The Conceptual Foundations of Quantum Mechanics

2019 ◽  
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Nonlocality ◽  
Standard Theory ◽  
Wave Mechanics ◽  
Many Worlds ◽  
Explanatory Role ◽  
Trade Offs ◽  
Quantum Phenomena

The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.

CONCEPTUAL FOUNDATIONS OF QUANTUM MECHANICS: THE ROLE OF EVIDENCE THEORY, QUANTUM SETS, AND MODAL LOGIC

1999 ◽  
Vol 10 (01) ◽  
pp. 29-62 ◽  
Author(s):  
GERMANO RESCONI ◽  
GEORGE J. KLIR ◽  
ELIANO PESSA
Keyword(s):  
Quantum Mechanics ◽  
Modal Logic ◽  
Set Theory ◽  
Possible Worlds ◽  
Evidence Theory ◽  
Foundations Of Quantum Mechanics ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
New Interpretation ◽  
Quantum Phenomena

Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

Relational Blockworld and Quantum Mechanics

2018 ◽  
Author(s):  
Michael Silberstein ◽  
W.M. Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Nonlocality ◽  
Global Constraints ◽  
Quantum Superposition ◽  
Delayed Choice ◽  
Counterfactual Definiteness ◽  
Main Thread ◽  
Block Universe ◽  
Contextual Emergence

The main thread of chapter 4 introduces some of the major mysteries and interpretational issues of quantum mechanics (QM). These mysteries and issues include: quantum superposition, quantum nonlocality, Bell’s inequality, entanglement, delayed choice, the measurement problem, and the lack of counterfactual definiteness. All these mysteries and interpretational issues of QM result from dynamical explanation in the mechanical universe and are dispatched using the authors’ adynamical explanation in the block universe, called Relational Blockworld (RBW). A possible link between RBW and quantum information theory is provided. The metaphysical underpinnings of RBW, such as contextual emergence, spatiotemporal ontological contextuality, and adynamical global constraints, are provided in Philosophy of Physics for Chapter 4. That is also where RBW is situated with respect to retrocausal accounts and it is shown that RBW is a realist, psi-epistemic account of QM. All the relevant formalism for this chapter is provided in Foundational Physics for Chapter 4.

scholarly journals A Phenomenological Reading of the Many-Worlds Interpretation of Quantum Mechanics

2020 ◽  
Author(s):  
Joaquin Trujillo
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Measurement Problem ◽  
Copenhagen Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
Standard Interpretation ◽  
Hermeneutic Phenomenological ◽  
Many Worlds Interpretation ◽  
The Many

The articles provides a phenomenological reading of the Many-Worlds Interpretation (MWI) of quantum mechanics and its answer to the measurement problem, or the question of “why only one of a wave function’s probable values is observed when the system is measured.” Transcendental-phenomenological and hermeneutic-phenomenological approaches are employed. The project comprises four parts. Parts one and two review MWI and the standard (Copenhagen) interpretation of quantum mechanics. Part three reviews the phenomenologies. Part four deconstructs the hermeneutics of MWI. It agrees with the confidence the theory derives from its (1) unforgiving appropriation of the Schrödinger equation and (2) association of branching universes with the evolution of the wave function insofar as that understanding comes from the formalism itself. Part four also reveals the hermeneutical shortcomings of the standard interpretation.

scholarly journals Measured distribution of cloud chamber tracks from radioactive decay: a new empirical approach to investigating the quantum measurement problem

2021 ◽  
Author(s):  
Jonathan Schonfeld
Keyword(s):  
Spatial Distribution ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Radioactive Decay ◽  
Foundations Of Quantum Mechanics ◽  
Radioactive Source ◽  
Cloud Chamber ◽  
Quantum Measurement Problem ◽  
Measured Distribution

Abstract Using publically available video of a cloud chamber with a very small radioactive source, I measure the spatial distribution of where tracks start, and consider possible implications. This is directly relevant to the quantum measurement problem and its possible resolution, and appears never to have been done before. The raw data are relatively uncontrolled, leading to caveats that should guide future, more tailored experiments. Track distributions from decays in cloud chambers represent a previously unappreciated way to probe the foundations of quantum mechanics, and a novel case of wavefunctions with macroscopic signatures.

Pure Wave Mechanics

2019 ◽  
pp. 143-161
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Physical Theory ◽  
Measurement Problem ◽  
Wave Mechanics ◽  
Linear Dynamics ◽  
Physical Systems ◽  
Relative State ◽  
Quantum Probabilities ◽  
Pure Wave Mechanics

Everett thought of the quantum measurement problem as one of providing a consistent description of nested measurement. He proposed solving the measurement problem by simply supposing that all physical systems whatsoever always obey the linear dynamics and hence never collapse. Dropping the collapse dynamics immediately solves the measurement problem, but it introduces two new problems: explaining determinate measurement records and explaining quantum probabilities. In addition to these, we also consider the problem of empirical coherence in the context of pure wave mechanics. We then discuss how Everett himself understood determinate records and probabilities in his relative-state formulation of pure wave mechanics. What he ultimately provided was an argument that his formulation of quantum mechanics was consistent and empirically faithful. We will see why this is a relative weak standard by which to judge the empirical adequacy of a physical theory.

Many Worlds and Such

2019 ◽  
pp. 162-189
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Physical Theory ◽  
Empirical Adequacy ◽  
Wave Mechanics ◽  
Many Worlds ◽  
Standard Quantum ◽  
Information Theoretic ◽  
Quantum Probabilities ◽  
The Relationship ◽  
Pure Wave Mechanics

We consider a number of radically different ways that Everett’s pure wave mechanics has been understood. Each of these reconstructions aims to provide a stronger variety of empirical adequacy than Everett’s own formulation of the theory. Among the alternative formulations of quantum mechanics we consider are splitting worlds, decohering worlds, many minds, many threads, and many maps. Each of these differs in its metaphysical commitments and, hence, in how it explains determinate measurement records and probabilities. We focus, in particular, on the problem of accounting for the standard quantum probabilities. To this end, we consider the relationship between typicality and probability and contrast synchronic and forward-looking probabilities. We conclude with a brief discussion of epistemological, pragmatic, and information-theoretic formulations of quantum mechanics. A recurring issue in this chapter concerns what it should mean for a physical theory to be empirically adequate.

scholarly journals SOLVING THE NONLOCALITY RIDDLE BY CONFORMAL QUANTUM GEOMETRODYNAMICS

2012 ◽  
Vol 10 (08) ◽  
pp. 1241013 ◽  
Author(s):  
ENRICO SANTAMATO ◽  
FRANCESCO DE MARTINI
Keyword(s):  
Differential Geometry ◽  
Quantum Mechanics ◽  
Configuration Space ◽  
Foundations Of Quantum Mechanics ◽  
Bell Inequalities ◽  
Dynamical Problem ◽  
Quantum Nonlocality ◽  
Bell’S Inequalities ◽  
The Common ◽  
Quantum Geometrodynamics

Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.

scholarly journals Measured distribution of cloud chamber tracks from radioactive decay

2021 ◽  
Author(s):  
Jonathan Schonfeld
Keyword(s):  
Spatial Distribution ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Radioactive Decay ◽  
Foundations Of Quantum Mechanics ◽  
Radioactive Source ◽  
Cloud Chamber ◽  
Raw Data ◽  
Measured Distribution

Abstract Using publically available video of a cloud chamber with a very small radioactive source, I measure the spatial distribution of where tracks start, and consider possible implications. This is directly relevant to the quantum measurement problem and its possible resolution, and appears never to have been done before. The raw data are relatively uncontrolled, leading to caveats that should guide future, more tailored experiments. Track distributions from decays in cloud chambers represent a previously unappreciated way to probe the foundations of quantum mechanics, and a novel case of wavefunctions with macroscopic signatures.

scholarly journals Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1338
Author(s):  
Stéphane Avner
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Hidden Variables ◽  
Granular Systems ◽  
Interpretation Of Quantum Mechanics ◽  
Linear Dynamical Systems ◽  
Wave Particle Duality ◽  
Realist Interpretation ◽  
Quantum Phenomena ◽  
High Level

The strange behavior of subatomic particles is described by quantum theory, whose standard interpretation rejected some fundamental principles of classical physics such as causality, objectivity, locality, realism and determinism. Recently, a granular relativistic electrodynamical model of the electron could capture the measured values of its observables and predict its mass from the stability of its substructure. The model involves numerous subparticles that constitute some tight nucleus and loosely bound envelope allegedly forming real waves. The present study examines whether such a substructure and associated dynamics allow fundamentally realist interpretations of emblematic quantum phenomena, properties and principles, such as wave-particle duality, loss of objectivity, quantization, simultaneous multipath exploration, collapse of wavepacket, measurement problem, and entanglement. Drawing inspiration from non-linear dynamical systems, subparticles would involve realist hidden variables while high-level observables would not generally be determined, as particles would generally be in unstable states before measurements. Quantum mechanics would constitute a high-level probabilistic description emerging from an underlying causal, objective, local, albeit contextual and unpredictable reality. Altogether, by conceiving particles as granular systems composed of numerous extremely sensitive fluctuating subcorpuscles, this study proposes the possible existence of a local fundamentally realist interpretation of quantum mechanics.

scholarly journals Randomness and Irreversiblity in Quantum Mechanics: A Worked Example for a Statistical Theory

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1643
Author(s):  
Yves Pomeau ◽  
Martine Le Berre
Keyword(s):  
Quantum Mechanics ◽  
Quantum Coherence ◽  
Many Worlds ◽  
Worked Example ◽  
Interpretations Of Quantum Mechanics ◽  
Level Atom ◽  
Novel Approach ◽  
Basic Equations ◽  
Quantum Phenomena ◽  
Coherent Pumping

The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant laser beam is a worked example where statistical interpretations of quantum mechanics still meet some difficulties because the basic equations are fully deterministic and unitary. In such a problem with two different time scales, the atom makes coherent optical Rabi oscillations between the two states, interrupted by random emissions (quasi-instantaneous) of photons where coherence is lost. To describe this system, we already proposed a novel approach, which is completed here. It amounts to putting a probability on the density matrix of the atom and deducing a general “kinetic Kolmogorov-like” equation for the evolution of the probability. In the simple case considered here, the probability only depends on a single variable θ describing the state of the atom, and p(θ,t) yields the statistical properties of the atom under the joint effects of coherent pumping and random emission of photons. We emphasize that p(θ,t) allows the description of all possible histories of the atom, as in Everett’s many-worlds interpretation of quantum mechanics. This yields solvable equations in the two-level atom case.

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