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1
A Primer of Important Natural Numbers and
Revisited Fundamental Physical Constants
Hans Hermann Otto
Materials Science and Crystallography, Clausthal University of Technology,
Clausthal-Zellerfeld, Lower Saxony, Germany
E-mail: hhermann.otto@web.de
Abstract
Some fundamental physical constants such as the gyromagnetic factor of the electron or its
charge need to be marginally revisited considering the altered relativistic correction
determined by the Information Relativity theory (IRT) of Suleiman. As a new important
natural number the fifth power of the golden mean is introduced. Also a conjecture is given
connecting Sommerfeld’s structure constant α with the galactic velocity ß
g
. This primer will
be constantly renewed and extended as the acceptance by the physical community progresses.
Introduction
The intention of this primer is to fasten the process of the revision of physical ‘constants’ due
to a changed relativistic mass correction, which is suggested by the new Information
Relativity theory (IRT) of Suleiman [1]. In contrast to the as yet applied relativistic mass
correction based on the Lorentz-Einstein theory [2]
,
where
is the rest mass of a moving body, v is its velocity, and c is the speed of light, the
new IRT approach for the relativistic mass correction resulted in [1]
,
where
is the recession velocity of a moving body.
A first relativistic mass correction of the experimental determined gyromagnetic factor
of
the electron was recently proposed [3] and should be confirmed or marginally corrected by
the researchers of the original work [4] [5] [6]. Then the Sommerfeld fine-structure constant α
[7] should be adequately corrected, and also the elementary charge of the electron as not
independently defined quantity. The ‘magic’ α constant is given by
,
2
where e is the elementary charge of the electron, h is Planck’s constant, c is the speed of light,
and
is the vacuum magnetic permeability. The most precise value of α resulted from
comparison of the experimentally measured and calculated value of the gyromagnetic factor
of the electron [4] [5] [6], and the most precise value of the Planck constant comes from
Kibble watt balance experiments [7].
Recently, a new seminal approach of structure and matter was given by Guynn [8] [9],
considering Thomas precession of rotating entities from elementary particles to galaxies. He
has verified the gyromagnetic factor of the electron almost up to its exorbitantly precise
experimental value. He impressively lead back QED to what it actually is, hardly more than a
construct.
However, if we speak of constancy respectively physical constants, we can state constancy
only during the small time period people have documented observations and measurements.
But over the time the cosmos existed, constancy may be questioned at all [10].
Fundamental Physical Constants and Important Natural Numbers
In Table 1 important physical and chemical constants as well as important natural numbers
were selected. The red colored quantities were fixed by definition, whereas the blue colored
constants should be revisited. Recently, the Rydberg ‘constant’ was derived for relativistic
conditions [11] [12], but should be further adapted using the IRT theory [1]. Additional
references [13] to [14] are recommended to the reader. As a new important natural number
that governs phase transitions from microscopic to cosmic scale and beyond, the fifth power
of the golden mean respectively its inverse is recommended [15]. Surprisingly, this number
multiplied with the circle constant yields the ratio between the in-sphere volume and the
pyramid volume of the Great Pyramid of Giza [16] [17].
We may point to other approximate relations recently found by the present author, when he
studied the seminal results of Preston Guynn [8] [9]
!" #$"$
%
$
%
Indeed, these relations can have important consequences, if one could confirm the conjecture
[8] [9]. Guynn’s approach is a cornucopia of overflowing ideas inspiring
metrologists to confirm or measure anew fundamental physical constants. The galactic
velocity
can also be approximated as scaled product of electromagnetic and strong
coupling constants [8] [18]
&'
!%%
(
%%
(
'")'
Vice versa one can determine accurately
(
using this relation, because the Milky Way
maximum galactic velocity is accurate to eight decimal places [8]
3
(
%$
$$ *!!'
Recently, Bhandari and Bhandari set out to demonstrate that an external energy source may
power our universe and that gravity may be due to cancellation of energy lines in the shadow
regions of mass objects, creating an energy vacuum that causes the gravitational force
between the masses [31]. We have just derived that their approach can be reformulated in a
formula in which the G constant is retained. However, the squared distance between the
centers of the masses is reciprocal in both the Newton formula and the new one [32] [33].
Reciprocity relations are frequently observed in physics. Most important is the reciprocal
duality between particles and waves [34]. The reciprocity relation between Sommerfeld’s
structure constant [24] and Guynn’s galactic velocity [8] is another prominent example.
However, Guynn recently also suggested that G is not a constant and suffers periodic
variations due to the influence of Jupiter’s orbit and alignment relative to the galaxy [35] [36].
Jupiter is by far the most massive planet in the solar system.
Recently we related the Higgs mass
+,
to the mass of proton plus electron using the
following result [37] [38]
+,
-
.
/
0
1
2
3$!*!'45678
where 9 is the golden mean and
represents a new (fundamental) angle, derived from our
Split-Sphere-Approach
:;<<=>?&!
@
!A*"*! B"B$C
9
$'''"#$'*"
9
0
1
2
3$!*!)45678
References
[1] Suleiman, R. (2019) Relativizing Newton. Nova Scientific Publisher, New York, 2020, 1-
207.
[2] Einstein, A. (1905) Zur Elektrodynamik bewegter Körper. Annalen der Physik und
Chemie 17, 891-921.
[3] Otto, H. H. (2020) Reciprocity as an Ever-Present Dual Property of Everything. Journal of
Modern Physics 11, 98-121.
[4] Odom, B. (2004) Fully Quantum Measurement of the Electron Magnetic Momentum.
Ph.D. Thesis, Harvard University, Massachusetts USA.
[5] Gabrielse, G., Hanneke, D., Kinoshita, T., Nio, M., and Odom, B. (2006) New
Determination of the Fine Structure Constant from Electron g Value and QED. Physical
Review Letters 97, 030802, 1-4.
4
[6] Gabrielse, G., Hanneke, D., Kinoshita, T., Nio, M., and Odom, B. (2007) Erratum: New
Determination of the Fine Structure Constant from the Electron g Value and QED. Physical
Review Letters 99, 039902, 1-2.
[7] Wood, B.M., Sanchez, C. A., Green, R. G., and Liard, J. O. (2017) A Summary of the
Planck constant determination using the NRC Kibble balance. Metrologia 54, 399-409.
[8] Guynn. P. (2018) Thomas precession is the basis for the structure of matter and space.
viXra: 1810.0456, 1-27.
[9] Otto, H. H. (2022) Comment to Guynn’s Fine-Structure Constant Approach. Journal of
Applied Physics and Mathematics 10, 2796-2804.
[10] Otto, H. H. (2023) Actually There is No Reason for Anything to be Constant At All.
ResearchGate.net.
[11] Suto, R. (2021) Theoretical and Experimental Values for the Rydberg Constant Do Not
Match.
Journal of Applied Mathematics and Physics 9, 1993-2003.
[12] Suto, K. (2023) The Physical Constant Called Rydberg Constant Does Not Exist. Journal
of Applied Physics and Mathematics 11, 2621-2629.
[13] von Klitzing, K., Dorda, G., and Pepper, M. (1980) New method for high accuracy
determination of the fine structure constant based on quantized Hall resistance. Physical
Review Letters 45, 494-497.
[14] Bettin, H. (2019) How the Avogadro constant was measured for the last time.
Chemeurope.com
[15] Otto, H. H. (2020) Phase Transitions Governed by the Fifth Power of the Golden Mean
and Beyond. World Journal of Condensed Matter Physics 10, 1-22.
[16] Otto, H. H. (2020) Magic Numbers of the Great Pyramid: A Surprising Result. Journal
of Applied Mathematics and Physics 8, 2063-2071.
[17] Otto, H. H. (2021) Ratio of In-Sphere Volume to Polyhedron Volume of the Great
Pyramid Compared to Selected Convex Polyhedral Solids. Journal of Applied Physics and
Mathematics 9, 41-56.
[18] Otto, H. H. (2022) Galactic Route to the Strong Coupling Constant α
s
(m
z
) and Its
Implication On the Mass Constituents of the Universe. Journal of Applied Mathematics and
Physics, Volume 10, 3572-3585.
[19] The NIST SP 959 CODATA Recommended Values of the Fundamental Constants of
Physics and Chemistry (2019). National Institute of Standards and Technology, Gaitherburg,
MD 20899, USA.
[20] NIST CODATA (2018) National Institute of Standards and Technology, Gaitherburg,
MD 20899, USA.
[21] Finch, S. R. (2003) Mathematical Constants. Cambridge University Press, New York.
[22] Otto, H.H. (2017) Continued Fraction Representation of Universal Numbers and
Approximation.
[23] He, J. H., Tian, D. and Otto, H. H. (2018) Is the half-integer spin a first level
approximation of the golden mean hierarchy? Results in Physics 11, 362-363.
Reserachgate.net, DOI: 10.13140/RG.2.2.20110.66884
[24] Sommerfeld, A. (1919) Atombau und Spektrallinien. Friedrich Vieweg & Sohn,
Braunschweig.
5
[25] Davis, R. S. (2017) Determining the value of the fine-structure constant from a current
balance: getting acquainted with some upcoming changes to the SI. American Journal of
Physics 85, 364.
[26] Li, Q. et al. (2018) Measurements of the gravitational constant using two independent
methods. Nature 560, 582-588.
[27] Jiang, Z. et al. (2013) On the gravimetric contribution to watt balance experiments.
Metrologia 50, 452-471.
[28] Ketterle, W. and Jamison, A. O. (2019) An atomic physics perspective on the new
kilogram defined by Planck’s constant. Physics Today?
[29] Tumasyan, A. et al. (2022) Measurement and QCD analysis of double-diffential inclusive
jet cross sections in proton-proton collisions at &D = 13TeV. Journal of High Energy Physics
142, 1-66.
[30] Mozafari, K. (2022) Unified Equation of Fundamental Forces’ Coupling Values, and the
Existence of Subsequent, Fifth and Other, Forces. Journal of Applied Mathematics and
Physics 10, 2499-2507.
[31] Bhandari, P. N. and Bhandari, N. (2022) Fundamental forces are not fundamental as our
3-D Universe is driven by an external energy source. ResearchGate.net, 1-19.
[32] Otto, H. H. (2023) Comment to Bhandari and Bhandari: Fundamental forces are not
fundamental as our 3-D Universe is driven by an external energy source. ResearchGate, 1-6.
[33] Otto, H. H. (2023) Reciprocity Relation Between Alternative Gravity Formulas.
ResearchGate, 1-3.
[34] Otto, H. H. (2020) Reciprocity as an Ever-Present Dual Property of Everything. Journal
of Modern Physics 11, 98-121.
[35] Guynn, P. (2021) Jupiter’s orbit and alignment relative to the galaxy is the physical basis
of periodic variations of gravitational constant G and the length of day.
viXra.org:2111.0073v1.
[36] Anderson J. D. et al. (2015) Measurement of Newton’s gravitational constant and the
length of day. arXiv.org/pdf/1504.00604.pdf.
[37] Otto, H. H. (2024) Creation of Paired Entities is Ever Governed by the Golden Mean:
About the Nested Repeatability of Living and Cosmic Processes and the Origin of the
Universe. viXra:2401.0117, 1-14.
[38] Otto, H. H. (2024) Higgs Boson Mass Relations and Hole Superconductivity.
viXra:2401.0023, 1-14.
6
Table 1. Fundamental Physical Constants and Important Natural Numbers
Numbers in parentheses are the one-sigma uncertainty in the last two digits of the given value [19].
The red colored constants have been fixed. The blue colored values must be revised by means of the
information relativity theory (IRT) [1]
Speed of light c 2.99792458·10
8
m s
-
1
[7] [19] [24]
Planck constant h 6.62607015·10
-
34
J Hz
-
1
Vacuum permittivity ε
0
8.8541878128(13)·10
-
12
F m
-
1
Vacuum permeability µ
0
1.25663706212(19)·10
-
6
NA
-
2
Electron mass m
e
9.1093837015(28)·10
-
31
kg
Electron charge e
0
1.602176634(83)·10
-
19
C
Gyromagnetic factor g
e
2.00231909… - [3]
2.00231930436182(52) - [5] [8] [19]
Sommerfeld constant α 0.0072973525693(11) - [19] [24] [25] Inverse α constant α
-
1
137.035999084(21) -
Klitzing resistance R
K
25812.80745… Ω
Klitzing speed v
K
4.37538252727·10
6
m s
-
1
Gravitation constant G 6.674484(78)·10
-
11
m
3
kg
-
1
s
-
2
[25] [35]
G/c
4
4
E
B
!#! !
%
$
FG
H
[33]
Gravity acceleration g
0
9.80665 *) m s
-
2
[20]
9.809280196(13) m s
-
2
[11] [27]
Boltzmann constant k 1.38064903(51)·10
-
23
JK
-
1
[19]
Bohr radius a
0
5.29177210903(80)·10
-
11
m
Bohr magneton µ
H
9.2740100783(28)·10
-
24
JT
-
1
Rydberg ‘constant’
I
J
1.0973731568160(21)
%
10
7
m
-
1
[11] [12] [19]
Galactic velocity ß
g
- 0.000739437964740 - [8][9]
Strong coupling constant
D
K
L
M
0.1170(19) - [18] [29] [30]
0.11700522 - [18] [29]
Calibration constants
N
O
%
P
%
8
$
'!#!$$'!$ )
%
$
Q
C
Isotopic mass
133
Cs 132.905451933(24) g·mol
-
1
[19]
∆ν
Cs
-
hfs
**) 9192631770 Hz
[19]
h·∆ν
Cs
/c
2
***) 6.777265111839
%
10
-
41
kg
Avogadro number N
A
6.02214076·10
23
mol
-
1
[19]
Numbers Symbol Numerical Value
Circle constant π 3.14159265358079… - [21 [22]
Golden mean φ 0.61803398874989… - [21] [22] [23]
φ
5
0.090169943749… - [15] [22]
φ
-
5
11.090169943749… -
α/π 0.002322819466 -
φ
5
·π 0.28327723… [15] [16]
Euler number e 2.7182818284… - [19] [21]
FCT numbers ****) δ
1
4.6692016091… - [21] δ
2
2.502907875095… -
δ
3
8.7210972… -
Constants Symbol Numerical value Unit Reference