Quantum Theory as an Emergent Phenomenon

The Statistical Dynamics of Global Unitary Invariant Matrix Models as the Precursor of Quantum Field Theory

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by Stephen Adler

Cambridge University Press

Due/Published July 2004, 240 pages, cloth

ISBN 0521831946

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This book develops a new approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with recent phenomenological proposals for stochastic modifications to Schrodinger dynamics. 2 figures

 Contents

Acknowledgement
Introduction and overview
1. Trace dynamics: the classical Lagrangian and Hamiltonian dynamics of matrix models
2. Additional generic conserved quantities
3. Trace dynamics models with global supersymmetry
4. Statistical mechanics of matrix models
5. The emergence of quantum field dynamics
6. Brownian motion corrections to Schrodinger dynamics
7. Discussion and outlook
Appendices
References.