  The Bohigas-Giannoni-Schmit (BGS) conjecture states that the Hamiltonian of a
microscopic analogue of a classical chaotic system can be modeled by a random
matrix from a Gaussian ensemble. Here, this conjecture is considered in the
context of a recently discovered geometric relationship between classical and
quantum mechanics. Motivated by BGS, we conjecture that the Hamiltonian of a
system whose classical counterpart performs a random walk can be modeled by a
family of independent random matrices from the Gaussian unitary ensemble. By
accepting this conjecture, we find a relationship between the process of
observation in classical and quantum physics, derive irreversibility of
observation and describe the boundary between the micro and macro worlds.
