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From classical to quantum physics

E.L. Albuquerque

Elsevier eBooksJan 1, 20240 citations

On the Structure of Charge in Classical and Quantum Physics

Benjamin H. Feintzeig

This paper takes up a suggestion that the structure associated with physical charge in quantum theories is best captured mathematically by the collection of charge representations of the quantum theory. In order to assess the evidence for this view, I investigate whether this charge structure has been preserved across theory change from classical to quantum physics. I show that one can analogously take charge structure in classical physics to be captured by the collection of charge representations of a classical theory. But one faces the potential problem that the collections of classical and quantum charge representations appear to not be isomorphic. I solve the problem by showing that if one attends carefully to more sophisticated category-theoretic tools for comparing structure, then one finds a precise and substantive sense in which charge structure is preserved from classical to quantum theories. I argue these results lead to greater understanding of inequivalent representations in quantum physics.This paper takes up a suggestion that the structure associated with physical charge in quantum theories is best captured mathematically by the collection of charge representations of the quantum theory. In order to assess the evidence for this view, I investigate whether this charge structure has been preserved across theory change from classical to quantum physics. I show that one can analogously take charge structure in classical physics to be captured by the collection of charge representations of a classical theory. But one faces the potential problem that the collections of classical and quantum charge representations appear to not be isomorphic. I solve the problem by showing that if one attends carefully to more sophisticated category-theoretic tools for comparing structure, then one finds a precise and substantive sense in which charge structure is preserved from classical to quantum theories. I argue these results lead to greater understanding of inequivalent representations in quantum physics.

Apr 21, 20260 citations

Entanglement is Necessary for Emergent Classicality in All Physical Theories

Jonathan G. Richens, John H. Selby, Sabri W. Al-Safi

One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance." These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance." These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.

arXiv:1610.00682Physical Review LettersAug 24, 201743 citations

Quantum Theory of the Classical

Wojciech Hubert Zurek

Bulletin of the American Physical SocietyMar 7, 20180 citations

From classical to quantum

Yun Li

Nature PhysicsJan 1, 20200 citations

A classical extension of quantum mechanics

Enrico G. Beltrametti, Slawomir Bugajski

A physically natural generalization of the notion of observable that encompasses both the classical and the quantum ones is derived. Based on it, the idea of the classical extension of a theory is developed; the states of the extended theory being the probability measures on the pure states of the original one. It is shown that quantum theory admits such a classical extension and that the qualifying features of quantum observables are preserved in the extended model.

Journal of Physics A Mathematical and GeneralJun 21, 1995133 citations

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