# Choice of Consistent Family, and Quantum Incompatibility

@article{Griffiths1998ChoiceOC, title={Choice of Consistent Family, and Quantum Incompatibility}, author={Robert B. Griffiths}, journal={Physical Review A}, year={1998}, volume={57}, pages={1604-1618} }

In consistent-history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories that it contains. It is argued that the framework is chosen by the physicist constructing a description of a quantum system on the basis of questions he wishes to address, in a manner analogous to choosing a coarse-graining of the phase space in classical statistical mechanics. The… Expand

#### Figures from this paper

#### 94 Citations

The regular histories formulation of quantum theory

- Mathematics, Computer Science
- 2012

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. Expand

Probabilities and Quantum Reality: Are There Correlata?

- Mathematics, Physics
- 2002

Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann's proposal for a quantum… Expand

A Consistent Quantum Ontology

- Computer Science, Physics
- 2011

The formalism of classical (Shannon) information theory applies without change in suitable quantum contexts, and this suggests the way in which quantum information theory extends beyond its classical counterpart. Expand

Bohmian mechanics and consistent histories

- Physics
- 1999

AbstractThe interpretations of a particular quantum gedanken experiment provided byBohmian mechanics and consistent histories are shown to contradict each other, bothin the absence and in the… Expand

Consistent resolution of some relativistic quantum paradoxes

- Physics
- 2002

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the… Expand

Se p 20 02 Probabilities and Quantum Reality : Are There Correlata ?

- 2002

Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann’s proposal for a quantum… Expand

Consistent quantum measurements

- Physics
- 2015

Abstract In response to recent criticisms by Okon and Sudarsky, various aspects of the consistent histories (CH) resolution of the quantum measurement problem(s) are discussed using a simple… Expand

Quantum Measure Theory: A New Interpretation

- Mathematics, Physics
- 2009

Quantum measure theory can be introduced as a histories based reformulation (and generalisation) of Copenhagen quantum mechanics in the image of classical stochastic theories. These classical models… Expand

Nature and location of quantum information

- Physics
- 2002

Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy… Expand

Progress in a Many-Minds Interpretation of Quantum Theory

- Mathematics, Physics
- 1999

In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory… Expand

#### References

SHOWING 1-10 OF 45 REFERENCES

Consistent histories and quantum reasoning.

- Physics, Medicine
- Physical review. A, Atomic, molecular, and optical physics
- 1996

A system of quantum reasoning for a closed system is developed by treating nonrelativistic quantum mechanics as a stochastic theory and the physical considerations which determine the choice of a framework are discussed. Expand

On the consistent histories approach to quantum mechanics

- Mathematics, Physics
- 1996

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnès, and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some… Expand

Consistent histories and the interpretation of quantum mechanics

- Mathematics
- 1984

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,… Expand

Consistent interpretations of quantum mechanics

- Physics
- 1992

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… Expand

Correlations in separated quantum systems: A consistent history analysis of the EPR problem

- Physics
- 1987

The familiar problem of two separated, noninteracting spin‐ 1/2 particles in a state of zero total spin is analyzed using the consistent history interpretation of quantum mechanics and shown to… Expand

CONSISTENT SETS YIELD CONTRARY INFERENCES IN QUANTUM THEORY

- Physics
- 1997

In the consistent histories formulation of quantum theory, the probabilistic predictions and retrodictions made from observed data depend on the choice of a consistent set. We show that this freedom… Expand

Complete description of a quantum system at a given time

- Mathematics
- 1991

A generalization of the description of a quantum system in the time interval between two measurements is presented. A new concept of a generalized state is introduced. Generalized states yield a… Expand

Quasiclassical dynamics in a closed quantum system.

- Physics, Medicine
- Physical review. A, Atomic, molecular, and optical physics
- 1996

We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional… Expand

THE INTERPRETATION OF QUANTUM MECHANICS*

- Physics
- The British Journal for the Philosophy of Science
- 1953

THE following pages are a reply to Erwin Schrodinger's article, ' Are There Quantum Jumps ? Parts I and II ' , published in August and November 1952, in this Journal. A discussion on this subject was… Expand

Consistent histories and the measurement problem

- Physics
- 1987

Abstract The Physical grounds and significance of Griffiths' “consistent histories” theory are investigated. A simple derivation of the consistency conditions is given. The question is studied… Expand