  Prequantum classical statistical field theory (PCSFT) is a model which
provides a possibility to represent averages of quantum observables, including
correlations of observables on subsystems of a composite system, as averages
with respect to fluctuations of classical random fields. PCSFT is a classical
model of the wave type. For example, "electron" is described by electronic
field. In contrast to QM, this field is a real physical field and not a field
of probabilities. An important point is that the prequantum field of e.g.
electron contains the irreducible contribution of the background field, vacuum
fluctuations. In principle, the traditional QM-formalism can be considered as a
special regularization procedure: subtraction of averages with respect to
vacuum fluctuations. In this paper we derive a classical analog of the
Heisenberg-Robertson inequality for dispersions of functionals of classical
(prequantum) fields. PCSFT Robertson-like inequality provides a restriction on
the product of classical dispersions. However, this restriction is not so rigid
as in QM. The quantum dispersion corresponds to the difference between e.g. the
electron field dispersion and the dispersion of vacuum fluctuations. Classical
Robertson-like inequality contains these differences. Hence, it does not imply
such a rigid estimate from below for dispersions as it was done in QM.
