  A numerical experiment based on a particle number-conserving quantum field
theory is performed for two initially independent Bose-Einstein condensates
that are coherently coupled at two temperatures. The present model illustrates
ab initio that the initial relative phase of each of the two condensates
doesn't remain random, but is distributed around integer multiple values of
$2\pi$ from the interference and thermalization of forward and backward
propagating matter waves at the Boltzmann equilibrium, that intrinsically
measures zero average phases for each of the two independent condensates.
Following this approach, focus is put on the original Gedanken experiment of
Anderson on whether a Josephson current between two initially separated
Bose-Einstein condensates occurs in a deterministic way or not, depending on
the initial phase distribution.
