Available via license: CC BY 4.0

Content may be subject to copyright.

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

DOI:

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

N. Butto

DOI:

10.4236/jhepgc.2021.71016 327 Journal of High Energy Physics, G

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-

N. Butto

DOI:

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

N. Butto

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

N. Butto

DOI:

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.

References

[1] Plank, M. (1900) Zur theorie des gesetzes der energieverteilung im normalspek-

trum.

Verhandlungen der Deutschen Physikalischen Gesellschaft

,

2, 237.

[2] Steiner, R., Williams, E.R., Liu, R. and Newell, D.B. (2007) Uncertainty Improve-

ments of the NIST Electronic Kilogram.

IEEE Transactions on Instrumentation and

Measurement

, 56, 592-596. https://doi.org/10.1109/TIM.2007.890590

[3] Massa, E. and Nicolaus, A. (2011) Special Issue International Determination of the

Avogadro Constant.

Metrologia

,

48, S1-119.

https://doi.org/10.1088/0026-1394/48/2/E01

N. Butto

DOI:

10.4236/jhepgc.2021.71016 331 Journal of High Energy Physics, G

ravitation and Cosmology

[4] Bettin, H.,

et al

. (2013) Accurate Measurements of the Avogadro and Planck Con-

stants by Counting Silicon Atoms.

Annalen der Physik

, 525, 680-687.

https://doi.org/10.1002/andp.201300038

[5] Mohr, P.J. and Taylor, B.N. (2005) CODATA Recommended Values of the Funda-

mental Physical Constants: 2002.

Reviews of Modern Physics

,

77, 1.

https://doi.org/10.6028/NIST.SP.959e2005

[6] Peacock, K.A. (2008) The Quantum Revolution—A Historical Perspective. Green-

wood Press, Westport and London.

[7] Butto, N. (2020) A New Theory on the Origin and Nature of the Fine Structure

Constant.

Journal of High Energy Physics

,

Gravitation and Cosmology

, 6, 579-589.

https://doi.org/10.4236/jhepgc.2020.64039

[8] Butto, N. (2020) New Mechanism and Analytical Formula for Understanding the

Gravity Constant G.

Journal of High Energy Physics

,

Gravitation and Cosmology

, 6,

357-367. https://doi.org/10.4236/jhepgc.2020.63029

[9] Butto, N. (2020) The Essence and Origin of the Magnetic Constant.

Journal of High

Energy Physics

,

Gravitation and Cosmology

, 6, 662-669.

https://doi.org/10.4236/jhepgc.2020.64045

[10] Butto, N. (2021) Revealing the Essence of Electric Permittivity Constant.

Journal of

High Energy Physics

,

Gravitation and Cosmology

, 7, 210-217.

[11] Dirac, P.A. (1930) A Theory of Electrons and Protons.

Proceedings of the Royal So-

ciety of London A

:

Mathematical

,

Physical and Engineering Sciences

, 126, 360-365.

https://doi.org/10.1098/rspa.1930.0013

[12] Condon, E.U. and Odishaw, H. (1958) Handbook of Physics, Section 29. Mcgraw-

Hill, New York, 2-50.

[13] Rauscher, E.A. (1968) Electron Interactions and Quantum Plasma Physics.

Journal

of Plasma Physics

, 2, 517-541. https://doi.org/10.1017/S0022377800004013

[14] Rauscher, E.A. (2004) Dynamic Plasma Excitation Modes of Propagation in the Io-

nosphere. PA Press, The University of Columbus, 277.

[15] Peebles, P.J.E. and Ratra, B. (2003) The Cosmological Constant and Dark Energy.

Reviews of Modern Physics

, 75, 559-606.

https://doi.org/10.1103/RevModPhys.75.559

[16] Bonvin, V.,

et al

. (2017) H0LiCOW V. New COSMOGRAIL Time Delays of HE

0435-1223: H0 to 3.8% Precision from Strong Lensing in a Flat ΛCDM Model.

Monthly Notices of the Royal Astronomical Society

, 465, 4914-4930.

https://doi.org/10.1093/mnras/stw3006

[17] Hudson, J.J.,

et al

. (2011) Improved Measurement of the Shape of the Electron.

Na-

ture

, 473, 493-496. https://doi.org/10.1038/nature10104

[18] Butto, N. (2020) Electron Shape and Structure: A New Vortex Theory.

Journal of

High Energy Physics

,

Gravitation and Cosmology

, 6, 340-352.

https://doi.org/10.4236/jhepgc.2020.63027

[19] Ball, P. (2007) Two Constants to Rule Us All.

Nature

.

https://doi.org/10.1038/news.2007.389

[20] Mohr, P.J., Taylor, B.N. and Newell, D.B. (2012) CODATA Recommended Values

of the Fundamental Physical Constants: 2010.

Journal of Physical and Chemical

Reference Data

, 41, Article ID: 043109.

https://doi.org/10.1103/RevModPhys.84.1527

[21] Schlamminger, S.,

et al

. (2015) A Summary of the Planck Constant Measurements

Using a Watt Balance with a Superconducting Solenoid at NIST.

Metrologia

, 52,

N. Butto

DOI:

10.4236/jhepgc.2021.71016 332 Journal of High Energy Physics, G

ravitation and Cosmology

L5-L8. https://doi.org/10.1088/0026-1394/52/2/L5

[22] Azuma, Y.,

et al

. (2015) Improved Measurement Results for the Avogadro Constant

Using a 28Si-Enriched Crystal.

Metrologia

, 52, 360-375.

https://doi.org/10.1088/0026-1394/52/2/360

[23] Zloshchastiev, K.G. (2011) Spontaneous Symmetry Breaking and Mass Generation

as Built-In Phenomena in Logarithmic Nonlinear Quantum Theory.

Acta Physica

Polonica B

, 42, 261-292.

[24] Avdeenkov, A.V. and Zloshchastiev, K.G. (2011) Quantum Bose Liquids with Loga-

rithmic Nonlinearity: Self-Sustainability and Emergence of Spatial Extent.

Journal

of Physics B

:

Atomic

,

Molecular and Optical Physics

, 44, Article ID: 195303.

https://doi.org/10.1088/0953-4075/44/19/195303

[25] Maxwell, J. (1873) A Treatise on Electricity and Magnetism. Sections 822 and 823.