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Olimpia Lombardi

Olimpia Lombardi
  • Senior Researcher
  • Superior Researcher at CONICET-National Scientific and Technical Research Council

About

177
Publications
125,139
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2,287
Citations
Current institution
CONICET-National Scientific and Technical Research Council
Current position
  • Superior Researcher
Additional affiliations
January 2008 - present
University of Buenos Aires
Position
  • Professor & Researcher

Publications

Publications (177)
Article
En este trabajo, proponemos un marco metafísico naturalista para una variante del posibilismo basada en una concepción bilocalizada de la modalidad. Luego de revisar problemas característicos de posiciones alternativas, exploramos la aplicación de este marco al caso de la interpretación modal-hamiltoniana de la mecánica cuántica. Finalmente, revisa...
Article
Full-text available
The concept of molecular structure is one of the most important concepts of chemistry. In fact, molecular structure is closely related to the concept of chemical substance and its set of properties, and it is the main factor in the explanation of reactivity. In fact, much of the behavior of substances is explained in terms of the structure of their...
Article
Full-text available
Although the electron density can be calculated with the formal resources of quantum mechanics, in physics it does not play the leading role that the quantum state does. In contrast, the concept of electron density is central in quantum chemistry. There is no doubt about how the electron density is computed in terms of the wave function of an atom...
Article
Full-text available
In the debate about the direction of time in physics, the concept of time reversal has been central. Tradition has it that time-reversal invariant laws are sufficient to state that the direction of time is non-fundamental or emergent. In this paper, we review some of the debates that have gravitated around the concept of time reversal and its relat...
Article
Full-text available
La figura de Roberto Torretti ha sido un faro para la filosofía de la ciencia internacional y en particular para la latinoamericana. En este comentario se recordarán algunos de sus más importantes trabajos. Su obra conjuga de un modo inmejorable erudición y sensibilidad filosófica con conocimiento científico experto.
Chapter
To which ontological category do quantum systems belong? Although we usually speak of particles, it is well known that these peculiar items defy several traditional metaphysical principles. In the present chapter these challenges will be discussed in the light of certain distinctions usually not taken into account in the debate about the ontologica...
Chapter
After the preeminence of logical positivism/empiricism during the most part of twentieth century, during the last decades many authors began to recognize the relevance of the Kantian thought for present-day philosophy of science. This chapter follows this general trend, adopting a realist reading of Kantian teachings. On this basis, I will delineat...
Article
Full-text available
While entanglement in the case of distinguishable particles is clearly understood, in the case of indistinguishable particles, there is still a wide debate regarding basic conceptual issues. Here, I will address two such issues. First, the debate almost always rests on a differentiated treatment of the cases of distinguishability and indistinguisha...
Article
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The identity criteria proposed by traditional metaphysics had to undergo a profound revision when quantum mechanics entered the scene with its characteristic indistinguishable systems. In this paper we apply Oscar Nudler's model of controversial spaces to analyze the controversy over identity in the field of quantum mechanics and propose the introd...
Article
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In previous works, an ontology of properties for quantum mechanics has been pro�posed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the tradition...
Article
Full-text available
In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditiona...
Article
Full-text available
En este artículo se argumenta que la existencia de leyes invariantes frente a inversión temporal no es condición indispensable para la existencia de la flecha del tiempo. Esta última puede definirse como una propiedad global y geométrica del espacio-tiempo que no se basa en consideraciones entrópicas ni requiere de la existencia de leyes no invaria...
Article
Full-text available
In the literature on the interpretation of quantum mechanics, not many works attempt to adopt a proactive perspective aimed at seeing how different interpretations can enrich each other through a productive dialogue. In particular, few proposals have been devised to show that different approaches can be clarified by comparing them, and can even com...
Chapter
Full-text available
This chapter explores the role played by the Quantum Theory of Atoms in Molecules (QTAIM) in the relation between molecular chemistry and quantum mechanics, in the conceptual framework of coarse graining. It is shown that the electron density is a coarse-grained magnitude when considered from the viewpoint of quantum mechanics. As a consequence, al...
Article
Full-text available
According to classical molecular chemistry, molecules have a structure, that is, they are sets of atoms with a definite arrangements in space and held together by chemical bonds. The concept of molecular structure is central to modern chemical thought given its impressive predictive power. It is also a very useful concept in chemistry education, du...
Preprint
Full-text available
Trabajos sobre la tabla periódica de los elementos desde la historia y filosofía de la química.
Article
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In the discourse of quantum mechanics it is usual to say that non-commuting observables cannot have definite values at the same time, or that they cannot be simultaneously measured. But, what does the term ‘cannot’ mean in this context? Does it stand for impossible? Should Heisenberg’s principle be read in terms of uncertainty or of indeterminacy?...
Article
Full-text available
The aim of the present article is to address the problem of entanglement in the case of indistinguishable particles from a perspective based on the algebraic formalism of quantum mechanics, which is the natural formal counterpart of an ontology of properties, devoid of the ontological category of individual. On the basis of this perspective, an alg...
Article
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Some authors, inspired by the theoretical requirements for the formulation of a quantum theory of gravity, proposed a relational reconstruction of the quantum parameter-time—the time of the unitary evolution, which would make quantum mechanics compatible with relativity. The aim of the present work is to follow the lead of those relational programs...
Preprint
Full-text available
In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for treating aggregates of items that do not belong to the traditional ca...
Conference Paper
Full-text available
Although the interpretation of the concept of information is not clear, even in the classical framework, new interpretive problems have arisen with the advent of the so-called quantum information, which combine the difficulties in understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself...
Article
Full-text available
In a recent article entitled “The problem of molecular structure just is the measurement problem”, Alexander Franklin and Vanessa Seifert argue that insofar as the quantum measurement problem is solved, the problems of molecular structure are resolved as well. The purpose of the present article is to show that such a claim is too optimistic. Althou...
Article
Full-text available
In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for treating aggregates of items that do not belong to the traditional ca...
Article
Full-text available
By moving away from the traditional reductionist reading of the quantum theory of atoms in molecules (QTAIM), in this paper we analyze the role played by QTAIM in the relationship between molecular chemistry and quantum mechanics from an emergentist perspective. In particular, we show that such a relationship involves two steps: an intra-domain eme...
Article
Full-text available
Although Bohr’s Correspondence Principle (CP) played a central role in the first versions of quantum mechanics, its original version seems to have no present-day relevance. The purpose of the present article is to show that the CP, with no need of being interpreted in terms of the quantum-to-classical limit, still plays a relevant role in the under...
Article
In this article, we reconstruct the Frauchiger and Renner argument, taking into account that the assertions of the argument are made at different times. To do this, we use a formalism of quantum histories, namely the Theory of Consistent Histories. We show that the supposedly contradictory conclusion of the argument requires computing probabilities...
Preprint
In this article we reconstruct the Frauchiger and Renner's argument [1] taking into account that the assertions of the argument are made at different times. In order to do that, we use a formalism that allows dealing with quantum properties at different times: the Theory of Consistent Histories. We show that the supposedly contradictory conclusion...
Preprint
Full-text available
In April 2016, Daniela Frauchiger and Renato Renner published an article online in which they introduce a Gedankenexperiment that led them to conclude that single-world interpretation of quantum theory cannot be self-consistent. In a new version of the paper, published in September 2018, the authors moderate their original claim by concluding that...
Article
Full-text available
Perhaps the hottest topic in the philosophy of chemistry is that of the relationship between chemistry and physics. The problem finds one of its main manifestations in the debate about the nature of molecular structure, given by the spatial arrangement of the nuclei in a molecule. The traditional strategy to address the problem is to consider chemi...
Article
Full-text available
The problem of the reduction of chemistry to physics has been traditionally addressed in terms of classical structural chemistry and standard quantum mechanics. In this work, we will study the problem from the perspective of the Quantum Theory of Atoms in Molecules (QTAIM), proposed by Richard Bader in the nineties. The purpose of this article is t...
Article
Full-text available
Currently, there are almost as many conceptions of emergence as authors who address the issue. Most literature on the matter focuses either on discussing, evaluating and comparing particular contributions or accounts of emergence, or on assessing a particular case study. Our aim in this paper is rather different. We here set out to introduce a dist...
Article
Full-text available
Las dificultades encontradas para pensar la química a partir de categorías que la filosofía había articulado tradicionalmente para la física tuvo como consecuencia la emergencia de un fértil campo de problemas específicos –la filosofía de la química–. Recientemente, nuevos desafíos surgen al analizar el nanomundo desde una perspectiva filosófica. E...
Article
Full-text available
In April 2016, Daniela Frauchiger and Renato Renner published an article online in which they introduce a Gedankenexperiment that led them to conclude that single-world interpretations of quantum theory cannot be self-consistent. In a new version of the paper, published in September 2018, the authors moderate their original claim by concluding that...
Preprint
Full-text available
According to classical molecular chemistry, molecules have a structure, that is, they are sets of atoms with a definite arrangements in space and held together by chemical bonds. The concept of molecular structure is central to modern chemical thought given its impressive predictive power. It is also a very useful concept in chemistry education, du...
Article
Full-text available
El objetivo del presente artículo es proponer una nueva interpretación del concepto de información en contextos comunicacionales: una interpretación físicocausal. Apelando a las teorías manipulabilistas de la causación, principalmente ensu versión intervencionista, buscaremos mostrar que la información comunicacional es una propiedad física que pod...
Article
Full-text available
Integrated Information Theory (IIT) intends to provide a principled theoretical approach able to characterize consciousness both quantitatively and qualitatively. By starting off identifying the fundamental properties of experience itself, IIT develops a formal framework that relates those properties to the physical substratum of consciousness. One...
Article
Full-text available
The aim of this paper is to offer a new interpretation of information: a causal.phvsical interpretation. We shall turn to manipulability theories of causation (mainly to its interventionist version) in order to show that "information" refers to a physical property, which we can manipulate to bring about communication situat ions. According to our a...
Article
In this paper, we shall describe a new account of information in communicational contexts, namely, a causal-deflationary one. Our approach draws from Timpson's deflationary view and supplies the field of philosophy of information with new tools that will help to clarify the underlying structure of communication: information is an abstract entity th...
Article
Full-text available
El objetivo del presente trabajo consiste en arrojar nueva luz sobre el problema de la irreversibilidad, señalando que en las discusiones sobre el tema no se ha tomado en cuenta suficientemente que la relación entre termodinámica y mecánica involucra relaciones teóricas en dos niveles: un nivel intra-teórico y un nivel inter-teórico. Intentaremos p...
Article
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In his recent Editorial Article, Jeffrey Seeman (2017) calls for the promotion of collaborative work among different disciplines, focusing on the case of the interaction between chemistry, the history of chemistry and the philosophy of chemistry. From a general viewpoint, it is difficult to disagree with this claim; moreover, the interest of scient...
Article
In spite of being a well articulated proposal, the theory of quantum histories (TQH), in its different versions, suffers from certain difficulties that have been pointed out in the literature. Nevertheless, two facets of the proposal have not been sufficiently stressed. On the one hand, it is a non-collapse formalism that should be technically appr...
Article
Full-text available
Two recent papers appeared in FOOP disagree regarding the role played by decoherence in quantum physics. On the one hand, Elise Crull considers that decoherence, by itself, solves many conceptual problems in quantum physics, with no need of interpretative considerations. On the other hand, Antonio Vassallo and Michael Esfeld reply by correctly clai...
Book
Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science which provides an up-to-date examination of developments in this field. The authors provide coherent definitions and theories of information, taking clearly defined approaches to considering information in connection with quantum mechan...
Article
Full-text available
The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was produced. Nevertheless, the work on the subject is, even at present, a superposition of several approaches expressed in different...
Chapter
Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science which provides an up-to-date examination of developments in this field. The authors provide coherent definitions and theories of information, taking clearly defined approaches to considering information in connection with quantum mechan...
Chapter
Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science which provides an up-to-date examination of developments in this field. The authors provide coherent definitions and theories of information, taking clearly defined approaches to considering information in connection with quantum mechan...
Article
Full-text available
Although during the last decades the philosophy of chemistry has greatly extended its thematic scope, the main difficulties appear in the attempt to link the chemical description of atoms and molecules and the description supplied by quantum mechanics. The aim of this paper is to analyze how the difficulties that threaten the continuous conceptual...
Chapter
Full-text available
The problem of the classical limit of quantum mechanics consists in explaining how the classical realm "emerges" from the quantum domain. Although along the history of quantum mechanics the problem has been addressed from many different perspectives, at present it is recognized that the classical limit also involves some kind of physical process, w...
Article
Full-text available
Resumen: A partir del fin de la Segunda Guerra Mundial se extiende, partiendo de los EEUU, una comprensión y uso de la ciencia subordinadas al proceso de producción. Esto determina el avance, sobre el campo científico, de un proceso de administración de la investigación y de la formación por parte del Estado y, a través de él, del aparato productiv...
Article
Full-text available
This open letter is the result of the intense epistolary exchange I had with Prof. Torretti for many years, which has highly enriched my philosophical thought. Here I point out our agreement in adopting a Kantian perspective, and in the acknowledgement of the role played by the pragmatic dimension in science. However, we drift apart regarding the w...
Article
Full-text available
Esta carta abierta es el resultado del intenso intercambio epistolar que he mantenido con el Prof. Torretti durante muchos años, y a través del cual me he enriquecido ampliamente en el pensar filosófico. Aquí señalo nuestros acuerdos en la adopción de una perspectiva de inspiración kantiana, y en el reconocimiento del papel que juega la dimensión p...
Article
Full-text available
Esta carta abierta es el resultado del intenso intercambio epistolar que he mantenido con el Prof. Torretti durante muchos años, y a través del cual me he enriquecido ampliamente en el pensar filosófico. Aquí señalo nuestros acuerdos en la adopción de una perspectiva de inspiración kantiana, y en el reconocimiento del papel que juega la dimensión p...
Article
Full-text available
The modal-Hamiltonian interpretation belongs to the modal family of interpretations of quantum mechanics. By endowing the Hamiltonian with the role of selecting the subset of the definite-valued observables of the system, it accounts for ideal and non-ideal measurements, and also supplies a criterion to distinguish between reliable and non-reliable...
Article
Full-text available
In the present paper we develop different arguments to show that there are no reasons to consider that there exists quantum information as qualitatively different than Shannon information. There is only one kind of information, which can be coded by means of orthogonal or non-orthogonal states. The analogy between Shannon’s theory and Schumacher’s...
Article
Full-text available
In the present paper we address the problem of optical isomerism embodied in the socalled “Hund’s paradox”, which points to the difficulty to account for chirality by means of quantum mechanics. In particular, we explain the answer to the problem proposed by the theory of decoherence. The purpose of this article is to challenge this answer on the b...
Article
Full-text available
Resumo This article focuses on the relationship between knowledge and representation. We consider the difficulties of the approaches that try to justify the representative character of models. We point out that the attempts to account for representation from a perspective that does not include the agent as a constitutive element lack enough philos...
Article
Full-text available
La filosofía de la información ha experimentado un enorme auge en los últimos años, consolidándose como un ámbito de indagación filosófica autónomo. Su tema de estudio, el concepto de información, es uno de los términos más comunes y extendidos en nuestros días, abarcando ámbitos tan disímiles como el lenguaje cotidiano y la mecánica cuántica. Esta...
Preprint
Full-text available
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. But in the last decades, several attempts to interpret it from a realist viewpoint have been proposed. Among them, modal interpretations supply a realist non-collapse account, a...
Article
Full-text available
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under the Galilean group, the invariance is usually not discussed in the case of the interpretation of the theory. Thi...
Article
Full-text available
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. However, in the last decades, several attempts to interpret it from a realist viewpoint have been proposed. Among them, modal interpretations supply a realist non-collapse accou...
Chapter
The ontological autonomy of the chemical world has been explicitly defended from a Kantian-rooted ontological pluralism, according to which the ontological priority of the physical world turns out to be a mere metaphysical prejudice. From the pluralist viewpoint, concepts like bonding, molecular shape and orbital refer to entities belonging to the...
Book
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¿Está nuestra realidad inexorablemente determinada o se encuentra librada al azar y la sorpresa? En el presente libro la cuestión del determinismo es abordada desde ámbitos muy diversos, desde la mecánica cuántica, la teoría del caos y la química microscópica en el área de las ciencias físicoquímicas, hasta la genética, la biología evolutiva del de...
Article
Full-text available
Although the use of the word ‘information’, with different meanings, can be traced back to antique and medieval texts (see Adriaans 2013), it is only in the 20th century that the term begins to acquire the present-day sense. Nevertheless, the pervasiveness of the notion of information both in our everyday life and in our scientific practice does no...
Article
Full-text available
The aim of the present paper is to supply an elucidation of the concept of information in the communicational context. For this purpose, two traditional interpretations of the concept of information, the epistemic and the physical interpretations, will be distinguished, and their specific problems will be considered. In particular, whereas the epis...
Article
Full-text available
The aim of this article is to offer a conceptual analysis of the notion of information, on the basis of the way in which it is defined by the theories of Claude Shannon and of Benjamin Schumacher. Against the position according to which there are two kinds of information of different natures, a classical information and a quantum information (defin...
Article
Full-text available
En el presente artículo abordaremos la cuestión del determinismo ontológico en física. Proponemos una elucidación del concepto de posibilidad que resulte útil para tratar el problema del determinismo ontológico en física, y mediante la cual pueda interpretarse el concepto de probabilidad de un modo signifi cativo para la práctica de la física teóri...
Article
Full-text available
In the field of the philosophy of physics, Christopher Timpson has published several works where he accurately designs an interpretation of the technical concept of information. In particular, he proposes a deflationary view about information, according to which the term ‘information’ is an abstract noun and, as a consequence, information is not pa...
Article
Full-text available
Focusing on Shannon information, this article shows that, even on the basis of the same formalism, there may be different interpretations of the concept of information, and that disagreements may be deep enough to lead to very different conclusions about the informational characterization of certain physical situations. On this basis, a pluralist v...
Article
Full-text available
The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearl...
Article
Full-text available
The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individ...
Article
Full-text available
The aim of this paper is to review a new perspective about decoherence, according to which formalisms originally devised to deal just with closed or open systems can be subsumed under a closed-system approach that generalizes the traditional account of the phenomenon. This new viewpoint dissolves certain conceptual difficulties of the orthodox open...
Article
In the present paper we develop different arguments to show that there are no reasons to consider that there exists quantum information as qualitatively different than Shannon information. There is only one kind of information, which can be coded by means of orthogonal or non-orthogonal states. The analogy between Shannon’s theory and Schumacher’s...
Conference Paper
Full-text available
Conscientes de que los entornos de educación virtuales acotan las posibilidades de orientar a los educandos en la formación de las capacidades necesarias para el proceso de aprendizaje y su desarrollo epistémico, nos proponemos diseñar un Desarrollo Experimental tendiente a salvar esta dificultad. Partiremos de la consideración del perfil de gradu...
Conference Paper
Partiremos de la consideración del perfil de graduados, procurado por los planes de las carreras, el Proyecto Institucional y las recomendaciones del CONFEDI, para determinar las capacidades cognitivas necesarias para alcanzarlo, por parte de nuestros alumnos. Caracterizaremos estas capacidades en términos psicopedagógicos y las vincularemos con es...
Chapter
The correlations between the outcomes of consecutive measurements are one of those issues so deeply entrenched in the quantum knowledge of physicists that, in many cases, they use them to test the acceptability of any proposal of interpretation of the theory. The aim of the present article is to show the serious obstacles that modal interpretations...
Article
Full-text available
Our purpose in this paper is to delineate an ontology for quantum mechanics that results adequate to the formalism of the theory. We will restrict our aim to the search of an ontology that expresses the conceptual content of the recently proposed modal-Hamiltonian interpretation, according to which the domain referred to by non-relativistic quantum...
Article
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The many-faced relationship between chemistry and physics is one of the most discussed topics in the philosophy of chemistry. In his recent book Reducing Chemistry to Physics. Limits, Models, Consequences, Hinne Hettema (Reducing chemistry to physics. Limits, models, consequences, Rijksuniversiteit Groningen, Groningen, 2012) conceives this relatio...
Article
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En su libro Time´s Arrow and Archimedes’ Point, Huw Price critica los argumentos de algunos cosmólogos contemporáneos acerca del origen cosmológico de la flecha del tiempo, quienes supuestamente no logran adoptar un punto de vista atemporal. En este artículo se analizan las críticas de Price a la propuesta de Stephen Hawking, argumentando que, si b...
Article
In the present article we approach the issue of ontological determinism in physics. We propose a clarification of the concept of possibility that is useful for addressing this issue. By means of this clarification, the concept of probability can be given an interpretation that is meaningful for the practice of theoretical physics. Finally, these cl...
Chapter
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En una caracterización muy general y deliberadamente vaga, reduccionismo es la posición filosófica que afirma que los ítems de un cierto ámbito pueden obtenerse, en algún sentido, a partir de los ítems de otro ámbito. La idea de reducción, estrechamente vinculada con el ideal de unificación, atraviesa el pensamiento filosófico occidental desde sus...
Article
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The general question to be considered in this paper points to the nature of the world described by chemistry: what is macro-chemical ontology like? In particular, we want to identify the ontological categories that underlie chemical discourse and chemical practice. This is not an easy task, because modern Western metaphysics was strongly modeled by...
Article
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This article focuses on the relationship between microevolution and macroevolution. The main purpose is to argue that up to the present time in the consolidation of the evolutionary synthesis macroevolution has been always conceived as dependent on microevolution. Such dependence was very clear in the synthesis, but seems to have been left aside by...
Article
In this chapter, we argue that both the problem of quantum indistinguishability in the philosophy of physics and the problem of identity in structures in the philosophy of mathematics are identical in a certain relevant sense; i.e., that they are two instances of the same general problem. This favors the idea that certain ontological questions are...
Article
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According to the environment-induced approach to decoherence (EID), the split of the Universe into the degrees of freedom which are of direct interest to the observer (the system) and the remaining degrees of freedom (the environment) is absolutely essential for decoherence. However, the EID approach offers no general criterion for deciding where t...
Article
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El propósito del presente trabajo consiste en abordar la pregunta por la ontología de la química cuántica. Para ello nos concentraremos en el concepto de enlace químico desde la perspectiva de los dos enfoques a través de los cuales la ecuación de Schrödinger se aplica a los sistemas químicos moleculares: la teoría del enlace de valencia (EV) y la...
Article
Full-text available
Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems but, since its actualization rule applies to closed systems, it seems to stand at odds of EID...
Article
Full-text available
Modal interpretations are non-collapse interpretations, where the quantum state of a system describes its possible properties rather than the properties that it actually possesses. Among them, the atomic modal interpretation (AMI) assumes the existence of a special set of disjoint systems that fixes the preferred factorization of the Hilbert space....

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