arXiv subjects

Jiri Soucek

Publications and source records attributed to Jiri Soucek.

4 recordsLinked to original sources

arXiv2010

Extended probability theory and quantum mechanics I: non-classical events, partitions, contexts, quadratic probability spaces

In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of Ωis replaced with the concept of an event as a partition. The partition is any set of disjoint non-empty subsets of Ω(i.e. partition=subset+its decomposition). Interpretation: elements inside certain part are indistinguishable, while elements from different parts are distinguishable. There are incompatible events, e.g {{e1},{e2}} and {e1,e2}. This is logical incompatibility analogical to the impossibility to have and simultaneously not to have the which-way information in the given experiment. The context is the maximal set of mutually compatible events. Each experiment has associated its context. In each context the extended probability is reduced to classical probability. Then the quadratic representation of events, partitions and probability measures is developed. At the end the central concept of quadratic probability spaces (which extend Kolmogorov probability spaces) is defined and studied. In the next paper it will be shown that quantum mechanics can be represented as the theory of Markov processes in the extended probability theory (Einstein's vision of QM).

quant-ph↗

arXiv2004

Testing QM : the Uncertainty Principle

We propose the experimental test of the uncertainty principle. From sub-quantum models it follows that the uncertainty principle may be not true on short time intervals of the order of a picosecond. The positive result of this experiment would signify the limits of QM.

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arXiv2001

The New Interpretation of Quantum Mechanics and Hidden Parameters

The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive number. The two-slit experiment, the mathematical formulation of the complex probability theory, the density matrix, Born's law and a possibility of hidden variables are discussed.

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arXiv2001

Subquantum Models: Basic Principles, Effects and Tests

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.

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