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# Exact formula for the fine-structure constant α in terms of the golden ratio φ

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## Abstract

The purpose of many sciences is to find the most accurate mathematical formula that can be found in the experimental value of fine-structure constant. Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However,no numerological explanation has ever been accepted by the physics community. In this paper we will present the exact expression for the fine-structure constant. A exact expression for the fine-structure constant in terms of the golden angle,the relativity factor and the fifth power of the golden mean. Finally we will present the continued fractions for the fine-structure constant.
Exact formula for the fine-structure constant α in terms of the golden ratio φ
Stergios Pellis
sterpellis@gmail.com
ORCID iD: 0000-0002-7363-8254
Greece
13 October 2021
Abstract
The purpose of many sciences is to find the most accurate mathematical formula that can be found in the
experimental value of fine-structure constant. Attempts to find a mathematical basis for this dimensionless constant
have continued up to the present time. However,no numerological explanation has ever been accepted by the physics
community. In this paper we will present the exact expression for the fine-structure constant. A exact expression for
the fine-structure constant in terms of the golden angle,the relativity factor and the fifth power of the golden mean:
α-1=360·φ-2-2·φ-3+(3∙φ)-5
Finally we will present the continued fractions for the fine-structure constant.
Keywords
Fine-structure constant , Dimensionless physical constants ,Golden ratio , Golden angle , Relativity factor , Fifth
power of the golden mean
1. Introduction
Golden ratio φ is an omnipresent number in nature,found in the architecture of living creatures as well as human
buildings,music,finance,medicine,philosophy,and of course in physics and mathematics including quantum
computation. It is the most irrational number known and a number-theoretical chameleon with a self-similarity
property. The golden ratio can be found in nearly all domains of Science,appearing when self-organization processes
are at play and expressing minimum energy configurations. Several non-exhaustive examples are given in biology
(natural and artificial phyllotaxis, genetic code and DNA) physics (hydrogen bonds,chaos, superconductivity),
astrophysics (pulsating stars,black holes), chemistry (quasicrystals,protein AB models),and technology (tribology,
resistors, quantum computing, quantum phase transitions, photonics). The fifth power of the golden mean appears in
Phase transition of the hard hexagon lattice gas model, Phase transition of the hard square lattice gas
model,One-dimensional hard-boson model, Baryonic matter relation according to the E-infinity theory,Maximum
quantum probability of two particles,Maximum of matter energy density,Reciprocity relation between matter and
dark matter,Superconductivity phase transition, etc. Among the numbers in the Fibonacci range,the numbers 5and 13
seem to be the most important. Whereas number 5 is involved in the definition of the golden mean,number 13 is
found as a helix repetition number for instance in tubulin protein,thought to be the location from where our thinking
and consciousness originates.
The fine-structure constant is one of the most fundamental constants of physics. It describes the strength of the force
of electromagnetism between elementary particles in what is known as the standard model of particle physics. In
particular, the fine-structure constant sets the strength of electromagnetic interaction between light (photons) and
charged elementary particles such as electrons and muons. The quantity α was introduced into physics by A.
Sommerfeld in 1916 and in the past has often been referred to as the Sommerfeld fine-structure constant. In order to
explain the observed splitting or fine structure of the energy levels of the hydrogen atom, Sommerfeld extended the
Bohr theory to include elliptical orbits and the relativistic dependence of mass on velocity. One of the most important
numbers in physics is the fine-structure constant α which defines the strength of the electro-magnetic field. It is a
dimensionless number independent of how we define our units of mass,length,time or electric charge. A change in
these units of measurement leaves the dimensionless constant unchanged. The number can be seen as the chance that
an electron emits or absorbs a photon. It’s a pure number that shapes the universe to an astonishing degree. Paul Dirac
considered the origin of the number «the most fundamental unsolved problem of physics». The constant is
everywhere because it characterizes the strength of the electromagnetic force affecting charged particles such as
electrons and protons. Many eminent physicists and philosophers of science have pondered why α itself has the value
that it does,because the value shows up in so many important scenarios and aspects of physics. Nobody has come up
with any ideas that are even remotely convincing. A similar situation occurs with the proton-electron mass ratio μ,not
because of its ubiquity,but rather how chemistry can be based on two key electrically charged particles of opposite
electric charge that are opposite but of seemingly identical magnitude while their masses have a ratio that is quite
large yet finite. These two questions have a huge bearing on why physics and chemistry behave the way they do. The
product of the two quantities appears,at least at first glance,not to be so important. There is a dream,which,albeit more
often not confessed,occupies the most secret aspirations of theoreticians and is that of reducing the various constants
of Physics to simple formula involving integers and transcendent numbers. The fine-structure constant plays an
important role in modern physics. Yet it continues to be a mystery as to exactly what it represents and why it has the
mystical value it has.
2. The search for mathematical expression for the fine-structure constant
The mystery about the fine-structure constant is actually a double mystery. The first mystery the origin of its
numerical value has been recognized and discussed for decades. The second mystery the range of its domain is
generally unrecognized.
— M. H. MacGregor (2007). The Power of Alpha.
When I die my first question to the Devil will be: What is the meaning of the fine structure constant?
— Wolfgang Pauli
“God is a pure mathematician!' declared British astronomer Sir James Jeans. The physical Universe does seem to be
organized around elegant mathematical relationships. And one number above all others has exercised an enduring
fascination for physicists: 137,0359991.... It is known as the fine-structure constant and is denoted by the Greek
letter alpha (α).”
― Paul Davies
“While twentieth-century physicists were not able to identify any convincing mathematical constants underlying the
fine structure, partly because such thinking has normally not been encouraged, a revolutionary suggestion was
recently made by the Czech physicist Raji Heyrovska, who deduced that the fine structure constant, ...really is
defined by the [golden] ratio ....”
Carl Johan Calleman, The Purposeful Universe: How Quantum Theory and Mayan Cosmology Explain the Origin
and Evolution of Life
The fine-structure constant plays an important role in modern physics. Yet it continues to be a mystery as to exactly
what it represents and why it has the mystical value it has. The elementary charge of electron e was proposed by
Stoney in 1894 and discovered by Thomson in 1896,then Planck introduced the energy quanta h∙ν in 1901 and
explained it as photon E=h∙ν by Einstein in 1905. Planck first noticed in 1905 that e2/c and h have the same
dimension. In 1909,Einstein found that there are two fundamental velocities in physics: c and e2/h requiring
explanation. He said, “It seems to me that we can conclude from h=e2/c that the same modification of theory that
contains the elementary quantum eas a consequence,will also contain as a consequence the quantum structure of
radiation.” Albert Einstein was the first to use a mathematical formula for the fine-structure constant α in 1909. This
expression is:
with numerical value α=0,00733038286 with an error accuracy of 0,45%. Later many scientists used other
mathematical formulas for fine-structure constant but they are not at all accurate. These are Jeans 1913,Lewis Adams
1914,Lunn in 1922,Peirles in 1928 and others. Arthur Eddington was the first to focus on its inverse value and
suggested that it should be an integer,that the theoretical value is α-1=136. In his original document 1929 he applied
the value:
α-1=16+1/2×16×(16-1)=136
However,the experiments themselves consistently showed that α-1137. This forced him to look for an error in his
original theory. He soon came to the conclusion that:
α-1=137
He thus argued that the extra unit was a consequence of the initial exclusion of every elementary particle pair in the
universe. In the document of 1929,Eddington considered that fine-structure constant relates in a simple way to the
cosmological constants,as given by the expression:
where Nthe cosmic number,the number of electrons and protons in the closed universe. Eddington always kept the
name and the symbol α:
The first to find an exact formula for the fine-structure constant αwas the Swiss mathematician Armand Wyler in
1969. Based on the arguments concerning the congruent group,the group consists of simple Lorentz transformations
such as the space-time dimensions that leave the Maxwell equations unchanged. The first form of the Wyler constant
type is:
With numerical value αw=0,00729735252... At the time it was proposed,they agreed with the experiment to be
within 1.5 ppm for the value α-1.
3. Measurement of the fine-structure constant
Based on the precise measurement of the hydrogen atom spectrum by Michelson and Morley in 1887,Arnold
Sommerfeld extended the Bohr model to include elliptical orbits and relativistic dependence of mass on velocity. He
introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fine-structure
constant was as the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the
speed of light in the vacuum. The 2018 CODATA recommended value of αis:
α=0.0072973525693(11) (1)
with standard uncertainty 0,0000000011×10-3 and relative standard uncertainty 1,5×10-10.For reasons of
convenience,historically the value of the reciprocal of the fine-structure constant is often specified. The 2018
CODATA recommended value is given by:
α-1=137,035999084(21) (2)
with standard uncertainty 0,000000021×10-3 and relative standard uncertainty 1,5×10-10.There is general
agreement for the value of α,as measured by these different methods. The preferred methods in 2019 are
measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry. The most
precise value of αobtained experimentally (as of 2012) is based on a measurement of g using a one-electron
so-called "quantum cyclotron" apparatus,together with a calculation via the theory of QED that involved 12672
tenth-order Feynman diagrams:
α-1=137,035999174(35) (3)
This measurement of αhas a relative standard uncertainty of 2,5×10-10.This value and uncertainty are about the
same as the latest experimental results. Further refinement of this work were published by the end of 2020,giving the
value:
α-1=137,035999206(11) (4)
with a relative accuracy of 81 parts per trillion.
4. Fine-structure Constant,Anomalous Magnetic Moment,Relativity Factor and the Golden Ratio that
Dr. Rajalakshmi Heyrovska in [8] has found that the golden ratio φ provides a quantitative link between various
known quantities in atomic physics,research in this book chapter entitled "The golden ratio in the creations of Nature
arises in the architecture of atoms and ions". While searching for the exact values of ionic radii and for the
significance of the ionization potential of hydrogen,Dr. Heyrovska has found that the Bohr radius can be divided into
two Golden sections pertaining to the electron and proton. More generally,it was found that φ is also the ratio of
anionic to cationic radii of any atom,their sum being the covalent bond length. After that she showed,among other
facts,that many bond lengths in organic and inorganic molecules behave additively,and are the sum of the covalent
and the ionic radii,whether partially or fully ionic or covalent. An interpretation and a value of the fine-structure
constant α-1 has been discovered in terms of the golden angle. Dr. Heyrovska proposed another interpretation of α
based on the observation that it is close to the golden angle. Fine-structure constant can also be formulated for the
first time exclusively in terms of the golden ratio as follows:
α-1=360·φ-2-2·φ-3
with numerical value:
α-1=137,03562809…
5. Exact formula for the fine-structure constant
There is a dream,which,albeit more often not confessed,occupies the most secret aspirations of theoreticians and is
that of reducing the various constants of Physics to simple formula involving integers and transcendent numbers. We
propose the exact formula for the fine-structure constant αin terms of in terms of the golden angle,the relativity
factor and the fifth power of the golden mean:
α-1=360·φ-2-2·φ-3+(3φ)-5 (5)
with numerical values:
α-1=137,03599916476564........ (6)
α=0,00729735256498292........ (7)
The numerical value (6) is the average of the measurements (2),(3) and (4). We believe that the formula (5) is the
exact formula for the fine-structure constant α.Another beautiful forms of the equations are:
(8)
Other equivalent expressions for the fine-structure constant are:
α-1=(362-3-4)·φ-2-(1-3-5)·φ-1 (9)
α-1=(362-3-4)+(3-4+2·3-5-364)·φ-1 (10)
α-1=1-2·φ-1+360·φ-2-3+(3∙φ)-5 (11)
α-10-2·φ-1+360·φ-2-3+(3∙φ)-5 (12)
α-10-2·φ-1+360·φ-2-3-241·3-5·φ-4-(3∙φ)-5 (13)
α-1=(174.474·φ+86.995)∙(243∙φ5)-1 (14)
α-1=(87.480·φ3-486·φ2+1)∙(243∙φ5)-1 (15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
6. Continued fraction for the fine-structure constant
The pattern of the continued fraction for the fine-structure constant is:
The continued fraction for the fine-structure constant is:
In the notation of Carl Friedrich Gauss the fine-structure constant is:
8. Conclusions
We presented new exact expression for the fine-structure constant αin terms of the golden angle,the relativity factor
and the fifth power of the golden mean:
α-1=360·φ-2-2·φ-3+(3∙φ)-5
New interpretation and a very accurate value of the fine-structure constant has been discovered in terms of the
golden radio. These equations are simple,elegant and symmetrical in a great physical meaning. These exact
expressions should be studied further.
References
[1] www.en.wikipedia.org/
[2] www.wolframalpha.com/
[3] www.math.stackexchange.com/
[4] www.mathworld.wolfram.com/
[5] www.numberempire.com/
[6] http://physics.nist.gov/cuu/Constants/
[7] Heyrovska,R. Golden Ratio Based Fine Structure Constant and Rydberg Constant for Hydrogen Spectra.
[8] Heyrovska,R. The Golden ratio,ionic and atomic radii and bond lengths. Molecular Physics,103,877-882 (2005)
[9] Heyrovska,R. The Golden ratio in the Creations of Nature Arises in the Architecture of Atoms and Ions. Chapter
12 in Book:"Innovations in Chemical Biology",Editor:Bilge Sener,Springer.com,January (2009).
[10] Heyrovska,R. and Narayan,S. Atomic Structures of Molecules Based on Additivity of Atomic and/or Ionic
Radii. AIP Conference Proceedings 1119,216 (2009)
http://precedings.nature.com/documents/3292/version/1
[11] Heyrovska,R.Dependence of the Length of the Hydrogen Bond on the Covalent and Cationic Radii of
Hydrogen,and Additivity of Bonding Distances. Chemical Physics Letters,432,348-351 (2006).
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https://arxiv.org/ftp/physics/papers/0509/0509207.pdf
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... We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: α -1 =360·φ -2 -2·φ -3 +(3•φ) -5 ...
... μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... Jeff Yee proposed in [10] that the Avogadro's number NA can be calculated from the Planck length lpl,the Bohr radius α0 and Euler's number e: ...
Article
Full-text available
In this paper in an elegant way will be present the simple unification of atomic physics and cosmology. We will show that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
... We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: α -1 =360·φ -2 -2·φ -3 +(3•φ) -5 ...
... μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... Jeff Yee proposed in [10] that the Avogadro's number NA can be calculated from the Planck length lpl,the Bohr radius α0 and Euler's number e: ...
Preprint
Full-text available
In this paper in an elegant way will be present the simple unification of atomic physics and cosmology. We will show that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
... However,no numerological explanation has ever been accepted by the physics community. We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: ...
... Other equivalent expressions for the proton to electron mass ratio are: µ 3 =7 -1 •165 3 •ln 11 10 7•µ 3 =(3•5•11) 3 •ln 11 (2•5) (9) Also other exact mathematical expression in [12] for the proton to electron mass ratio is: μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... So the new formula for the Planck length lpl is: (43) Jeff Yee proposed in [10] that the mole and charge are related by deriving Avogadro's number from three constants,the Bohr radius,the Planck length and Euler's number. The fundamental unit of length in this unit system is the Planck length lpl. ...
Article
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
... However,no numerological explanation has ever been accepted by the physics community. We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: ...
... Other equivalent expressions for the proton to electron mass ratio are: µ 3 =7 -1 •165 3 •ln 11 10 7•µ 3 =(3•5•11) 3 •ln 11 (2•5) (9) Also other exact mathematical expression in [12] for the proton to electron mass ratio is: μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... So the new formula for the Planck length lpl is: (43) Jeff Yee proposed in [10] that the mole and charge are related by deriving Avogadro's number from three constants,the Bohr radius,the Planck length and Euler's number. The fundamental unit of length in this unit system is the Planck length lpl. ...
Preprint
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
... However,no numerological explanation has ever been accepted by the physics community. We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: ...
... Other equivalent expressions for the proton to electron mass ratio are: µ 3 =7 -1 •165 3 •ln 11 10 7•µ 3 =(3•5•11) 3 •ln 11 (2•5) (9) Also other exact mathematical expression in [12] for the proton to electron mass ratio is: μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... So the new formula for the Planck length lpl is: (43) Jeff Yee proposed in [10] that the mole and charge are related by deriving Avogadro's number from three constants,the Bohr radius,the Planck length and Euler's number. The fundamental unit of length in this unit system is the Planck length lpl. ...
Article
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
... We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: α -1 =360·φ -2 -2·φ -3 +(3•φ) -5 ...
... μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... Jeff Yee proposed in [10] that the Avogadro's number NA can be calculated from the Planck length lpl,the Bohr radius α0 and Euler's number e: ...
Article
Full-text available
In this paper in an elegant way will be present that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
... We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: α -1 =360·φ -2 -2·φ -3 +(3•φ) -5 ...
... μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... Jeff Yee proposed in [10] that the Avogadro's number NA can be calculated from the Planck length lpl,the Bohr radius α0 and Euler's number e: ...
Preprint
Full-text available
In this paper in an elegant way will be present that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
... However,no numerological explanation has ever been accepted by the physics community. We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: ...
... Other equivalent expressions for the proton to electron mass ratio are: µ 3 =7 -1 •165 3 •ln 11 10 7•µ 3 =(3•5•11) 3 •ln 11 (2•5) (9) Also other exact mathematical expression in [12] for the proton to electron mass ratio is: μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... So the new formula for the Planck length lpl is: (43) Jeff Yee proposed in [10] that the mole and charge are related by deriving Avogadro's number from three constants,the Bohr radius,the Planck length and Euler's number. The fundamental unit of length in this unit system is the Planck length lpl. ...
Article
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
... However,no numerological explanation has ever been accepted by the physics community. We propose in [10] the exact formula for the fine-structure constant α with the golden angle,the relativity factor and the fifth power of the golden mean: ...
... Other equivalent expressions for the proton to electron mass ratio are: µ 3 =7 -1 •165 3 •ln 11 10 7•µ 3 =(3•5•11) 3 •ln 11 (2•5) (9) Also other exact mathematical expression in [12] for the proton to electron mass ratio is: μ=6·π 5 +π -3 +2·π -6 +2·π -8 +2·π -10 +2·π -13 +π -15 (10) with numerical value: ...
... So the new formula for the Planck length lpl is: (43) Jeff Yee proposed in [10] that the mole and charge are related by deriving Avogadro's number from three constants,the Bohr radius,the Planck length and Euler's number. The fundamental unit of length in this unit system is the Planck length lpl. ...
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In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
... There is a dream,which,albeit more often not confessed,occupies the most secret aspirations of theoreticians and is that of reducing the various constants of Physics to simple formula involving integers and transcendent numbers. Fine-structure constant can also be formulated in [9] exclusively in terms of the golden angle,the relativity factor and the fifth power of the golden mean: The numerical value (7) is the average of the measurements (2),(3) and (4). We believe that the formula (10) is the exact formula for the fine-structure constant α. ...
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New interpretation and a very accurate value of the fine-structure constant has been discovered in terms of the golden radio. In this paper we will present the exact expression for the fine-structure constant in terms of the golden angle,the relativity factor and the fifth power of the golden mean. Finally we will present the continued fractions for the fine-structure constant.
Article
Full-text available
In this paper will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. Also that the gravitational fine-structure constant is the coupling constant for the fifth force. This article will be followed by the energy wave theory and the fractal space-time theory.
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A new interpretation and a very accurate value of the fine-structure constant has been discovered in terms of the Archimedes constant. The equation is simple,elegant and symmetrical in a great physical meaning. This accurate expression is the most impressive since it is simple and contains just a few prime numbers and the Archimedes constant.
Article
Full-text available
In this paper in an elegant way will be present the simple unification of atomic physics and cosmology. We will show that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
Article
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
Article
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
Article
Full-text available
In this paper in an elegant way will be present that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
Article
Full-text available
In this paper in an elegant way will be present the simple unification of the fundamental interactions. We will calculate the unity formulas that connect the coupling constants of the fundamental forces. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincaré dodecahedral space. Finally will be presented the law of the gravitational fine-structure constant followed by ratios of maximum and minimum theoretical values for natural quantities. This article will be followed by the energy wave theory and the fractal space-time theory.
Article
Full-text available
New interpretation and a very accurate value of the fine-structure constant has been discovered in terms of the golden radio. In this paper we will present the exact expression for the fine-structure constant in terms of the golden angle,the relativity factor and the fifth power of the golden mean. Finally we will present the continued fractions for the fine-structure constant.
Article
Full-text available
A new interpretation and a very accurate value of the fine-structure constant has beendiscovered in terms of the madelung constant b2(2). The equation is simple,elegant andsymmetrical in a great physical meaning. This accurate expression is the most impressivesince it is simple and contains just a few prime numbers and the madelung constant. Theseprime numbers can be possibly connected to finite groups. Also we will present thecontinued fraction for the fine-structure constant.
Article
Full-text available
In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant. This article will be followed by the energy wave theory and the fractal space-time theory.