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Textbooks give as basic constants of physics (in the kg m s System):

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.

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Textbooks give as basic constants of physics (in the kg m s System):

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  1. Expression of the dimensionless constants of nature as function of proton and electron propertiesKarl Otto Greulich, Fritz Lipmann Institute, Beutenbergstr. 11 D 07745 Jena kog @ fli-leibniz.de The spectroscopic fine structure constant a = 1 / 137.037, the ratio of proton and electron mass b = 1836.12 and the gravitation factor g = 2.2683 * 1039, are expressed as combination of proton mass and electron- and Planck - mass and length. When me, mproton and re are expressed as multiples of the corresponding Planck units, i. e. with mproton = mproton* mpl, me= me* mpl and re = re * 0.5 * lpl, the system of dimensionless constants of nature becomes a = re * meb = mproton/ me g =re /mproton The longstanding question whether a, bandg 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.

  2. Textbooks give as basic constants of physics (in the kg m s System): mp = 1.673 *10-27 kg me = 9.110 *10-31 kg ko e2 = 23.067 *10-29 N m2 h = 6.625 *10-34 J s c = 2.998 * 108 m / s G = 6.672 * 10 –11 N m2 / kg2 From these constants, more basic dimensionless constants are derived which allow calculating all values above: a = ko e2 / (hc) = 1 / 137.037 fine structure constant, ratio of Coulomb interaction and strong interaction ”It (a) is one of the greatest damn mysteries of physics: A magic number with no understanding by man” and ”we don’t 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 b = mp / me = 1836.12 ratio of proton versus electron mass g = ko e2 / (me *mp * G) = 2.268 * 1039 ratio of Coulomb interaction and gravitation (g ) 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

  3. The Planck Unitsa) Mathematicallythe only combinations of G(gravitation constant),h(Planck const. = h / 2p), c (vacuum speed of light),which give a length, mass, time etc. for examplemPl = √ h * c / G= 2.17645 * 10 - 8 kglPl = √ h * G / c3 = 1.61624 * 10- 35 mb) PhysicallyThe Planck length is the de Broglie wavelength of the Planck mass and simultaneously its Schwarzschild radiusAn attempt to localise a Planck mass in a volume with dimensions of the Planck length results in a black (micro) hole

  4. Expression of electron and proton properties as multiples of Planck unitsre = re / (0.5 * lPl) = 1.4086 * 10-15 m / 1.61624 * 10- 35 m = 1.7430 * 1020me = me / mpl = 9.110 *10-31 kg / 2.17645 * 10- 8 kg = 4.1857 * 10-23mproton= m proton / mPl = 0.768 * 10-19Deriving aFrom the definition of Planck mass and Planck length -------> the de Broglie relationship for these two units can be derivedmPl = √ h * c / GlPl = √ h * G / c3 ====>mPl * lPl = h / cTextbook: re = koe2 / 2 * me * c2 ====> koe2 = 2 * re * me * c2a = koe2 / h * c = 2 * re * me * c2 / (h * c) = 2 * re * me * c / ha= 2 * re* me / lPl * mPl=re* meCheck of resultre * me =1.7430 * 1020* 4. 18572 * 10-23= 7.2957 * 10-3 =1 /137.06

  5. Deriving gmPl = √h * c / GlPl = √h * G / c3 G = lPl2 c3 / h G = h c / mPl ==> G = c2 * lPl / mPlg = koe2 / (me* mproton * G) = koe2* mPl *c2 / ( me * mproton * lPl) g = koe2 * mPl * mPl * c2 / ( me * mproton * h / c) (with de Broglie : h = mPl * lPl * c)g= a * mPl * mPl / ( me * mproton)= re * me / (me * mproton )g = re / mproton= 1.7430 * 1020/0.768 * 10-19 = 2.268 * 1039

  6. What type of force K is this ???K = ko*e1* e2 / r2with ko = Coulomb constant, e1 and e2 two different charges and r the distance between them

  7. Gravitation expressed as Coulomb interactionTextbook Result of this consideration G = ko e2 / (me *mproton * g) = ko e2 * mproton/ (me*mproton* re) mProton / m Proton =1 / m pland me = me * mpl= ko e2 / (me *mPl*mPl* re) re*me = aG= ko e2 / (a * mPl2)The gravitational force between two masses m1 and m2 then becomesKgrav = G * m1 * m2 / r2 =Kgrav = ko e2 * m1 * m2 / (a * mPl2* r2)Kgrav = (1 / a) ko*e1* e2 / r2where e1 = e *m1 / mPl and e2 = e *m2 / mPlThe gravitational force between two masses is identical to the Coulomb force between two opposite charges, which are defined by e * m / mpl.

  8. Conclusion”It (a) is one of the greatest damn mysteries of physics: A magic number with no understanding by man” and ”we don’t know what .... to do... to make this number come out- without putting it in secretly”a = re * meperhaps not too exciting, it may have been put in secretlyb = mproton/ metrivial“(g ) is simply the largest number the almighty God could write during the first day of creation”. g = re /mproton that really opens the path to some new considerationsThe longstanding question whether a, bandg 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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