {(c^{*})^{35}}{(\mu _{0}^{*})^{9}(R^{*})^{7}}}=2^{295}\pi ^{157}3^{21}\alpha ^{26}\color {red}(\Omega ^{15})^{15}\color {black}=}$ 0.326 103 528 6170... 10301 ${\displaystyle {\frac {(u^{17})^{35}}{(u^{56})^{9}(u^{13})^{7}}}=1}$ ${\displaystyle (v^{35})/(r^{7})^{9}({\frac {v^{5}}{r^{9}}})^{7}=1}$
${\displaystyle {\frac {c^{9}e^{4}}{m_{e}^{3}}}=}$ 0.170 514 342... 1092 ${\displaystyle {\frac {(c^{*})^{9}(e^{*})^{4}}{(m_{e}^{*})^{3}}}=2^{97}\pi ^{49}3^{9}\alpha ^{5}(\color {red}\Omega ^{15})^{5}\color {black}=}$ 0.170 514 368... 1092 ${\displaystyle {\frac {(u^{29})(u^{-27})(u^{17})}{(u^{19})}}=1}$ ${\displaystyle (v^{9})({\frac {r^{3}}{v^{3}}})^{4}/({\frac {r^{4}}{v}})^{3}=1}$
${\displaystyle {\frac {k_{B}}{e^{2}m_{e}c^{4}}}=}$ 73 095 507 858. ${\displaystyle {\frac {(k_{B}^{*})}{(e^{*})^{2}(m_{e}^{*})(c^{*})^{4}}}={\frac {3^{3}\alpha ^{6}}{2^{3}\pi ^{5}}}=}$ 73 035 235 897. ${\displaystyle {\frac {(u^{29})}{(u^{-27})^{2}(u^{15})(u^{17})^{4}}}=1}$ ${\displaystyle ({\frac {r^{10}}{v^{3}}})/({\frac {r^{3}}{v^{3}}})^{2}({\frac {r^{4}}{v}})(v)^{4}=1}$
${\displaystyle {\frac {hc^{2}em_{p}}{G^{2}k_{B}}}=}$ 3.376 716 ${\displaystyle {\frac {(h^{*})(c^{*})^{2}(e^{*})(m_{p}^{*})}{(G^{*})^{2}(k_{B}^{*})}}={\frac {2^{11}\pi ^{3}}{\alpha ^{2}}}=}$ 3.381 506 ${\displaystyle {\frac {(u^{19})(u^{17})^{2}(u^{-27})(u^{15})}{(u^{6})^{2}(u^{29})}}=1}$ ${\displaystyle ({\frac {r^{13}}{v^{5}}})v^{2}({\frac {r^{3}}{v^{3}}})({\frac {r^{4}}{v^{1}}})/({\frac {r^{5}}{v^{2}}})^{2}({\frac {r^{10}}{v^{3}}})=1}$

#### Fine structure constant

${\displaystyle {\frac {2(h^{*})}{(\mu _{0}^{*})(e^{*})^{2}(c^{*})}}=2({2^{3}\pi ^{4}\Omega ^{4}})/({\frac {\alpha }{2^{11}\pi ^{5}\Omega ^{4}}})({\frac {2^{7}\pi ^{4}\Omega ^{3}}{\alpha }})^{2}(2\pi \Omega ^{2})=\color {red}\alpha \color {black},\;{\frac {u^{19}}{u^{56}(u^{-27})^{2}u^{17}}}=1,\;({\frac {r^{13}}{v^{5}}})({\frac {1}{r^{7}}})({\frac {v^{6}}{r^{6}}})({\frac {1}{v}})=1}$
Table 6. fine structure constant (units = scalars = 1)
CODATA 2014 natural constant*
${\displaystyle {\frac {2h}{\mu _{0}e^{2}c}}=\color {red}\alpha \color {black}=}$ 137.035 999 139(31) ${\displaystyle {\frac {2(h^{*})}{(\mu _{0}^{*})(e^{*})^{2}(c^{*})}}=\color {red}\alpha \color {black}}$
${\displaystyle {\sqrt {\frac {2^{11}\pi ^{3}G^{2}k_{B}}{hc^{2}em_{p}}}}=}$ 137.133 167 47 ${\displaystyle {\sqrt {\frac {2^{11}\pi ^{3}(G^{*})^{2}(k_{B}^{*})}{(h^{*})(c^{*})^{2}(e^{*})(m_{p}^{*})}}}=\color {red}\alpha \color {black}}$
${\displaystyle ({\frac {2^{3}\pi ^{5}k_{B}}{3^{3}e^{2}m_{e}c^{4}}})^{1/6}=}$ 137.054 833 44 ${\displaystyle ({\frac {2^{3}\pi ^{5}(k_{B}^{*})}{3^{3}(e^{*})^{2}(m_{e}^{*})(c^{*})^{4}}})^{1/6}=\color {red}\alpha \color {black}}$
${\displaystyle {\frac {2^{9}\pi ^{2}t_{p}}{m_{P}^{4}\epsilon _{0}}}=}$ 137.119 576 89 ${\displaystyle {\frac {2^{9}\pi ^{2}(t_{p})^{*}}{(m_{P}^{*})^{4}(\epsilon _{0}^{*})}}=\color {red}\alpha \color {black}}$

### Mathematical electron (scalars = 1)

The electron is an example of a combination that is dimensionless (units = scalars = 1). The electron function (the mathematical formula for the electron) fe can be defined, for example, in terms of ALT where AL as an ampere-meter (ampere-length = e*c) are the units for a magnetic monopole.

${\displaystyle T=\pi {\frac {r^{9}}{v^{6}}},\;u^{-30}}$
${\displaystyle \sigma _{e}={\frac {3\alpha ^{2}AL}{2\pi ^{2}}}={2^{7}3\pi ^{3}\alpha \Omega ^{5}}{\frac {r^{3}}{v^{2}}},\;u^{-10}}$
${\displaystyle f_{e}={\frac {\sigma _{e}^{3}}{2T}}={\frac {(2^{7}3\pi ^{3}\alpha \Omega ^{5})^{3}}{2\pi }},\;units={\frac {(u^{-10})^{3}}{u^{-30}}}=1,scalars=({\frac {r^{3}}{v^{2}}})^{3}{\frac {v^{6}}{r^{9}}}=1}$
${\displaystyle f_{e}=4\pi ^{2}(2^{6}3\pi ^{2}\alpha \Omega ^{5})^{3}=.23895453...x10^{23},\;units=1}$

#### Electron parameters

Associated with the electron are dimensioned parameters, these parameters however are a function of the base MLTVA units, the formula fe dictating the frequency of these units. By setting MLTVA to their SI Planck unit equivalents;

electron mass ${\displaystyle m_{e}={\frac {M}{f_{e}}}}$ (M = Planck mass)

electron wavelength ${\displaystyle \lambda _{e}=2\pi Lf_{e}}$ (L = Planck length)

elementary charge ${\displaystyle e=A\;T}$ (T = Planck time)