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t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of…

General Physics · Physics 2007-05-23 B. G. Sidharth

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…

Quantum Physics · Physics 2008-11-26 D. A. Slavnov

Contextuality lays at the heart of quantum mechanics. In the prevailing opinion it is considered as a signature of 'quantumness' that classical theories lack. However, this assertion is only partially justified. Although contextuality is…

Quantum Physics · Physics 2015-02-26 Pawel Blasiak

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…

Quantum Physics · Physics 2014-08-14 Peter Janotta , Haye Hinrichsen

We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…

Quantum Physics · Physics 2007-05-23 M. S. Torres , J. M. A. Figueiredo

After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…

History and Philosophy of Physics · Physics 2018-01-22 Stephen Boughn

The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such…

Artificial Intelligence · Computer Science 2013-01-08 Diederik Aerts , Marek Czachor , Sandro Sozzo

Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…

Statistical Mechanics · Physics 2025-05-23 Marco Baldovin , Giacomo Gradenigo , Angelo Vulpiani , Nino Zanghì

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…

Quantum Physics · Physics 2007-05-23 Werner Stulpe

Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum Mechanics in presence of non-interacting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary…

Quantum Physics · Physics 2009-11-07 M. Correggi , G. Morchio

An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…

Artificial Intelligence · Computer Science 2022-06-06 V. I. Yukalov

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…

Probability · Mathematics 2015-09-01 E. N. Dzhafarov , J. V. Kujala

We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures research'. We concentrate…

Quantum Physics · Physics 2007-05-23 Diederik Aerts

In a fundamental formulation of the quantum mechanics of a closed system such as the universe as a whole, three forms of information are needed to make predictions for the probabilities of alternative time histories of the closed system .…

General Relativity and Quantum Cosmology · Physics 2021-03-16 James B. Hartle

Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…

Quantum Physics · Physics 2007-05-23 Antonio Cassa

This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of…

Quantum Physics · Physics 2013-01-09 Jeffrey Bub

Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…

Quantitative Methods · Quantitative Biology 2007-08-15 Hernan G. Garcia , Jané Kondev , Nigel Orme , Julie A. Theriot , Rob Phillips

Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood…

Quantum Physics · Physics 2026-02-27 Jianqi Sheng , Dongkai Zhang , Lixiang Chen
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