Compatible Quantum Theory

Abstract

Formulations of quantum mechanics can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'Compatible Quantum Theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory requires a macroscopic mechanism for selecting a physical framework, which is part of the macroscopic theory (MAQM). Detailed definitions and proofs are presented in the appendices

References in corpus (21)

• Classical Equations for Quantum Systems
• Quantum probabilities as Bayesian probabilities
• Quantum Mechanics as Quantum Measure Theory
• Operationally Invariant Information in Quantum Measurements
• Statistical Mechanics: A Selective Review of Two Central Issues
• Understanding quantum measurement from the solution of dynamical models
• QBism, the Perimeter of Quantum Bayesianism
• The Interpretation of Quantum Mechanics: Many Worlds or Many Words?
• An Introduction to Consistent Quantum Theory
• Quasiclassical Coarse Graining and Thermodynamic Entropy
• The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem
• Linearly Positive Histories: Probabilities for a Robust Family of Sequences of Quantum Events
• The quasiclassical realms of this quantum universe
• Anomalies of weakened decoherence criteria for quantum histories
• The New Quantum Logic
• Quantum Locality
• Quantum Histories
• A Consistent Quantum Ontology
• Annotated Interview with a QBist in the Making
• A short introduction to the quantum formalism[s]
• Weak Decoherence and Quantum Trajectory Graphs

Cited by in corpus (3)

• Particle Path Through a Nested Mach-Zehnder Interferometer
• What is quantum mechanics? A minimal formulation
• Diagnosing the Trouble With Quantum Mechanics