Quantum Mechanics

In 1927, Paul Dirac first explicitly introduced the idea that electrodynamical processes can be evaluated by decomposing them into virtual, energy non-conserving subprocesses. This mode of reasoning structured a lot of the perturbative evaluations of quantum electrodynamics during the 1930s. Although the physical picture connected to Feynman diagrams is no longer based on energy non-conserving transitions but on off-shell particles, emission and absorption subprocesses still remain their fundamental constituents. This article will access the introduction and the initial reception of this (...) picture of subsequent transitions by conceiving of concepts, models, and their representations as tools for the practitioners. I will argue for a multi-factorial explanation of Dirac’s initial, verbally explicit introduction: the mathematical representation he had developed was highly suggestive and already partly conceptualized; Dirac was philosophical flexible enough to talk about transitions when no actual transitions, according to the general interpretation of quantum mechanics of the time, occurred; and, importantly, Dirac eventually used the verbal exposition in the same paper in which he introduced it. The direct impact of PST on the conception of quantum electrodynamical processes will be exemplified by its reflection in diagrammatical representations. The study of the diverging ontological commitments towards PST immediately after its introduction opens up the prehistory of a philosophical debate that stretches out into the present: the dispute about the representational and ontological status of the physical picture connected to the evaluation of the perturbative series of QED and QFT. (shrink)

In this paper, we challenge a wide-spread assumption among philosophers that contemporary physics supports physical state monism. This is the claim that the causal powers of a system supervene upon the ‘lower-level’ laws and the lower-level state of the cosmos (as represented by our ‘best physics’). On this view, it makes sense to ignore a macroscopic system’s higher-level properties in determining its causal powers, since any higher-level powers are merely artifacts of our special interests. We argue that this assumption is (...) common both to microphysicalism, which carves the cosmos into a set of microscopic constituents, and priority monism, which posits a single cosmic substance, but is incompatible with any form of physical pluralism that attributes irreducibly higher-level powers to entities of intermediate scales. We consider a number of case studies in contemporary physics which fail to support the thesis of state monism. We argue that the causal powers of many systems are (determined by) higher-level, macroscopic properties that are neither reducible nor weakly emergent, and that contemporary physics is compatible with some kind of pluralism that affirms that these entities are robustly real. A pluralist ontology is likely to have implications for discussions of free will and agency. (shrink)

Quantum mechanics predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic \-random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on infinite-dimensional Hilbert (...) spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real \, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

Multilocation – the notion of an object being at two places – is a central notion in metaphysics. According to a widespread view, multilocation is problematic but metaphysically possible. In effect, it has been claimed that in a quantum world, multilocation is not simply possible but actual. This article provides a new argument against the latter claim: there is no quantum multilocation.

In 1966, Paul Feyerabend published a short essay on the relation between dialectical materialist philosophy and Niels Bohr’s quantum theory, in which he develops several provocative ideas about the...

The two-state-vector formalism presents a time-symmetric approach to the standard quantum mechanics, with particular importance in the description of experiments having pre- and post-selected ensembles. In this paper, using the correspondence limit of the quantum harmonic oscillator in the two-state-vector formalism, we produce harmonic oscillators that possess a classical behavior while having a complex-valued position and momentum. This allows us to discover novel effects that cannot be achieved otherwise. The proposed classical behavior does not describe the classical physics in the (...) usual sense since this behavior is subjected to the feature that only after the final measurement is performed, as a boundary condition, the complex-valued classical effects occur between the initial and the final boundary conditions. This classical behavior breaks down if one does not follow the decided boundary conditions during the experiment, since otherwise, one will contradict the impossibility of retrocausality. (shrink)

Typicality is routinely invoked in everyday contexts: bobcats are typically short-tailed; people are typically less than seven feet tall. Typicality is invoked in scientific contexts as well: typical gases expand; typical quantum systems exhibit probabilistic behaviour. And typicality facts like these support many explanations, both quotidian and scientific. But what is it for something to be typical? And how do typicality facts explain? In this paper, I propose a general theory of typicality. I analyse the notion of a typical property. (...) I provide a formalism for typicality explanations, and I give an account of why typicality explanations are explanatory. Along the way, I show how typicality facts explain a variety of phenomena, from everyday phenomena to the statistical mechanical behaviour of gases. Finally, I argue that typicality is not the same thing as probability. (shrink)

An Aristotelian philosophy of nature offers an alternative to reduction for the conception of the inter-theoretical relationships between molecular chemistry and quantum mechanics. A basic ingredient for such an approach is an ontology of fundamental causal powers, and this work aims to develop such an ontology by drawing on quantum-chemical entities, particularly, the electron density. This notion is central to the Quantum Theory of Atoms in Molecules, a theory of molecular structure developed by Richard F. W. Bader, which describes molecules (...) and atoms in terms precisely of the electron density. Then, by identifying a philosophical tension in Bader’s discourse about the nature of electron density, the work will analyze this central notion in terms of the categorical/dispositional distinction regarding properties. The central idea is that electron density can be conceived as categorical and dispositional at once, and this very characterization can avoid Bader’s philosophical tension. (shrink)

The ideas of quantum simulation and advances in quantum algorithms to solve quantum chemistry problems have been discussed. Theoretical proposals and experimental investigations both have been studied to gauge the extent to which quantum computation has been applied to solve quantum chemical problems till date. The distinctive features and limitations of the application of quantum simulation on chemical systems and current approaches to define and improve upon standard quantum algorithms have been studied in detail. The possibility and consequences of designing (...) an efficient quantum computer that can address chemical problems have been assessed. The experimental realization of quantum supremacy defies the conventional belief of chemists, that millions of qubits would be required to solve fundamental chemistry problems. It is predicted that quantum simulation of quantum chemistry problems will radically revolutionize this field. (shrink)

UNBELIEVABLE, many (hundreds) “great” or small thinkers did the same thing in 2006-2007 and later: they published the same ideas, UNBELIEVABLE similar to my ideas from 2002-2005! They believe they would be considered co-authors of the same new framework of thinking.

Due primarily to technological advances over the last decade, quantum research has become a key priority area for science and technology policy all over the world. With this manifesto, we wish to prevent quantum technology from running into fiascos of implementation at the interface of science and society. To this end, we identify key stumbling blocks and propose recommendations.

In this volume I offer a compact history of the concepts of probability and statistics as well as a review of the most relevant interpretations of these notions. In the second part of the volume I explore the meaning of probability, statistics and their interpretations with respect to the developement of physical theories - from classical mechanics to quantum mechanics. -/- (ISBN: 978-8889891322).

This book examines how major interpretations of quantum theory are progressing toward a more unified understanding and experience of nature. It offers subtle insights to address core issues of wave-particle duality, the measurement problem, the mind/body problem, determinism/indeterminism/free will, and the nature of consciousness. It draws from physics, consciousness studies, and 'ancient Vedic science' to outline a new holistic interpretation of quantum theory. Accessible and thought-provoking, it will be profoundly integrating for scholars and researchers in science and technology, in philosophy, (...) and also in South Asian studies. (shrink)

Published in 1934, this monograph was one of the first introductory accounts of the principles which form the physical basis of the Quantum Theory, considered as a branch of mathematics. The exposition is restricted to a discussion of general principles and does not attempt detailed application to the wide domain of atomic physics, although a number of special problems are considered in elucidation of the principles. The necessary fundamental mathematical methods – the theory of linear operators and of matrics – (...) are developed in the first chapter so this could introduce anyone to the new theory. This is an interesting snapshot of scientific history. (shrink)

The aim of this paper is to invalidate the hypothesis that human consciousness is necessary in the quantum measurement process. In order to achieve this target, I propose a considerable modification of the Schrödinger’s cat and the Dead-Alive Physicist thought experiments, called “PIAR”, short for “Physicist Inside the Ambiguous Room”. A specific strategy has enabled me to plan the experiment in such a way as to logically justify the inconsistency of the above hypothesis and to oblige its supporters to rely (...) on an alternative interpretation of quantum mechanics in which a real world of phenomena exists independently of our conscious mind and where observers play no special role. Moreover, the description of the measurement apparatus will be complete, in the sense that the experiment, given that it includes also the experimenter, will begin and end exclusively within a sealed room. Hence, my analysis will provide a logical explanation of the relationship between the observer and the objects of her/his experimental observation; this and a few other implications will be discussed in the fourth section and in the conclusions. (shrink)

Most theories of quantum mechanics do not offer clear yes/no empirical answers to all questions that seem at face value. The Many-Worlds Interpretation, originated by Hugh Everett in the late 1950s, is unique for its unambiguous envisioning of reality: our universe is one of the numerous parallel universes that frantically branch off from each other nanoseconds by nanoseconds. In many of these worlds, there exist exact replicas of you and me, all evolving independently. My thesis exhibition, entitled Wholly Quantum, articulates (...) this controversial theory in a visual way. Through a hybrid of electronics, lights, and sculptures, the exhibition recasts reality within an utterly surreal framework and investigates the battle between a single reality versus a multitude of realities, what we perceive versus what reality is. This paper, as one of the two components of my thesis, carries out my research and creative experiments on the phenomena of reality and perception. (shrink)

Interactionist dualism is often rejected based on the claim that the physical world is causally closed. Another claim against interactionist dualism is that, were it to hold, it would violate energy/momentum conservation or the second law of thermodynamics. Here I show that the phase of the quantum wave function may provide a loophole in the causal closure of the world through which the mind can affect behavior without violating any physical law.

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry—and thus of causation—in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum (...) systems. I show that by exploiting a connection between the amount of entanglement in a quantum state and the algorithmic complexity of that state, one can use recently developed tools for causal inference to identify a causal asymmetry—and a notion of causation—in the dynamical evolution of quantum systems. (shrink)

In this article, I discuss the criticisms raised against Thomas Kuhn’s Black-Body Theory. These criticisms concern two issues: how to understand Planck’s position with regards to the quantization of energy in 1901, and how to understand the book’s relation to The Structure of Scientific Revolutions. Both criticisms, I argue, concern the notion of a paradigm: the first concerns how Boltzmann acted as an exemplar for Planck, and the second whether the book provides a paradigm change. I will then argue that (...) both criticisms presume a conceptualization of paradigms that does not align well with Kuhn’s conceptualization of it in both Structure and later work: they assume, more specifically, that sharing a paradigm presupposes sharing an interpretation of it, and that paradigm changes are essentially identical to gestalt switches. On the basis of this, I will then argue that the criticisms are misguided, that Kuhn’s position regarding Planck’s work is in fact quite close to the indetermination-view developed by some of his critics, and that the book fits Structure quite well. In conclusion, I will then reflect on how the narrative provided in Black-Body Theory connects with Kuhn’s views on the relation between history and philosophy of science. (shrink)

We introduce a sequent system which is Gentzen algebraisable with orthomodular lattices as equivalent algebraic semantics, and therefore can be viewed as a calculus for orthomodular quantum logic. Its sequents are pairs of non-associative structures, formed via a structural connective whose algebraic interpretation is the Sasaki product on the left-hand side and its De Morgan dual on the right-hand side. It is a substructural calculus, because some of the standard structural sequent rules are restricted—by lifting all such restrictions, one recovers (...) a calculus for classical logic. (shrink)

I propose an account of probability in the Everett interpretation of quantum mechanics. According to the account, probabilities are objective chances of centered propositions. As I show, the account solves a number of problems concerning the role of probability in the Everett interpretation. It also challenges an implicit assumption, concerning the aim and scope of fundamental physical theories, that is made throughout the philosophy of physics literature.

E=mc2: What did he miss? Rethinking Einstein as a circular theory. Producing philosophical, physical, and psychological fusion.

The quantum transition probability assignment is an equiareal transformation from the annulus of symplectic spinorial amplitudes to the disk of complex state vectors, which makes it equivalent to the equiareal projection of Archimedes. The latter corresponds to a symplectic synchronization method, which applies to the quantum phase space in view of Weyl’s quantization approach involving an Abelian group of unitary ray rotations. We show that Archimedes’ method of synchronization, in terms of a measure-preserving transformation to an equiareal disk, imposes the (...) integrality of the quantum of action, and requires the extension of the classical moment map from the real line to the circle. Additionally, the same synchronization method is encoded in the structure of the Heisenberg group, viewed as a principal bundle with a connection, whose curvature and anholonomy is expressed in terms of area bounding loops in relation to the underlying Abelian shadow on a symplectic plane. In this manner, we show that the geometric phase pertains to the minimal synchronized area \ of the 2-d symplectic Abelian shadow of the symplectic ball, modulo \. The integrality condition naturally leads to the consideration of modular commutative observables pertaining to the role of the discrete Heisenberg group. We prove that the structural transition from non-commutativity to modular commutativity in accordance to Weyl’s group-theoretic commutation relations takes place via universal factorization through the discrete Heisenberg group. In this way, we derive a homology-theoretic formulation of the synchronization method in terms of the area-bounding cells of the modular lattice \ in relation to any Abelian symplectic shadow. Thus, we finally obtain the physical interpretation of the analytic representation of quantum states as theta functions corresponding to the sections of a complex line bundle with an integral symplectic structure. (shrink)

Beginning with the Everett–DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. Here we propose a decomposition of a state vector into branches by finding the minimum of a measure of the mean squared quantum complexity of the branches in the branch decomposition. In a non-relativistic formulation of this proposal, branching occurs repeatedly (...) over time, with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen randomly according to the Born rule. In a Lorentz covariant version, the real world is a single random draw from the set of branches at asymptotically late time, restored to finite time by sequentially retracing the set of branching events implied by the late time choice. The complexity measure depends on a parameter b with units of volume which sets the boundary between quantum and classical behavior. The value of b is, in principle, accessible to experiment. (shrink)

Authoritative appraisals have qualified this book as an “axiomatic” theory. However, given that its essential content is no more than an analogy, its theoretical organization cannot be axiomatic. Indeed, in the first edition Dirac declares that he had avoided an axiomatic presentation. Moreover, I show that the text aims to solve a basic problem. A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors non-axiomatically. Four characteristic features of a new model of organizing (...) a theory were recognized. A careful examination of Dirac’s text shows that it actually applied this kind of organization of a theory, confirming formally what Kronz and Lupher suggested through intuitive categories, i.e. Dirac’s formulation of Quantum mechanics represents a distinct theoretical approach from von Neumann’s axiomatic approach. However, since the second edition Dirac has changed his approach: although relying again on analogy, his theory refers to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest that a new foundation of this theory needs to be found. (shrink)

We report to which extent elementary particles and the nucleons can be described by an Ansatz that is alternative to the established standard model, and can still yield predicted results that reproduce the observed ones, without using the formalism of quantum mechanics. The different Ansatz is motivated by the attempt to explain known properties of elementary particles as a consequence of an inner structure, in contrast to the approach of the standard model, where the properties are ascribed to point-like particles. (...) Based on the assumption of the existence of photons, the possibility of the creation of fermion and anti-fermion in an interaction of two photons of equal energy is shown. The properties of these created elementary material particles are found to agree with the ones observed. Also the possibility of the creation of a neutron by interaction of two photons of equal energy is shown. In this case, the newly formed neutron rests in the center of the collision system as a combined system of the localized two photons. The created neutron is shown to have the known properties of the neutron, and in addition, to have a definite shape of definite size. The proton is described as the particle formed by decay of the neutron, also owning the observed properties, and in addition a definite shape. For all particles described by the Ansatz, their properties are consequences of an inner structure. The merits of the alternative description as compared to the standard model and the application of quantum mechanics are discussed. (shrink)

Broadly, there are two approaches to consciousness, viz. the scientific and the rishi. In the scientific approach, consciousness is an emergent phenomenon of matter. This can be referred to as the matter route to consciousness. In the rishi route, consciousness is an infused phenomenon wherein matter is infused with spirit. īśāvāsyamidaṃsarvaṃ, yatkiñcajagatyāṃjaga, Ishopanishad declares. It implies all matter is infused with consciousness. This can be referred to as the spirit route to consciousness. Now there is a need to combine the (...) two approaches to consciousness. It implies recognizing the impact of consciousness on Space and Time and on Energy and Matter. This also implies viewing the world through the lens of STC and EMC. This essay strives to do this. (shrink)

According to Ernest Nagel, determinism is central to the scientific enterprise. Faced with the claim that determinism fails in quantum mechanics, Nagel proposed a notion of determinism which does not rely on a fundamental level of description, and can play a role in different scientific disciplines irrespective of their reducibility to physics. Nagel argues that determinism ultimately plays the role of a guiding principle in scientific research. In this way, Nagel argues that determinism has an enduring relevance in all domains (...) of science, from quantum physics to the social sciences. (shrink)

A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.” Such an extraordinary feature may appear unattainable in any realistic and simple theory of physics. In this paper, I propose a definition of strong determinism and contrast (...) it with those of standard determinism and super-determinism. Next, I discuss its consequences for explanation, causation, prediction, fundamental properties, free will, and modality. Finally, I present the first example of a realistic, simple, and strongly deterministic physical theory--the Everettian Wentaculus. As a consequence of physical laws, the history of the Everettian multiverse could not have been different. If the Everettian Wentaculus is empirically equivalent to other quantum theories, we can never empirically find out whether or not our world is strongly deterministic. Even if strong determinism fails to be true, it is closer to the actual world than we have presumed, with implications for some of the central topics in philosophy and foundations of physics. (shrink)

Absolute nothing is the absence of our universe and its laws. Without these rules, nothingness has infinite potential. This implies that within the infinite probability of nothing, infinity can emerge. This would be expressed through infinite universes like our own. Infinite of these universes will differ by several particles, appearing and disappearing for no reason other than fulfilling every possibility. This universe is the product of a greater realisation of infinity and we can test this theory via the measurement of (...) our universe’s most fundamental particles appearing and disappearing for no discernible internal reason (random to our perspective). (shrink)