[Paper Review] A Synopsis of the Minimal Modal Interpretation of Quantum Theory

Jacob A. Barandes, David Kagan|arXiv (Cornell University)|May 26, 2014

Quantum Mechanics and Applications7 references3 citations

TL;DR

This paper proposes the Minimal Modal Interpretation (MMI) of quantum theory as a realist, Lorentz-invariant framework that assigns definite ontic states to quantum systems, including open systems, via an underlying interpolating dynamics. It derives the Born rule from unitary evolution and decoherence, resolves the measurement problem by eliminating the need for wave-function collapse or a Heisenberg cut, and ensures ontological stability through a consistent, local dynamics grounded in the density matrix evolution.

ABSTRACT

We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. Our interpretation---which we claim is ultimately compatible with Lorentz invariance---reformulates wave-function collapse in terms of an underlying interpolating dynamics, makes it possible to derive the Born rule from deeper principles, and resolves several open questions regarding ontological stability and dynamics.

Motivation & Objective

• To provide a realist interpretation of quantum theory that assigns definite ontic states to quantum systems, including open systems, without relying on an ad hoc measurement postulate.
• To eliminate the problematic Heisenberg cut by treating measurements as ordinary interactions governed by unitary dynamics.
• To derive the Born rule as a consequence of decoherence and density matrix evolution, rather than as a fundamental postulate.
• To ensure compatibility with Lorentz invariance and locality by formulating dynamics in terms of an underlying interpolating ontology.
• To resolve foundational issues such as the quantum Zeno effect, Wigner’s friend, and Schrödinger’s cat through a consistent, non-epistemic ontology.

Proposed method

• The interpretation assigns definite ontic states to quantum systems based on the unitary evolution of the density matrix, extending the classical notion of state trajectories to Hilbert space.
• It introduces an interpolating dynamics that continuously tracks the actual ontic state of a system, even during interactions with the environment, avoiding discontinuous collapse.
• The Born rule is derived from the statistical behavior of this underlying dynamics under decoherence, which suppresses interference between macroscopically distinct branches.
• The framework treats all systems—including observers—as quantum systems with definite ontic states, thereby avoiding circularity in measurement definitions.
• It draws an analogy with classical gauge theories (e.g., electromagnetism), where different gauge choices (e.g., unitary vs. Lorenz gauge) represent equivalent formulations, with MMI corresponding to a physically meaningful 'unitary gauge'.
• The interpretation is formulated to be manifestly locally causal and Lorentz-invariant by ensuring that the dynamics of each subsystem depend only on its local environment and density matrix evolution.

Experimental results

Research questions

• RQ1 How can a realist interpretation of quantum theory assign definite ontic states to open quantum systems without invoking wave-function collapse?
• RQ2 Can the Born rule be derived from unitary dynamics and decoherence rather than being postulated?
• RQ3 How can the measurement problem be resolved without introducing a fundamental distinction between quantum and classical systems?
• RQ4 Is it possible to construct a Lorentz-invariant quantum interpretation that maintains ontological stability and locality?
• RQ5 What is the role of decoherence in establishing the emergence of definite outcomes and probabilities in quantum theory?

Key findings

• The Minimal Modal Interpretation provides a consistent, realist ontology for quantum systems by assigning definite ontic states that evolve continuously along trajectories in Hilbert space, even for open systems.
• The Born rule emerges naturally as a consequence of decoherence acting on the underlying interpolating dynamics, rather than being postulated.
• The interpretation avoids the Heisenberg cut by treating all interactions—including measurements—as unitary processes governed by the same dynamical rules.
• The framework is fundamentally compatible with Lorentz invariance, as the dynamics are locally causal and defined through the density matrix evolution.
• The interpretation resolves foundational paradoxes such as Wigner’s friend and Schrödinger’s cat by assigning definite, consistent ontic states to all systems, including observers.
• The model draws a parallel with classical gauge theories, where the 'unitary gauge' (MMI) provides a physically meaningful ontology, while other gauges (e.g., density-matrix-based many-worlds) are mathematically equivalent but less ontologically transparent.