Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
arXiv:gr-qc/0607072 · doi:10.1007/s10773-007-9592-y
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 during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem and the problem of time in reparametrization invariant theories as for example in canonical quantum gravity. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem.
arXiv comment23 pages, Few changes and added references in v2
References in corpus (24)
- Classical Equations for Quantum Systems
- Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
- Consistent Histories and Quantum Reasoning
- Choice of Consistent Family, and Quantum Incompatibility
- Time-of-arrival in quantum mechanics
- Quantum Observables and Recollapsing Dynamics
- On the Generality of Refined Algebraic Quantization
- A Uniqueness Theorem for Constraint Quantization
- Somewhere in the Universe: Where is the Information Stored When Histories Decohere?
- Relational time in generally covariant quantum systems: four models
- Zeno dynamics yields ordinary constraints
- A Review of the Decoherent Histories Approach to Quantum Mechanics
- Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems
- Time-of-arrival probabilities and quantum measurements
- Observables and a Hilbert Space for Bianchi IX
- Anomalies of weakened decoherence criteria for quantum histories
- Life in an Energy Eigenstate: Decoherent Histories Analysis of a Model Timeless Universe
- Decoherent Histories Approach to the Arrival Time Problem
- SL(2,R) model with two Hamiltonian constraints
- Decoherent histories analysis of the relativistic particle
- Group quantization of parametrized systems I. Time levels
- Invariant Class Operators in the Decoherent Histories Analysis of Timeless Quantum Theories
- Unusual quantum states: nonlocality, entropy, Maxwell's daemon, and fractals
- Relational evolution of the degrees of freedom of generally covariant quantum theories
Cited by in corpus (8)
- Arrival Times, Complex Potentials and Decoherent Histories
- Quantum Arrival Time Formula from Decoherent Histories
- Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect
- On the Relationship Between Complex Potentials and Strings of Projection Operators
- Decoherent Histories of Spin Networks
- Contrary Inferences in Consistent Histories and a Set Selection Criterion
- Amplitudes for Spacetime Regions and the Quantum Zeno Effect: Pitfalls of Standard Path Integral Constructions
- Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory