Quantum Theory as an Emergent Phenomenon
The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory

This 2004 book develops an approach to the conceptual foundations of quantum mechanics.

Stephen L. Adler (Author)

9780521115971, Cambridge University Press

Paperback, published 23 July 2009

240 pages
24.4 x 17 x 1.3 cm, 0.39 kg

"The book describes in detail a rich mathematical framework out of which a new physical description of nature can emerge. The chapters are well organized; the presentation is clear, rigorous, very attractive, and accessible to mathematical as well as theoretical physicists. It is recommended to everyone who wants to learn more about the fascinating field of the foundations of physics and the continuing efforts scientists are making to formulate a clear and coherent picture of physical phenomena." - Angelo Bassi, Universitat Munchen

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an 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 phenomenological proposals for stochastic modifications to Schrödinger dynamics.

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 Schrödinger dynamics
7. Discussion and outlook
Appendices
References.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Physics [PH], Philosophy of science [PDA]