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.

Science and exile: David Bohm, the cold war, and a new interpretation of quantum mechanics

2005 ◽  
Vol 36 (1) ◽  
pp. 1-34 ◽  
Author(s):  
OLIVAL FREIRE
Keyword(s):  
Quantum Mechanics ◽  
Cold War ◽  
Cultural Context ◽  
Foundations Of Quantum Mechanics ◽  
Interpretation Of Quantum Mechanics ◽  
Causal Interpretation ◽  
David Bohm ◽  
New Interpretation ◽  
The Cold War ◽  
American Physicist

ABSTRACT In the early 1950s the American physicist David Bohm (1917-1992) produced a new interpretation of quantum mechanics and had to flee from McCarthyism. Rejected at Princeton, he moved to Sãão Paulo. This article focuses on the reception of his early papers on the causal interpretation, his Brazilian exile, and the culture of physics surrounding the foundations of quantum mechanics. It weighs the strength of the Copenhagen interpretation, discusses the presentation of the foundations of quantum mechanics in the training of physicists, describes the results Bohm and his collaborators achieved. It also compares the reception of Bohm's ideas with that of Hugh Everett's interpretation. The cultural context of physics had a more significant influence on the reception of Bohm's ideas than the McCarthyist climate.

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.

History, Causation, and the Many-Worlds Interpretation of Quantum Mechanics

2019 ◽  
pp. 1-22
Author(s):  
Bruce S. Bennett ◽  
Moletlanyi Tshipa
Keyword(s):  
Quantum Mechanics ◽  
Possible Worlds ◽  
Interpretation Of Quantum Mechanics ◽  
Quantum Level ◽  
Many Worlds ◽  
Starting Conditions ◽  
Many Worlds Interpretation ◽  
Historical Causation ◽  
The Many ◽  
The Universe

AbstractThe Many-Worlds Interpretation (MWI) is a theory in physics which proposes that, rather than quantum-level events being resolved randomly as according to the Copenhagen Interpretation, the universe constantly divides into different versions or worlds. All physically possible worlds occur, though some outcomes are more likely than others, and therefore all possible histories exist. This paper explores some implications of this for history, especially concerning causation. Unlike counterfactuals, which concern different starting conditions, MWI concerns different outcomes of the same starting conditions. It is argued that analysis of causation needs to take into account the divergence of outcomes and the possibility that we inhabit a less probable world. Another implication of MWI is convergent history: for any given world there will be similar worlds which are the result of different pasts which are, however, more or less probable. MWI can assist in thinking about historical causation and indicates the importance of probabilistic causation.

scholarly journals Muitos mundos e a interpretação ondulatória: revendo a conexão à luz da filosofia Schorödingeriana

2016 ◽  
Vol 19 (3) ◽  
pp. 343
Author(s):  
Caroline Elisa Murr
Keyword(s):  
Quantum Mechanics ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
Many Worlds Interpretation ◽  
Single World

http://dx.doi.org/10.5007/1808-1711.2015v19n3p343This paper presents Erwin Schrödinger’s Wave Interpretation of Quantum Mechanics, with the main goal of comparing it to the so called Many Worlds Interpretation, of which Bryce DeWitt is the most important figure. It is commonly said that DeWitt’s and Everett’s Interpretations are equivalent, and both would have been inspired by Schrödinger’s wave-like approach. This paper claims those stances to be superficial, requiring a more detailed exam of the philosophical grounds held by the authors, besides other distinguishing details. A connexion may be established concerning the rejection of the quantum collapse, although one should be careful about the meaning of the term in each standpoint. This article also shows the balance of Schrödinger’s Interpretation of Quantum Mechanics in regard to his philosophy in a wider sense. Finally, it concludes that detaching Schrödinger’s interpretation from Many Worlds is more coherent with his philosophical assumptions; he conceives a single world containing infinite possibilities.

scholarly journals FOUNDATIONS OF QUANTUM MECHANICS: DECOHERENCE AND INTERPRETATION

2011 ◽  
Vol 20 (05) ◽  
pp. 861-875 ◽  
Author(s):  
OLIMPIA LOMBARDI ◽  
JUAN SEBASTIAN ARDENGHI ◽  
SEBASTIAN FORTIN ◽  
MARTIN NARVAJA
Keyword(s):  
Quantum Mechanics ◽  
General Framework ◽  
Deep Understanding ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Decoherence ◽  
Interpretation Of Quantum Mechanics ◽  
The Third ◽  
Closed Systems

In this paper, we review Castagnino's contributions to the foundations of quantum mechanics. First, we recall his work on quantum decoherence in closed systems, and the proposal of a general framework for decoherence from which the phenomenon acquires a conceptually clear meaning. Then, we introduce his contribution to the hard field of the interpretation of quantum mechanics: the modal-Hamiltonian interpretation solves many of the interpretive problems of the theory, and manifests its physical relevance in its application to many traditional models of the practice of physics. In the third part of this work we describe the ontological picture of the quantum world that emerges from the modal-Hamiltonian interpretation, stressing the philosophical step toward a deep understanding of the reference of the theory.

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.

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