Foundations of Physics. Vol. 26. No. 6, 1996
Statistical Mechanics and the
Ontological Interpretation
D. Bohm ~'-" and B. J. Hiley I
Receired July II, 1995
plete our ontological hsterpretathm of quantum theoo" we have to conchMe
a treatment of quantunt statistical mechanics, The basic concepts ill the onto-
Iogk'al approach are the particle and the wave./imction. Tile densio, matrix cannot
play a Jitndamental role here. Ther(~[bre quaatutn statistical mechanics will require
a .[ia'ther statistical distribution oz,er wave.[imctk)ns ill addithm to the distrihttthm
of particles that hate a .v~ec(fied wave fimcthm. Ulthnately the ~lw,e fimcthm of
the unit'erse will be required, hut we show that if the anil,erse ill not ill thelvna-
dynamic equilibrium then it cmt be treated in terms of weakO: #iteracting httge
scale colzstituents that are rery nearly illdependent of each other, ltt this way we
ohtailt the same results as those of the usual approach u'ithht the fi'amework of the
ontoh~gical illterpretation.
1. INTRODUCTION
In the ontological or causal interpretation developed by Bohm ~ and
extended by Bohm and Hiley, ~-'~ the description of reality includes the
~pecification of the wave function as well as the positions of all the par-
ticles. In it there is i1o place for giving the density matrix the kind of
fundamental significance that is ascribed to it in the usual interpretation/3)
Rather, the wave function must always correspond to what is called a pure
~tate in the usual interpretation. This consists of a statistical ensemble of
systems having the same form of wave fuction, but different positions of the
particles. In what is generally called a "mixed state," however, not only
will there be a statistical ensemble of particle positions, but also of wave
functions.
Department of Physics, Birkbeck College, University of London, Malet Street, London
WCI E 7HX, United Kingdom.
: Professor D. Boh
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