## Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field TheoryQuantum 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. |

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### Contents

the classical Lagrangian and Hamiltonian dynamics of matrix models | 21 |

2 Additional generic conserved quantities | 39 |

3 Trace dynamics models with global supersymmetry | 64 |

4 Statistical mechanics of matrix models | 75 |

5 The emergence of quantum field dynamics | 117 |

6 Brownian motion corrections to Schrödinger dynamics and the emergence of the probability interpretation | 156 |

7 Discussion and outlook | 190 |

Appendices | 193 |

212 | |

220 | |

### Other editions - View all

Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of ... Stephen L. Adler No preview available - 2009 |

Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of ... Stephen L. Adler No preview available - 2004 |

### Common terms and phrases

adjointness Adler analog anti-self-adjoint anticommutators apparatus argument assume assumption Born rule bosonic bosonic and fermionic c-number canonical algebra canonical ensemble Ceff classical coefficients commute conserved quantities constraints corresponding cyclic identities deﬁned degrees of freedom derivative discussion dynamical variables emergent quantum theory energy energy-driven equations of motion evolution factor fluctuations give global unitary invariance Grassmann Heff Heisenberg picture Hilbert space ieff ieff¯h implies integration measure Lorentz matrix elements matrix models monomial obey parameter particle partition function phase space phase space variables Poincar´e invariant Poisson bracket polynomials properties quantum field theory quantum mechanics restricted right-hand side rleff self-adjoint side of Eq spinor statistical mechanics structure supersymmetry symmetric term in Eq tion trace dynamics models trace functional trace Hamiltonian trace Lagrangian ueff underlying trace dynamics unitary fixing unitary transformations vanishing variations vector reduction Ward identities Wightman functions xreff xueff zero