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For want of a more natural proposal, it is generally assumed that theback-reaction of a quantised matter field on a classical metric is given by theexpectation value of its energy-momentum tensor, evaluated in a specifiedstate. This proposal can be expected to be quite sound only when thefluctuations in the energy-momentum tensor of the quantum field are negligible.Based on this condition, a dimensionless criterion has been suggested earlierby Kuo and Ford for drawing the limits on the validity of this semiclassicaltheory. In this paper, we examine this criterion for the case of a toy model,constructed with two degrees of freedom and a coupling between them thatexactly mimics the behaviour of a scalar field in a Friedmann universe. Toreproduce the semiclassical regime of the field theory, in the toy model, oneof degrees of freedom is assumed to be classical and the other quantummechanical. Also the backreaction is assumed to be given by the expectationvalues of the quantum operators involved in the equations of motion for theclassical system. Motivated by the same physical reasoning as Kuo and Ford, we,here, suggest another criterion, one which will be shown to perform morereliably as we evaluate these criterions for different states of the quantumsystem in the toy model. Finally, from the results obtained we conclude thatthe semiclassical theory being considered for the toy model is reliable, duringall stages of its evolution, only if the quantum system is specified to be incoherent like states. The implications of these investigations on field theoryare discussed.Comment: 20 pages in Te

Limits on the Validity of the Semiclassical Theory — A Minisuperspace Example