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Information and measurement in generally covariant quantum theory

S. Jay Olson, Jonathan P. Dowling

Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the covariant formalism, and use it to interpret the measurement process. We find that the time ordering of measurements emerges as an entropy relationship in the state of the observers, giving unique probabilities for multiple measurements. This approach suggests a new, fully self-contained probability interpretation for generally covariant quantum physics, which makes use of a quantum mechanical description of the observer, in contrast to standard quantum mechanics which assumes an external, classical observer.Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the covariant formalism, and use it to interpret the measurement process. We find that the time ordering of measurements emerges as an entropy relationship in the state of the observers, giving unique probabilities for multiple measurements. This approach suggests a new, fully self-contained probability interpretation for generally covariant quantum physics, which makes use of a quantum mechanical description of the observer, in contrast to standard quantum mechanics which assumes an external, classical observer.

arXiv:quant-ph/0701200Jan 28, 20072 citations

Tunneling Times and Weak Measurementsa

Aephraim M. Steinberg

Annals of the New York Academy of SciencesApr 1, 19952 citations

Covariance Systems on the Projective Line

Nicola Pinamonti, M. Toller

We study the positive-operator-valued measures on the projective real line covariant with respect to the projective group, assuming that the energy is a positive operator. This problem is similar to the more complicated problem of finding the positive-operator-valued measures on the compactified Minkowski space-time covariant with respect to the conformal group. It also describes a time-of-arrival observable for a free particle covariant with respect to linear canonical transformations.

arXiv:quant-ph/0001109Jan 29, 20000 citations

Tunneling times through a barrier with inelasticity

Arya Paul, A. Saha, Swarnali Bandopadhyay +1 more

arXiv:quant-ph/0607038The European Physical Journal DMar 8, 20078 citations

MODEL STUDY OF TUNNELING TIMES (SUMMARY)

Z.-H. Huang, Paul H. Cutler, T. E. Feuchtwang +3 more

Le Journal de Physique ColloquesNov 1, 19890 citations

In Search Of A Covariant Quantum Measure

Sumati Surya

In the quantum measure approach, quantum theory is viewed as a generalisation of classical stochastic theory rather than of classical deterministic theory. An observable or "be-able" is thus a quantum measurable set in an appropriate event algebra. Thus, the observables in quantum cosmology are covariant quantum measurable sets. In a quantum system with a strongly positive quantum measure or decoherence functional one can construct a vector valued measure whose domain is the algebra of events or physical questions. Using results in the literature, this allows us to specify when a vector valued measure on finite time events can be extended to a measure over infinite time, or equivalently, covariant events. For the class of complex percolation dynamics we show that there is a generic obstruction to this process and that covariant observables can be constructed only for a very restricted class of dynamics.In the quantum measure approach, quantum theory is viewed as a generalisation of classical stochastic theory rather than of classical deterministic theory. An observable or "be-able" is thus a quantum measurable set in an appropriate event algebra. Thus, the observables in quantum cosmology are covariant quantum measurable sets. In a quantum system with a strongly positive quantum measure or decoherence functional one can construct a vector valued measure whose domain is the algebra of events or physical questions. Using results in the literature, this allows us to specify when a vector valued measure on finite time events can be extended to a measure over infinite time, or equivalently, covariant events. For the class of complex percolation dynamics we show that there is a generic obstruction to this process and that covariant observables can be constructed only for a very restricted class of dynamics.

Journal of Physics Conference SeriesJul 8, 201111 citations

Tunneling Times with Covariant Measurements

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