Several experiments have suggested that the complete indistinguishability of quantum systems is to be considered a real phenomenon. Experiments such as the HOM effect, the existence of BECs, the path identity cases, and many others are physical realities of today. Physicists `explain’ these phenomena using different models, such as Bohmian mechanics, relational quantum mechanics or the QBism approach. Most of these models are constructed within a standard mathematical framework, meaning standard mathematics, where all things can, even if only in principle, be distinguished from one another, so complete indistinguishability can only be mimicked. These approaches may work for physical purposes but are debatable regarding logical and metaphysical questions. If we accept that such questions are at least part of the philosophical aspect of quantum physics, then we are authorised to analyse them and try to offer an alternative. Looking for an alternative, we consider Alain Aspect’s and Anton Zeilinger’s views about quantum realism, opting for Aspect’s acceptance of some kind of reality behind the wave-function, while Zeilinger suggests that everything comes from information. In our opinion, the case is the opposite: it is information that comes from the existence of things. The aim of this paper is to justify why we think that the underlying reality (in Aspect’s sense) can be seen as a quantum ontology of non-individuals.
Several experiments have suggested that the complete indistinguishability of quantum systems is to be considered a real phenomenon. Experiments such as the HOM effect, the existence of BECs, the path identity cases, and many others are physical realities of today. Physicists `explain’ these phenomena using different models, such as Bohmian mechanics, relational quantum mechanics or the QBism approach. Most of these models are constructed within a standard mathematical framework, meaning standard mathematics, where all things can, even if only in principle, be distinguished from one another, so complete indistinguishability can only be mimicked. These approaches may work for physical purposes but are debatable regarding logical and metaphysical questions. If we accept that such questions are at least part of the philosophical aspect of quantum physics, then we are authorised to analyse them and try to offer an alternative. Looking for an alternative, we consider Alain Aspect’s and Anton Zeilinger’s views about quantum realism, opting for Aspect’s acceptance of some kind of reality behind the wave-function, while Zeilinger suggests that everything comes from information. In our opinion, the case is the opposite: it is information that comes from the existence of things. The aim of this paper is to justify why we think that the underlying reality (in Aspect’s sense) can be seen as a quantum ontology of non-individuals.
The topics of identity, individuality and indiscernibility had already entered the domain of the philosophy of physics, mainly in what respects the philosophy of quantum theories. In this paper, I present the main ideas of an underlying metaphysics that considers the basic entities of quantum physics as non-individuals, that is, as entities to which the standard theory of identity of classical logic and standard mathematics (set theory) does not apply. Two things must be emphasized: the first is that we pursue Erwin Schrödinger’s ideas that the notion of identity (or sameness ) does not apply to quantum things; the second is to follow Heinz Post’s claim that the non-individuality of quantum entities ‘must be introduced right at the start’ and not by taking individuals and making them pretend to be non-individuals ‘by hand’, say by confining them to non-rigid structures. Thus, this paper should be regarded as an attempt to justify the metaphysics of non-individuals and the logical systems that cope with them, although these systems are here only referred to. We also answer some criticisms that have been directed to such a view. The paper is directed to an audience of both physicists interested in foundations and philosophers of physics. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.
In the non-reflexive formulation of quantum physics, attention is given to a metaphysical view of quantum objects (q-objects) as non-individuals, characterised as entities to which the standard notion of identity lacks sense. The reference to the nature of q-objects is usually omitted in other interpretations and the most we can find is some vague reference to “to each [quantum] system we associate a Hilbert space”, and nothing more is said about them; we need to infer from the theory their characteristics, and it gives us several alternatives. One of them, to be justified here in broad aspects, is the non-individual view. It is important to enlighten that we are not trying to just find a way to deal with quantum entities but to defend a possible ontology of non-individuals, which can be applied also to ‘particles’ arising from quantum fields. Our account is based on two assumptions: (i) the ‘classical theory of identity’ does not apply to q-objects, and (ii) their non-individuality must be attributed from the start, that is, as a primitive notion and not ‘made a posteriori’ say by assuming symmetry principles. The underlying logic is called non-reflexive because the reflexive law of identity ∀x(x=x) is supposed not to hold for q-objects. Since all the details demand a lot of space, here we only sketch and justify our view. The references provide a more detailed account.
The notion of an individual and the related issues on individuation are topics that appear in the philosophical discussion ever since the antiquity. The idea of an individual thing is intuitively clear: an individual is something of a specific kind that is a unity, having its own identity, and being so that it is possible at least in principle to discern it from any other individual, even of similar species. But when we try to leave the intuitive realm and push this idea to a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical contexts. In this work, we shall be concerned with some aspects of this intuitive concept of an individual and on some related facts about individuation taken from recent discussions that arose ever since the inception of quantum theory, pushing the discussion to a “logical” view, which in our opinion is still lacking in the usual debates on such issues. In the final part of the paper, we propose a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and we try to justify such a move. In most of the uses of the expression “quantum theory”, we shall not make explicit the distinction between the non-relativistic and the relativistic approaches, although they of course are quite different, for we think that the problems as we shall present them appear in both versions. But, as the text goes, the context will distinguish between them and these questions will become clear to the reader.
In this article we try to justify a way of looking for an alternative approach to quantum mechanics based on a non-classical logic. The main motivation is both to accommodate a metaphysical view according to which quantum objects are non-individuals and to introduce, so to say, these objects within the formalism, for as we know, the usual formalism treats of states of quantum systems and not (directly) of quantum systems properly speaking. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. Our way of looking to these concepts motivate us to construct a metaphysical view according to which quantum objects do not present identity criterion (they are ‘non-individuals’), and then we try to construct a quantum theory based on such a view, which is grounded on a non-classical logic, termed non-reflexive. From the formal point of view, the main motivation comes from the fact that in using classical logic and classical set theory (such as ZFC), we are necessarily committed to individuals, and non-individuals can be considered only by assuming ‘strong’ symmetry principles, which mask the basic idea involving non-individuality. In the core of the article, due to questions of space, only the main philosophical arguments are presented, but in two appendixes we outline, firstly, quasi-set theory, the non-reflexive mathematical framework that sustain our view, and a bottom-top construction of a quantum mechanics based on quasi-set theory.
According to scientific realism, science gives us an approximately true description of what the world is like. But what does it mean? In this chapter, we focus on the ontological and metaphysical aspects of this discussion. That is, we are concerned with the following questions: what there is, according to our best scientific theories? And how are these things that theories say exist? We start from the assumption that a genuine scientific realism must deal with these issues. Taking non-relativistic quantum mechanics as a case study, we discuss some of the challenges currently faced by a genuinely realistic stance. We argue, first, that in the ontological aspect, realists are in the same boat as science, that is, without sufficient epistemic justification to adopt the belief in the entities postulated by a single quantum theory, given that experience (currently) is not able to decide between rival theories; in the metaphysical aspect, realists also encounter problems with theory choice, given the possibility of associating more than one metaphysical theory with the description of the entities postulated by each quantum theory. The same goes for structuralist alternatives, since, even if we accept that scientific theories are committed to the existence of structures, but not objects, we still do not know what structures are, metaphysically. Finally, we move forward in the discussion with the meta-Popperian method, which serves to reduce the metaphysical alternatives associated with the ontological postulates of scientific theories. We may not know what the correct alternative is, but we have been able to progressively check which metaphysical alternatives are incompatible with each scientific theory.
Introduction It is not exaggeration to claim that one of the major divides in the foundations of non-relativistic quantum mechanics derives from the way physicists and philosophers understand the status of the wave function. On the instrumentalist side of the camp, the wave function is regarded as a mere instrument to calculate probabilities that have been established by previous measurement outcomes. On the other “realistic” camp, the wave function is regarded as a new physical entity or a physical field of some sort. While both sides agree about the existence of quantum “particles” (the so-called theoretical entities), and therefore reject the radical agnosticism about them preached by van Fraassen (1980), the various “realistic” (and consequently, instrumentalist) philosophies of quantum mechanics are typically formulated in different, logically independent ways, so their implications need to be further investigated. For instance, on the one hand it seems plausible to claim that a realistic stance about the wave function is not the only way to defend “realism” about quantum theory. One can support a “flash” or a “density-of-stuff ” ontology (two variants of GRW), or an ontology of particles with well-defined positions (as in Bohmian mechanics), as primitive ontologies for observer-independent formulations of quantum mechanics (Allori, Goldstein, Tumulka and Zanghí, 2008). “Primitive ontologies”, as here are understood, are not only a fundamental ground for other ontological posits, but also entail a commitment to something concretely existing in spacetime (see also Allori, 2013). On the other hand, however, it is still debated whether such primitive ontologies can be autonomous from some form of realism about the wave function (Albert, 1996). In order to discuss this problem, we begin with a preliminary clarification of the meaning of “realism” and “instrumentalism” in physics, which are often subject to ideological and abstract discussions that often have little to do with the practice of physics (Section 9.2).