Abstract
In this paper we argue that physical theories, including quantum mechanics, refer to some kind of ‘objects’, even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some ‘new kind’ while still adhering to the logico-mathematical framework we use to deal with classical objects. The use of such apparatus would hinder us from being in complete agreement with the ontological novelties the theories of quanta seem to advance. Thus, we join those who try to investigate a ‘logic of quantum mechanics’, but from a different point of view: looking for a formal foundation for a supposed new ontology. As a consequence of this move, we can revisit Einstein’s ideas on physical reality and propose that, by considering a new kind of object traditionally termed ‘non-individuals’, it is possible to sustain that they still obey some of Einstein’s conditions for ‘physical realities’, so that it will be possible to talk of a ‘principle of separability’ in a sense which is not in complete disagreement with quantum mechanics. So, Einstein’s departure from quantum mechanics might be softened at least concerning a form of his realism, which sees separated physical objects as distinct ‘physical realities’.
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Notes
Ian Thompson discussed several ‘quantum ontologies’, namely, the ontologies of particles, of events, of waves, of propensities and the wave-particle complementarity ontology, all of them with positive and negative points. But, as he says, all of them are ways of describing “different possibilities for the individual things which exist in the quantum world” (cf. [33, §4.3]). Here we shall leave the discussion about string-like theories out, like superstring theory for, as said Glashow, it does not exist as a theory yet: “[superstring theory] does not now exist, may never exist, and is probably not even a sensible concept” [17, p. 77].
The anonymous referee of this paper recalled that in quantum field theories the very notion of ‘object’ is left out in prol of a wider concept of field, to which the use non-standard logics would be in question. He is completely right, but even without entering in this discussion, which would demand another paper at least, the idea of a field was introduced to elaborate local physical laws and turned to be more comfortable than that of particles, the particles ‘arising’ from the fields in a certain way. We think that even by assuming fields in the basic ontology, the ontological discussion is still here as the cat’s grin, for we still accelerate ‘particles’ and speak of them. What rests is the necessity of distinguishing the mathematical model we are dealing with from the ‘objects’ (either particles or excited fields) we are assuming they represent.
The reader may be thinking in complementary propositions here. But we would like to say that we do not regard complementary propositions as being the negation of one another, strictly speaking. In [7], the idea is discussed, which will not be considered here, mainly because complementarity does not appear in classical physics.
Let us insist in the philosophical aspect of this necessity. There are interesting approaches to quantum mechanics given entirely within classical logic and mathematics; see [24]. In this framework, physics surely works, but the philosophical problems we are pointing out have no clear explanation.
See [14] for further references and comments.
In the particular case of physical theories, due to the need of higher-order languages, some further intricacies would have to be taken into account. We shall not bother with them here.
This point was not considered by the mentioned authors, but surely can be related to their ideas.
This idea was developed in a series of previous papers; see [13].
If relativistic concepts are to be considered, then even the cardinal of such a collection is to be questioned; see [34].
This interpretation can and has been challenged.
Howard calls our attention to a letter from Einstein to Eduard Study where he says that “I concede that the natural sciences concern the ‘real’, but I am still not a realist” [19, §5].
We would like to thank an anonymous referee for pressing this point.
This is associated to what Schrödinger [32] had anticipated, in saying that this kind of formulation “gets off on the wrong foot” by initially assigning object labels and then permuting them before extracting combinations of appropriate symmetry.
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A first version of this paper was prepared by the first author for a short course given in the Universidad del Valle, in Cali, Colombia, in 2005, during the Symposium “Einstein: científico, filósofo y humanista”. The text was corrected and revised in several parts, and the bibliography was updated. We thank the audience of the symposium for kind remarks and suggestions, and Ian Thompson for an earlier discussion about these issues.
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Krause, D., Arenhart, J.R.B. Separability and Non-Individuality: Is It Possible to Conciliate (At Least A Form Of) Einstein’s Realism with Quantum Mechanics?. Found Phys 44, 1269–1288 (2014). https://doi.org/10.1007/s10701-014-9808-y
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DOI: https://doi.org/10.1007/s10701-014-9808-y