Inge S. Helland

This book presents a comprehensive treatment of quantum theory using theoretical variables as its foundation. The work progresses from fundamental quantum mechanical principles to sophisticated applications in quantum field theory and gravity. It provides rigorous mathematical frameworks while establishing connections between theoretical physics and practical engineering applications and includes: Presents an advanced treatment of quantum theory across two interconnected parts Examines Bell experiments, quantum probability, information theory, and connections to relativity Extends these foundations to explore quantum field theory, gravity, and noise theory Bridges the gap between theoretical physics and engineering applications Covers topics from Yang-Mills fields, quantum gravity to neural networks and biomedical applications of quantum electrodynamics Addresses quantum measurement of gravitons, Hawking radiation, classical and quantum neural networks with practical examples Provides mathematical frameworks for understanding quantum phenomena in applied contexts Particularly suitable for graduate students and researchers in physics, mathematics, and engineering disciplines seeking to understand quantum phenomena across theoretical and applied domains. This title has been co-published with Manakin Press. Taylor & Francis does not sell or distribute the print edition in India, Pakistan, Nepal, Bhutan, Sri Lanka and Bangladesh.

In the literature, quantum mechanics is founded by a very abstract set of postulates. For several reasons I propose that this set should be replaced by straightforward postulates based on the notion of conceptual variables, a notion generalizing the statisticians' parameters: In his mind, any observer/ actor in each given situation may have several conceptual variables. Some of these are accessible, can in some future be given numerical values by measurements or experiments. The notion of a maximal accessible conceptual variable is crucial. This can be motivated by an assumption to the effect that all physical variables in the actor's context have parallels in his mind. Examples are given. Under weak technical conditions, basic postulates of quantum mechanics can be shown to be implied by a postulate assuming that the actor in his mind has two related maximally accessible variables. Some specific symmetry conditions are needed. The notion of being related has a precise definition. A parallel development can be based on conceptual variables shared by a group of communicating observers.

This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given. In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory. The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings.The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.

This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given. In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory. The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings.The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.

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.

Culture, in fact, also plays an important role in science which is, per se, a multitude of different cultures. The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods. Of course, these three domains should not be taken as equals in any sense. But the book holds the important claim that it is possible to develop a common language which, at least to a certain extent, can create direct links and build bridges. From this point of departure, the book will be of interest to the following three types of scientists — statisticians, quantum physicists and chemometricians — and in particular, statisticians and physicists who are interested in interdisciplinary research. Written at a level that is accessible to general readers, not only the academics, the book will appeal to graduate students and mathematically educated persons of all disciplines as well as philosophers, pure and applied mathematicians, and the general public.