The geometry of quantum potential : entropic information of the vacuum

344 Pages·2018·3.326 MB·English

by  Fiscaletti, Davide

THE GEOMETRY
OF QUANTUM
POTENTIAL
Entropic Information of the Vacuum
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THE GEOMETRY
OF QUANTUM
POTENTIAL
Entropic Information of the Vacuum
Davide Fiscaletti
SpaceLife Institute, Italy
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
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Published by
World Scientific Publishing Co. Pte. Ltd.
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British Library Cataloguing-in-Publication Data
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THE GEOMETRY OF QUANTUM POTENTIAL
Entropic Information of the Vacuum
Copyright © 2018 by World Scientific Publishing Co. Pte. Ltd.
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ISBN 978-981-3227-97-2
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Contents
Introduction ix
Chapter 1. The Geometry of the Quantum Potential
in Different Contexts 1
1.1 Bohm’s Original 1952 Approach on the Quantum
Potential . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Geometrodynamic Information of the Quantum
Potential . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.1 Gro¨ssing’s thermodynamic approach to the
quantum potential . . . . . . . . . . . . . . . 16
1.2.2 Quantum potential as an information
channel of a special superfluid vacuum. . . . 29
1.3 About the Link Between Weyl Geometries and the
Quantum Potential . . . . . . . . . . . . . . . . . . . 36
1.3.1 Weyl’s conformal geometrodynamics . . . . . 37
1.3.2 Santamato’s geometric interpretation
of quantum mechanics . . . . . . . . . . . . . 41
1.3.3 Novello’s, Salim’s and Falciano’s approach
of quantum mechanics as a manifestation of
the non-euclidean geometry . . . . . . . . . . 46
1.4 The Quantum Potential in the Relativistic Domain . 49
1.4.1 The quantum potential in Bohm’s
approach to Klein-Gordon relativistic
quantum mechanics . . . . . . . . . . . . . . 50
1.4.2 About a Bohmian approach to the Dirac
relativistic quantum mechanics . . . . . . . . 61
v
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vi The Geometry of Quantum Potential
1.5 The Quantum Potential in Relativistic Quantum
Field Theory . . . . . . . . . . . . . . . . . . . . . . 74
1.5.1 The quantum potential in bosonic quantum
field theory . . . . . . . . . . . . . . . . . . . 76
1.5.2 The quantum potential in fermionic
quantum field theory . . . . . . . . . . . . . 85
1.6 The Quantum Potential in Bohmian
Quantum Gravity . . . . . . . . . . . . . . . . . . . . 91
1.6.1 Bohm’s quantum potential in relativistic
curved space-time . . . . . . . . . . . . . . . 92
1.6.2 Bohm’s quantum potential in
quantum gravity . . . . . . . . . . . . . . . . 97
1.7 The Quantum Potential in Bohmian Quantum
Cosmology . . . . . . . . . . . . . . . . . . . . . . . . 110
1.7.1 F. Shojai’s and A. Shojai’s
geometrodynamic approach to Wheeler-de
Witt equation . . . . . . . . . . . . . . . . . 112
1.7.2 Pinto-Neto’s results about bohmian
quantum cosmology . . . . . . . . . . . . . . 118
1.7.3 The quantum potential ... and
the cosmological constant . . . . . . . . . . . 124
1.8 About the Quantum Potential in the Treatment
of Entangled Qubits . . . . . . . . . . . . . . . . . . 127
Chapter 2. Quantum Entropy and Quantum Potential 137
2.1 The Quantum Entropy as the Ultimate Source
of the Geometry of Space in the Non-Relativistic
Domain . . . . . . . . . . . . . . . . . . . . . . . . . 138
2.2 The Quantum Entropy in Bohm’s Approach
to the Klein-Gordon Relativistic Quantum
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 157
2.3 About the Quantum Entropy in a Bohmian
Approach to the Dirac Relativistic
Quantum Mechanics . . . . . . . . . . . . . . . . . . 164
2.4 Perspectives of the Quantum Entropy in Bohm’s
Relativistic Quantum Field Theory . . . . . . . . . . 172
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Contents vii
2.5 The Quantum Entropy as the Ultimate Source
of the Geometry of Space in the Relativistic
de Broglie-Bohm Theory in Curved Space-Time . . . 178
2.6 The Quantum Entropy as the Ultimate Source
of the Geometry of Space in Bohmian
Quantum Gravity . . . . . . . . . . . . . . . . . . . . 182
2.7 The Quantum Entropy as the Ultimate Source
of the Geometry of Space in Bohmian
Quantum Cosmology . . . . . . . . . . . . . . . . . . 185
2.8 About the Geometrodynamics of Bohm’s Quantum
Potential in an Entropic Approach in the Condition
of Fisher Information . . . . . . . . . . . . . . . . . . 189
Chapter 3. Immediate Quantum Information and
Symmetryzed Quantum Potential 203
3.1 The Symmetrized Quantum Potential
in the Non-relativistic Domain. . . . . . . . . . . . . 204
3.2 The Quantum Geometry in the Symmetrized
Quantum Potential Approach . . . . . . . . . . . . . 222
3.3 The Symmetrized Quantum Potential Approach
in the Relativistic de Broglie-Bohm Theory
in Curved Space-time . . . . . . . . . . . . . . . . . . 228
3.4 Towards a Symmetrized Extension of Bohm’s
Relativistic Quantum Field Theory . . . . . . . . . . 235
3.5 The Symmetrized Quantum Potential for Gravity
in the Context of Wheeler-deWitt Equation . . . . . 243
Chapter 4. The Quantum Potential ... and the
Quantum Vacuum 251
4.1 The Space-time Arena and the Quantum
Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . 251
4.2 Bohm’s Quantum Potential Approach
as the Epistemological Foundation of the
Quantum Vacuum . . . . . . . . . . . . . . . . . . . 254
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viii The Geometry of Quantum Potential
4.3 From Bohm’s View to Kastner’s Possibilist
Transactional Interpretation and Chiatti’s
and Licata’s Approach about Transactions . . . . . . 256
4.4 From Transactions ... to a Three-dimensional
Timeless Non-local Quantum Vacuum ... to
the Emergence of the Geometrodynamics
of Standard Quantum Theory from the
Non-local Quantum Vacuum . . . . . . . . . . . . . . 262
4.5 About the Behaviour of Subatomic Particles in
the Three-dimensionalTimeless Non-local Quantum
Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . 280
4.6 Unifying Perspectives of the Non-local Quantum
Potential of the Vacuum . . . . . . . . . . . . . . . . 282
Conclusions 293
References 301
Index 321
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Introduction
Phenomena studied by quantum physics are far outside the range
of parameters of our daily experience. The behaviour and the
evolution of quantum systems do not seem to be compatible with
a description in visualizable terms. Quantum physics turns out to
appear extremely exotic, unnatural and mysterious to us because
of our incapability to visualize a subatomic particle (such as an
electron) and its motion or the uncertainty principle or the processes
of creation and annihilation of quanta in the quantum vacuum.
Ifinclassicalphysicssystemscanbeanalysedintermsofelements
ofinformationrepresentedbyacertainnumberofwell-definedstates,
which are determined by the values of a certain number of physical
quantities (such as position and speed) and our ignorance about the
knowledge of the state of the system is owed to the loss of the
ability to follow information, in quantum mechanics the physical
variables of a system do not seem to have a well defined value at
each instant and thus the ignorance seems to be intrinsic to the
nature of objects. In the study of the microscopic world it seems
that there is no way to avoid the introduction of the probability
and that, when a property of an object is measured, its state
turns out to be modified dramatically by virtue of the irreversible
interaction with the measurement apparatus. Quantum mechanics
leads to develop an entirely new kind of programme in order to
studyphysicalprocesses —withrespecttoclassical physics— which
takes account of the fact that each system can be found in a state
ix