Open Quantum Physics and Environmental Heat Conversion into Usable Energy, Volume 3

167 Pages·2022·17.394 MB·English

by  Eliade Stefanescu

Open Quantum Physics and
Environmental Heat Conversion
Into Usable Energy

(Volume 3)

Authored by
Eliade Stefanescu
(cid:38)(cid:72)(cid:81)(cid:87)(cid:72)(cid:85)(cid:3)(cid:82)(cid:73)(cid:3)(cid:36)(cid:71)(cid:89)(cid:68)(cid:81)(cid:70)(cid:72)(cid:71)(cid:3)(cid:54)(cid:87)(cid:88)(cid:71)(cid:76)(cid:72)(cid:86)(cid:3)(cid:76)(cid:81)(cid:3)(cid:51)(cid:75)(cid:92)(cid:86)(cid:76)(cid:70)(cid:86)(cid:3)(cid:82)(cid:73)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:53)(cid:82)(cid:80)(cid:68)(cid:81)(cid:76)(cid:68)(cid:81)(cid:3)(cid:36)(cid:70)(cid:68)(cid:71)(cid:72)(cid:80)(cid:92)
Academy of Romanian Scientists
Bucharest
Romania
(cid:50)(cid:83)(cid:72)(cid:81)(cid:3)(cid:52)(cid:88)(cid:68)(cid:81)(cid:87)(cid:88)(cid:80)(cid:3)(cid:51)(cid:75)(cid:92)(cid:86)(cid:76)(cid:70)(cid:86)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:40)(cid:81)(cid:89)(cid:76)(cid:85)(cid:82)(cid:81)(cid:80)(cid:72)(cid:81)(cid:87)(cid:68)(cid:79)(cid:3)(cid:43)(cid:72)(cid:68)(cid:87)(cid:3)(cid:38)(cid:82)(cid:81)(cid:89)(cid:72)(cid:85)(cid:86)(cid:76)(cid:82)(cid:81)(cid:3)(cid:76)(cid:81)(cid:87)(cid:82)(cid:3)(cid:56)(cid:86)(cid:68)(cid:69)(cid:79)(cid:72)(cid:3)(cid:40)(cid:81)(cid:72)(cid:85)(cid:74)(cid:92)
Volume # (cid:22)
Author: Eliade Stefanescu
ISSN (Online): 2542-5072
ISSN (Print): 2542-5064
ISBN (Online): 978-981-5051-09-4
ISBN (Print): 978-981-5051-10-0
ISBN (Paperback): 978-981-5051-11-7
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CONTENTS
PREFACE ................................................................................................................................................... i
DEDICATION ............................................................................................................................................ iii
CHAPTER 1 INTRODUCTION ............................................................................................................... 1
CONCLUSION ................................................................................................................................. 14
CHAPTER 2 QUANTUM PARTICLE AS A DISTRIBUTION OF MATTER .................................... 15
CONCLUSION ................................................................................................................................. 17
CHAPTER 3 QUANTUM PARTICLE IN THE GRAVITATIONAL FIELD ...................................... 19
3.1. CURVED TIME-SPACE COORDINATES ............................................................................. 20
3.2. CURVED PHYSICAL SYSTEM IN THE TOTAL UNIVERSE ........................................... 25
3.3. THE MASS CONSERVATION AS A RELATIVISTIC INVARIANCE .............................. 34
3.4. HARMONIC OSCILLATIONS AND METRIC TENSOR DENSITY ................................. 36
3.5. GAUSS AND STOKES THEOREMS WITH COVARIANT DERIVATIVES ..................... 38
3.6. GEODESICS ............................................................................................................................... 41
3.7. THE CURVATURE TENSOR ................................................................................................. 44
3.8. BIANCI RELATIONS AND EINSTEIN’S LAW OF GRAVITATION ................................ 51
3.9. NEWTON’S GRAVITATION EQUATION AND RED SHIFT ........................................... 54
3.10. GRAVITATIONAL FIELD WITH SPHERICAL SYMMETRY – THE
SCHWARZSCHILD SOLUTION ................................................................................................... 57
3.11. QUANTUM PARTICLE IN A SPHERICAL GRAVITATIONAL FIELD AND BLACK
HOLE ................................................................................................................................................. 68
3.12. EINSTEIN’S LAW OF THE GRAVITATIONAL FIELD AND THE BLACK HOLE
DYNAMICS ...................................................................................................................................... 77
CONCLUSION ................................................................................................................................. 88
CHAPTER 4 CHARGED QUANTUM PARTICLE IN GRAVITATION AND
ELECTROMAGNETIC FIELDS .............................................................................................................. 90
4.1. QUANTUM PARTICLE DYNAMICS IN ELECTROMAGNETIC
FIELD ................................................................................................................................................. 91
4.2. QUANTUM PARTICLE IN A GRAVITATIONAL WAVE AND THE
GRAVITON SPIN ............................................................................................................................. 100
4.3. PROPAGATION WAVE FUNCTIONS ................................................................................... 109
CONCLUSION ................................................................................................................................. 128
CHAPTER 5 THE LEAST ACTION AND MATTER-FIELD DYNAMICS IN GRAVITATIONAL
FIELD ......................................................................................................................................................... 130
5.1. GRAVITATION ACTION ........................................................................................................ 130
5.2. MATTER ACTION ................................................................................................................... 138
5.3. ELECTROMAGNETIC FIELD ACTION ............................................................................. 141
5.4. ELECTRIC CHARGE ACTION AND THE TOTAL MATTER-FIELD ACTION ............ 149
CONCLUSION ................................................................................................................................. 152
REFERENCES ……………………………………..……………………………………………............................. 154
SUBJECT I NDEX .................................................................................................................................... 155
i
PREFACE
In the first two volumes, we approached the openness of a physical system, from
coupling to a complex dissipative environment of Fermions, Bosons, and a free
electromagnetic field. Essentially, the open description of a system of interest starts
with the dynamics of the total system, including the environment, and consists of
the reduction of the system dynamics on the environmental coordinates to
dissipative dynamics, with coefficients depending on the coupling matrix elements,
the densities of the environmental states, and the occupation probabilities of these
states, as a function of temperature. Various empirical descriptions of coupling with
the environment violated fundamental principles of quantum mechanics as the
uncertainty principle, the zero-point vibration, and the positivity of the density
matrix. A positive application of the dissipative dynamics was discovered in the
seventies b(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:7)(cid:11)(cid:3)(cid:8)(cid:12)(cid:13)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:7)(cid:14)(cid:15)(cid:3)(cid:16)(cid:10)(cid:15)(cid:13)(cid:17)(cid:18)(cid:3)(cid:17)(cid:19)(cid:12)(cid:10)(cid:13)(cid:5)(cid:20)(cid:6)(cid:3)(cid:8)(cid:17)(cid:21)(cid:10)(cid:16)(cid:17)(cid:3)(cid:10)(cid:3)(cid:22)(cid:20)(cid:22)(cid:12)(cid:9)(cid:10)(cid:18)(cid:3)(cid:13)(cid:20)(cid:20)(cid:9)(cid:11)(cid:3)
especially in nuclear physics, only in the eighties, when Sandulescu and Scutaru
applied this equation to deep inelastic collisions of heavy ions. However, this
equation, much used today, is very unsatisfactory, being a phenomenological one,
with terms for all the system operators, with unspecified dissipation coefficients.
Consequently, in the nineties, and the early 2000s, I obtained master equations for
Fermions, Bosons, and a coherent electromagnetic field, with explicit microscopic
coefficients for the dissipative coupling with other Fermions, Bosons, and the free
electromagnetic field, and terms for non-Markovian effects. Based on these
equations, I showed that the entropy of a matter-field system could spontaneously
decrease, not only increase as it is asserted by the second law of thermodynamics,
for molecular systems. In this framework, I invented a semiconductor device
converting environmental heat into usable energy. A theoretical description of this
device, and of the quantum mechanical and statistical fundamentals are the objects
of the first two volumes. However, in the approach of these fundamentals, I found
that a general solution of the Schrödinger equation in the coordinate space does not
correctly describe the particle dynamics, according to the Hamilton equations. A
correct description is obtained only with propagation wave functions when the
Hamiltonian of the time-dependent phase is replaced by the Lagrangian. In this
volume, with the relativistic Lagrangian, for a quantum particle, I obtain a more
physical description, as an invariant quantity of matter propagating in space, with
the mass determined by the dynamic characteristics of the matter density. Quantum
mechanics is obtained from the general theory of relativity. I use the formalism of
Dirac, who was the big architect of quantum mechanics, and the general theory of
relativity. In the whole universe, where it is curved on other dimensions, I regard
(cid:3)
ii
our four-dimensional physical universe to be an open system, describing the
inertial-gravitational dynamics.
CONSENT FOR PUBLICATION
Not applicable.
CONFLICT OF INTEREST
The author declares that he has no affiliation with any organization or entity from
afinancial point of view in the subject matter or materials discussed in this book.
ACKNOWLEDGEMENT
Declared none.
Eliade Stefanescu
Center of Advanced Studies in Physics of the Romanian Academy
Academy of Romanian Scientists
Bucharest
Romania
(cid:3)
iii
DEDICATION

I dedicate this book
to my grandson Alex and my granddaughter Julia
and to all young people tending to really understanding the world they live in
Open Quantum Physics, 2022, Vol. 3, 1-14 1
CHAPTER 1

Introduction
Abstract: We consider the two basic theories of the standard physics: (1) the theory
of relativity, as a four-dimensional time-space description of our universe, with the
invariance of the time-space interval which leads to the Lorentz transformation, and
(2) quantum mechanics, based on the Schrödinger equation, with a solution called
wave function. However, we find that this equation is very unsatisfactory, describing
fully unlocalized free particles, any initially localized particle rapidly spreading in
space, in disagreement with the fundamental Hamilton equations. In agreement with
the Hamilton equations, we describe a quantum particle by propagation wave
functions in the coordinate and momentum spaces, with the Lagrangian in the time
dependent phase instead of the Hamiltonian coming from the Schrödinger equation.
With the relativistic Lagrangian, we obtain wave functions describing invariant
distributions propagating in space.
Keywords: Light velocity, Time-space interval, Lorentz transformation,
Hamiltonian, Kinetic energy, Potential energy, Mass, Schrödinger equation,
Operator, Heisenberg picture, Schrödinger picture, Hamilton equation, Wave
function, Wave packet, Group velocity, Standard deviation, Mean value,
Commutation, Lagrangian, Proper time, Momentum, Conjugate space, Metric
tensor.
The standard physics is based on two different descriptions:
(1) the theory of relativity [1], which we consider here in Dirac’s formalism [2], as
an analytic description of a continuous distribution of matter in a time-space
system of coordinates
(cid:2) (cid:3) (cid:2) (cid:3) (cid:2) (cid:3)
x(cid:5) x(cid:4) (cid:5) x0 (cid:5)ct,x1,x2,x3 (cid:5) x0 (cid:5)ct,xi , (1.1)
c
where is a universal constant, called the light velocity, and
(2) quantum mechanics [3], as a statistical description of a ssyysstteeeemmm pppuunnccttuuaall
particles, any particle randomly having different coordinnaatteess rrr (cid:5) xxxx11111 (cid:6) y11 (cid:6)z11
(cid:2) (cid:3)(cid:3) x y z
, with probabilities determined by a wave function (cid:7) t,r .
The theory of relativity is based on the invariance of the time-space interval, which
(cid:8)
in two orthogonal systems S and S of a flat space is
ds2 (cid:5)dx02 (cid:9)dx12 (cid:9)dx22 (cid:9)dx32 (cid:5)ds(cid:8)2 (cid:5)dx0(cid:8)2 (cid:9)dx1(cid:8)2 (cid:9)dx2(cid:8)2 (cid:9)dx3(cid:8)2, (1.2)
Eliade Stefanescu
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