# Expression of the dimensionless constants of nature as function of proton and electron properties Karl Otto Greulich, Fritz Lipmann Institute, Beutenbergstr.

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Expression of the dimensionless constants of nature as function of proton and electron properties Karl Otto Greulich, Fritz Lipmann Institute, Beutenbergstr. 11 D 07745 Jena kog @ fli-leibniz.de The spectroscopic fine structure constant = 1 / 137.037, the ratio of proton and electron mass and the gravitation factor = 2.2683 * 10 39, are expressed as combination of proton mass and electron- and Planck - mass and length. When m e, m proton and r e are expressed as multiples of the corresponding Planck units, i. e. with m proton = m proton * m pl, m e = m e * m pl and r e = r e * 0.5 * l pl, the system of dimensionless constants of nature becomes = r e * m e = m proton / m e = r e / m proton The longstanding question whether and have changed during ageing of the Universe can now be reduced to the question whether properties of the electron (and Proton) or the Planck units have changed. Gravitation can be expressed as a subclass of Coulomb interaction.

Textbooks give as basic constants of physics (in the kg m s System): m p = 1.673 *10 -27 kg m e = 9.110 *10 -31 kg k o e 2 = 23.067 *10 -29 N m 2 h = 6.625 *10 -34 J s c = 2.998 * 10 8 m / s G = 6.672 * 10 –11 N m 2 / kg 2 From these constants, more basic dimensionless constants are derived which allow calculating all values above: = k o e 2 / ( c) = 1 / 137.037 fine structure constant, ratio of Coulomb interaction and strong interaction It ( ) is one of the greatest damn mysteries of physics: A magic number with no understanding by man and we dont know what.... to do... to make this number come out- without putting it in secretly R.Feynman 1985 QED - The strange theory of light.., p. 129 = m p / m e = 1836.12 ratio of proton versus electron mass = k o e 2 / (m e * m p * G) = 2.268 * 10 39 ratio of Coulomb interaction and gravitation ) is simply the largest number the almighty God could write during the first day of creation. George Gamow, see J.D. Barrow 2004 The Constants of Nature, p.110 FOM2005 2

The Planck Units a) Mathematically the only combinations of G (gravitation constant ), (Planck const. = h / 2, c (vacuum speed of light), which give a length, mass, time etc. for example m Pl = * c / G = 2.17645 * 10 - 8 kg l Pl = * G / c 3 = 1.61624 * 10 - 35 m b) Physically The Planck length is the de Broglie wavelength of the Planck mass and simultaneously its Schwarzschild radius An attempt to localise a Planck mass in a volume with dimensions of the Planck length results in a black (micro) hole

Expression of electron and proton properties as multiples of Planck units r e = r e / (0.5 * l Pl ) = 1.4086 * 10 -15 m / 1.61624 * 10 - 35 m = 1.7430 * 10 20 m e = m e / m pl = 9.110 *10 -31 kg / 2.17645 * 10 - 8 kg = 4.1857 * 10 -23 m proton = m proton / m Pl = 0.768 * 10 -19 Deriving From the definition of Planck mass and Planck length -------> the de Broglie relationship for these two units can be derived m Pl = * c / G l Pl = * G / c 3 ====> m Pl * l Pl = / c Textbook: r e = k o e 2 / 2 * m e * c 2 ====> k o e 2 = 2 * r e * m e * c 2 k o e 2 / * c = 2 * r e * m e * c 2 / ( * c) = 2 * r e * m e * c / = 2 * r e * m e / l Pl * m Pl = r e * m e Check of result r e * m e = 1.7430 * 10 20 * 4. 18572 * 10 -23 = 7.2957 * 10 -3 = 1 /137.06

Deriving m Pl = * c / G l Pl = * G / c 3 G = l Pl 2 c 3 / G = c / m Pl ==> G = c 2 * l Pl / m Pl = k o e 2 / (m e * m proton * G) = k o e 2 * m Pl *c 2 / ( m e * m proton * l Pl ) = k o e 2 * m Pl * m Pl * c 2 / ( m e * m proton * / c ) (with de Broglie : = m Pl * l Pl * c) = * m Pl * m Pl / ( m e * m proton ) = r e * m e / (m e * m proton ) = r e / m proton = 1.7430 * 10 20 / 0.768 * 10 -19 = 2.268 * 10 39

What type of force K is this ??? K = k o * e 1 * e 2 / r 2 with k o = Coulomb constant, e 1 and e 2 two different charges and r the distance between them

Gravitation expressed as Coulomb interaction Textbook Result of this consideration G = k o e 2 / (m e * m proton * ) = k o e 2 * m proton / (m e * m proton * r e ) m Proton / m Proton =1 / m pl and m e = m e * m pl = k o e 2 / (m e * m Pl * m Pl * r e ) r e *m e = G= k o e 2 / ( * m Pl 2 ) The gravitational force between two masses m 1 and m 2 then becomes K grav = G * m 1 * m 2 / r 2 = K grav = k o e 2 * m 1 * m 2 / ( * m Pl 2 * r 2 ) K grav = (1 / ) k o * e 1 * e 2 / r 2 where e 1 = e *m 1 / m Pl and e 2 = e *m 2 / m Pl The gravitational force between two masses is identical to the Coulomb force between two opposite charges, which are defined by e * m / m pl.

ConclusionIt ( ) is one of the greatest damn mysteries of physics: A magic number with no understanding by man and we dont know what.... to do... to make this number come out- without putting it in secretly = r e * m e perhaps not too exciting, it may have been put in secretly = m proton / m e trivial ) is simply the largest number the almighty God could write during the first day of creation. = r e / m proton that really opens the path to some new considerations The longstanding question whether and have changed during ageing of the Universe can now be reduced to the question whether properties of the electron (and Proton) or the Planck units have changed.

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