Quantum theory as an emergent phenomenon : the statistical mechanics of matrix models as the precursors of quantum field theory

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. Half-title......Page 2 Title......Page 4 Copyright......Page 5 Dedication......Page 6 Contents......Page 8 Acknowledgements......Page 11 Introduction and overview......Page 14 1 The quantum measurement problem......Page 15 2 Reinterpretations of quantum mechanical foundations......Page 19 2.2 Bohmian mechanics......Page 20 2.4 Everett's "many worlds" interpretation......Page 21 3.2 The quantum measurement problem......Page 22 3.4 Infinities and nonlocality......Page 23 3.6 The cosmological constant......Page 24 3.7 A concrete proposal......Page 25 4 An overview of this book......Page 26 5 Brief historical remarks on trace dynamics......Page 31 1.1 Bosonic and fermionic matrices and the cyclic trace identities......Page 34 1.2 Derivative of a trace with respect to an operator......Page 37 1.3 Lagrangian and Hamiltonian dynamics of matrix models......Page 40 1.4 The generalized Poisson bracket, its properties, and applications......Page 42 1.5 Trace dynamics contrasted with unitary Heisenberg picture dynamics......Page 45 2.1 The trace "fermion number" N......Page 52 2.2 The conserved operator C......Page 55 2.3 Conserved quantities for continuum spacetime theories......Page 65 2.4 An illustrative example: a Dirac fermion coupled to a scalar Klein-Gordon field......Page 71 2.5 Symmetries of conserved quantities under.........Page 75 3.1 The Wess-Zumino model......Page 77 3.2 The supersymmetric Yang-Mills model......Page 80 3.3 The matrix model for M theory......Page 83 3.4 Superspace considerations and remarks......Page 85 4 Statistical mechanics of matrix models......Page 88 4.1 The Liouville theorem......Page 89 4.2 The canonical ensemble......Page 94 4.3 The microcanonical ensemble......Page 101 4.4 Gauge fixing in the partition function*......Page 106 4.5 Reduction of the Hilbert space modulo i_{eff}......Page 113 4.6 Global unitary fixing*......Page 119 5 The emergence of quantum field dynamics......Page 130 5.1 The general Ward identity......Page 132 5.2 Variation of the source terms......Page 137 5.3 Approximations/assumptions leading to the emergence of quantum theory......Page 141 5.4 Restrictions on the underlying theory implied by further Ward identities......Page 152 5.5 Derivation of the Schrodinger equation......Page 160 5.6 Evasion of the Kochen-Specker theorem and Bell inequality arguments......Page 164 6 Brownian motion corrections to Schrödinger dynamics and the emergence of the probability interpretation......Page 169 6.1 Scenarios leading to the localization and the energy-driven stochastic Schrodinger equations......Page 170 6.2 Proof of reduction with Born rule probabilities......Page 183 6.3 Phenomenology of stochastic reduction - reduction rate formulas......Page 187 6.4 Phenomenology of energy-driven reduction......Page 188 6.5 Phenomenology of reduction by continuous spontaneous localization......Page 198 7 Discussion and outlook......Page 203 Appendices......Page 206 Appendix B: Algebraic proof of the Jacobi identity for the generalized Poisson bracket......Page 207 Appendix C: Symplectic structures in trace dynamics......Page 211 Appendix D: Gamma matrix identities for supersymmetric trace dynamics models......Page 214 Appendix E: Trace dynamics models with operator gauge invariance......Page 217 Appendix F: Properties of Wightman functions needed for reconstruction of local quantum field theory......Page 219 Appendix G: BRST invariance transformation for global unitary fixing......Page 221 References......Page 225 Index......Page 233 "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 is 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."--Jacket Although it is our most successful physical theory, quantum mechanics 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, in fact, an emergent phenomenon arising from a more profound level of dynamics. Quantum mechanics is our most successful physical theory but raises conceptual issues that perplex physicists and philosophers of science. This book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but in fact an emergent phenomenon arising from a deeper level of dynamics Stephen Adler tackles the perplexing conceptual issues raised by the quantum theory of mechanics. He develops a new approach to the subject, based on the proposal that quantum theory is not a complete, final theory, but is an emergent phenomenon arising from a deeper level of dynamics