of the Ministry of Education.

1 2 JIŘ´I SOUČEK Abstract. 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 τ) can be arbitrarily close to QM. The parameter τ defines a relaxation time and on time intervals shorter than τ , 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.