Table Of ContentTHE PRINCIPLE OF THE COMMON CAUSE
The Common Cause Principle says that every correlation is either due to a direct
causal effect linking the correlated entities, or is brought about by a third factor,
a so-called common cause. The principle is of central importance in the philos
ophy of science, especially in causal explanation, causal modeling, and in the
foundations of quantum physics.
Written for philosophers of science, physicists and statisticians, this book con
tributes to the debate over the validity of the Common Cause Principle, by proving
results that bring to the surface the nature of explanation by common causes. It
provides a technical and mathematically rigorous examination of the notion of
common cause, providing an analysis not only in terms of classica! probability
measure spaces, which is typical in the available literature, but also in quantum
probability theory. The authors provide numerous open problems to further the
debate and encourage future research in this field.
G AB o R Ho F E R -s z AB 6 is a Senior Research Fellow in the Institute of Philos
ophy, Research Center for Humanities at the Hungarian Academy of Sciences. His
main fields of research are the foundations of quantum mechanics, interpretations
of probability, and probabilistic causality.
M I K L 6 s R É DE I is Professor in the Department of Philosophy, Logie and
Methodology of Science at the London School of Economics and Politica! Science.
His research interests are philosophy and the foundations of physics.
LA s z L 6 E. s z AB 6 is Professor in the Department of Logie, Institute of Phi
losophy at Eotvos Lorand University, Budapest. His research focuses on the
philosophy of space and time, causality, the EPR-Bell problem, the interpretation
of probability, and a physicalist account of mathematics.
THE PRINCIPLE OF THE
COMMON CAUSE
GABOR HOFER-SZABÒ
Research Center far the Humanities, Budapest
MIKLÒS RÉDEI
London School of Economics and Politica! Science
LASZLÒ E. SZABÒ
Eotvos Lortind University, Budapest
U
CAMBRIDGE
V
UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS
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Cambridge University Press
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© G. Hofer-Szab6, M. Rédei, L. E. Szab6 2013
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take piace without the written
permission of Cambridge University Press.
First published 2013
Printed and bound in the United Kingdom by the MPG Books Group
A catalog record for this publication is available from the British Library
Library ofCongress Cataloging in Publication data
Hofer-Szab6, Gabor.
The principle of the common cause I Gabor Hofer-Szab6, Eotvos Lorand University,
Budapest, Mikl6s Rédei, London School of Economics and Political Science,
Lazsl6 E. Szab6, Eotvos Lorand University, Budapest.
pages cm
Includes bibliographical references and index.
ISBN 978-1-107-01935-5 (hardback)
I. Causation. 2. Science-Philosophy. 3. Physics-Philosophy. I. Rédei, Mik.16s.
II. Szab6, Lazsl6 E. III. Title.
Ql 75.32.C38H64 2013
122--dc23 2012044990
ISBN 978-1-107-01935-5 Hardback
Cambridge University Press has no responsibility for the persistence or
accuracy of URLs for external or third-party internet websites referred to
in this publication, and does not guarantee that any conteni on such
websites is, or will remain, accurate or appropriate.
Contents
Preface
page vii
Introduction and overview
1
2 The Common Cause Principle
11
2.1 Reichenbach's notion of common cause 11
2.2 Reichenbach's Common Cause Principle
13
2.3 Notes and bibliographic remarks
17
3 Common cause extendability of probability spaces 18
3.1 Common cause (in)completeness and extendability 18
3.2 Classica! probability spaces are common cause extendable 24
3.3 Notes and bibliographic remarks 28
4 Causally closed probability theories 29
4.1 Causal closedness and common cause closedness 29
4.2 Atomicity and common cause closedness 34
4.3 Notes and bibliographic remarks
50
5 Common common causes
51
5.1 Common causes and common common causes 51
5.2 Common causes are not common common causes 52
5.3 Notes and bibliographic remarks
59
6 Common cause extendability of nonclassical probability spaces 60
6.1 Quantum probability spaces are common cause extendable 62
6.2 Atomicity and common cause closedness in nonclassical
probability theory 69
6.3 Notes and bibliographic remarks 79
V
vi Contents
7 Reichenbachian common cause systems 80
7 .1 Common cause partitions 80
7 .2 Existence and properties of common cause systems 82
7.3 Notes and bibliographic remarks 95
8 Causal closedness of quantum field theory 97
8.1 The Common Cause Principle in algebraic relativistic
quantum field theory 97
8.2 The Common Cause Principle in lattice quantum field theory 116
8.3 Notes and bibliographic remarks 132
9 Reichenbach's Common Cause Principle and EPR correlations 134
9.1 Einstein-Podolsky-Rosen (EPR) correlations 134
9.2 Local and nonconspiratorial common cause systems 139
9.3 Notes and bibliographic remarks 171
10 Where do we stand? 173
Appendix 180
A.1 Boolean algebras 180
A.2 Classica! probability measure spaces 182
A.3 Measure theoretic atomicity 184
A.4 Orthocomplemented lattices 185
A.5 von Neumann algebras 188
References 193
Index 201
Preface
This book summarizes and develops further in some respects the results of research
the authors have undertaken in the past severa} years on the problem of explain
ing probabilistic correlations in terms of (Reichenbachian) Common Causes.
The results have been published by the authors of this book in a number of
papers, partly in collaborations with each other and with other colleagues; these
papers form the basis of the present book. We wish to thank especially Balazs
Gyenis, Zalan Gyenis, Inaki San Pedro, Stephen J. Summers, and Péter Vecsemyés
for the cooperation on the topic of the book and in particular for allowing us to use
materia} in joint publications.
In our work we also have benefited greatly from collaborations and informa}
discussions with a number of other colleagues. These include Nuel Belnap, Arthur
Fine, Jeremy Butterfield, Rob Clifton, Gerd Grasshoff, David Malament, Tomasz
Placek, Samuel Portman, Elliott Sober, Leszek Wronski, and Adrien Wi.ithrich -
we thank them all for their interest in our work and for their readiness to share with
us their insights and views.
The research that the book is based on was partially supported by severa} small
grants from the Hungarian National Science Found (OTKA). Tue final writing was
facilitated by the OTKA grant with contract number K100715.
G. Hofer-Szab6 (Budapest)
M. Rédei (London)
L. E. Szab6 (Budapest)
Vll
