The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.
The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.
We begin this work calculating Halliwell's propagator in the case of a Mixmaster universe with small anisotropy. Afterwards in the context of the Decoherence Model we introduce in our system terms that comprise the self-measurement of the universe of this model by higher multipoles of matter. Analyzing self-measurement with the Restricted Path Integral Formalism we obtain Halliwell's modified propagator and find that a gauge invariant physical time emerges as consequence of this process. The conditions leading to Wheeler-DeWitt dynamics are also obtained. The comparison of our results with those of the isotropic case will enable us to conclude that the number of conditions to be satisfied in order to have Halliwell's regime is in the anisotropic situation bigger than in an isotropic universe. We obtain also in terms of the parameters of the measurement process an expression for the threshold in time beyond which the scale factors of this model are meaningless.