## Ensembles on Configuration Space: Classical, Quantum, and by Michael J. W. Hall, Marcel Reginatto

By Michael J. W. Hall, Marcel Reginatto

This e-book describes a promising method of difficulties within the foundations of quantum mechanics, together with the size challenge. The dynamics of ensembles on configuration area is proven right here to be a helpful instrument for unifying the formalisms of classical and quantum mechanics, for deriving and increasing the latter in quite a few methods, and for addressing the quantum dimension challenge. an outline of actual structures via ensembles on configuration area could be brought at a really primary point: the fundamental development blocks are a configuration house, chances, and Hamiltonian equations of movement for the chances. The formalism can describe either classical and quantum platforms, and their thermodynamics, with the most distinction being the alternative of ensemble Hamiltonian. in addition, there's a common manner of introducing ensemble Hamiltonians that describe the evolution of hybrid platforms; i.e., interacting platforms that experience specified classical and quantum sectors, taking into consideration constant descriptions of quantum platforms interacting with classical size units and quantum topic fields interacting gravitationally with a classical spacetime.

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**Extra info for Ensembles on Configuration Space: Classical, Quantum, and Beyond**

**Example text**

1) Similarly, there can be no physical distinction between the joint function S(x, y) and the pair of individual functions S X (x) and SY (y). Now, as discussed in Chap. 2, the conservation of probability requires that all physical quantities are insensitive under addition of a constant to S. More precisely, observables are independent under any transformation of the form S → S + c, where c is independent of the configuration space of the ensemble. 2) up to an arbitary additive constant of no physical significance.

Rev. A 69, 052113 (2004) 9. : Weak values as interference phenomena. Phys. Rev. A 91, 032116 (2015) 10. : Nonrelativistic Mechanics. W. A. Benjamin, Reading, Massachusetts (1973) 11. : Quantum properties of classical Fisher information. Phys. Rev. A 62, 012107 (2000) 12. : Lectures on Quantum Field Theory, Chaps. 14–15. Academic, New York (1966) 13. : Quantization of Gauge Systems, Chap. 1. Princeton University Press, New Jersey (1992) 14. : The Quantum Theory of Fields, vol. I. Cambridge University Press, Cambridge (1995) 15.

However, some combinations of states have never been observed, including coherent superpositions of integer and half-integer spins, electric charges, and Schrödinger’s cat. Possible explanations for why such superpositions are not observed fall into two logical categories: 1. measurement superselection rules: such superpositions may be allowed, but physical limitations on measurement prevent their observation; 2. state superselection rules: such superpositions are not physically allowed. State superselection rules are stronger than measurement superselection rules (one cannot observe what does not exist), and are clearly constraints on possible states of quantum ensembles.