The search for a link between electricity and gravity is actively pursued by the scientific community. My notes, including a brief presentation, can be found in the following documents. A summary is outlined in a table below.

"There is no unified field that we can experience. There is instead a unique field we always experience in its electric and gravitational duality"

An analysis of the tensor matrix where the diagonals are made close to zero show a point of instability which allow us to switch from a gravitational to an electric field. The consequence is a Planck black hole yielding new mathematical relationships among basic constants. The concept of time loses its meaning when going from our world to the black hole and the need to merge together the electric quantities with all the others brings about an apparent dimensional imbalance. Actually all equations are balanced because of quantity Wu also shown as (2π)4. All numbers are in accordance with the MKSA system even if its definition of electrical quantities were not devised for a future integration with quantum gravitation. The standard value for the Planck time is numerically very close to the ratio between gravity and electric force in an electron: its difference, disregarding a π2 factor, is only 0.2%. This is not a coincidence as they both refer to the same particle and the small difference is between a rotating and a non-rotating particle.

 Initial data

 c = 299792458       h = 6.62606944283x10-34       G = 6.672918952267x10-11

 Non-rotating particle

Planck time   tp

(π h G / c5)1/2

2.3950197x10-43

Planck mass   M

h / tp c2

3.0782613x10-8

Apparent Planck mass M0

M tp1/2

1.5064684x10-29

Planck permittivity   εp

(tp / 4 π2)1/4

8.825459772x10-12

Planck charge   Q

M (4 π εp G)1/2

2.648116x10-18

 Rotating particle - initial electron

Toroidal ratio of unitary force / unitary time Wu

(2 π)4 Q u2 / tu

1558.54545654

Initial fine struct. const.  α0

(tp Wu  / Q2)1/2

7.295873175x10-3

Initial electron charge e0

Q / (2 / α0 - 1)1/2

1.60233838x10-19

 Relations among fundamental constants

Vacuum fine structure constants

  Solve:

α3 - 2 α2 + (2 π)5 (π G / c3 h)1/2/107 = 0

or:                 α3 - 2 α2 + tp Wu  / 2 ε0 h c = 0

7.2973525719x10-3

1.999973470767

-7.270823339x10-3

G with current known data

α2 (2 - α)2 (e / 4 π2)4 c5 / π h

6.6729191x10-11

 Electron data

Charge   e

Q / (α / α0) (2 / α - 1)1/2

or:                     (Wu  t/ α (2 - α))1/2

1.602176549x10-19

Electron fine structure constants

  Solve:

α2 - 2 α + tp Wu  / e2  0

7.2973525719x10-3

1.99270264743

Permittivity   ε0

εp / (α / α0)2 (1 - α / 2)

8.8541878176x10-12

Mass   me

M0 (α/2)1/2 (α/α0)12 (1-α/2)3/8 ((2-α)/(2-α0))1/4

9.10938272x10-31

Magnetic moment   μe
(Qh/4πM0) (α0/α)11/4((2-α)/(2-α0))7/(1-α/2)5/8

9.28476422x10-24

Electric force  e2/4 π ε0

Q2 α / 8 π εp

2.307077307x10-28

Gravitational force Fg

π ε 03 e2 (α / α0)32 (1 - α / 2)19/4 ((2 - α) / (2 - α0))1/2

5.53724511x10-71

Gravitational / electric force ratio   Fg / Fe

tp (α / α0)24 (1 - α / 2)3/4 ((2 - α) / (2 - α0))1/2

2.40011251x10-43

Magnetic moment / Bohr magneton ratio  μe / μB

(e0 / e)29/2 (α / α0)3 (1 - α / 2)1/4

1.001159652180758

 Electric field from gravitational variation

Materialization time   te

h / me c2

8.0932998x10-21

Gravit. field variation Δg G me / te 7.51067848x10-21
Electric field  e / 4 π ε0 Δg M / Q (α/α0)23 (1-α/2)1/4 ((α/2)(2-α)/(2-α0))1/2

1.439964471x10-9

With the exception of G, at 1.15 standard deviations, all other numbers are within one standard deviation if compared with the latest CODATA listing. All results are obtained from three basic constants only: c, h, G.


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