Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such (...) students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study. (shrink)

Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose (...) a legitimate view of the world. (shrink)

Written by an internationally renowned philosopher, this volume offers a three-part philosophical interpretation of quantum physics. The first part reviews the basics of quantum mechanics, outlining their philosophical interpretation and summarizing their results; the second outlines the mathematical methods of quantum mechanics; and the third section blends the philosophical ideas of the first part and the mathematical formulations of the second part to develop a variety of interpretations of quantum mechanics. 1944 edition.

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the (...) measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem. (shrink)

It is argued that certain recent advances in the construction of a theory of the collapses of Quantum Mechanical wave functions suggest the possibility of new and improved foundations for statistical mechanics, foundations in which epistemic considerations play no role.

The revolution brought about by quantum mechanics in the early 20th century was nothing short of remarkable. It shattered the foundational principles of classical physics, giving rise to a plethora of controversial and intriguing conceptual questions. Questions that still perplex and confound the scientific community today. Is the quantum mechanical description of physical reality complete? Are the objects of nature truly inseparable? And most importantly, do objects not have a specific position before measurement, and are there non-causal (...) quantum jumps? These vital problems continue to garner more attention as time passes, particularly with the fading of positivism. If you're a student seeking to explore the fascinating philosophical foundations of quantum mechanics, this book might be just what you need. Written in Persian, brings you closer to the heart of quantum controversies and the fascinating world of quantum mechanics. (shrink)

In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons.The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his (...) calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent.A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms. (shrink)

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary account (...) of the nature of quantum information. Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

The following article by Grete Hermann arguably occupies an important place in the history of the philosophical interpretation of of quantum mechanics. The purpose of Hermann's writing on natural philosophy is to examine the revision of the law of causality which quantum mechanics seems to require at a fundamental level of theoretical description in physics. It is Hermann's declared intention to show that quantum mechanics does not disprove the concept of causality, "yet has clarified (...) [it] and has removed from it other principles which are not necessarily connected to it." She attempts to show that this most "obvious" counter-example to the aprioricity of causality, quantum theory, is in fact not a counter-example at all. (shrink)

Brukner and Dakić proposed a very simple axiom system as a foundation for quantum theory. It implies the qubit and quantum entanglement. Because this axiom system aims at the core of our understanding of nature, it must be brought to the forum of the philosophy of nature. For philosophical reasons, a completely denied champion of quantum theory, imaginarity i, is added into this axiom system. In relation to Bell’s inequality, this leads to a deeper ‘philosophical’ understanding of (...) quantum nature based on qubits and entanglement. Both opens a way as well as one can get to the fundamental Schrödinger equation of quantum mechanics with the help of a complex valued Brownian motion. (shrink)

Rotations in Quantum Mechanics are a very well-known subject. When one is faced with rotations related to the SO group, for instance, all the underlying operators are well-known and built from their classical counterparts. However, when it comes to represent rotations related to the SU group, it is always argued that there is no classical counterpart from which the expressions for the quantum mechanical operators can be built. The approach is always done using matrix representation. In the (...) way of this aproach, one assumes that the operators related to SU are pseudovectors and end up with the weird result that only rotations by multiples of \ would bring the system to its original situation. In Olavo we have shown that any half-integral spin system can be represented in the Schrödinger picture by solving a Schrödinger equation with well defined expressions for the SU differential operators. It turned out that two of these operators are symmetric tensors, not pseudovectors or antisymmetric tensors. In this paper we use these results to dismiss with the \ conundrum. (shrink)

Starting from a set of assumptions mainly of an “operational” or experimentally based nature, a derivation of quantum mechanics is presented, with the aim of clarifying the essential features of the theory and their interpretation. Various properties of quantum mechanics such as the addition of amplitudes, the calculation of probabilities, de Broglie's equations, and energy-momentum conservation are derived from first principles. It is investigated whether quantum amplitudes may be constructed from quantities of higher order than (...) complex numbers. Measurable physical quantitics, as traditionally understood, are seen to play a role distinct from and supplementary to the behavior of the quantum amplitudes themselves. This is related to two distinct aspects of the nature of time in the context of quantum mechanics. (shrink)

This book provides an introduction to the conceptual foundations of quantum mechanics, from classical mechanics and a discussion of the quantum phenomena that undermine our classical intuitions about how the physical world works, to the quantum measurement problem and alternatives to the standard von Neumann-Dirac formulation.

Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schr¨ odinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose (...) in the context of a theory known as Bohmian mechanics, to which this article is an introduction. (shrink)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be (...) modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to (...) expect certain kinds of 'time observables' to find a representation within quantum theory, including clock operators and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on reflection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack. (shrink)

In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to Lawvere that illuminates and unifies the different perspectives on self-reference.

In this paper we unravel the connection between the quantum mechanical formalism and the Central limit theorem (CLT). We proceed to connect the results coming from this theorem with the derivations of the Schrödinger equation from the Liouville equation, presented by ourselves in other papers. In those papers we had used the concept of an infinitesimal parameter δx that raised some controversy. The status of this infinitesimal parameter is then elucidated in the framework of the CLT. Finally, we use (...) the formal apparatus developed in our previous papers and the results of the present one to advance an alternative objective interpretation of quantum mechanics in which its relations with the classical framework are made explicit. The relations between our approach and those using the Wigner–Moyal transformation are also addressed. (shrink)

This book tells the fascinating story of the people and events behind the turbulent changes in attitudes to quantum theory in the second half of the 20th century. The huge success of quantum mechanics as a predictive theory has been accompanied, from the very beginning, by doubts and controversy about its foundations and interpretation. This book looks in detail at how research on foundations evolved after WWII, when it was revived, until the mid 1990s, when (...) most of this research merged into the technological promise of quantum information. It is the story of the quantum dissidents, the scientists who brought this subject from the margins of physics into its mainstream. It is also a history of concepts, experiments, and techniques, and of the relationships between physics and the world at large, touching on themes such as the Cold War, McCarthyism, Zhdanovism, and the unrest of the late 1960s. (shrink)

This volume provides a unique overview of recent Italian studies on the foundations of quantum mechanics and related historical, philosophical and epistemological topics.

I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein’s historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, (...) whose degree of freedom in space–time has a discrete spectrum, relative to classical observers in space–time. This description is covariant with respect to coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics. (shrink)

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

The concepts of measurement and measurable quantity are discussed. A probabilistic interpretation independent of the arrow of time is recommended and a definition of quantizable physical systems is given. The space of states of information about the physical system is Schwarz space rather than Hilbert space.

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are (...) usually categorically rejected, because of Bell’s powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions. (shrink)

Enormous and significant progress has been made in the important areas of entanglement, quantum computing and harnessing energy from the vacuum, which includes a sound theoretical basis, using the Einstein-Sachs theories to develop an anti-symmetric general relativity (AGR) approach to a higher topology O(3) electrodynamics. These developments also lead to the application of the Aharonov-Bohm effect and the Yang-Mills theory to the higher topology O(3) electrodynamics, as well as a deeper understanding and appreciation of these effects and their impact (...) on modern physics. The door is now open for the further development and unification of physics, including the gravitational, electromagnetic, weak, and strong forces, using the AGR approach. (shrink)

Karl Popper and Paul Feyerabend were among the most influential philosophers of science of the twentieth century. Extensive studies have been dedicated to the development of their controversial relationship, which saw Feyerabend turning from a student and supporter of Popper to one of his harshest critics. Yet, it is not as well known that the rift between Popper and Feyerabend arose mainly in the context of their studies on the foundations of quantum mechanics, which has been the (...) main subject of their discussions for about two decades. This paper reconstructs in detail their diatribe over the foundations of quantum mechanics, emphasising also the major role that their personal relationship played in their distancing. (shrink)

On several levels, there is now a debate whether the concept of God can be made compatible with modern science. In an attempt to elucidate this debate, I give an account of my own experiences from writing a book on the foundation of quantum mechanics. In my opinion, one can give two independent arguments for the existence of God by taking as departure an epistemic (knowledge-based) interpretation of quantum theory. However, I also argue that any religious belief (...) should be the result of an existential choice governed by each person’s own context (history and culture). In particular, I give my account of Christianity as a religion connected to our western culture, how one as a scientist can relate to the relevant dogmas. (shrink)

Statistical mechanics is often taken to be the paradigm of a successful inter-theoretic reduction, which explains the high-level phenomena (primarily those described by thermodynamics) by using the fundamental theories of physics together with some auxiliary hypotheses. In my view, the scope of statistical mechanics is wider since it is the type-identity physicalist account of all the special sciences. But in this chapter, I focus on the more traditional and less controversial domain of this theory, namely, that of explaining (...) the thermodynamic phenomena.What are the fundamental theories that are taken to explain the thermodynamic phenomena? The lively research into the foundations of classical statistical mechanics suggests that using classical mechanics to explain the thermodynamic phenomena is fruitful. Strictly speaking, in contemporary physics, classical mechanics is considered to be false. Since classical mechanics preserves certain explanatory and predictive aspects of the true fundamental theories, it can be successfully applied in certain cases. In other circumstances, classical mechanics has to be replaced by quantum mechanics. In this chapter I ask the following two questions: I) How does quantum statistical mechanics differ from classical statistical mechanics? How are the well-known differences between the two fundamental theories reflected in the statistical mechanical account of high-level phenomena? II) How does quantum statistical mechanics differ from quantum mechanics simpliciter? To make our main points I need to only consider non-relativistic quantum mechanics. Most of the ideas described and addressed in this chapter hold irrespective of the choice of a (so-called) interpretation of quantum mechanics, and so I will mention interpretations only when the differences between them are important to the matter discussed. (shrink)

Different realistic attitudes towards wavefunctions and quantum states are as old as quantum theory itself. Recently Pusey, Barret and Rudolph on the one hand, and Auletta and Tarozzi on the other, have proposed new interesting arguments in favor of a broad realistic interpretation of quantum mechanics that can be considered the modern heir to some views held by the fathers of quantum theory. In this paper we give a new and detailed presentation of such arguments, (...) propose a new taxonomy of different realistic positions in the foundations of quantum mechanics and assess the scope, within this new taxonomy, of these realistic arguments. (shrink)

This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why correlations between simultaneous events occurring far apart cannot be explained by local mechanisms, and why, nevertheless, the quantum theory can be understood in terms of matter in motion. No need to worry, as some people do, whether a cat can be both dead and alive, whether the moon is there when nobody looks at it, (...) or whether quantum systems need an observer to acquire definite properties. The author's inimitable and even humorous style makes the book a pleasure to read while bringing a new clarity to many of the longstanding puzzles of quantum physics. (shrink)