[Paper Review] Background freedom leads to many-worlds with local beables and probabilities

Ovidiu Cristinel Stoica|arXiv (Cornell University)|Sep 18, 2022

Quantum Mechanics and Applications4 citations

TL;DR

This paper proposes a new interpretation of quantum mechanics—many-spacetimes interpretation (MSTI)—where background independence in quantum gravity leads to a natural dissociation of the wavefunctional into classical space-states, each with local beables and definite geometry. Interference is suppressed at macroscopic scales due to geometric incompatibility, leading to absolute decoherence and a derivation of the Born rule from the distribution of space-states, thereby providing a natural foundation for the many-worlds interpretation with ontologically real, classical-like worlds.

ABSTRACT

I argue that background freedom in quantum gravity automatically leads to a dissociation of the quantum state into states having a classical space. That is, interference is not completely well-defined for states with different space geometries, even if their linear combination is. Interference of states with different space geometry is still allowed at small scales, but precluded at macro-scales. Macrostates, including measuring devices, appear classical. The distribution of space geometries automatically gives the Born rule. The dissociation entails a kind of absolute decoherence, making the ad-hoc wavefunction collapse unnecessary. This naturally leads to a new version of the many-worlds interpretation, in which: 1) the classical space-states form an absolute preferred basis, 2) at any time, the resulting micro-branches are like classical worlds, with objects in space, 3) macro-branches stop interfering, even though micro-branches can interfere (as they should), 4) the space geometries converge at the Big-Bang, favoring macro-branching towards the future, 5) the wavefunctional becomes real by absorbing the phases in the global U(1) gauge, 6) ontologically, the wavefunctional consists of many gauged space-states, each of them counting as a world by having local beables (the space geometry and the classical fields), 7) the density of the classical space-states automatically obeys the Born rule.

Motivation & Objective

• To resolve foundational issues in quantum mechanics, particularly the preferred basis problem and the emergence of classicality, within a background-independent quantum gravity framework.
• To derive the Born rule not as an ad hoc postulate but as a consequence of the distribution of classical space-states in the wavefunctional.
• To provide a natural, ontology-based version of the many-worlds interpretation that avoids the need for wavefunction collapse and postulates local beables.
• To reconcile quantum gravity with the many-worlds interpretation by showing that background freedom inherently leads to macroscopic branching and classical spacetime structure.
• To establish a physically realist interpretation where each space-state with definite geometry and classical fields counts as a distinct world with ontological status.

Proposed method

• Formulate the wavefunctional in terms of Riemannian 3-geometries $\gamma_{ab}$ on spatial slices $\Sigma$, using the Wheeler-DeWitt equation $\widehat{\mathsf{H}}\underline{\Psi} = 0$ as the fundamental constraint.
• Define classical space-states as configurations $ (\Sigma, \gamma_{ab}, \phi_\gamma) $, where $\phi_\gamma$ are classical fields on a 3-manifold with definite metric, forming the ontic basis of the theory.
• Show that interference between states with different spatial geometries is suppressed at macroscopic scales due to background freedom, leading to irreversible branching.
• Derive the Born rule by interpreting the density of space-states in the wavefunctional as a probability measure for self-location in a given world.
• Make the wavefunctional real by absorbing phases into a global U(1) gauge of the classical fields, preserving unitarity while eliminating complex phases from the ontology.
• Justify counting each space-state as a world by identifying local beables (metric $\gamma$, fields $\phi_\gamma$) that satisfy classical dynamics and allow for world-identity.

Experimental results

Research questions

• RQ1 How does background independence in quantum gravity lead to the emergence of classical spacetime and suppress interference between different geometries?
• RQ2 Can the Born rule be derived from the distribution of classical space-states in the wavefunctional, rather than being postulated?
• RQ3 Does background freedom naturally lead to a preferred basis for branching, eliminating the need for ad hoc decoherence or collapse postulates?
• RQ4 Can a many-worlds interpretation be formulated with local beables and a realist ontology, where each space-state corresponds to a distinct world?
• RQ5 How does the structure of the wavefunctional in background-free quantum gravity lead to time-asymmetric branching and classical probabilities?

Key findings

• Background freedom in quantum gravity suppresses interference between quantum states with different space geometries at macroscopic scales, leading to a natural form of absolute decoherence.
• The wavefunctional dissociates into classical space-states, each with definite 3-geometry and classical fields, which serve as the ontological basis for the theory.
• The distribution of space-states across macro-branches reproduces the Born rule as the probability measure for self-location in a given world.
• The wavefunctional can be made real by absorbing phases into a global U(1) gauge of the classical fields, eliminating complex numbers from the ontology while preserving unitarity.
• Each space-state, with its local beables (metric and classical fields), constitutes a distinct world, justifying the counting of worlds in the many-worlds framework.
• The branching structure is time-asymmetric, with space-states converging at the Big Bang and diverging toward the future, naturally explaining the arrow of time in quantum measurement.