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The Origin and Nature of the Planck Constant

Journal of High Energy Physics, Gravitation and Cosmology, 2021, 7, 324-332
ISSN Online: 2380-4335
ISSN Print: 2380-4327
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
Planck’s constant
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
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.
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
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
would quantize at an integral multiple of
. 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
that the action of atoms is quantized and that
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
Journal of High Energy Physics
vitation and Cosmology
, 324-332.
November 5, 2020
January 26, 2021
January 29, 2021
Copyright ©
2021 by author(s) and
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
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Open Access
N. Butto
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
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
at that moment.
Another way to measure it is via the X-ray crystal density (XRCD) method
[3]. This method measures the Avogadro constant
A to establish a mass scale
by counting the number of atoms in a silicon single crystal sphere using the
XRCD approach,
, 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
= 6.6260693 × 1034 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
has a specific quantitative
value [6].
In previous articles, the nature and the origin of the fine structure constant
[7], the gravitational constant
[8], magnetic constant
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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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
in which electromagnetic waves
(such as light) propagate through the vacuum, is related to the electric constant
0 and magnetic constant
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
71.9 2.4 3.0 km s Mpc 2.33 10 s
= +− = ×
, where the number of km in an
Mpc is 3.09 × 1019. Considering that the inertial mass of the
Observable Universe
3 56
2 0.8720532288 10 kgM c HG= = ×
and the volume of the universe is
( )
3 81 3
UU 0
4 3 4 3 8.9364367479 10 mV R cH
= = = ×ππ
, the cosmological density
is calculated to be
3. Elementary Particles as Vortices
The angular momentum (spin) of an electron indicates that there is an internal
N. Butto
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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
that moves the vortex is directly related to the
pressure that creates the vortex, known as the dynamic pressure
and the area
The dynamic pressure
) representing the fluid kinetic energy is expressed
is the density of the fluid and
v = c
is the velocity of the fluid.
Therefore, the internal force of the vortex is
12F cA
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,
= 2π
F cr
= π
. (4)
If we multiply and divide the right hand side of the equation by time
we obtain
F ct r c t
The quantity
is equivalent to the distance
2 is equivalent to the vo-
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ravitation and Cosmology
is equivalent to the mass
, and 1/
is equivalent to the frequency
F mcf
The energy of the rotating electron around its axis is
= force × distance. The
distance that an electron rotates in one cycle is 2π
; therefore,
2E rcmf= π
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
would be constant in
time; therefore, the circulation or the vorticity is Γe = 2π
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
e is an angular mo-
mentum; therefore, 2π
is a constant.
If we consider the Compton wavelength, 2.4263102367(11) × 1012 m, to be
one rotation of a vortex that has a core circumference of 2π
the Compton ra-
dius is 2.4263102367(11) × 1012/2π
3.86 × 1013 m.
If the radius of the core of the vortex is 3.86 × 1013 m,
= 2.99792458 × 108
m∙s−1, and
is the rest mass of an electron
o = 9.10938356 × 1031 kg, the an-
gular momentum is 2π
= 6.61997943364 × 1034 kg∙m2∙s−1, which is within
the range of the discrepancies in the experimental values.
How is 2π
related to the Planck constant?
According to Planck theory, for photons of a frequency
, energy is given by
E hf=
and the electron’s rest mass energy
0 can be represented by the following formula:
E mc=
h mc f=
If the frequency
= 1/
, then
h mc t=
In a vortex, the time necessary to complete one revolution is
2t rc= π
If we substitute the value of
in Equation (12) into Equation (11),
we obtain
2h r cm= π
. (13)
Γe = 2π
= Γe
e, and Γe
e = 7.274, then
= Γe
= 3.86 × 1013 m.
This is the value of the Compton radius.
Examining the mathematical equations by dimensional analysis gives
which is the dimension of action,
, the energy multiplied by time; therefore, it
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10.4236/jhepgc.2021.71016 329 Journal of High Energy Physics, G
ravitation and Cosmology
is natural to think of
in terms of action principles.
E r cmf hfπ
= =
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-
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
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 =
, and from quantum
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ravitation and Cosmology
mechanics the standard Compton wavelength,
, of a particle is given by
λ =
. This indicates that
= 2π
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.
The author would like to thank Enago ( 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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... 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 radiation 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 [4]. So, mass can be converted into energy and vice versa. ...
A closed system has different quantized level of Energy states. It can absorb energy depending on surrounding and its available quantized energy level. On absorption of energy the mass of the system increases as per Einstein’s mass energy relationship that is energy absorbed into system gets converted into mass. The system at higher energy state, having higher mass tends to come into available lower energy state depending on its surrounding, thereby releasing its energy in another form. During releasing energy mass of the closed system gets reduced. So, mass of a closed system is a function of energy. The mass will be minimum when the system is at zero energy level and will increase with its energy level.
... In this case, the frequency indicates the number of times a wave EM passes within 1 s. Planck's constant is the energy contained in a wave [42]. Therefore, we have 2 E rmcf hf π = = Next, the Planck constant is accurately determined by experiments and describes the ratio between the energy and frequency of photon. ...
Full-text available
New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of $N_A = 6.022 140 76(12) \times 10^{23}$ mol$^{-1}$. The X-ray crystal density method has thus achieved the target relative standard uncertainty of $2.0 \times 10^{-8}$ necessary for the realization of the definition of the new kilogram.
Full-text available
Researchers at the National Institute of Standards and Technology have been using a watt balance, NIST-3, to measure the Planck constant $h$ for over ten years. Two recently published values disagree by more than one standard uncertainty. The motivation for the present manuscript is twofold. First, we correct the latest published number to take into account a recently discovered systematic error in mass dissemination at the Bureau International des Poids et Mesures (BIPM). Second, we provide guidance on how to combine the two numbers into one final result. In order to adequately reflect the discrepancy, we added an additional systematic uncertainty to the published uncertainty budgets. The final value of $h$ measured with NIST-3 is $h = 6.626\,069\,36(37)\times 10^{-34}\,\mbox{J\,s}$. This result is $77(57) \times 10^{-9}$ fractionally higher than $h_{\mathrm{90}}$. Each number in parentheses gives the value of the standard uncertainty in the last two digits of the respective value and $h_{\mathrm{90}}$ is the conventional value of the Planck constant given by $h_{\mathrm{90}}\equiv 4 /( K_{\mathrm{J-90}}^2 R_{\mathrm{K-90}})$, where $K_{\mathrm{J-90}}$ and $R_{\mathrm{K-90}}$ denote the conventional values of the Josephson and von Klitzing constants, respectively.
We present a new measurement of the Hubble Constant H0 and other cosmological parameters based on the joint analysis of three multiply imaged quasar systems with measured gravitational time delays. First, we measure the time delay of HE 0435-1223 from 13-yr light curves obtained as part of the COSMOGRAIL project. Companion papers detail the modelling of the main deflectors and line-of-sight effects, and how these data are combined to determine the time-delay distance of HE 0435-1223. Crucially, the measurements are carried out blindly with respect to cosmological parameters in order to avoid confirmation bias. We then combine the time-delay distance of HE 0435-1223 with previous measurements from systems B1608+656 and RXJ1131-1231 to create a Time Delay Strong Lensing probe (TDSL). In flat Λ cold dark matter (ΛCDM) with free matter and energy density, we find H0 = 71.9-3.0+2.4 km s⁻¹ Mpc⁻¹ and ΩΛ = 0.62-0.35+0.24. This measurement is completely independent of, and in agreement with, the local distance ladder measurements of H0. We explore more general cosmological models combining TDSL with other probes, illustrating its power to break degeneracies inherent to other methods. The joint constraints from TDSL and Planck are H0 = 69.2-2.2+1.4 km s⁻¹ Mpc⁻¹, ΩΛ = 0.70-0.01+0.01 and Ωk = 0.003-0.006+0.004 in open ΛCDM and H0 = 79.0-4.2+4.4 km s⁻¹ Mpc⁻¹, Ωde = 0.77-0.03+0.02 and w = -1.38-0.16+0.14 in flat wCDM. In combination with Planck and baryon acoustic oscillation data, when relaxing the constraints on the numbers of relativistic species we find Neff = 3.34-0.21+0.21 in NeffΛCDM and when relaxing the total mass of neutrinos we find ∑mν =0.182 eV in mνλCDM. Finally, in an open wCDM in combination with Planck and cosmic microwave background lensing, we find H0 = 77.9-4.2+5.0 km s⁻¹ Mpc⁻¹, Ωde = 0.77-0.03+0.03, Ωk = -0.003-0.004+0.004 and w = -1.37-0.23+0.18.
Described by Einstein as “the most important event in physics since Newton's time,” the discovery by James Clerk Maxwell that a vast array of phenomena could be united by four elegant formulas remains one of the greatest successes of modern physics. This book, based on the third originally published in 1891, presents the original work which underpins the electronic revolution in the 20th century and which inspired both Lorentz’s theories on the electron and Einstein's theory of relativity. Volume II covers magnetism and electromagnetism.