The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with what we know about (...) classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided. (shrink)

We support the authors' claims, except that we point out that also quantum structure different from quantum probability abundantly plays a role in human cognition. We put forward several elements to illustrate our point, mentioning entanglement, contextuality, interference, and emergence as effects, and states, observables, complex numbers, and Fock space as specific mathematical structures.

We elaborate on a new interpretation of quantum mechanics which we introduced recently. The main hypothesis of this new interpretation is that quantum particles are entities interacting with matter conceptually, which means that pieces of matter function as interfaces for the conceptual content carried by the quantum particles. We explain how our interpretation was inspired by our earlier analysis of non-locality as non-spatiality and a specific interpretation of quantum potentiality, which we illustrate by means of the example of two interconnected (...) vessels of water. We show by means of this example that philosophical realism is not in contradiction with the recent findings with respect to Leggett’s inequalities and their violations. We explain our recent work on using the quantum formalism to model human concepts and their combinations and how this has given rise to the foundational ideas of our new quantum interpretation. We analyze the equivalence of meaning in the realm of human concepts and coherence in the realm of quantum particles, and how the duality of abstract and concrete leads naturally to a Heisenberg uncertainty relation. We illustrate the role played by interference and entanglement and show how the new interpretation explains the problems related to identity and individuality in quantum mechanics. We put forward a possible scenario for the emergence of the reality of macroscopic objects. (shrink)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: [email protected] , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected] . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

It is shown that the Hilbert-Bernays-Quine principle of identity of indiscernibles applies uniformly to all the contentious cases of symmetries in physics, including permutation symmetry in classical and quantum mechanics. It follows that there is no special problem with the notion of objecthood in physics. Leibniz's principle of sufficient reason is considered as well; this too applies uniformly. But given the new principle of identity, it no longer implies that space, or atoms, are unreal.

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced (...) here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show (...) that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts. (shrink)

Department of History and Philosophy of Science. University of Cambridge, Free School Lane, Cambridge CB2 3RH This paper is concerned with the question of whether atomic particles of the same species, i. e. with the same intrinsic state-independent properties of mass, spin, electric charge, etc, violate the Leibnizian Principle of the Identity of Indiscernibles, in the sense that, while there is more than one of them, their state-dependent properties may also all be the same. The answer depends on what exactly (...) the state-dependent properties of atomic particles are taken to be. On the plausible interpretation that these should comprise all monadic and relational properties that can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the individual particles, then the weakest form of the Principle is shown to be violated for bosons, fermions and higher-order paraparticles, treated in first quantization *Some of the arguments inn this paper appeared in a thesis submited by one of us (S.F.) In partial fulfilment of the requirements for the PhD degree of the University of London, in 1984. entitled 'Identity and ‘Individuality in Classical and Quantum Physics’. (shrink)

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', (...) allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision. (shrink)

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics (...) laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in (...) the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

According to classical physics particles are basic building blocks of the world. These classical particles are distinguishable objects, individuated by unique combinations of physical properties. By contrast, in quantum mechanics the received view is that particles of the same kind are physically indistinguishable from each other and lack identity. This doctrine rests on the quantum mechanical symmetrization postulates together with the “factorist” assumption that each single particle is represented in exactly one factor space of the tensor product Hilbert space of (...) a many-particle system. Even though standard in theoretical physics and the philosophy of physics, the assumption of factorism and the ensuing indistinguishability of particles are problematic. Particle indistinguishability is irreconcilable with the everyday meaning of “particle”, and also with how this term is used in the practice of physics. Moreover, it is a consequence of the standard view that identical quantum particles remain indistinguishable even in the classical limit, which makes a smooth transition to the classical particle concept impossible. Lubberdink and Dieks and Lubberdink have proposed an alternative conception of quantum particles that does not rely on factorism and avoids these difficulties. We further explain and discuss this alternative framework here. One of its key consequences is that particles in quantum theory are not fundamental but emergent; another that once they have emerged, quantum particles are always physically distinguishable and thus possess a physically grounded identity. (shrink)

In the first half of this two-part article, we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now (...) also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms. (shrink)

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics (...) laboratories. This is the first part of a two-part article. In the second part we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space. (shrink)

We show that data collected from corpuses of documents violate the Clauser-Horne-Shimony-Holt version of Bell’s inequality and therefore indicate the presence of quantum entanglement in their structure. We obtain this result by considering two concepts and their combination and coincidence operations consisting of searches of co-occurrences of exemplars of these concepts in specific corpuses of documents. Measuring the frequencies of these co-occurrences and calculating the relative frequencies as approximate probabilities entering in the CHSH inequality, we obtain manifest violations of the (...) latter for all considered corpuses of documents. In comparing these violations with those analogously obtained in an earlier work for the same combined concepts in psychological coincidence experiments with human participants, also violating the CHSH inequality, we identify the entanglement as being carried by the meaning connection between the two considered concepts within the combination they form. We explain the stronger violation for the corpuses of documents, as compared to the violation in the psychology experiments, as being due to the superior meaning domain of the human mind and, on the other side, to the latter reaching a broader domain of meaning and being possibly also actively influenced during the experimentation. We mention some of the issues to be analyzed in future work such as the violations of the CHSH inequality being larger than the ‘Cirel’son bound’ for all of the considered corpuses of documents. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in (...) the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

We analyse the way in which the principle that ‘the whole is greater than the sum of its parts’ manifests itself with phenomena of visual perception. For this investigation we use insights and techniques coming from quantum cognition, and more specifically we are inspired by the correspondence of this principle with the phenomenon of the conjunction effect in human cognition. We identify entities of meaning within artefacts of visual perception and rely on how such entities are modelled for corpuses of (...) texts such as the webpages of the World-Wide Web for our study of how they appear in phenomena of visual perception. We identify concretely the conjunction effect in visual artefacts and analyse its structure in the example of a photograph. We also analyse quantum entanglement between different aspects of meaning in artefacts of visual perception. We confirm its presence by showing that well elected experiments on images retrieved accordingly by Google Images give rise to probabilities and expectation values violating the Clauser Horne Shimony Holt version of Bell’s inequalities. We point out how this approach can lead to a mathematical description of the meaning content of a visual artefact such as a photograph. (shrink)

In the first half of this two-part article, we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now (...) also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms. (shrink)

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics (...) laboratories. This is the first part of a two-part article. In the second part we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...) parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras. They are combined into a uniform system via a mechanism preventing the simultaneous realization of perspectives. Gleason’s theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic macro-systems using the framework of symbolic dynamics. Finally, we discuss several ideas that are useful for justifying complementarity in cognitive systems. (shrink)

We analyze different aspects of our quantum modeling approach of human concepts and, more specifically, focus on the quantum effects of contextuality, interference, entanglement, and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, (...) that is, prototype theory, exemplar theory, and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and we shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this article by analyzing human concepts and their dynamics. (shrink)

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses, in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and (...) individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter. (shrink)

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on (...) a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. (shrink)

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us caapble of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach.

We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so-called transformers of information, basic processes are information processes and statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of flows of information in cognitive and social systems, since (...) a p-adic metric gives a quite natural description of the ability to form associations. (shrink)

According to classical physics _particles_ are basic building blocks of the world. These classical particles are distinguishable objects, individuated by unique combinations of physical properties. By contrast, in quantum mechanics the received view is that particles of the same kind (“identical particles”) are physically indistinguishable from each other and lack identity. This doctrine rests on the quantum mechanical (anti)symmetrization postulates together with the “factorist” assumption that each single particle is represented in exactly one factor space of the tensor product Hilbert (...) space of a many-particle system. Even though standard in theoretical physics and the philosophy of physics, the assumption of factorism and the ensuing indistinguishability of particles are problematic. Particle indistinguishability is irreconcilable with the everyday meaning of “particle”, and also with how this term is used in the practice of physics. Moreover, it is a consequence of the standard view that identical quantum particles remain indistinguishable even in the classical limit, which makes a smooth transition to the classical particle concept impossible. Lubberdink (1998; 2009) and Dieks and Lubberdink (2011) have proposed an alternative conception of quantum particles that does not rely on factorism and avoids these difficulties. We further explain and discuss this alternative framework here. One of its key consequences is that particles in quantum theory are not fundamental but _emergent_; another that once they have emerged, quantum particles are always physically distinguishable and thus possess a physically grounded identity. (shrink)

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.

Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein–Podolsky–Rosen’s reality criterion and Heisenberg’s uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of (...) non-spatial and non-local entities. (shrink)

Elaboramos aquí una nueva interpretación propuesta recientemente de la teoría cuántica, según la cual las partículas cuánticas son consideradas como entidades conceptuales que median entre los pedazos de materia ordinaria los cuales son considerados como estructuras de memoria para ellos. Nuestro objetivo es identificar qué es lo equivalente para el ámbito cognitivo humano de lo que el espacio-tiempo físico es para el ámbito de las partículas cuánticas y de la materia ordinaria. Para ello, se identifica la noción de "historia" como (...) el equivalente en la esfera cognitiva humana de lo que la materia ordinaria es en el ámbito físico cuántico. Analizamos también el papel desempeñado por los conectivos lógicos de disyunción y de conjunción con respecto a la noción de localidad. De manera similar a lo que hemos hecho en investigaciones anteriores referidas a esa nueva interpretación de la teoría cuántica, se utiliza el entorno cognitivo específico de la Internet para dilucidar las comparaciones que hacemos entre el ámbito cognitivo humano y el ámbito físico cuántico. We elaborate the new interpretation of quantum theory that we recently proposed, according to which quantum particles are considered conceptual entities mediating between pieces of ordinary matter which are considered to act as memory structures for them. Our aim is to identify what is the equivalent for the human cognitive realm of what physical space-time is for the realm of quantum particles and ordinary matter. For this purpose, we identify the notion of 'story' as the equivalent within the human cognitive realm of what ordinary matter is in the physical quantum realm, and analyze the role played by the logical connectives of disjunction and conjunction with respect to the notion of locality. Similarly to what we have done in earlier investigations on this new interpretation of quantum theory, we use the specific cognitive environment of the Internet to elucidate the comparisons we make between the human cognitive realm and the physical quantum realm. (shrink)

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to (...) the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. (shrink)