# Signal-locality, uncertainty, and the subquantum *H*-theorem. I

### Antony Valentini

*International School for Advanced Studies, Strada Costiera 11, 34014 Trieste,
Italy *
**(Originally published in ***Physics Letters A* 156, No.1-2, June 1991)

ABSTRACT: We begin a statistical mechanics bsed on the pilot-wave formulation
of quantum theory, without making the assumption that the probability density
*P* is equal to |*Psi*|^2. Instead, this relation is shown to arise
statistically from an "*H*-theorem", based on assumptions similar to
those of classical statistical mechanics (rather than postulating subquantum
"fluid fluctuations", as done by Bohm and Vigier). The theorem is proved by
constructing a subquantum entropy which, when coarse-grained, increases with
time, reaching a maximum when *P* = |*Psi*|^2.

# Signal-locality, uncertainty, and the subquantum *H*-theorem. II

### Antony Valentini

*International School for Advanced Studies, Strada Costiera 11, 34014 Trieste,
Italy *
**(Originally published in ***Physics Letters A* 158, No.1-2, August 1991)

ABSTRACT: In the pilot-wave formulation, signal-locality and the uncertainty principle are
shown to be valid only for the equilibrium distribution *P*=|*Psi*|^2
(which arises from the subquantum *H*-theorem proved earlier). The *H*-theorem
then explains the emergence of effective locality and uncertainty from a
deeper nonlocal and deterministic theory. In order to explain the
present uneasy "peaceful coexistence" (or "conspiracy") between relativity
and quantum theory, we suggest that a subquantum analogue of Boltzmann's
heat death has actually happened in the real universe.