Probing the Meaning of Quantum Mechanics: Superpositions, Dynamics, Semantics and Identity: Quantum Mechanics and Quantum Information: Physical, Philosophical and Logical Approaches (Cagliari, Italy 23–25 July 2014)

371 Pages·2016·4.43 MB·English

Probing the Meaning of
Quantum Mechanics
Superpositions, Dynamics, Semantics and Identity
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Probing the Meaning of
Quantum Mechanics
Superpositions, Dynamics, Semantics and Identity
Quantum Mechanics and Quantum Information: Physical,
Philosophical and Logical Approaches
Cagliari, Italy 23 – 25 July 2014
Editors
Diederik Aerts
Brussels Free University (VUB), Belgium
Christian de Ronde
University of Buenos Aires, Argentina &
Brussels Free University (VUB), Belgium
Hector Freytes
Università di Firenze, Italy
Sven Aerts
Università degli studi di Cagliari, Italy
World Scientific
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PROBING THE MEANING OF QUANTUM MECHANICS
Superpositions, Dynamics, Semantics and Identity
Copyright © 2016 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 978-981-3146-27-3
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EDITORIAL PREFACE
Quantummechanicsisrecognizedtodayasoneofthemostsuccessfulphys-
ical theories ever. However, its interpretation is still problematic, or more
specifically,anunderstandingofwhatquantummechanicstalksaboutdoes
notexistyet.Althoughthefeaturesthatareconsideredattheoriginofthese
problems — Schr¨odinger’s cat situation, entanglement, non-separability
and contextuality — are well identified and nowadays resources of well-
established technical applications, we continue to lack a semantic and a
conceptual representation explaining the relation of quantum theory to
physical reality.
Independently of the many developments in the 20th Century, dur-
ing the last decades quantum mechanics has given rise to a new techno-
logical era, a revolution taking place today especially within the field of
quantuminformationprocessing,reachingfromquantumteleportationand
cryptographyto quantumcomputation. This developmentis relatedto the
philosophy of quantum mechanics which addresses epistemic and ontic in-
terpretations, the meaning of individuality and identity, of quantum pos-
sibility, objective probability and chance, free will and causality. Next to
the philosophical foundations also the logical and mathematical structure
of the theory is consideredinthe presentbook. The underlying mathemat-
ical structure relatedto quantummechanics is basedonavectorialHilbert
space, which was employed in 1932 by John von Neumann in his famous
book Mathematical Foundations of Quantum Mechanics. Few years later,
in 1936, John von Neumann and Garret Birkhoff published a seminal pa-
per titled “The logic of quantum mechanics”. The subject of that paper
was an investigation of the logical structure underlying the language of
quantum mechanics, establishing a link between logic, language and quan-
tum mechanics. From this standpoint several schools in the foundations of
quantum mechanics and quantum logic with different approachesfollowed.
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The differences in approach have still grown over time, up to the present
day. The quantum logical approaches consider many different aspects of
quantum mechanics such as: truth notions, the logic related to superpo-
sitions and entanglement, modal approaches, logical systems associated to
quantum computational gates and categorical approaches. These topics
define a new extensive area of investigation in modern quantum logic and,
at the same time, provide a deep contribution to the understanding of the
theoryofquanta.Allthesedifferentsubjectsrelatedtoquantummechanics
are discussed and analyzed in the present book.
This book attempts to address foundational questions in an interdisci-
plinary manner considering the physical, philosophical, mathematical and
logical aspects of quantum mechanics. Going from philosophy of quan-
tum mechanics to quantum logic, from categorical approaches to quantum
informationprocessing,the originalityofthis bookresidesinthe multiplic-
ity of approaches which focus on the common aim, to grasp the meaning
of the theory of quanta. We believe that the advancement of such under-
standing will be possible, not through the strict separation of smaller and
smallersubjectsofresearch,butontheverycontrary,throughthecommon
sharing and discussion of multiple perspectives that come from different
fields.
The novelty of the book comes from the multiple perspectives put for-
ward by top researchers in quantum mechanics, from Europe as well as
North and South America, discussing the meaning and structure of the
theory of quanta. The book comprises in a balanced manner physical,
philosophical, logicaland mathematical approachesto quantum mechanics
andquantuminformation.Fromquantumsuperpositionsandentanglement
to dynamics and the problem of identity, from quantum logic, computa-
tion andquasi-settheoryto the categoryapproachandteleportation,from
realism and empiricism to operationalism and instrumentalism, the book
touches from different perspectives some of the most intriguing questions
related to one of the most important physical theories of our time. From
Buenos Aires to Brussels and Cagliari,from Florence to Florian´opolis, the
interaction between different groups is reflected in the many different ar-
ticles. This book is interesting not only to the specialists but also to the
general public attempting to get a graspon some of the most fundamental
questions of present quantum physics.
D. Aerts, C. de Ronde, H. Freytes & R. Giuntini.
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ACKNOWLEDGMENTS
Thepresentbookwasinspiredbythefirsteditionoftheinternationalmeet-
ing “Quantum Mechanics and Quantum Information: Physical, Philosoph-
ical and Logical approaches” that took place at the University of Cagliari
(Italy) in July 2014.
We are particularly grateful to the Regione Sardegna that has par-
tially supported this international meeting within the Regional project:
“Modeling the uncertainty: Quantum Theory and Imaging Processing”,
(Legge Regionale 7 Agosto 2007,n.7, Promozionedella ricerca scientifica e
dell’innovazione tecnologica in Sardegna).
A special thanks to the National Research Council CONICET
(Argentina) and the Centre Leo Apostel CLEA(Bruxelles) that also spon-
sored this conference.
Last but not least, thanks to the Scientific Committee, composed of
Diederik Aerts, Maria Luisa Dalla Chiara, Desio Crause and Newton da
Costa,andtotheOrganizingCommittee,composedofChristiandeRonde,
Hector Freytes, Giuseppe Sergioli and Antonio Ledda.
Cagliari, May 13th, 2016
Roberto Giuntini
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CONTENTS
1. On the Notion of Truth in Quantum Mechanics:
A Category-TheoreticStandpoint 1
V. Karakostas and E. Zafiris
2. A Logical Account of Quantum Superpositions 44
D. Krause and J. R. B. Arenhart
3. Mixing Categories and Modal Logics in the Quantum Setting 60
G. Cina`
4. Binary Gates in Three Valued Quantum Computational
Logics 76
G. Sergioli, A. Ledda and R. Giuntini
5. The GTR-Model: A Universal Framework for
Quantum-Like Measurements 91
D. Aerts and M. S. de Bianchi
6. ‘Probabilistic Knowledge’ as ‘Objective Knowledge’ in
QuantumMechanics:PotentialImmanentPowersInstead
of Actual Properties 141
C. de Ronde
7. On When a Semantics is not a Good Semantics:
The Algebraisation of Orthomodular Logic 179
T. Kowalski, F. Paoli and R. Giuntini