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Nová axiomatizace kvantové mechaniky
Souček, Jiří
In this paper we describe a new (complete) axiomatization of quantum mechanics (QM) in which we add axioms describing the concept of an observation. We show that new axioms are clear and evident and based on common sense. Our approach is based on the idea of the observation of properties of an individual measuring system. We distinguish two concepts of a state: the properties of an individual measuring system and the state of an ensemble of systems. Then we prove that the ontic model of QM is inconsistent. This is our main result. This implies the necessity to consider “non-realistic” models for QM in which it is not true that each wave-function describes a possible state of an individual system. Our axiomatization is based on the postulate of the existence of definite outputs of an experiment. Thus the evident reality of the existence of definite outputs implies that our axiomatization is true and verifiable.
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Nová observační axiomatizace kvantové mechaniky, nekonsistence ontického modelu kvantové mechaniky a konec kvantové nelokality
Souček, Jiří
In this paper we describe a new axiomatization of quantum mechanics (QM) in which we replace the concept of the measurement by the concept of the observation. We shall describe and discuss this axiomatization in details. We show that new axioms are clear and evident and based on the common sense. Our approach is based on the idea of the observation of the individual state of the individual measuring system. We distinguish two concepts of a state: the individual state of the individual measuring system and the state of an ensemble of systems. Then we prove that the ontic model of QM (where the wave function describes the state of the individual system) is inconsistent. This is our main result. It implies that the "standard von Neumann's text-book QM" is inconsistent. This implies the necessity to consider "non-realistic" models for QM. Moreover we show that the proofs of Bell's theorem and of quantum nonlocality are not valid in these "nonrealistic" models for QM. This implies that there is no valid proof of the quantum nonlocality.
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The principle of anti-superposition in QM and the local solution of the Bell’s inequality problem
Souček, Jiří
In this paper we identify the superposition principle as a main source of problems in QM (measurement, collapse, non-locality etc.). Here the superposition principle for individual systems is substituted by the anti-superposition principle: no non-trivial superposition of states is a possible individual state (for ensembles the superposition principle is true). The modified QM is based on the anti-superposition principle and on the new type of probability theory (Extended Probability Theory [1]), which allows the reversible Markov processes as models for QM. In the modified QM the measurement is a process inside of QM and the concept of an observation of the measuring system is defined. The outcome value is an attribute of the ensemble of measured systems. The collapse of the state is substituted by the Selection process. We show that the derivation of Bell’s inequalities is then impossible and thus QM remains a local theory. Our main results are: the locality of the modified QM, the local explanation of EPR correlations, the non-existence of the wave-particle duality, the solution of the measurement problem. We show that QM can be understood as a new type of the statistical mechanics of many-particle systems.
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Exact methods in trade (model approximation)
Zeithamer, Tomáš ; Drozen, František (advisor) ; Jablonský, Josef (referee) ; Malý, Josef (referee) ; Kloc, Karel (referee)
The paper deals with quantum economy. It means the methods of quantum mechanics are applied in the study of economic processes. The scalar abstract economic quantities are constructed as follows: general abstract economic quantity F , average abstract economic quantity FA, marginal abstract economic quantity FM, marginal average abstract economic quantity FMA, average marginal abstract economic quantity FAM, elasticity of abstract economic quantity EF. All the abstract economic quantities mentioned above are constructed as mappings. The general theory of abstract economic quantities is utilized in a construction of the abstract total gross profit TGP. The set of static models of total gross profit TGP is constructed in the case that the first unit gross profit is slowly changed with time while the second unit gross profit is quickly changed with time in comparison with the first unit gross profit.
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