Quantum Structural Studies. Classical Emergence from the Quantum Level

484 Pages·2016·4.053 MB·English

by  Ruth E Kastner, Jasmina Jeknić-Dugić, George Jaroszkiewicz (eds.)

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Library of Congress Cataloging-in-Publication Data
Names: Kastner, Ruth E., 1955– editor. | Jeknić-Dugić, Jasmina, editor. |
Jaroszkiewicz, George, editor.
Title: Quantum structural studies : classical emergence from the quantum level /
edited by, Ruth E. Kastner (University of Maryland, College Park, USA),
Jasmina Jeknić-Dugić (University of Niš, Serbia),
George Jaroszkiewicz (The University of Nottingham, UK).
Description: Hackensack, NJ : World Scientiic, [2016] |
Includes bibliographical references and index.
Identiiers: LCCN 2016032484| ISBN 9781786341402 (hc ; alk. paper) |
ISBN 1786341409 (hc ; alk. paper)
Subjects: LCSH: Quantum systems. | Quantum theory. | Degree of freedom. | Atomic structure.
Classiication: LCC QC174.13 .Q35 2016 | DDC 530.12--dc23
LC record available at https://lccn.loc.gov/2016032484
British Library Cataloguing-in-Publication Data
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About the Editors
Ruth E. Kastner received her BS, cum laude with high honors in
physics, and after picking up an MS in physics from the University
of Maryland, College Park, in 1992, decided to pursue her interest
in the foundational aspects being studied at the UMCP Philosophy
Department. She received her PhD in Philosophy (History and
Philosophy of Science) with Jeffrey Bub as her dissertation advisor
in 1999. She has won two National Science Foundation awards
for her study of interpretational issues in quantum theory and is
Research Associate in the Foundations of Physics Group at UMCP.
She wrote the first book on the length treatment of the Transac-
tional Interpretation (The Transactional Interpretation of Quantum
Mechanics: The Reality of Possibility, Cambridge University Press,
2012) and followed that with a conceptual presentation of TIQM
for the general reader (Understanding Our Unseen Reality: Solving
Quantum Riddles, Imperial College Press, 2015). She has over two

dozen peer reviewed publications and regularly attends international
conferences on Foundations of Physics, where she is often an invited
speaker. She currently resides in upstate New York.
Jasmina Jekni´c-Dugi´c received her BS degree in physics in 2000
whenshedecidedtoventureintonuclearsciencesandtechnology.She
visited numerous nuclear research centers in Europe, notably IRES
in Strasbourg (France) and UCL in Louvain-la-Neuve (Belgium)
that resulted in obtaining her MS degree in physics and in starting
her academic career as a Teaching Assistant at Department of
v
vi About the Editors
Physics, Faculty of Science and Mathematics, University of Niˇs,
Serbia. While working in applied field of nuclear science, numerous
open questions and challenges emerged and established her future
permanent interest in the foundational topics and issues of quantum
theory,quantumdecoherenceandopenquantumsystemstheory.The
research work and scientific publications in these fields earned her
position of Associate Professor at Department of Physics, University
of Niˇs, Serbia. With collaborators, she published (2013) the first
bookonthetop-down,minimalistandnon-interpretationalapproach
to quantum structuralism with an emphasis on the team’s original
results,andcurrentlypursuesaspecificparadigm of local timeinthe
foundations of quantum theory.
George Jaroszkiewicz earned a degree in Mathematical Physics
from the University of Edinburgh and then completed his PhD in
high energy particle physics with Dr. Peter Landshoff at the Depart-
ment of Applied Mathematics and Theoretical Physics (DAMTP),
University ofCambridge,UK.AwardedaBritishCouncilFellowship,
he spent most of 1977 at the Theoretical Physics Department,
University ofWarsaw,Poland,workingwithProf.Krolikowskionthe
colored quark model. On his return to Britain in 1977, Jaroszkiewicz
spenttwoyearsasaPost-DoctoralFellowatthePhysicsDepartment,
University of Kent at Canterbury, England, working on theoretical
end experimental spin-echo nuclear magnetic resonance with John
Strange. Thiswas followed by two years as a Post-Doctoral Fellow in
theDepartmentofPhysicalChemistry,UniversityofOxford,working
onthesimulationofdiluteaqueoussolutions,withGrahamRichards.
In 1981, Jaroszkiewicz was appointed lecturer in the Department of
Mathematics (now School of Mathematical Sciences), University of
Nottingham, UK.Overthenextthreedecades,Jaroszkiewicz worked
on discrete time mechanics and quantized detector networks (an
observer-centered approach to quantum mechanics). A major theme
throughouthasbeenhispreoccupationwiththetimeconcept.Hehas
published two books: Principles of Discrete Time Mechanics (CUP,
2014) and Images of Time (OUP, 2016). Current projects include a
monograph on quantized detector networks, currently scheduled for
April 2017 with Oxford University Press.
Contents
About the Editors v
1. Quantum Structures: An Introduction 1
R. E. Kastner, J. Jekni´c-Dugi´c and G. Jaroszkiewicz
Historical Aspects 21
2. Bohr’s Diaphragms 23
T. Bai and J. Stachel
3. “It Ain’t Necessarily So”: Interpretations and
Misinterpretations of Quantum Theory 53
J. Stachel
Philosophical Aspects 75

4. Beyond Complementarity 77
R. E. Kastner
5. Representational Realism, Closed Theories and the
Quantum to Classical Limit 105
C. de Ronde
6. Principles of Empiricism and the Interpretation
of Quantum Mechanics 137
G. Jaroszkiewicz
vii
viii Contents
Specific Interpretive Approaches and Ontologies 173
7. Primitive Ontology and the Classical World 175
V. Allori
8. Fluidodynamical Representation and Quantum Jumps 201
L. Chiatti and I. Licata
9. Minkowski Spacetime and QED from Ontology of Time 225
C. Baumgarten
10. The Quantum State as Spatial Displacement 333
P. Holland
11. Symmetry and Natural Quantum Structures
for Three-Particles in One-Dimension 373
N. L. Harshman
12. Quantum to Classical Transitions via Weak
Measurements and Post-Selection 401
E. Cohen and Y. Aharonov
13. Bound States as Fundamental Quantum Structures 427
R. E. Kastner
Methodological Approaches 433
14. A Top-down View of the Classical Limit
of Quantum Mechanics 435
S. Fortin and O. Lombardi
15. A Top-down versus a Bottom-up Hidden-variables
Description of the Stern–Gerlach Experiment 469
M. Arsenijevi´c, J. Jekni´c-Dugi´c and M. Dugi´c
Index 485
Chapter 1
Quantum Structures: An Introduction
R.E. Kastner∗, J. Jekni´c-Dugi´c† and G. Jaroszkiewicz‡
∗Foundations of Physics Group,
University of Maryland, College Park, USA
†Department of Physics,
Faculty of Science and Mathematics, University of Niˇs, Serbia
‡School of Mathematical Sciences,
The University of Nottingham, UK
1. Introduction
Quantum mechanics offers a striking, genuinely novel observation:
it is possible to obtain more information about a closed composite
system than about the subsystems constituting that system. This
is symptomatic of the highly nontrivial concept of a quantum
subsystem: specifically, there is much more to the “subsystem”
concept in quantum mechanics than there is in classical physics.

In classical physics, complete knowledge about the total state
of a system is equivalent to a complete knowledge about the state
of every constituent subsystem. This accounts for the primary
role of subsystems in classical physics, and the fact that the lack of
knowledge about subsystems is subjective, i.e. observer–dependent.
There are no fundamental physical limits in this regard, since there
is no classical information limit at the fundamental physical level.
This view of the classical world is typically interpreted as follows:
every single classical system exists in space independently of any
other physical system at every instant of time. Physical subsystems
1
2 R. E. Kastner, J. Jekni´c-Dugi´c and G. Jaroszkiewicz
(“constituting particles”) are as physically realistic as the physical
objects they build.
Mathematically, thisideaisrepresentedbytheCartesianproduct
of a set of ontologically fundamental degrees of freedom (and
analogously for continuous fields). In addition, in classical physics,
useful artificial degrees of freedom can be defined; for example,
the center of mass of an extended composite system. Mathematical
manipulations with such constructed degrees of freedom do not
directly describe the behavior of a realistic physical object. Thus,
a description based on such mathematical degrees of freedom is
typically incomplete and approximate, but is assumed ultimately to
be reducible to the dynamics of the fundamental degrees of freedom.
This reductionistic attitude is sometimes criticized even in the
context of classical physics: there is a conceptual and formal gap
between the fundamental and the apparently emergent degrees of
freedom [6]. Nevertheless, the primary role of the fundamental
degrees of freedom is rarely, if at all, challenged in the physics litera-
ture: the existence of fundamental degrees of freedom is assumed to
be a necessary condition for the emergent behavior that is observed.
However, this view face a serious challenge in the quantum
mechanical context for at least the following two reasons. First,
knowledgeofacompositesystem’sstatedoesnotimply,orassumeor
require knowledge about, the subsystems’ states. If the total system
is in a pure state |Ψ(cid:1), the subsystems are statistically described
by “reduced density matrices” (“reduced statistical operators”) that
are sometimes referred to as “improper mixtures”. For a bipartite

1 + 2 system, a pure state, |Ψ(cid:1), can be always represented by a
Schmidt canonical form, |Ψ(cid:1)= c |i(cid:1) ⊗|i(cid:1) , |c |2 = 1; with the
i i 1 2 i i
orthonormalized bases, (cid:3)i|j(cid:1) = δ , α = 1,2. Provided |c | < 1,∀i,
α α ij i
(cid:1) (cid:1)
the reduced (subsystems) mixed states ρˆ are obtained via the
α
tracing out operation such that ρˆ2 (cid:5)= ρˆ , α = 1,2. The point is that
α α
|Ψ(cid:1)(cid:3)Ψ| =(cid:5) ρˆ ⊗ ρˆ , i.e. that the αth subsystem cannot be assumed
1 2
to be in the ρˆ state. Rather, the subsystems’ states are not well
α
defined.
Second, there is no unique ensemble description of a mixed
quantum state ρˆ. The formalism of quantum mechanics allows a