  We investigate the representation of the geometrical information of the
universe in terms of the eigenvalues of the Laplacian defined on the universe.
We concentrate only on one specific problem along this line: To introduce a
concept of distance between universes in terms of the difference in the
spectra.
  We can find out such a measure of closeness from a general discussion. The
basic properties of this `spectral distance' are then investigated. It can be
related to a reduced density matrix element in quantum cosmology. Thus,
calculating the spectral distance gives us an insight for the quantum
theoretical decoherence between two universes. The spectral distance does not
in general satisfy the triangular inequality, illustrating that it is not
equivalent to the distance defined by the DeWitt metric on the superspace.
  We then pose a question: Whether two universes with different topologies
interfere with each other quantum mechanically? We concentrate on the
difference in the orientabilities. Several concrete models in 2-dimension are
set up, and the spectral distances between them are investigated: Tori and
Klein's bottles, spheres and real projective spaces. Quite surprisingly, we
find many cases of spaces with different orientabilities in which the spectral
distance turns out to be very short. It may suggest that, without any other
special mechanism, two such universes interfere with each other quite strongly.
