We argue that the notion of pure sate within Standard Quantum Mechanics is presently applied within the specialized literature in relation to two mutually inconsistent definitions. While the first provides a basis-dependent definition which makes reference to the certain prediction of measurement outcomes, the latter provides a purely abstract invariant definition which lacks operational content. In this work we derive a theorem which exposes the serious inconsistencies existent within these two incompatible definitions of purity.

In de Ronde and Massri it was argued against the orthodox definition of quantum entanglement in terms of pure and separable states. In this paper we attempt to discuss how the logos categorical approach to quantum mechanics is able to provide an objective formal account of the notion of entanglement—completely independent of both purity and separability—in terms of the potential coding of intensive relations and effective relations. We will show how our novel redefinition allows us to provide an anschaulich content (...) to the notion of entanglement, erasing in this way the “spookiness” still present within its orthodox understanding in terms of space-time separated collapse particles. (shrink)

This paper presents and critically discusses the “logos approach to quantum mechanics” from the point of view of the current debates concerning the relation between metaphysics and science. Due to its alleged direct connection with quantum formalism, the logos approach presents itself as a better alternative for understanding quantum mechanics than other available views. However, we present metaphysical and methodological difficulties that seem to clearly point to a different conclusion: the logos approach is on an epistemic equal footing among alternative (...) realist approaches to quantum mechanics. (shrink)

In recent years, much research has been devoted to exploring contextuality in systems that are not strictly quantum, like classical light, and many theory-independent frameworks for contextuality analysis have been developed. It has raised the debate on the meaning of contextuality outside the quantum realm, and also on whether—and, if so, when—it can be regarded as a signature of non-classicality. In this paper, we try to contribute to this debate by showing a very simple “thought experiment” or “toy mechanism” where (...) a classical object (i.e., an object obeying the laws of classical physics) is used to generate experimental data violating the KCBS inequality. As with most thought experiments, the idea is to simplify the discussion and to shed light on issues that in real experiments, or from a purely theoretical perspective, may be cumbersome. We give special attention to the distinction between classical realism and classicality, and to the contrast between contextuality within and beyond quantum theory. (shrink)

In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed in order to allow a restoration of a classical “common sense” understanding of what there is. In particular, we discuss a solution to (...) Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM —originally proposed by Isham, Butterfiled and D ̈oring— in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological reading of the quantum formalism and the need to restore an objective conceptual representation and understanding of quantum physical reality. (shrink)

In this paper we consider the notion of quantum entanglement from the perspective of the logos categorical approach [26, 27]. Firstly, we will argue that the widespread distinctions, on the one hand, between pure states and mixed states, and on the other, between separable states and entangled states, are completely superfluous when considering the orthodox mathematical formalism of QM. We will then argue that the introduction of these distinctions within the theory of quanta is due to another two completely unjustified (...) metaphysical presuppositions, namely, the idea that there is a “collapse” of quantum states when being measured and the idea that QM talks about “elementary particles”. At distance from these distinctions and taking the logos approach as a standpoint, we will propose an objective formal account of the notion of entanglement in terms of potential coding which introduces the necessary distinction between intensive relations and effective relations. We will also discuss how this new definition of entanglement provides an anschaulich content to this —supposedly “spooky”— quantum relational feature. (shrink)

In this paper we attempt to consider quantum superpositions from the perspective of the logos categorical approach presented in [26]. We will argue that our approach allows us not only to better visualize the structural features of quantum superpositions providing an anschaulich content to all terms, but also to restore —through the intensive valuation of graphs and the notion of immanent power— an objective representation of what QM is really talking about. In particular, we will discuss how superpositions relate to (...) some of the main features of the theory of quanta, namely, contextuality, paraconsistency, probability and measurement. (shrink)

In this paper we investigate the history of relationalism and its present use in some interpretations of quantum mechanics. In the first part of this article we will provide a conceptual analysis of the relation between substantivalism, relationalism and relativism in the history of both physics and philosophy. In the second part, we will address some relational interpretations of quantum mechanics, namely, Bohr’s relational approach, the modal interpretation by Kochen, the perspectival modal version by Bene and Dieks and the relational (...) interpretation by Rovelli. We will argue that all these interpretations ground their understanding of relations in epistemological terms. By taking into account the analysis on the first part of our work, we intend to highlight the fact that there is a different possibility for understanding quantum mechanics in relational terms which has not been yet considered within the foundational literature. This possibility is to consider relations in ontological terms. We will argue that such an understanding might be capable of providing a novel approach to the problem of representing what quantum mechanics is really talking about. (shrink)

In this paper we we will argue against the orthodox definition of quantum entanglement which has been implicitly grounded on several widespread presuppositions which have no relation whatsoever to the formalism of QM. We will show how these presuppositions have been introduced through a naive interpretation of the quantum mathematical structure which assumes dogmatically that the theory talks about "small particles" represented by pure states which suddenly "collapse" when a measurement takes place. In the second part of this paper we (...) will present a non-collapse approach to QM which makes no use whatsoever of particle metaphysics, escaping the need to make reference to space-time separability or the restriction to certain predictions of definite valued binary properties. Our paper ends up concluding the essential need to redefine the notion of quantum entanglement, at least in the cases of: i) non-collapse interpretations of QM; or, ii) any other interpretation which abandons the idea that QM makes reference to "small particles". (shrink)

In this paper we compare two different notions of 'power', both of which attempt to provide a realist understanding of quantum mechanics grounded on the potential mode of existence. For this propose we will begin by introducing two different notions of potentiality present already within Aristotelian metaphysics, namely, irrational potentiality and rational potentiality. After discussing the role played by potentiality within classical and quantum mechanics, we will address the notion of causal power which is directly related to irrational potentiality and (...) has been adopted by many interpretations of QM. We will then present the notion of immanent power which relates to rational potentiality and argue that this new concept presents important advantages regarding the possibilities it provides for understanding in a novel manner the theory of quanta. We end our paper with a comparison between both notions of 'power', stressing some radical differences between them. (shrink)

Quantum contextuality and its ontological meaning are very controversial issues, and they relate to other problems concerning the foundations of quantum theory. I address this controversy and stress the fact that contextuality is a universal topological property of quantum processes, which conflicts with the basic metaphysical assumption of the definiteness of being. I discuss the consequences of this fact and argue that generic quantum potentiality as a real physical indefiniteness has nothing in common with the classical notions of possibility and (...) counterfactuality, and that also it reverses, in a way, the classical mirror-like relation between actuality and definite possibility. (shrink)