Classical equations for quantum systems.

@article{GellMann1993ClassicalEF,
  title={Classical equations for quantum systems.},
  author={Gell-Mann and Hartle},
  journal={Physical review. D, Particles and fields},
  year={1993},
  volume={47 8},
  pages={
          3345-3382
        }
}
  • Gell-Mann, Hartle
  • Published 21 October 1992
  • Physics
  • Physical review. D, Particles and fields
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. A formulation of quantum mechanics is used that predicts probabilities for the individual members of a set of alternative coarse-grained histories that decohere, which means that there is negligible quantum interference between the individual histories in the set… 

Figures from this paper

The Quantum Mechanics of Closed Systems

A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative

Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime

These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does

Decoherent Histories Quantum Mechanics and Copenhagen Quantum Mechanics

We discuss the relation between our approach to quantum mechanics, based on coarsegrained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in

The regular histories formulation of quantum theory

TLDR
It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance.

On the Consistency of the Consistent Histories Approach to Quantum Mechanics

TLDR
The present work questions the validity of claims offered by CH proponents asserting that it solves many interpretational problems in quantum mechanics, and critically examines the proposed notion of a realm-dependent reality.

Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History

Decoherent histories quantum theory is reformulated with the assumption that there is one “real” fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real

Alternative decohering histories in quantum mechanics

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

Quasiclassical coarse graining and thermodynamic entropy

Our everyday descriptions of the universe are highly coarse grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical

Spacetime Coarse Grainings and the Problem of Time in the Decoherent Histories Approach to Quantum Theory

Abstract We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system

Quasiclassicality and Quantum Measurement

We address two problems arising in the quantum measurement process: A rigorous definition of quasiclassical systems and its implications for the observed collapse of the wave function.For a
...

References

SHOWING 1-10 OF 89 REFERENCES

Quantum mechanics of history: The decoherence functional in quantum mechanics.

TLDR
A condition for approximate decoherence is proposed, and it is argued that most probability sum rules will be satisfied to approximately the same degree, and an inequality bounding the size of the off-diagonal terms of thedecoherence functional is derived.

Alternative decohering histories in quantum mechanics

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

Consistent histories and the interpretation of quantum mechanics

The usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times,

Consistent interpretations of quantum mechanics

Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the

Logical reformulation of quantum mechanics. I. Foundations

The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic

The emergence of classical properties through interaction with the environment

The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to

Environment-induced superselection rules

We show how the correlations of a quantum system with other quantum systems may cause one of its observables to behave in a classical manner. In particular, "reduction of the wave packet," postulated

Logical reformulation of quantum mechanics. III. Classical limit and irreversibility

This paper deals with two questions: (1) It contains a proof of the fact that consistent quantum representations of logic tend to the classical representation of logic when Planck's constant tends to

Logical reformulation of quantum mechanics. IV. Projectors in semiclassical physics

This is a technical paper providing the proofs of three useful theorems playing a central role in two kinds of physical applications: an explicit logical and mathematical formulation of the
...