scholarly journals Contextuality in Classical Physics and Its Impact on the Foundations of Quantum Mechanics

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 968
Author(s):  
Fritiof Wallentin
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
Mixed States ◽  
Classical Physics ◽  
Von Neumann ◽  
Foundations Of Probability ◽  
Classical Statistical Mechanics ◽  
Quantum Phenomenon ◽  
Pure States ◽  
Ordinary Quantum

It is shown that the hallmark quantum phenomenon of contextuality is present in classical statistical mechanics (CSM). It is first shown that the occurrence of contextuality is equivalent to there being observables that can differentiate between pure and mixed states. CSM is formulated in the formalism of quantum mechanics (FQM), a formulation commonly known as the Koopman–von Neumann formulation (KvN). In KvN, one can then show that such a differentiation between mixed and pure states is possible. As contextuality is a probabilistic phenomenon and as it is exhibited in both classical physics and ordinary quantum mechanics (OQM), it is concluded that the foundational issues regarding quantum mechanics are really issues regarding the foundations of probability.

scholarly journals THE BALANCE OF QUANTUM CORRELATIONS FOR A CLASS OF FEASIBLE TRIPARTITE CONTINUOUS VARIABLE STATES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345024 ◽  
Author(s):  
STEFANO OLIVARES ◽  
MATTEO G. A. PARIS
Keyword(s):  
Conservation Laws ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Noisy Environment ◽  
Mixed States ◽  
Von Neumann ◽  
Entanglement Of Formation ◽  
Pure States ◽  
Gaussian Quantum Discord

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi–Winter-like conservation laws involving Gaussian entanglement of formation (EoF), Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.

scholarly journals Irreversibility in quantum mechanics

2004 ◽  
Vol 2004 (1) ◽  
pp. 75-83 ◽  
Author(s):  
R. C. Bishop ◽  
A. Bohm ◽  
M. Gadella
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Boundary Conditions ◽  
Liouville Equation ◽  
Quantum Systems ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Classical Physics ◽  
Von Neumann ◽  
Signal Features

Time asymmetry and irreversibility are signal features of our world. They are the reason of our aging and the basis for our belief that effects are preceded by causes. These features have many manifestations called arrows of time. In classical physics, some of these arrows are described by the increase of entropy or probability, and others by time-asymmetric boundary conditions of time-symmetric equations (e.g., Maxwell or Einstein). However, there is some controversy over whether probability or boundary conditions are more fundamental. For quantum systems, entropy increase is usually associated with the effects of an environment or measurement apparatus on a quantum system and is described by the von Neumann-Liouville equation. But since the traditional (von Neumann) axioms of quantum mechanics do not allow time-asymmetric boundary conditions for the dynamical differential equations (Schrödinger or Heisenberg), there is no quantum analogue of the radiation arrow of time. In this paper, we review consequences of a modification of a fundamental axiom of quantum mechanics. The new quantum theory is time asymmetric and accommodates an irreversible time evolution of isolated quantum systems.

scholarly journals PURE STATES, MIXED STATES AND HAWKING PROBLEM IN GENERALIZED QUANTUM MECHANICS

2004 ◽  
Vol 19 (27) ◽  
pp. 2037-2045 ◽  
Author(s):  
A. E. SHALYT-MARGOLIN
Keyword(s):  
Black Holes ◽  
Quantum Mechanics ◽  
Density Matrix ◽  
Flat Space ◽  
Uncertainty Relations ◽  
Mixed States ◽  
High Entropy ◽  
High Energies ◽  
Pure States ◽  
Heisenberg's Uncertainty Principle

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As before, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck's remnants of black holes appearing in the assumption of the generalized uncertainty relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the holographic principle. Because of this, a conjecture is made about the possibility for obtaining the generalized uncertainty relations from the covariant entropy bound at high energies in the same way as Bousso has derived Heisenberg's uncertainty principle for the flat space.

Mathematical Foundations of Quantum Mechanics

2018 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
Theoretical Physics ◽  
Mathematical Framework ◽  
Von Neumann ◽  
New Science ◽  
Freeman Dyson ◽  
And Mathematics ◽  
Mathematical Foundations ◽  
First Time

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics—a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. This new edition of this classic work has been completely reset in TeX, making the text and equations far easier to read. The book has also seen the correction of a handful of typographic errors, revision of some sentences for clarity and readability, provision of an index for the first time, and prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson have been added. The result brings new life to an essential work in theoretical physics and mathematics.

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