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Journal of High Energy Physics, Gravitation and Cosmology, 2021, 7, 324-332
https://www.scirp.org/journal/jhepgc
ISSN Online: 2380-4335
ISSN Print: 2380-4327
DOI:
10.4236/jhepgc.2021.71016 Jan. 29, 2021 324 Journal of High Energy Physics, G
ravitation and Cosmology
The Origin and Nature of the Planck Constant
Nader Butto
Dania, Petah-Tikva, Israel
Abstract
Planck’s constant
h
is a fundamental physical constant defined in the realm of
quantum theory and is determined only by physical measurement and cannot
be calculated. To this day, physicists do not have a convincing explanation for
why action in microcosm is quantized or why
h
has a specific quantitative
value. Here, a new theory is presented based on the idea that the elementary
particles are vortices of a condensed superfluid vacuum. The vortex ha
s a
conserved angular momentum that can be calculated by applying hydrody-
namic laws; in this way, the numerical value of Planck’s constant can be ob-
tained. Therefore, the Planck constant is not a fundamental constant but an
observable parameter of the elementary particle as a vortex that has constant
vorticity and conserved angular momentum. This theory may offer a unique
and comprehensive understanding of Planck’s constant and open a new pers-
pective for a theory of everything.
Keywords
Planck’s Constant, Angular Momentum, Compton Radius, Vorticity
1. Introduction
Max Planck’s attempts to provide a theoretical explanation for the empirically
discovered laws of blackbody radiation yielded Planck’s constant
h
that first ap-
peared in physics theory in 1900 [1]. He proposed the quantum hypothesis stat-
ing that the energy of a harmonic oscillator with an oscillation frequency
ν
would quantize at an integral multiple of
hν
. Therefore, Planck’s constant is the
currently accepted quantum (smallest quantity) of energy possible within a
photon and relates the energy in one quantum (photon) of electromagnetic rad-
iation to the frequency of that radiation. The implication of discovery of
h
was
that the action of atoms is quantized and that
h
represents the fundamental unit
of action for discrete atomic-scale systems. It has become an integral component
of modern atomic and subatomic physics and has profound importance in
How to cite this paper:
Butto, N. (2021
)
The Origin and Nature of the Planck Co
n-
stant
.
Journal of High Energy Physics
,
Gr
a-
vitation and Cosmology
,
7
, 324-332.
https://doi.org/10.4236/jhepgc.2021.71016
Received:
November 5, 2020
Accepted:
January 26, 2021
Published:
January 29, 2021
Copyright ©
2021 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.2021.71016 325 Journal of High Energy Physics, G
ravitation and Cosmology
technology, understanding of reality, and understanding of life.
The estimated value of Planck’s constant according to the 1998 CODATA was
determined based on balancing electric and gravitational forces in a so-called
watt balance [2]. In this scheme, the weight of a test mass is compared to the
force generated by a coil, the electric power of which is accurately measured via
the Josephson and quantum-Hall effects. The number chosen for the numerical
value of the
h
is such that, at the time of adopting the definition, one kilogram is
equal to the mass of the international prototype currently used for the definition
of mass, within the uncertainty of the combined best estimates of the value of the
h
at that moment.
Another way to measure it is via the X-ray crystal density (XRCD) method
[3]. This method measures the Avogadro constant
N
A to establish a mass scale
by counting the number of atoms in a silicon single crystal sphere using the
XRCD approach,
i.e.
, probing the regular arrangement of atoms in a perfect lat-
tice, and then multiplying it by the known mass of a silicon atom (the 28Si iso-
tope) [4].
The CODATA Recommended Values of the Fundamental Physical Constants
used these measurement results and the measurement results of the abovemen-
tioned watt balance method as a basis to determine Planck’s constant, which is
h
= 6.6260693 × 10−34 J s [5].
Progress is made every year in measuring Planck’s constant; however, little
progress has been made in understanding its nature. Planck’s constant is
thought to be a fundamental physical constant defined in the realm of quantum
theory; however, thus far, physicists do not have a convincing explanation for
why action in the microcosm is quantized or why
h
has a specific quantitative
value [6].
In previous articles, the nature and the origin of the fine structure constant
[7], the gravitational constant
G
[8], magnetic constant
μ
0 [9] and electric per-
mittivity [10] were described.
In this paper, we provide a new theory to describe the origin of Planck’s con-
stant and to reveal the constant’s intrinsic nature. The starting point is the su-
perfluid nature of the vacuum, which explains the vortex nature of the elemen-
tary particles. Thereafter, applying the classical laws of hydrodynamics to the
vortex to calculate the vorticity and angular momentum of the vortex, an analyt-
ical formulation is presented to obtain the numerical value of the constant.
2. Superfluid Vacuum
Although the theory of quantum mechanics is not predicted based upon any
property of space, the idea of space is frequently used to justify mathematical
procedures and to imply the amounts of detailed space properties such as the
speed of light in a vacuum governed by the vacuum permeability and permittiv-
ity. During the early years of quantum mechanics, Paul Dirac theorized that va-
cuum was actually filled with particles in negative energy states [11], therefore
N. Butto
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10.4236/jhepgc.2021.71016 326 Journal of High Energy Physics, G
ravitation and Cosmology
giving rise to the concept of the “physical vacuum,” which is not empty at all. In
quantum electrodynamics, the vacuum is a state with no matter particles and
photons but with vacuum fluctuations and with a finite energy called the va-
cuum energy. The vacuum is defined as the state with the lowest possible energy
and a superfluid behavior. The superfluidity of the vacuum is the basis for Max-
well’s equations, special relativity, and general relativity.
The classical behavior of the electromagnetic field is described by Maxwell’s
equations, which predict that the speed of light
c
in which electromagnetic waves
(such as light) propagate through the vacuum, is related to the electric constant
ε
0 and magnetic constant
μ
0. Special relativity is derived from Maxwell’s equa-
tions. Einstein clearly realized that both special and general relativity were based
on fluid dynamical models [12].
Nonetheless, the microscopic structure of the vacuum is currently largely un-
known according to quantum field theory. Even in the absence of real particles,
the vacuum is always filled by pairs of created and annihilated virtual particles,
and it is predicted that these invisible particles could materialize for a short time
and exert a measureable force. Therefore, the physical vacuum is assumed to be
a non-trivial medium, not empty but rather filled with quantum mechanical ze-
ro-point energy and characterized as behaving like a frictionless fluid with ex-
tremely low viscosity, in which one can associate a certain energy and density
with extremely high thermal conductivity. Therefore, the vacuum energy has
real physically observable consequences, and its properties can be observed as
having real physical effects [13] [14].
The vacuum extends everywhere, has no size, shape, center, direction, time, or
extent, and is immovable. Therefore, the vacuum density is generally viewed as a
fundamental property of the cosmos, its magnitude should not depend on
whether we choose subatomic, astronomical, or cosmological methods to assess
its value.
The vacuum density value depends primarily on general relativity, and has
been determined using astronomical observations of the curvature of space-time
and the expansion of the universe. The expansion of the universe has been stu-
died using several different methods; however, the Wilkinson Microwave Aniso-
tropy Probe mission represents a major step toward precision in calculating the
Hubble constant and the vacuum density [15].
The most recent result [16], indicates that the value of the Hubble constant is
18 1
0
71.9 2.4 3.0 km s Mpc 2.33 10 s
H
−−
= +− = ×
, where the number of km in an
Mpc is 3.09 × 1019. Considering that the inertial mass of the
Observable Universe
is
3 56
U0
2 0.8720532288 10 kgM c HG= = ×
and the volume of the universe is
( )
3
3 81 3
UU 0
4 3 4 3 8.9364367479 10 mV R cH
= = = ×ππ
, the cosmological density
is calculated to be
27 3
UU
9.75839983 10 kg mMV
−
= ×
.
3. Elementary Particles as Vortices
The angular momentum (spin) of an electron indicates that there is an internal
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ravitation and Cosmology
rotation that confers its rest mass. It has become obvious that not only an inter-
nal oscillation but also some type of internal motion at the speed of light is
present. Therefore, the seemingly empty space that surrounds electrons is com-
posed of “virtual particles” and electrons are inseparable from the clouds of vir-
tual particles that surround them.
Quantum mechanics predicts that an electron is composed a cloud of proba-
bilities. Although the precise measuring of the form of this cloud is beyond the
capability of modern methods, the current model predicts that electrons are
slightly aspheric, with a distortion characterized by the electric dipole moment.
However, no experiment has ever detected this deviation [17]. Therefore, we
propose that elementary particles, such as quarks and electrons, are irrotational
circular vortices of frictionless superfluid space with concentric streamlines gen-
erated from the primordial vacuum during the Big Bang. The rate of rotation of
the fluid is greatest at the center and decreases progressively with distance from
the center until there is no gradient pressure on the boundaries of the vortex
where the flow is laminar and the friction is zero. In such a case, the absence of
friction would make it impossible to create or destroy the vortex motion. If the
negative suction point-volume in the center of the vortex does not have suffi-
cient energy to drag the virtual photons to the speed of light, a stable situation
cannot occur [18].
In previous article [19], the electron properties have been accurately described
using classical laws of hydrodynamics and describing the electron as a vortex.
4. Hydrodynamics of the Vortex
In hydrodynamics, the force
F
that moves the vortex is directly related to the
pressure that creates the vortex, known as the dynamic pressure
Pd,
and the area
A
:
d
F PA=
.
(1)
The dynamic pressure
(Pd
) representing the fluid kinetic energy is expressed
as
2
12
d
Pv
ρ
=
,
(2)
where
ρ
is the density of the fluid and
v = c
is the velocity of the fluid.
Therefore, the internal force of the vortex is
2
12F cA
ρ
=
.
(3)
The area of the vortex is approximately a circle, and its radius when the vortex
is extended will cause the vortex radius to double in size. Therefore,
A
= 2π
r
2
and
22
F cr
ρ
= π
. (4)
If we multiply and divide the right hand side of the equation by time
t
we obtain
2
F ct r c t
ρ
π=
.
(5)
The quantity
ct
is equivalent to the distance
L
,
L
π
r
2 is equivalent to the vo-
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10.4236/jhepgc.2021.71016 328 Journal of High Energy Physics, G
ravitation and Cosmology
lume
Q
,
ρQ
is equivalent to the mass
m
, and 1/
t
is equivalent to the frequency
f
;
therefore,
F mcf
=
.
(6)
The energy of the rotating electron around its axis is
E
= force × distance. The
distance that an electron rotates in one cycle is 2π
r
; therefore,
2E rcmf= π
.
(7)
This energy is the energy assigned to virtual particles. In this case, the fre-
quency indicates the number of passages of one electromagnetic wave within
one second of time. Planck’s constant is the energy found within one wave.
In hydrodynamics, the velocity of a fluid element instantaneously passing
through a given point in space in a vortex with a radius
r
would be constant in
time; therefore, the circulation or the vorticity is Γe = 2π
r
e
c.
This is a fundamen-
tal constant for every vortex, as long as it exists in time and space, and vanishes
only upon the destruction of the vortex. The quantity Γe
m
e is an angular mo-
mentum; therefore, 2π
r
e
cm
e
is a constant.
If we consider the Compton wavelength, 2.4263102367(11) × 10−12 m, to be
one rotation of a vortex that has a core circumference of 2π
r,
the Compton ra-
dius is 2.4263102367(11) × 10−12/2π
=
3.86 × 10−13 m.
If the radius of the core of the vortex is 3.86 × 10−13 m,
c
= 2.99792458 × 108
m∙s−1, and
m
is the rest mass of an electron
m
o = 9.10938356 × 10−31 kg, the an-
gular momentum is 2π
rcm
= 6.61997943364 × 10−34 kg∙m2∙s−1, which is within
the range of the discrepancies in the experimental values.
How is 2π
rcm
related to the Planck constant?
According to Planck theory, for photons of a frequency
f
, energy is given by
E hf=
,
(8)
and the electron’s rest mass energy
E
0 can be represented by the following formula:
2
0
E mc=
.
(9)
Therefore,
2
h mc f=
.
(10)
If the frequency
f
= 1/
t
, then
2
h mc t=
.
(11)
In a vortex, the time necessary to complete one revolution is
e
2t rc= π
.
(12)
If we substitute the value of
t
in Equation (12) into Equation (11),
we obtain
e
2h r cm= π
. (13)
If
Γe = 2π
r
e
c
,
h
= Γe
m
e, and Γe
=
h/m
e = 7.274, then
r
e
= Γe
/
2π
c
= 3.86 × 10−13 m.
This is the value of the Compton radius.
Examining the mathematical equations by dimensional analysis gives
M L
2/
T,
which is the dimension of action,
i.e.
, the energy multiplied by time; therefore, it
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DOI:
10.4236/jhepgc.2021.71016 329 Journal of High Energy Physics, G
ravitation and Cosmology
is natural to think of
h
in terms of action principles.
Therefore,
2e
E r cmf hfπ
= =
.
(14)
5. Discussion
The Planck constant and the speed of light are the two fundamental constants
that rule the universe [20]. The speed of light is related to the strength of gravity,
and Planck’s constant relates energy to the frequency of a particle of light. All
other constants, such as the charge or mass of an electron or the strength of the
nuclear forces, can be described in relation to these two “dimensional” con-
stants.
Planck’s
h
is very small and only comes into play at the “quantum” scale of
very small things.
The effect of fixing the numerical value of the Planck constant is a definition
of the unit kg∙m2∙s−1 (the unit of the physical quantity called action). Its value has
been determined experimentally using the XRCD and watt balance approaches.
However, there are significant discrepancies between the available experimental
values for the Planck constant [21].
Most recently in 2015, researchers from National Institute of Standards and
Technology (NIST), USA) researchers reported a single value (NIST-15) for
h
with an uncertainty of 5.6 parts in 108 based on all the data obtained using their
current watt balance [22]. Furthermore, also in 2015, the International Avogadro
Collaboration (IAC) reported a new value (IAC-15) with an uncertainty of 2.0
parts in 108 on the basis of the XRCD method; this value also fulfilled the condi-
tion of the second quantitative requirements of the Consultative Committee for
Mass and Related Quantities for determinations of the Planck constant [23].
Progress is made every year in measuring Planck’s constant; however, little
progress has been made in understanding its nature.
We present a new perspective of an old idea that the electron is a vortex of
superfluid vacuum. Superfluid vacuum theory proposes the mass generation
mechanism, which may replace or supplement the electroweak Higgs mechan-
ism. It has been shown that the masses of the elementary particles could emerge
as the result of interactions with the superfluid vacuum, similar to the gap gen-
eration mechanism in superconductors [24] [25]. The super fluidity of the va-
cuum is the basis for Maxwell’s equations. In deriving these equations, Maxwell
made certain assumptions about the nature of the medium that carried electrici-
ty, magnetism, and light. The primary assumption used by Maxwell was that the
underlying medium could be described using the perfect fluid vortex theory de-
veloped by Helmholtz. Therefore, we propose that the electron is an irrotational
circular vortex of frictionless superfluid space with concentric streamlines and
that is applies hydrodynamics to express the angular momentum of the vortex to
connect it to Planck’s constant.
From the Planck-Einstein equation we obtain
h =
2π
r
e
cm
, and from quantum
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10.4236/jhepgc.2021.71016 330 Journal of High Energy Physics, G
ravitation and Cosmology
mechanics the standard Compton wavelength,
λ
, of a particle is given by
λ =
h/mc
and
h
=
λcm
. This indicates that
λ
= 2π
r
e; therefore, the Compton wave-
length is the same as the electron core circumference. We obtained the Compton
radius (which is different from the classical radius) and calculated the angular
momentum of the core vortex, which gave the same value of Planck’s constant.
This is the first time, to our knowledge, that the Planck constant has been de-
rived from an analytical formula based on the proposed theory, which explains
the hydrodynamic mechanism of the angular constant as the origin of its quan-
titative value and provides a precise value of the Planck constant that can be ex-
pressed with a coherent set of units according to the International System of
Units (SI units). The effect of fixing the numerical value of the Planck constant is
a definition of the unit kg∙m2∙s−1.
6. Conclusions
Planck’s constant is an expression of the angular momentum of a frictionless
vortex elementary particle composed of the condensed vacuum and generated in
the Big Bang from massless virtual photons that acquire mass when moving in
the vortex at the speed of light, as described by Higgs theory. The circulation in
the vortex is constant, and the angular momentum of the vortex is conserved. By
taking the Compton wavelength to be the circumference of the core vortex, we
calculated the Compton wavelength and the angular momentum of the vortex to
obtain the value of the Planck constant.
We conclude that the Planck constant is not a fundamental constant but an
observable parameter of the elementary particle as a vortex, which expresses the
circulation conserved momentum of the vortex. This theory may offer a unique
and deeper understanding of Planck’s constant and change the definitions of units
to establish practical realizations by ever-increasingly accurate experiments.
Acknowledgments
The author would like to thank Enago (https://www.enago.com/) for the English
language and peer reviewers review.
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.
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