Continuous measurement of mini-superspace variables by higher multipoles

Abstract

The density matrix rho ( alpha , phi ; alpha ', phi ') on the mini-superspace corresponding to a Friedmann universe with scale factor alpha containing a (homogeneous) massive scalar field phi is investigated on the basis of the linear coupling model of higher multipoles as proposed by Halliwell and Hawking (1985). The wavefunctions for all multipoles of the matter field and for the tensor modes of the metric are calculated explicitly. They can be considered as continuously measuring alpha and phi . It turns out that in this way the 'intrinsic time variable' alpha is rendered a perfectly classical quantity in not allowing the observation of superpositions of different alpha , while phi can be regarded to be defined within the width of a narrow Gaussian.