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)

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.

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)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems with only one adjustable property cannot carry more than a single message at a time. We demonstrate that this is true for the photons in the double-slit experiment, and that this is what leads to the fundamental limit on measuring the complementary aspect of the photons. Next, we illustrate that systems with a single adjustable property exhibit other (...) quantum behaviors, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert space formalism of quantum mechanics as well as the Born probability rule. Our derivation demonstrates the physical foundation of quantum theory. (shrink)

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)

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 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)

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)

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.

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)

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.

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)

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)

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.

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)

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)

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)

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)

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)

In 1966 the Brazilian physicist Klaus Tausk (b. 1927) circulated a preprint from the International Centre for Theoretical Physics in Trieste, Italy, criticizing Adriana Daneri, Angelo Loinger, and Giovanni Maria Prosperi`s theory of 1962 on the measurement problem in quantum mechanics. A heated controversy ensued between two opposing camps within the orthodox interpretation of quantum theory, represented by Leon Rosenfeld and Eugene P. Wigner. The controversy went well beyond the strictly scientific issues, however, reflecting philosophical and political (...) commitments within the context of the Cold War, the relationship between science in developed and Third World countries, the importance of social skills, and personal idiosyncrasies. (shrink)

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)

If quantum mechanics is correct and there is a finite upper bound for the speed of causal influences (e.g., the speed of light), then quantum mechanics is complete (i.e., it does not admit a more detailed description in terms of hidden variables). Here I show that the conclusion holds if we replace the assumption of bounded velocity by the assumption that there is a finite upper bound to the memory a finite physical system can store (...) (e.g., the Holevo bound). On the way to this conclusion I first show that, although the quantum violation of an inequality valid for any non-contextual model can be explained with a classical contextual model, the inequality can be promoted to a Bell inequality in which, if the model is contextual, then it must be also non-local. This suggests that there is something non-classical in any contextual explanation of the individual systems, and leads us to the question of which are the minimum resources (and specifically memory) any contextual explanation should consume. (shrink)

This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, (...) but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of 'superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an "arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author's earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory. (shrink)

This is the first book in a two-volume series. The present volume introduces the basics of the conceptual foundations of quantum physics. It appeared first as a series of video lectures on the online learning platform Udemy.]There is probably no science that is as confusing as quantum theory. There's so much misleading information on the subject that for most people it is very difficult to separate science facts from pseudoscience. The goal of this book is to make you (...) able to separate facts from fiction with a comprehensive introduction to the scientific principles of a complex topic in which meaning and interpretation never cease to puzzle and surprise. An A-Z guide which is neither too advanced nor oversimplified to the weirdness and paradoxes of quantum physics explained from the first principles to modern state-of-the-art experiments and which is complete with figures and graphs that illustrate the deeper meaning of the concepts you are unlikely to find elsewhere. A guide for the autodidact or philosopher of science who is looking for general knowledge about quantum physics at intermediate level furnishing the most rigorous account that an exposition can provide and which only occasionally, in few special chapters, resorts to a mathematical level that goes no further than that of high school. It will save you a ton of time that you would have spent searching elsewhere, trying to piece together a variety of information. The author tried to span an 'arch of knowledge' without giving in to the temptation of taking an excessively one-sided account of the subject. What is this strange thing called quantum physics? What is its impact on our understanding of the world? What is ‘reality’ according to quantum physics? This book addresses these and many other questions through a step-by-step journey. The central mystery of the double-slit experiment and the wave-particle duality, the fuzzy world of Heisenberg's uncertainty principle, the weird Schrödinger's cat paradox, the 'spooky action at a distance' of quantum entanglement, the EPR paradox and much more are explained, without neglecting such main contributors as Planck, Einstein, Bohr, Feynman and others who struggled themselves to come up with the mysterious quantum realm. We also take a look at the experiments conducted in recent decades, such as the surprising "which-way" and "quantum-erasure" experiments. Some considerations on why and how quantum physics suggests a worldview based on philosophical idealism conclude this first volume. This treatise goes, at times, into technical details that demand some effort and therefore requires some basics of high school math (calculus, algebra, trigonometry, elementary statistics). However, the final payoff will be invaluable: Your knowledge of, and grasp on, the subject of the conceptual foundations of quantum physics will be deep, wide, and outstanding. Additionally, because schools, colleges, and universities teach quantum physics using a dry, mostly technical approach which furnishes only superficial insight into its foundations, this manual is recommended for all those students, physicists or philosophers of science who would like to look beyond the mere formal aspect and delve deeper into the meaning and essence of quantum mechanics. The manual is a primer that the public deserves. (shrink)

The time-dependent Schrödinger equation has been derived from three assumptions within the domain of classical and stochastic mechanics. The continuity equation isnot used in deriving the basic equations of the stochastic theory as in the literature. They are obtained by representing Newton's second law in a time-inversion consistent equation. Integrating the latter, we obtain the stochastic Hamilton-Jacobi equation. The Schrödinger equation is a result of a transformation of the Hamilton-Jacobi equation and linearization by assigning the arbitrary constant ħ=2mD. An (...) experiment is proposed to determine ħ and to test a hypothesis of the theory directly. A mathematical apparatus is formulated from the Jacobian formalism to derive physical parameters from ψ(x, t) and to obtain operators for the boundary cases of the theory. The operator formalisms are compared by means of a well-known solution in the quantum theory. (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)

We scan Paul K. Feyerabend's work in philosophy of physics and of science more generally for insights that could be useful for the contemporary debate on the foundations of quantum mechanics. We take as our starting point what Feyerabend has actually written about quantum mechanics, but we extend our analysis to his general views on realism, objectivity, pluralism, and the relation between physics and philosophy, finding that these more general views could in fact offer many interesting (...) insights for physicists and philosophers working on quantum foundations. (shrink)

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.

Several contemporary interpretations of quantum mechanics use the concept of information as a tool for addressing and explaining the quantum world. In the article, I focus on Zeilinger-Brukner's informational foundations of quantum theory. I propose that with a phenomenological approach—which, unlike most of the contemporary interpretations of quantum mechanics, exceeds the mere dichotomy between realism and anti-realism—we can address the epistemological questions re-opened by IFQT and the parts of the interpretation that are recognized as (...) problematic by its critics. After the phenomenological supplementation IFQT can provide both, ontic and epistemic answer to the question "Why quantum?" As we apply Husserl's concept of the world as our common objective ground to the IFQT explanation, we can make a justifiable step away from the solipsism/subjectivism, which is, according to the critics, the main problem of IFQT. Thus, I propose in conclusion, a phenomenological approach to quantum physics can offer a background for the much needed dialog between realists and anti-realists as well as for a comprehensive contemporary interpretation of the quantum world. (shrink)

An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with a given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can emerge. However, the concept does not allow philosophically crucial free will decisions. The quantum world and its conjugate evolve independently, and one can replace fixed final states on each side just with a common matching one. This change allows for external manipulations (...) done in the quantum world and its conjugate, which do not otherwise alter the basic quantum dynamics. In a big bang/big crunch universe, the expanding part can be attributed to the quantum world and the contracting one to the conjugate one. The obtained bi-linear picture has several noteworthy consequences. (shrink)

It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from “Copenhagen” to “many worlds” are critically revisited. The difficulties for intuitive models of quantum physics are pointed out and possible solutions proposed. In particular the existence of discrete states, the quantum jumps, the alleged lack of objective properties, measurement theory, the probabilistic character of quantum physics, the wave–particle duality and the Bell inequalities are analyzed. The sketch of a (...) realistic picture of the quantum world is presented. It rests upon the assumption that quantum mechanics is a stochastic theory whose randomness derives from the existence of vacuum fields. They correspond to the vacuum fluctuations of quantum field theory, but taken as real rather than virtual. (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)

The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave- functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave- function in this interpretation is best regarded as ψ-ontic and incomplete.

These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The "standard" formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on (...) the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the "quantum logic" approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics. (shrink)

In the literature on the interpretation of quantum mechanics, not many works attempt to adopt a proactive perspective aimed at seeing how different interpretations can enrich each other through a productive dialogue. In particular, few proposals have been devised to show that different approaches can be clarified by comparing them, and can even complement each other, improving or leading to a more fertile overall approach. The purpose of this paper is framed within this perspective of complementation and mutual (...) enrichment. In particular, the Relational Quantum Mechanics and the Modal-Hamiltonian Interpretation are compared, highlighting their differences and points of contact. The final purpose is to show that, in spite of their disagreements, they are not contradictory but, on the contrary, they can be made compatible from an overarching perspective and can even complement each other in a fruitful way. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing (...) the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

The London and Bauer monograph occupies a central place in the debate concerning the quantum measurement problem. Gavroglu has previously noted the influence of Husserlian phenomenology on London's scientific work. However, he has not explored the full extent of this influence in the monograph itself. I begin this paper by outlining the important role played by the monograph in the debate. In effect, it acted as a kind of 'lens' through which the standard, or Copenhagen, 'solution' to the measurement (...) problem came to be perceived and, as such, it was robustly criticized, most notably by Putnam and Shimony. I then spell out the Husserlian understanding of consciousness in order to illuminate the traces of this understanding within the London and Bauer text. This, in turn, yields a new perspective on this 'solution' to the measurement problem, one that I believe has not been articulated before and, furthermore, which is immune to the criticisms of Putnam and Shimony. (shrink)

The debate about constructivism in physics has led to different kinds of questions that can be conventionally framed in two classes. One concerns the mathematics that is considered for the theoretical development of physics. The other is concerned with the experimental parts of physical theories. It is unnecessary to observe that the intersection between our two classes of problems is far from being empty. In this paper we will mainly deal with topics belonging to the second class. However, let (...) us briefly mention some important problems that have been debated in the framework of our first class. For instance, the following: to what extent do the undecidability and incompleteness results of classical mathematics affect fragments of physical theories, in such way as to have a “real physical meaning”? are the mathematical arguments that seem to be essential for physics justifiable in the framework of traditional mathematical constructivism?The first question has recently been investigated by Pitowski, Penrose, da Costa, Doria, Mundici, Svozil and others. As expected by most logicians, one can construct undecidable sentences whose physical meaning seems to be hardly questionable. This happens both in classical and in quantum mechanics. (shrink)

John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections (...) focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history. (shrink)

An axiomatic theory is formulated which describes a class of “yes-no” experiments, involving a fixed basic source, a fixed basic detector, and various filters. It is assumed that all filters considered can be constructed from a setP of primitive filters by composition and stochastic selection. Two physically plausible axioms are formulated which allow us to define the concept of asystem in the present context (cf. Definition2.4). To each system we can attach anorder unit module ( $^\circ \hat V, ^\circ \hat (...) V_ + , |1\rangle , \langle 1|$ ) (cf. Definition5.1) whereby ( $^\circ \hat V, ^\circ \hat V_ + , |1\rangle ,$ ) is acomplete, separable order unit space. Two additional axioms are proposed which have the effect that the space ( $^\circ \hat V, ^\circ \hat V_ + , |1\rangle ,$ ) becomes isomorphic to the order unit space underlying a JB-algebra, at least in the case where $^\circ \hat V$ isfinite dimensional (cf. Corollary7.9). (shrink)

A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the “virtual” paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born’s rule; therefore, (...) Bell’s type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system. (shrink)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are (...) given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics.These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble.Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the center of masses of large macroscopic systems do satisfy Newton’s laws. (shrink)

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains (...) in its own structure the possibility of describing real objects in an observer-independent way. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed (...) the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (shrink)