Abstract
Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions.
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Notes
What is special for a classical system, is that ‘observables’ can be described by functions on the state space. This is the main reason that, a measurement corresponding to such an observable, can be left out of the description of the theory ‘in case one is not interested in the change of state provoked by the measurement’, but ‘only interested in the values of the observables’. It is in this respect that the situation is very different for a quantum system. Observables can also be described, as projection valued measures on the Hilbert space, but ‘no definite values can be attributed to such a specific observable for a substantial part of the states of the system’. For a quantum system, contrary to a classical system, it is not true that ‘either a property or its negation is actual’.
Einstein designed, in the by now famous EPR ‘paper’ [13], a definition of when a physical quantity could be considered an element of physical reality within quantum mechanics. By using this definition Einstein, Podolsky and Rosen argued against the completeness of the quantum theory. For a general discussion see [16].
In an analogous fashion as Décio Krause has developed a Q-set theory which accounts for indistinguishable particles with a formal calculus “right from the start” [21].
These words, according to Heisenberg himself, led him to the development of the indetermination principle in his foundational paper of 1927.
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Acknowledgements
The authors wish to thank an anonymous referee for his/her careful reading of our manuscript and useful comments. This work was partially supported by the following grants: Ubacyt 2011/2014 635, FWO project G.0405.08 and FWO-research community W0.030.06. CONICET RES. 4541-12 (2013–2014).
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da Costa, N., de Ronde, C. The Paraconsistent Logic of Quantum Superpositions. Found Phys 43, 845–858 (2013). https://doi.org/10.1007/s10701-013-9721-9
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DOI: https://doi.org/10.1007/s10701-013-9721-9