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.

scholarly journals If quantum mechanics is the solution, what should the problem be?

2020 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Real Problem ◽  
Many Worlds ◽  
Interpretations Of Quantum Mechanics ◽  
Wave Particle Duality ◽  
History Of ◽  
The Common ◽  
Universal Law

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum mechanics is only partly relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”

scholarly journals If quantum mechanics is the solution, what should the problem be?

2020 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Real Problem ◽  
Many Worlds ◽  
Interpretations Of Quantum Mechanics ◽  
Wave Particle Duality ◽  
History Of ◽  
The Common ◽  
Universal Law

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum mechanics is only partly relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”

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.

Distinguishing the multiverse from an echo: Quantum Mechanics and

2008 ◽  
Vol 20 (1) ◽  
pp. 245-257
Author(s):  
Donald Spector
Keyword(s):  
Quantum Mechanics ◽  
Copenhagen Interpretation ◽  
Many Worlds ◽  
Equal Footing ◽  
Interpretations Of Quantum Mechanics

can be understood as a play about the tension between two views of reality, embodied in the Copenhagen and Many Worlds Interpretations of quantum mechanics. To Didi and the audience, the second act seems to be an echo of the first, but an echo implies an original and a copy. In fact, the two acts are on an equal footing, representing parallel versions of the selfsame day. Ultimately, emerges as an exploration of the existential conflict that arises when an adherent of the Copenhagen Interpretation is confronted with a Many Worlds universe.

scholarly journals If quantum mechanics is the solution, what should the problem be?

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Real Problem ◽  
Many Worlds ◽  
Interpretations Of Quantum Mechanics ◽  
Wave Particle Duality ◽  
History Of ◽  
The Common ◽  
Universal Law

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum mechanics is only partly relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”

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