Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Decoherence, einselection, and the quantum origins of the classical

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Criticism and the Growth of Knowledge. Edited by I. Lakatos and A. Musgrave. Pp. viii, 282. £3·50, paperback £1. 1970. (Cambridge University Press.)

It comes as something ofa surprise to reflect that the New York Review ofBooks is now over twenty years old. Even people of my generation (that is, old enough to remember the revolutionary 196os but not young enough to have taken a very exciting part in them) think of the paper as eternally youthful. In fact, it has gone through years of relatively quiet life, yet, as always in a competitive journalistic market, it is the controversies that attract the interest of the reader and to which the history (especially an admittedly impressionistic survey that tries to include something of the intellectual context in which a journal has operated) must give some attention. Not all the attacks which the New York Review has attracted, both early in its career and more recently, are worth more than a brief summary. What do we now make, for example, of Richard Kostelanetz's forthright accusation that 'The New York Review was from its origins destined to publicize Random House's (and especially [Jason] Epstein's) books and writers'?1 Well, simply that, even if the statistics bear out the charge (and Kostelanetz provides some suggestive evidence to support it, at least with respect to some early issues), there is nothing surprising in a market economy about a publisher trying to push his books through the pages of a journal edited by his friends. True, the New York Review has not had room to review more than around fifteen books in each issue and there could be a bias in the selection of

http://www.jstor.org/stable/pdfplus/3507774.pdf

The New York Review of Books

What is randomness? probability? certainty? knowledge? These are old and difficult questions, and we shall not focus on them here. Nonetheless, we shall obtain sharp, striking conclusions concerning the relationship between these concepts.

Quantum Equilibrium and the Origin of Absolute Uncertainty

It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell This is true both for classical distributions on the phase space and for quantum density matrices Here we show that a much stronger statement holds for quantum systems Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble This clarifies, expands and justifies remarks made by Schrodinger in 1952

Canonical Typicality

Preface. I: Bohmian Mechanics: Background and Fundamentals. 1. The Causal Quantum Theory Program J.T. Cushing. 2. Bohmian Mechanics as the Foundation of Quantum Mechanics D. Durr, et al. 3. Pilot-Wave Theory of Fields, Gravitation and Cosmology A. Valentini. 4. Contextuality in Bohmian Mechanics L. Hardy. 5. Global Existence and Uniqueness of Bohmian Trajectories K. Berndl. 6. Scattering Theory from a Bohmian Perspective M. Daumer. 7. Is Quantum Mechanics Universal? P.R. Holland. II: Applications and Further Developments of Bohmian Mechanics. 8. The `Tunneling-Time Problem' for Electrons C.R. Leavens. 9. Local Bohmian Mechanics E.J. Squires. 10. About Position Measurements Which Do Not Show the Bohmian Particle Position Y. Aharonov, L. Vaidman. 11. An Ontological Interpretation of Boson Fields P.N. Kaloyerou. 12. De Broglie, Bohm and the Boson C. Dewdney, G. Horton. 13. A Realistic Formulation of Quantum Field Theory T.M. Samols. 14. Attaching Theories of Consciousness to Bohmian Quantum Mechanics D.N. Page. III: Historical, Conceptual and Philosophical Perspectives Related to Bohmian Mechanics. 15. Bohm and the `Inevitability' of Acausality M. Beller. 16. On the Interpretation of Bohmian Mechanics A. Fine. 17. Tension in Bohm's Interpretation of Quantum Mechanics M. Baublitz, A. Shimony. 18. An Epistemological Critique of Bohmian Mechanics R. Collins.19. Elementary Quantum Metaphysics D.Z. Albert. 20. Space-Time in the Quantum World T. Maudlin. 21. Cause and Effect in the Pilot-Wave Interpretation of Quantum Mechanics H.R. Brown, et al. 22. Is the Bohm Theory Local? M. Dickson. IV: Comparisons with Some Other Programs. 23. Modal Interpretations and Bohmian Mechanics J. Bub. 24. Remarks on Consistent Histories and Bohmian Mechanics A. Kent. 25. Bohm' Theory Versus Dynamical Reduction G.-C. Ghirardi, R. Grassi. Bibliography. The Authors. Index.

Bohmian mechanics and quantum theory : an appraisal

Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrodinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ``matter'' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter.

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On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory

Despite the uncertainty principle, the predictions of nonrelativistic quantum mechanics permit particles to have precise positions at all times.

Sheldon Goldstein

Papers

Quantum Equilibrium and the Origin of Absolute Uncertainty

Canonical Typicality

Bohmian mechanics and quantum theory : an appraisal

On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory

Bohmian mechanics and quantum field theory