Overview
Presents basic assumptions that imply a link between statistical theory and quantum theory
Offers strong arguments for an epistemic interpretation of quantum mechanics, and describes epistemic foundations
Provides a simple interpretation of quantum states as question-and-answer pairs
Derives the Born formula and the Schrödinger equation under weak conditions on the epistemic process
Discusses the philosophical implications of this approach to quantum theory, including in a macroscopic setting
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Table of contents (6 chapters)
Keywords
- Bell’s inequality
- Born’s formula
- epistemic process
- complementarity
- conceptual variable
- conditionality principle
- epistemic conceptual variable
- Schrödinger equation
- inaccessible conceptual variable
- interpretation of quantum states
- likelihood principle
- quantum state
- quantum theory
- rationality
- spin
- sufficiency principle
About this book
This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes – which can be e.g. statistical investigations or quantum mechanical measurements, and refer to processes that are used to gain knowledge about something. The book addresses a range of topics, including a derivation of the Born formula from reasonable assumptions, a derivation of the Schrödinger equation in the one-dimensional case, and a discussion of the Bell inequality from an epistemic perspective. The book describes a possible epistemic foundation of quantum theory. Lastly, it presents a general philosophical discussion of the approach, which, principally speaking, is not restricted to the micro-world. Hence the book can also be seen as a motivation for further research into quantum decision theory and quantum models for cognition. The book will benefit a broad readership, including physicists and statisticians interested in the foundation of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.
Authors and Affiliations
About the author
Inge S. Helland completed his cand.mag (B.S.) in mathematics and physics at the University of Bergen in 1970. After a research fellowship at The Niels Bohr Institute, Copenhagen in fall 1971, he turned to statistics, and completed his cand.real. (M.S.) at the University of Bergen in 1973. He was a fellow at the University of Bergen from 1973 to1978, including a research stay at the University of California, Berkeley in 1977 and 1978. He was then an Associate Professor of Statistics at the Agricultural University of Norway, later Norwegian University of Life Sciences, from 1978 to 1983, and Professor at the same university from 1983 to 1996. He obtained his dr. philos. degree on limit theorems for stochastic processes from the University of Oslo in 1980, and was Professor of Statistics at the University of Oslo from 1996 to 2012, when he went took on an emeritus position. His research covers a large area of theoretical and applied statistics, including proposing a statistical model connected to the chemometricians’ partial least squares algorithm.
Bibliographic Information
Book Title: Epistemic Processes
Book Subtitle: A Basis for Statistics and Quantum Theory
Authors: Inge S. Helland
DOI: https://doi.org/10.1007/978-3-319-95068-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2018
Softcover ISBN: 978-3-030-06968-1Published: 20 December 2018
eBook ISBN: 978-3-319-95068-6Published: 21 September 2018
Edition Number: 1
Number of Pages: XI, 164
Number of Illustrations: 1 b/w illustrations
Topics: Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Quantum Physics, Epistemology, Philosophy of Science, Statistical Theory and Methods, Statistical Physics and Dynamical Systems