Quantum Logic

Mittelstaedt, Peter

doi:10.1007/978-94-009-9871-1

Cited by 151 publications

(42 citation statements)

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“…. For difficulties in the domain of Quantum Physics see Mittelstaedt (1978Mittelstaedt ( , 2004, Weingartner (2004Weingartner ( , 2009Weingartner ( , 2010. The criteria originate in a paper devoted to give a solution of the problem of verisimilitude in the sense of rehabilitating Popper's original idea by restricting the logical consequence class to relevant consequentelements only (cf.…”

Section: The Motivating Criteria Rc and Rdmentioning

confidence: 99%

Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

Weingartner

2011

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The present article shows that there are consistent and decidable manyvalued systems of propositional logic which satisfy two or all the three criteria for non-trivial inconsistent theories by da Costa (1974). The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6-valued system of propositional logic for avoiding difficulties in several domains of empirical science (Weingartner (2009)).

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Section: The Motivating Criteria Rc and Rdmentioning

confidence: 99%

Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

Weingartner

2011

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“…The totality of formally true implications can be summarised in a calculus which contains "beginnings" ⇒ A ≤ B and rules A ≤ B ⇒ C ≤ D. Here, we distinguish the calculus L Q of formally true logical propositions and the calculus S Q of formally true sequential propositions. [Mittelstaedt, 1978;Stachow, 1980].…”

Section: Quantum Logicmentioning

confidence: 99%

“…The described approach to quantum mechanics which starts from the relaxed quantum ontology O(Q) and leads finally to the quantum mechanical Hilbert space, is sometimes considered as an a priori justification of quantum theory [Mittelstaedt, 1978]. The term "a priori" seems to be legitimated here, since the starting point of this approach are the most general preconditions of a scientific language of physics, i.e.…”

Section: Is Quantum Mechanics a Priori Valid?mentioning

confidence: 99%

“…In recent years many interesting logical systems for unsharp propositions were proposed. [Dalla Chiara 1993, 1995, Foulis 1997, Giuntini 1989, 1990, Mittelstaedt 1978 However, it is still an open question whether in this way a consistent operational approach to quantum mechanics can be obtained. Up to now the logical systems mentioned were not yet reconstructed in an operational way starting from a formal language of unsharp propositions.…”

Section: Is Quantum Mechanics a Priori Valid?mentioning

confidence: 99%

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Quantum Physics and Classical Physics—In the Light of Quantum Logic

Mittelstaedt

2005

Int J Theor Phys

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In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. -We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Solèr condition and Piron's result one obtains the classical Hilbert spaces. -However, this approach is not fully convincing. There is no plausible justification of Solèr's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics. The dualism of Copenhagen interpretationEven today, 75 years after the discovery of quantum mechanics many quantum physicists are convinced that the Copenhagen interpretation is still the right way for understanding quantum physics. According to this interpretation we have to distinguish two distinct worlds, the quantum world of microscopic entities and the classical world of our everyday experience which is subject to classical physics. In the quantum world we are confronted with many strange features, complementarity, nonindividuality, nonlocality, and the loss of determinism. However, the apparatuses which measure and register the properties of the quantum system as well as the human observer, who reads the observed data are parts of the classical world that is free from the quantum physical absurdities mentioned. For describing and interpreting quantum physics we can use common language and classical logic.We will query this doctrine here for several reasons. Firstly, during the last decades it became obvious that quantum mechanics is not restricted to the microscopic world of nuclei, atoms, and molecules but can be applied also to 1

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“…180] says, "the orthodox interpretation begins to sound like 'mumbo-jumbo', a collection of empty words that indicate only that we really do not understand quantum theory", and quotes Gell-Mann [117] to the effect that "The fact that an adequate philosophical presentation has been so long delayed is no doubt caused by the fact that Niels Bohr brainwashed a whole generation of theorists into thinking that the job was done fifty years ago". 260 …”

Section: A Few Commentators On Bohrmentioning

confidence: 99%