In Search Of A Covariant Quantum Measure
2011
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.
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