A surprisingly close relationship between
gravitation and electrostatic interaction
Karl Otto Greulich, Fritz Lipmann Institute, Beutenbergstr. 11 D 07745 Jena
http://www.fli-leibniz.de/www_kog/ Then click the symbol for Physics
Despite their formal identity, the physical core of gravitation and
electrostatic interaction is seen to be quite different.
When, however, both, the gravitation constant G and the Coulomb
constant are expressed in terms of Planck units it turns out that
G = k0e2 / (a * mPlanck2) and the gravitational force is
Kgrav = (1 / a) ko e1*e2 / r2
where a is the fine structure constant and mPlanck the Planck mass. The
charges e1 and e2 can be calculated from the elementary charge e and the
masses m1 and m2 which exert the gravitational force as e1 = e *m1 / mPlanck
and e2 = e * m2 / mPlanck. Thus it formally appears as if the gravitational
force is simply an electrostatic force between (very small) “gravitational
charges” e1 and e2, which are narrowly correlated with the mass.
Reference K.O. Greulich Expression of the dimensionless constants of nature as function of proton and electron properties
Verhandlungen der DPG 3/2006 Gr 303.1 http://www.fli-leibniz.de/www_kog (then click the symbol Phi for physics)
The Planck particle: the smallest black hole
Max Planck had combined G, c and h so that a mass, length, time ….. results
The Planck mass is only mass for which ►de Broglie wavelength = Schwarzschild radius
and, as will turn out t h a t mass, for which the „gravitational“ charge = e
Mass in Planck masses √ ħ* c / G = 2.17 * 10 - 8 kg = 4.18 * 1023 electron masses ≈ 1.22×1019 GeV/c2
y axis:
Diameter in Planck lengths √ħ * G / c3 = 1.61* 10- 35 m
x axis :
3.5
This „particle“ will be the basis
of the following discussion
3
2.5
2
1.5
Schwarzschild
radius smaller
than de Broglie
wavelength
No black hole
possible
1
Schwarzschild radius larger
than de Broglie wavelength
it "hides" the mass
0.5
0
0
0.5
1
1.5
2
2.5
The gravitation constant
G = ko e2 / (me * mproton * g)
can be expressed as
G= ko e2 / (a * mPl2)
See http://www.fli-leibniz.de/www_kog/ Then click the symbol for Physics
K.O. Greulich Expression of the dimensionless constants of nature as function of proton and
electron properties Verhandlungen der DPG 3/2006 Gr 303.1 second last slide
or verify using
G =6,67 * 10-11 Nm2/kg2
ko=9 *109 Nm2/C2
mPl = 2.17645 * 10- 8 kg
a =1/137.037
e =1,6 * 10-19 C
Gravitation expressed as Coulomb interaction
Result of the previous slide
G= ko e2 / (a * mPl2)
The gravitational force between two masses m1 and m2 then becomes
Kgrav = G * m1 * m2 / r2
Kgrav = ko e2 * m1 * m2 / (a * mPl2 * r2)
Kgrav = ko** e1* e2 / r2
This is n o t the electrostatic force, it is still gravitation
where e1 = e *m1 / √ a mPl and e2 = e *m2 / √ a mPl
or
e1 = rPl *m1 / √ a and e2 = rPl * m2 * √ a
where rPl is the true specific charge of the Planck particle
and rPl / √ a its specific gravitational charge (8,62 * 10-11 Cb / kg)
Conclusion
Karl Otto Greulich, Fritz Lipmann Institute, Beutenbergstr. 11 D 07745 Jena
http://www.fli-leibniz.de/www_kog/ Then click the symbol for Physics
Gravitation can be completely rewritten as electrostatics when
one assigns to matter a very small gravitational charge density of
e / (mPl
√ a)
= 8,62 * 10-11 Cb / kg =
√ G / ko
where e is the elementary charge, mPl the mass of of the Planck particle,
G, ko and a the gravitational, Coulomb and fine structure constant
The actual gravitational charge of a given mass is then
m * e / (mPl√ a)
So far unexplained is why gravitation is only attractive