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arXiv:1407.2858

Truth problem in the context of interpretations of quantum logic

Sergey B. Kulikov

Published Jul 10, 2014• 0 citations
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Abstract

The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a context of modal expansions of quantum logic. It is found the way for solution of the problem of detection of features of creation of quantum-mechanical researches as a single case of semantics of "the possible worlds". Studies in the field of logic foundation of quantum physics receive the status of "possible quantum mechanics". Therefore they can be presented not simply as "truth" and "false" distinction within judgments about the physical phenomena but also as display logically possible and (or) impossible, necessary and (or) casual constructions of physical sciences.

DOI
10.48550/arxiv.1407.2858

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The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a context of modal expansions of quantum logic. It is found the way for solution of the problem of detection of features of creation of quantum-mechanical researches as a single case of semantics of "the possible worlds". Studies in the field of logic foundation of quantum physics receive the status of "possible quantum mechanics". Therefore they can be presented not simply as "truth" and "false" distinction within judgments about the physical phenomena but also as display logically possible and (or) impossible, necessary and (or) casual constructions of physical sciences.
The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to come to more general problem of the coherence between the scope of quantum mechanical and quantum logical studies on the basis of principle of the indiscernibility of identicals entered by G. Leibnitz and developed by S. Kripke. At the same time it’s revealed the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a context of modal expansions of quantum logic.
The aim of the article is to analyze the ontological foundations of quantum mechanics and the relationship of various interpretations of quantum mechanics with the question of truth in scientific knowledge. The theoretical material (various interpretations of quantum mechanics) was analyzed. The research methods were analysis, comparative-historical and institutional approaches. On the basis of the study, it can be concluded that physicists are only able to predict the probabilities of physical phenomena or processes, without any knowledge of the structure of entity in itself. The study helps to complement the theoretical picture of the ontology of quantum mechanics and to get an idea about the development prospects of the methodology of physical sciences. We should not ascribe properties that are unobservable in experience to the entity because science can truly interpret only the representation of entity in itself in experience and the ways of dealing with it, not future events or possible states of the entity. Otherwise, science “slides” down to the level of dialectical (rhetorical) exercises based not on true premises, but on generally accepted or “authoritative” biases, which gives room to extreme forms of relativism and takes natural scientists away from studying nature to inventing empirically unsupported hypotheses. When, in accordance with the Cartesian ontology, the scientist assumes that the entity is as the “subject” observes it (that is, the “reflection” of the entity in consciousness is identified with entity in itself), this assumption leads the scientist to attempts to “scientifically” describe the future events or the possible states of the entity. The criterion for the truth of a scientific theory put forward by Einstein in his dispute with Bohr remains a fundamentally unattainable ideal. Cognition of nature is probabilistically and fundamentally incomplete since a person can consciously comprehend natural phenomena only within the framework of their representation in the existing being. The probabilistic nature of quantum mechanics is due to the impossibility of knowing things as they exist by themselves, that is, as they exist outside of representation in the mind of the observer. This does not mean that physical entities did not exist before their knowledge: they existed potentially, but were not valid for the observer, that is, conscious. Quantum physics is as incomplete as any other physical theory when compared with an unattainable ideal, but this fact does not negate its truth for modern scientists since quantum theory is based on the results of verified experiments.
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What do we expect of a quantum logical interpretation of quantum mechanics worthy of the name? In what sense should it resolve the paradoxes? What scope should it have? Should quantum logic, if it is successful in the micro world, replace classical logic in the macro world and in mathematics? We distinguish between two kinds of quantum logical interpretations of quantum mechanics. An example of the first kind, the activist kind, will do much more than simply rewrite the assertions that quantum mechanics makes about the quantum world in an unfamiliar notation - in the elementary language of quantum mechanics. It will offer a solution to the major puzzles of quantum mechanics. It will show that the paradoxes of quantum mechanics can be resolved if we do away with classical logic and replace it with quantum logic, at least in our descriptions of quantum phenomena. It may defend a form of quantum-mechanical realism, a sort of quantum logical particle view of quantum systems, protecting it from the paradoxes that classical logic would impose on it. The second kind of quantum logical interpretation, the passive or quietist kind, is less ambitious. A quietist interpretation offers a solution to the paradoxes only in the following sense. It will assert that quantum mechanics, when it describes quantum phenomena in the elementary language, need not generate paradox, that the so-called paradoxes are not even formulable in quantum logic.