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Adler Stephen L. Quantum Theory as an Emergent Phenomenon

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Adler Stephen L. Quantum Theory as an Emergent Phenomenon
Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, 2004. — 238 p.
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 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 Schroedinger dynamics.
Introduction and overview
The quantum measurement problem
Reinterpretations of quantum mechanical foundations
Motivations for believing that quantum mechanics is incomplete
An overview of this book
Brief historical remarks on trace dynamics
Trace dynamics: the classical Lagrangian and Hamiltonian dynamics of matrix models
Bosonic and fermionic matrices and the cyclic trace identities
Derivative of a trace with respect to an operator
Lagrangian and Hamiltonian dynamics of matrix models
The generalized Poisson bracket, its properties, and applications
Trace dynamics contrasted with unitary Heisenberg picture dynamics
Additional generic conserved quantities
The trace “fermion number” N
The conserved operator C
Conserved quantities for continuum spacetime theories
An illustrative example: a Dirac fermion coupled
to a scalar Klein–Gordon field
Symmetries of conserved quantities under p F <-> q F
Trace dynamics models with global supersymmetry
The Wess–Zumino model
The supersymmetric Yang–Mills model
The matrix model for M theory
Superspace considerations and remarks
Statistical mechanics of matrix models
The Liouville theorem
The canonical ensemble
The microcanonical ensemble
Gauge fixing in the partition function
Reduction of the Hilbert space modulo i eff
Global unitary fixing
The emergence of quantum field dynamics
The general Ward identity
Variation of the source terms
Approximations/assumptions leading to the emergence of quantum theory
Restrictions on the underlying theory implied by further Ward identities
Derivation of the Schroedinger equation
Evasion of the Kochen–Specker theorem and Bell inequality arguments
Brownian motion corrections to Schroedinger dynamics and the emergence of the probability interpretation
Scenarios leading to the localization and the energy-driven stochastic Schroedinger equations
Proof of reduction with Born rule probabilities
Phenomenology of stochastic reduction – reduction rate formulas
Phenomenology of energy-driven reduction
Phenomenology of reduction by continuous spontaneous localization
Discussion and outlook
Modifications in real and quaternionic Hilbert space
Algebraic proof of the Jacobi identity for the generalized Poisson bracket
Symplectic structures in trace dynamics
Gamma matrix identities for supersymmetric trace dynamics models
Trace dynamics models with operator gauge invariance
Properties of Wightman functions needed for reconstruction of local quantum field theory
BRST invariance transformation for global unitary fixing
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