The Essence and Origin of the Magnetic Constant

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Journal of High Energy Physics, Gravitation and Cosmology, 2020, 6, 663-670
https://www.scirp.org/journal/jhepgc
ISSN Online: 2380-4335
ISSN Print: 2380-4327
DOI:
10.4236/jhepgc.2020.64045 Sep. 29, 2020 663 Journal of High Energy Physics, G
ravitation and Cosmology
The Essence and Origin of
the Magnetic Constant
Nader Butto
Rabin Medical Center, Dgania, Petah-Tikva, Israel
Abstract
In this study, the essence and origin of the magnetic constant are discussed
and a mechanism that allows real estimations of the magnetic constant based
upon the vacuum density description is proposed. By considering the vacuum
as a liquid with a measurable density and the electron as a vortex, hydrody-
namic laws are applied to measure the diminished momentum of a ro
tating
electron in a vacuum, thus obtaining a value similar to the experimentally de-
rived value of the magnetic constant. A consequence of this description is that
the magnetic constant can be expressed as the shear stress per unit time of the
vacuum; this means that it is an observable vacuum parameter and not a fun-
damental constant.
Keywords
Magnetic Constant, Magnetic Permeability, Shear Stress, Vacuum Density,
Vacuum Viscosity
1. Introduction
Physical constants are physical quantities that are generally believed to be both
universal in nature and constant over time. It is generally assumed that the val-
ues of fundamental constants such as the magnetic constant
μ0
, electric constant
ε0
, and speed of light in a vacuum
c
are the same throughout space-time poten-
tially because they depend on the vacuum’s superfluid characteristics.
Universal but dimensioned physical constants such as these are generally re-
ferred to as
fundamental
physical
constants
. Regardless of the theoretical status
of these quantities, the fact that they are constant (independent of both the time
and position of the measurement) must necessarily be verified experimentally.
In previous articles [1], the nature and the origin of the fine structure constant
was described. Furthermore, new mechanism and analytical formula for under-
standing the gravity constant
G
was presented [2].
How to cite this paper:
Butto, N. (2020
)
The Essence and Origin of the Magnetic
Constant
.
Journal of High Energy Physics
,
G
ravitation and Cosmology
,
6
, 663-670.
https://doi.org/10.4236/jhepgc.2020.64045
Received:
August 19, 2020
Accepted:
September 26, 2020
Published:
September 29, 2020
Copyright © 20
20 by author(s) and
Scientific
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access

N. Butto
DOI:
10.4236/jhepgc.2020.64045 664 Journal of High Energy Physics, G
ravitation and Cosmology
In this article magnetic constant essence and origin are discussed.
To date, no theory has been able to explain the real essence or precise origin of
the magnetic constant or magnetic permeability although its name implies that it
expresses the permeability of the vacuum and the degree to which it allows mag-
netic fields to expand. The magnetic constant can be defined as a fundamental
invariant quantity and is one of three components of Maxwell’s equations that
define
free
space
. The classical behavior of the electromagnetic field is described
by these equations, which predict that the speed
c
with which electromagnetic
waves (such as light) propagate through the vacuum is related to the electric
constant
ε
0 and magnetic constant
μ
0 as follows [3]:
00
1
c
εµ
=
(1)
This equation implies that the speed at which electromagnetic radiation propa-
gates depends on the permittivity and permeability of the vacuum, which are
widely considered to be absolute fundamental constants that are invariant in the
vacuum.
The magnetic field produced by an electric current or a moving electric charge
in a vacuum gives rise to the magnetic permeability. In classical electromagnetic
theory, free space resists the formation or propagation of magnetic field-induced
photons. In classical physics, free space, which is sometimes referred to as the
vacuum
of
free
space
, corresponds to a theoretically perfect vacuum and is con-
sidered to be a reference medium [4] [5].
In a classical vacuum,
µ
0 has a precisely defined value, namely [6] [7]
7 2 6 22
0
4 10 N A 1.2566370614 10 m kg A s
µ
−−
=× ≈ ×⋅ ⋅π
.
This paper discusses the essence and origin of the magnetic constant
μ
0, and
its dependence on the density of the vacuum. Its value is obtained by applying
hydrodynamic laws and calculating the shear stress of the vacuum.
2. The Nature of the Vacuum
Several widely accepted theories, such as special relativity, relativistic quantum
field theory, and superfluid vacuum theory, indicate that the vacuum is a fluid
with a well-known density. However, its microscopic structure is still largely
unknown despite being a subject of intense studies in the field of superfluid va-
cuum theory.
Maxwell’s equations combine electrical and magnetic effects and mathemati-
cally quantify their interactions. They were explicitly developed as fluid dynam-
ical models; thus, they require an underlying physical medium. In deriving these
equations, Maxwell made certain assumptions about the nature of the medium
that carries electromagnetic waves. The primary assumption was that it could be
described using the perfect fluid vortex theory developed by Hemlholtz [8].
Likewise, relativistic quantum field theory also assumes the physical vacuum
to be a non-trivial medium with a certain associated energy because the concept
of absolutely empty space contradicts the postulates of quantum mechanics. Ac-

N. Butto
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ravitation and Cosmology
cording to quantum field theory, pairs of virtual particles are continually being
created and annihilated even in the absence of real particles.
In previous article [9], a new theory of gravitation was presented, according to
which the gravitation force is a pull force due to vortex formation of the vacuum.
The vortex curves the vacuum (space-time) around it, attract and condense en-
ergy and dust to its center to form the mass. The gradient pressure in the vortex
creates a flow that upon interaction with an object transfers a part of its mo-
mentum to the object and pushes it toward the center.
Superfluid vacuum theory [10] [11] [12] [13] describes the physical vacuum as
a quantum superfluid that behaves like a frictionless fluid with extremely high
thermal conductivity. It is a perfect fluid in the sense that it is nonparticulate and
has no structural memory,
i.e.
, once changed, it has no tendency to return to its
former condition. The theory also proposes a mass generation mechanism that
may replace or supplement the electroweak Higgs theory. It has been shown that
masses of elementary particles could arise from their interaction with the super-
fluid vacuum, which is similar to the gap generation mechanism in supercon-
ductors [14] [15].
Vacuum energy density is generally viewed as a fundamental property of the
universe, with a magnitude that is independent of the method used to assess its
value,
i.e.
, whether it is subatomic, astronomical, or cosmological. Although there
is no consensus as to its value, the most generally accepted estimate relies mainly
on general relativity and is based on astronomical observations that determine
the curvature of space-time and the expansion of the universe. The universe’s
expansion can be measured based on the following relationship between a ga-
laxy’s velocity
v
and its distance
d
[16]:
0
v Hd=
, (2)
where
H
0 is Hubble’s constant. This is known as Hubble’s Law and is based on
the idea that the universe is constantly expanding; thus, galaxies are receding
from each other at a constant speed per unit distance. Thus, more distant objects
move more rapidly than nearby ones.
It is important to note that studies into the universe’s expansion rate have
shown that its average density is close to the critical density in which gravita-
tional attraction will eventually balance this expansion and halt it. In his theory
of general relativity, Einstein demonstrated that matter causes the surrounding
space to curve, thus giving rise to gravity. Both the overall geometry and fate of
the universe are controlled by the density of the matter within it.
The universe’s density
ρ
is typically expressed as a fraction of the critical den-
sity
ρ
cr via Ω =
ρ
/
ρ
cr. If Ω is less than 1 (known as an
open
universe
), the un-
iverse’s final fate will be a
cold
death
” where gravity cannot stop its expansion
and it expands forever, albeit at an ever-decreasing rate. If Ω is greater than 1
(known as a
closed
universe
), gravity eventually halts the universe’s expansion
and causes it to recollapse. Finally, if Ω is exactly equal to 1 (known as a
flat
un-
iverse
), the universe’s density is equal to the critical density and expansion will
halt only after an infinite time.

N. Butto
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ravitation and Cosmology
Currently, summing the estimated contributions to the total density parameter
Ω0 gives 1.02 ± 0.02, thus indicating that the universe’s density is close to critical.
In the standard cosmological model, the critical density (which defines the
boundary between an open and closed universe) is represented as follows [17]:
( )
22 29 3
0
cr
31.88 10 g cm ,
8
Hh
G
ρ
−
= = ×
π
(3)
where
H
0 = 71 km/s/Mpc,
G
is Newton’s gravitational constant, and h ≡ H /71
km/sec∙Mpc. The most recent result [18] estimated the cosmological density
ρ
to
be 11.11 (±1.05) 10−27 kg/m3.
Considering that the inertial mass of the observable universe
Mu
is as follows:
356
0
0.8720532288 10 kg,
2
u
c
MHG
= = ×
(4)
and that its volume
Vu
, given its observed radius
Ru
, is
3381 3
3
0
448.9364367479 10 m ,
33
u
u
Rc
VH
ππ
= = = ×
(5)
the cosmological density can be estimated as follows:
27 3
9.75839983 10 kg m .
u
u
M
V
−
= ×
(6)
The best estimate of the cosmological density is that it is between 9.75839983
× 10−27 and 11.11 (±1.05) × 10−27 kg/m3.
3. Magnetic Constant and Shear Stress
It is commonly accepted that quantum waves can travel in an ideal vacuum, thus
implying that an ideal vacuum behaves like both a liquid and a gas. Thus, the
vacuum energy has real observable physical consequences and its properties can
be observed through these physical effects [19] [20].
This paper proposes the magnetic permeability as an equivalent to the shear
stress per unit area of the vacuum, which depends on the vacuum density. Thus,
the shear stress of the vacuum will now be calculated to demonstrate that it is
equivalent to the magnetic permeability (constant).
Magnetic permeability and viscosity have much in common. The magnetic
permeability of free space is defined as the amount of resistance encountered
while forming a magnetic field in a classical vacuum. As stated above, its value is
defined as
µ
0 = 4π × 10−7 N∙A−2 [21].
Viscosity is the degree to which a fluid opposes relative motion between two
of its surfaces that are moving at different velocities. Therefore, a fluid’s viscosity
is often referred to as its thickness and is a measure of its resistance to gradual
deformation by shear or tensile stress.
While considering the vacuum as a fluid, its viscous resistance is related to the
virtual particles present. These particles represent aspects of the fields they are
used to describe, and the speed of light in a vacuum is an intrinsic property of
the electromagnetic field.

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ravitation and Cosmology
The specific resistance of a conductor can be thought of as the diminished mo-
mentum of the electrons passing along the conductor’s length. Thus, electrical
resistance
R
has units of Ohms, which is defined as kg∙m/s, per m of conductor.
The idea that electrons can be considered as vortices was first proposed by
Helmholtz in 1858 [22], and treated mathematically by Maxwell, who applied his
theory of molecular vortices to magnetic phenomena [23]. According to Helm-
holtz’s theory, particles are vortically moving ring-shaped masses of a homoge-
neous, incompressible, frictionless fluid. Vortices, namely portions of fluid in
rotational motion, will always exist out of the same portion of fluid and are im-
mune to dissipation,
i.e.
, will continue to exist forever.
In previous article [24], a new theory is proposed in which the electron has a
structure and a shape. The electron is a frictionless vortex with conserved mo-
mentum made out of virtual photons that acquire mass when moving in the
vortex at the speed of light. The vortex shape electron allowed to resolve the
enigmatic wave-particle duality [25].
According to the vortex theory of the electron, an electron is a vortex rotating
around its axis, experiences some resistance owing to interaction with the adja-
cent vacuum. Its diminished momentum
P
is determined by dividing the mo-
mentum, which given by the vacuum density
ρ
and vortex angular velocity
ū
, by
the vortex circumference
λ
:
,Pu
ρ
λ
=
(7)
where
uc=
,
i.e.
, 3
×
108 m/s, and the vacuum density
ρ
= 9.7583993 × 10−27
kg/m3. The vortex circumference
2r
λ
= π
, where
r
is its radius. If
r
is consi-
dered as the Compton radius of the electron, 3.86 × 10−13 m, then the electron
vortex circumference is 2.4263102367 (11) × 10−12 m, which is the CODATA
2014 value for the electron’s Compton wavelength [26].
Using these values, the electron’s diminished momentum can be calculated as
follows:
62
1.206572 10 N s A ,
c
P
ρ
λ
−
== ×⋅
(8)
which is of the same order of magnitude as the magnetic constant
µ
0. However,
the units in Equation (8) express the shear stress and are different from those for
the magnetic constant.
Momentum has units of kg∙m/s. Linear momentum is a conserved quantity;
this means that the linear momentum of a closed system (
i.e.
, one that is not af-
fected by external forces) cannot change. Momentum can equivalently be ex-
pressed in Newton seconds (N∙s). In hydrodynamics, the units of a fluid’s dy-
namic (shear) viscosity are (N∙s)/m2 = Pa∙s. Thus, the shear stress
τ
can be inter-
preted as the rate of change of momentum
p
per unit area
A
(rate of momentum
flux) of an arbitrary control surface as follows:
,
x
mu
p
AA
τ
= =
(9)

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ravitation and Cosmology
where
ux
is the component of the average velocity of the molecules flowing pa-
rallel to
x
plane through the unit area that is perpendicular to it, and
m
is the
mass of fluid flowing through the surface per unit time.
For a Newtonian fluid, when the stress is parallel to the surface, the shear
stress
τ
per unit area is proportional to the rate of change of the velocity with
respect to the distance and is represented as follows:
d,
d
x
u
y
τµ
=
(10)
where
τ
=
F/A
and d
ux
/d
y
is the local shear velocity for a unit area parallel to the
x-z
plane, moving along the
x
-axis. The proportionality factor
μ
in this formula
known as the
dynamic
viscosity.
Therefore, the shear stress is the dynamic vis-
cosity per unit area and has units of (N∙s)/m2.
Since the magnetic constant’s units are N/A2, this indicates that it can be ex-
pressed as the shear stress per unit time or the dynamic viscosity per unit area
and time. Therefore, an electron rotating in a vacuum experiences shear stress
that diminishes its momentum, and this is equal to the magnetic constant. The
shear stress depends on the vacuum’s viscosity, which is related to its density.
Therefore, the magnetic permeability is the rate of change of momentum per
unit area and time that the electron encounters when rotating around its axis in
a vacuum.
4. Conclusions
This paper has proposed a new interpretation of the essence and origin of the
magnetic constant. An electron is considered as a vortex rotating in a superfluid
vacuum, and the interaction length of the electron is equal to the Compton wa-
velength. Calculating diminished momentum of the rotating electron yields a
value in the same range as the accepted magnetic constant value.
This result strongly suggests that the magnetic constant is related to the struc-
ture and properties of a physical vacuum, a medium that can be characterized by
specific properties such as density, viscosity, and speed. Therefore, the magnetic
constant is not a fundamental constant, but it is the diminished momentum of a
rotating electron, which depends on the vacuum density. Its momentum per unit
area is equivalent to its dynamic viscosity, which has units of (N∙s)/m2, while the
rate of change of its momentum per unit area and time gives the change in the
electron’s dynamic viscosity per unit area and time. It is an expression of the
force per unit area, acting parallel to an infinitesimal surface element due to
vacuum viscosity.
This study opens up a new approach to determine the nature and essence of
the fundamental constants of nature, related to vacuum density and thus to re-
duce the number of fundamental constants to one. The origin and essence of
gravitation constant G, fine structure constants was published in previous papers
[1] [2], electric constant
ε0
, speed of light
c
constant and Planck constant will be
presented in separate papers in the near future.

N. Butto
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ravitation and Cosmology
Limitations
The superfluid nature of the vacuum still needs to be confirmed experimentally.
In addition, even though the idea of electrons having a vortex structure is not
new, it must still be confirmed by experimental research.
Acknowledgements
The author would like to thank Enago (https://www.enago.com/) for the English
language review.
This research did not receive any specific grant from funding agencies in the
public, commercial, or not-for-profit sectors.
Correspondence and requests for materials should be addressed to
nader.butto@gmail.com.
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa-
per.
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