  We present models in which the indeterministic feature of Quantum Mechanics
is represented in the form of definite physical mechanisms. Our way is
completely different from so-called hidden parameter models, namely, we start
from a certain variant of QM - deterministic QM - which has most features
similar to QM, but the evolution in this theory is deterministic. Then we
introduce the subquantum medium composed of so-called space-like objects. The
interaction of a deterministic QM-particle with this medium is represented by
the random force, but it is the random force governed by the probability
amplitude distribution. This is the quantum random force and it is very
different from classical random force. This implies that in our models there
are no Bell`s inequalities and that our models (depending on a certain
parameter tau) can be arbitrarily close to QM. The parameter tau defines a
relaxation time and on time intervals shorter than tau, the evolution violates
Heisenberg`s uncertainty principle and it is almost deterministic - spreading
of the wave packet is much slower than in QM. Such type of short-time effects
form the bases of proposed tests, which can, in principle, define limits of
validity of QM. The proposed experiments are related to the behavior of quantum
objects on short time intervals, where we expect the behavior different from
QM. The main proposed feature is violation of uncertainty relations on short
time intervals.
