REDUCTIONS OF STATE VECTORS IN THE THEORY OF WIENER AND SIEGEL

Frederik Jozef Belinfante

A. M. Jayannavar

Mićo Đurđević, Milan Vujičić, Fedor Herbut

The three known demonstrations that there exist contextual hidden variables (HV) that reproduce quantum mechanics (the HV theories of Bohm–Bub, Wiener–Siegel, and Gudder) are shown to be special cases of a generalized Gudder’s theory defined in this work. Within this scheme, a symplectic HV theory is introduced for which it is argued that it is physically more useful than Gudder’s theory because it makes possible the definition of a Hamiltonian subquantum dynamical law that reproduces in a natural way the Schrödinger equation. On the other hand, the symplectic HV theory contains as concrete realizations a slightly modified theory of Bohm–Bub and the theory of Wiener and Siegel.

Mark P. Davidson

It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the forward and backward time derivatives are different for these diffusions. A new variational approach to stochastic mechanics based on trace dynamics is introduced. It is shown that Yasue's method and Guerra and Morato's method can both be generalized to allow for any diffusion constant in a stochastic model of Schrodinger's equation, and that they can all also describe dissipative diffusion. Then it is shown that the trace dynamical theory seems to only describe dissipative diffusion unless an extra quantum mechanical potential term is added to the Hamiltonian. The differential space theory of Wiener and Siegel is reconsidered as a useful tool in this framework, and is generalized to stochastic processes instead of deterministic ones for the hidden trajectories of observables. It is proposed that the natural measure space for Wiener-Siegel theory is Haar measure for random unitary matrices. A new interpretation of the polychotomic algorithm is given.

David Z. Albert, Lev Vaidman A

Norbert Wiener Centenary Congress, Vidyadhar S. Mandrekar, P. R. Masani

Wiener-Kolmogorov conception of the stochastic organization of nature by S. Molchanov The Wiener programme in statistical physics. Is it feasible in the light of recent developments? by O. Penrose The mathematical ramifications of Wiener's program in statistical physics by L. Gross Potential capacity before and after Wiener by D. R. Adams Generalized harmonic analysis and Gabor and wavelet systems by J. J. Benedetto Wiener-Hopf equations and linear systems by J. Bart, I. Gohberg, and M. A. Kaashoek Complex harmonic analysis in the aftermath of Paley-Wiener by P. Malliavin Amalgam spaces and generalized harmonic analysis by H. G. Feichtinger Wiener space and nonlinear quantum field theory by I. Segal Wiener and Feynman--path integrals and their applications by S. Albeverio Optical coherence before and after Wiener by J. R. Klauder Wiener and the problem of Hidden Parameters in quantum mechanics by E. A. Carlen Finite path integrals by E. F. Thomas Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory by R. L. Warnock The role of Leibniz and Haldane in Wiener's cybernetics by G. Gale Quantum mechanical coherence, resonance, and mind by H. P. Stapp What is mind that the brain may order it? by K. H. Pribram Shannon-Wiener information and stochastic complexity by J. Rissanen Sharp norm comparison of Martingale maximal functions and stochastic integrals by D. L. Burkholder Stochastic analysis on Wiener space by S. Watanabe Stochastic filtering: A part of stochastic nonlinear analysis by G. Kallianpur The theory of learning before and after Wiener by N. K. Bose Sensory and motor prostheses in the aftermath of Wiener by R. W. Mann On Wiener's thought in the computer as an aid in visualizing higher-dimensioanl forms and its modern ramifications by D. Roseman Norbert Wiener and the future of cybernetics by P. R. Masani Letter to Norbert Wiener from John von Neumann Scientific impact of the work of C. E. Shannon by B. McMillan Citation and award of the Norbert Wiener Centenary Medal to Professor C. E. Shannon (in absentia) by J. Ramaekers Wiener and the art of communication by D. Gabor Academic vita of Norbert Wiener Doctoral students of Norbert Wiener Bibliography of Norbert Wiener Defense Department documents List of participants (Norbert Wiener centenary congress).