[Paper Review] Alternative Decohering Histories in Quantum Mechanics

Murray Gell‐Mann, James B. Hartle|arXiv (Cornell University)|May 14, 2019

History of Computing Technologies52 citations

TL;DR

The paper advances the decoherent (consistent) histories framework for quantum cosmology, introducing strong decoherence, full sets of histories, and equivalence classes to characterize a quasiclassical realm and measures of classicality.

ABSTRACT

We continue our efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasiclassical realm of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe. We introduce and define the notion of strong decoherence. We replace the notion of maximal sets of alternative decohering histories by defining the more useful concept of "full" sets of alternative strongly decohering histories. These full sets fall into equivalence classes each of which is characterized by a basis in Hilbert space. Finally we describe our continuing efforts to find measures of classicality --- measures that could be applied to such full sets of alternative strongly decohering so as to characterize a quasiclassical realm.

Motivation & Objective

• Motivate a framework to explain the quasiclassical realm as an emergent feature from the universe’s quantum state and dynamics.
• Introduce strong decoherence and full sets of histories to avoid observer-centric descriptions.
• Define equivalence classes of histories based on a common basis and generalized records.
• Investigate measures of classicality that can distinguish quasiclassical behavior within full sets.

Proposed method

• Define the decoherence functional with properties: Hermiticity, positivity, normalization.
• Introduce strong decoherence and the associated generalized records R_alpha (C_alpha rho = R_alpha rho).
• Define full sets of histories as maximal, completely fine-grained histories within an equivalence class of a shared basis R_alpha.
• Characterize equivalence classes of full sets by the common basis in Hilbert space (one-dimensional projections).
• Discuss qualitative features of quasiclassical realms via hydrodynamic-like variables and their decoherence.
• Propose information-theoretic measures (S tilde rho, hat S) to quantify classicality across history sets.

Experimental results

Research questions

• RQ1 What is the appropriate notion of decoherence that allows exact probabilities for histories?
• RQ2 How can one define and utilize full sets and equivalence classes of decohering histories to describe a quasiclassical realm?
• RQ3 What measures can effectively characterize classicality within full sets of histories?
• RQ4 How can hydrodynamic-like variables emerge as part of a quasiclassical realm from the universe’s Hamiltonian and initial state?

Key findings

• Strong decoherence (C_alpha rho = R_alpha rho) provides a robust condition tied to generalized records.
• Full sets of histories are organized into equivalence classes characterized by a common basis in Hilbert space (R_alpha projections).
• Equivalence classes admit representations as projections onto hydrodynamic-like variables that decohere with the density matrix rho.
• A maximal set of histories is not required for a quasiclassical realm; a full set may suffice and avoids excessive redundancy.
• Two proposed measures (S tilde rho and hat S) illustrate how to assess or optimize for classicality within and across history sets.