  We investigate the quantum dynamics of the isotropic Universe in the presence
of a free massless scalar field, playing the role of a physical clock. The
Hilbert space is constructed via a direct analogy between the Wheeler-DeWitt
equation in the minisuperspace and a relativistic scalar one in physical space.
In particular, we show how the introduction of a "turning point" in the
Universe evolution allows to overcome an intrinsic ambiguity in representing
the expanding and collapsing Universe. In this way, the positive and negative
frequencies are simply identified with time reversed states. The main subject
of the present analysis is the construction of a horizon operator, whose
quantum behavior is investigated when Polymer Quantum Mechanics is implemented
to describe the asymptotic evolution near the initial singularity. The reason
of this choice is motivated by the intrinsic spreading of localized wavepackets
when the polymer dispersion relation governs the quantum dynamics. The evidence
that the mean value of the quantum horizon operator follows its semiclassical
behavior (corrected for polymerization) is a clear indication that a concept of
causality can be restored also in the quantum cosmological picture.
