Memory exhibits episodic superposition, an analog of the quantum superposition of physical states: Before a cue for a presented or unpresented item is administered on a memory test, the item has the simultaneous potential to occupy all members of a mutually exclusive set of episodic states, though it occupies only one of those states after the cue is administered. This phenomenon can be modeled with a nonadditive probability model called overdistribution (OD), which implements fuzzy-trace theory's distinction between verbatim (...) and gist representations. We show that it can also be modeled based on quantum probability theory. A quantum episodic memory (QEM) model is developed, which is derived from quantum probability theory but also implements the process conceptions of global matching memory models. OD and QEM have different strengths, and the current challenge is to identify contrasting empirical predictions that can be used to pit them against each other. (shrink)

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to (...) restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions. (shrink)

Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.

A novel approach to quantization is shown to allow for superpositions of the cosmological constant in isotropic and homogeneous mini-superspace models. Generic solutions featuring such superpositions display: i) a unitary evolution equation; ii) singularity resolution; iii) a cosmic bounce. Explicit cosmological solutions are constructed. These exhibit characteristic bounce features including a ‘super-inflation’ regime with universal phenomenology that can naturally be made to be insensitive to Planck-scale physics.

Marinov''s critique I argue, is vitiated by its failure to recognize the distinctive role of superposition within the distributed connectionist paradigm. The use of so-called subsymbolic distributed encodings alone is not, I agree, enough to justify treating distributed connectionism as a distinctive approach. It has always been clear that microfeatural decomposition is both possible and actual within the confines of recognizably classical approaches. When such approaches also involve statistically-driven learning algorithms — as in the case of ID3 — the (...) fundamental differences become even harder to spot. To see them, it is necessary to consider not just the nature of an acquired input-output function but the nature of the representational scheme underlying it. Differences between such schemes make themselves best felt outside the domain of immediate problem solving. It is in the more extended contexts of performance DURING learning and cognitive change as a result of SUBSEQUENT training on new tasks (or simultaneous training on several tasks) that the effects of superpositional storage techniques come to the fore. I conclude that subsymbols, distribution and statistically driven learning alone are indeed not of the essence. But connectionism is not just about subsymbols and distribution. It is about the generation of whole subsymbol SYSTEMS in which multiple distributed representations are created and superposed. (shrink)

Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account (...) contradiction, as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions. (shrink)

Bonaventura Cavalieri has been the subject of numerous scholarly publications. Recent students of Cavalieri have placed his geometry of indivisibles in the context of early modern mathematics, emphasizing the role of new geometrical objects, such as, for example, linear and plane indivisibles. In this paper, I will complement this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geometrical objects. In Cavalieri’s practice, superposition is a means (...) of both manipulating geometrical objects and drawing inferences. Finally, I will suggest that an integrated approach, namely, one which strives to understand both objects and activities, can illuminate the history of mathematics. (shrink)

This article develops a commentary to Charles Brainerd, Zheng Wang and Valerie F. Reyna's article entitled “Superposition of episodic memories: Overdistribution and quantum models” published in a special number of topiCS 2013 devoted to quantum modelling in cognitive sciences.

With the interaction interpretation, the Lorentz transformation of a system arises with selection from a superposition of its states in an observation-interaction. Integration of momentum states of a mass over all possible velocities gives the rest-mass energy. Static electrical and magnetic fields are not found to form such a superposition and are to be taken as irreducible elements. The external superposition consists of those states that are reached only by change of state of motion, whereas the internal (...) superposition contains all the states available to an observer in a single inertial coordinate system. The conjecture is advanced that states of superposition may only be those related by space-time transformations (Lorentz transformations plus space inversion and charge conjugation). The continuum of external and internal superpositions is examined for various masses, and an argument for the unity of the super-positions is presented. (shrink)

In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this schema the claim that superpositions may involve contradictions, (...) as in the case of the Schrödinger's cat, which is both alive and dead. We argue that this claim is a misreading of the quantum case. Finally, we sketch a new form of quantum logic that involves three kinds of negations and present the relationships among them. The paper is a first approach to the subject, introducing some main guidelines to be developed by a `syntactical' logical approach to quantum superpositions. (shrink)

This paper aims first and foremost to unravel and clarify an interesting 17th century controversy around superposition in projectiles, which allegedly existed between the French Jesuit Honoré Fabri and the Italian physicist and astronomer Giovanni Alfonso Borelli. This conflict ? initially described by the English mathematician John Wallis in a letter from 1670 to the secretary of the Royal Society ? has been erroneously identified with Fabri's Dialogi physici (1669), a work written in response to Borelli's De vi percussionis (...) (1669). In fact, this ?conflict? was nothing but Wallis's account of a contradiction between Borelli's above mentioned work and Fabri's Tractatus physicus de motu locali from 1646, while Fabri's 1669 work expressed views very different from those contained in his Tractatus physicus. I will try here to reconstruct Fabri's change of heart between 1646 and 1669 concerning projectiles and superposition, while tracing the real bone of contention between (the later) Fabri and Borelli ? superimposing contrary motions ? to its Aristotelian origins. My analysis will lead me to problematize the way modern historians usually interpret the relation between Aristotle's physical thinking and projectile theories of early modern theoreticians (e.g. Nicollò Tartaglia's). (shrink)

Those who interpret quantum mechanics literally are forced to follow some variant of Everett's relative state formulation (or "many worlds" interpretation). It is generally assumed that this is a rather bizarre result that many physicists (especially cosmologists) have been forced into because of the evidence. I look at the history of philosophy, however, reveals that rationalism has always flirted with this very idea, from Parmenides to Leibniz to modern times. I will survey some of the philosophical history, and show how (...) the so-called paradox of quantum superposition can be considered a consequence of basic rationalist assumptions such as the principle of sufficient reason and the identity of indiscernibles. (shrink)

A distinction is made between superpositional and non-superpositional quantum computers. The notion of quantum learning systems - quantum computers that modify themselves in order to improve their performance - is introduced. A particular non-superpositional quantum learning system, a quantum neurocomputer, is described: a conventional neural network implemented in a system which is a variation on the familiar two-slit apparatus from quantum physics. This is followed by a discussion of the advantages that quantum computers in general, and quantum neurocomputers in particular, (...) might bring, not only to our search for more powerful computational systems, but also to our search for greater understanding of the brain, the mind, and quantum physics itself. (shrink)

We suggest a new answer to this intriguing question and argue that the answer may have implications for the solutions to the measurement problem. The main basis of our analysis is the doctrine of psychophysical supervenience. First of all, based on this doctrine, we argue that an observer in a quantum superposition or a quantum observer has a definite conscious experience, which is neither disjunctive nor illusive. The inconsistency of this result with the bare theory is further analyzed, and (...) it is shown that an appropriate use of the strategy of analyzing the disposition of an observer to answer a particular question also leads to the same result. Next, we argue that this new result seems to disfavor Everett's and Bohm's approaches to quantum mechanics when considering the doctrine of psychophysical supervenience. This suggests that dynamical collapse theories are in the right direction to solve the measurement problem. Thirdly, we analyze the concrete content of the conscious experience of a quantum observer. It is argued that the mental content of a quantum observer is related to both the amplitude and relative phase of each branch of the superposition she is physically in, and it is composed of the mental content corresponding to every branch of the superposition. In addition, we argue that when assuming the modulus squared of the amplitude of each branch determines the vividness of the mental content corresponding to the branch, the structured tails problem of dynamical collapse theories can be solved. (shrink)

While it has often been proposed that, fundamentally, Lorentz-invariance is not respected in a quantum theory of gravity, it has been difficult to reconcile deviations from Lorentz-invariance with quantum field theory. The most commonly used mechanisms either break Lorentz-invariance explicitly or deform it at high energies. However, the former option is very tightly constrained by experiment already, the latter generically leads to problems with locality. We show here that there exists a third way to integrate deviations from Lorentz-invariance into quantum (...) field theory that circumvents the problems of the other approaches. The way this is achieved is an extension of the standard model in which photons can have different speeds without singling out a preferred restframe, but only as long as they are in a quantum superposition. Once a measurement has been made, observables are subject to the laws of special relativity, and the process of measurement introduces a preferred frame. The speed of light can take on different values, both superluminal and subluminal (with respect to the usual value of the speed of light), without the need for Lorentz-invariance violating operators and without tachyons. We briefly discuss the relation to deformations of special relativity and phenomenological consequences. (shrink)

We consider the superposition of macroscopically distinguishable states for a measuring process whose time evolution is described by the Schrödinger equation. We ask whether it is possible to observe interference effects due to the above mentioned superposition and how to observe them, taking into consideration an experiment performed by other authors. We find a necessary condition in order to be able to observe these effects. We also point out some very serious difficulties in observing them and analyse the (...) connection between some of these difficulties and the Wigner-Araki-Yanase theory. We try to explain why the whole problem seems to us to be far from having a solution and we suggest some paths we think worthy of further investigation. (shrink)

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrödinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann’s 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their (...) seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics. (shrink)

I show in this paper why the universality of quantum mechanics at all scales, which implies the possibility of Schrodinger's Cat and Wigner's Friend thought experiments, cannot be experimentally confirmed, and why macroscopic superpositions in general cannot be observed or measured, even in principle. Through the relativity of quantum superposition and the transitivity of correlation, it is shown that from the perspective of an object that is in quantum superposition relative to a macroscopic measuring device and observer, the (...) observer is already sufficiently well correlated to the measuring device that once the object correlates to the measuring device, there is no time period in which the observer can perform an appropriate interference experiment to show that the measuring device is in a superposition. (shrink)

This paper attempts an interpretation of Everett''s relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like worlds or minds. Starting from Everett''s quantum mechanical model of an observer, it is argued that an observer''s belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are (...) constructed. From an analysis of these subjective states and their dynamics it is argued that Everett''s pure wave mechanics is subjectively consistent with von Neumann''s classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed. (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 finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of (...) the density matrices induced by the experiments or `measurements' is the Lüders mixture operation as in QM. And finally by moving the machinery into the n-dimensional vector space over ℤ₂, different basis sets become different outcome sets. That `non-commutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over ℤ₂ that can model many characteristic non-classical results of QM. (shrink)

In [7] the authors of this paper argued in favor of the possibility to consider a Paraconsistent Approach to Quantum Superpositions. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints -coming from present technical and experimental developments in QM- that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against the PAQS [1, 2, 3]. In [11, 12] it (...) was argued that their reasoning presupposes a metaphysical stance according to which the physical representation of reality must be exclusively considered in terms of the equation: Actuality = Reality. However, from a different metaphysical standpoint their problems disappear. It was also argued that, if we accept the idea that quantum superpositions exist in a potential realm, it makes perfect sense to develop QM in terms of a paraconsistent approach and claim that quantum superpositions are contradictory, contextual existents. Following these ideas, and taking as a standpoint an interpretation in terms of the physical notions of power and potentia put forward in [10, 12, 15], we present a paraconsistent formalization of quantum superpositions that attempts to capture the main features of QM. (shrink)

Non-Philosophy is a rigorous practice that can have useful applications for academic researchers and political activists alike. Utilizing its methods and frameworks, it is possible to bring Peace into the endless War of sectarian tendencies in which "the Left" is mired. In the following paper, we apply the technique of Non-Philosophy to Josh Moufawad-Paul's pamphlet "Maoism or Trotskyism," taking it as an instance of occasional material to be transformed. An important aspect of this analysis is a syntactical deployment of Non-Philosophy (...) not always found in non-philosophical texts: here our dualysis proceeds by double superposition. We effectuate two non-philosophical clones, using the first in order to recursively effectuate a second. First, we transform Trotskyism by isolating its philosophical and auto-positional structure, then we use this radicalized Trotskyism in order to transform Moufawad-Paul's Maoist polemic. The result is a radicalized Maoism-Trotskyism opening the way towards a productive and integrative Peace between Trotskyism and Maoism. (shrink)

This book examines the relevance of François Laruelle’s innovative notion of non-standard philosophy to critical and constructive discourses in the humanities, bringing together essays from prominent Anglophone scholars of Laruelle’s work and includes a contribution from Laurelle himself.

This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are (...) constructed. From an analysis of these subjective states and their dynamics it is argued that Everett's pure wave mechanics is subjectively consistent with von Neumann's classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed. (shrink)

We provide a new semantics and a slightly different formalisation for the propositional logic with superposition introduced and studied in Tzouvaras [. Propositional superposition logic...

We investigate how the sentence choice semantics for propositional superposition logic developed in Tzouvaras could be extended so as to successfully apply to first-order superposition logic. There are two options for such an extension. The apparently more natural one is the formula choice semantics based on choice functions for pairs of arbitrary formulas of the basis language. It is proved however that the universal instantiation scheme of first-order logic, $\varphi \rightarrow \varphi $, is false, as a scheme of (...) tautologies, with respect to FCS. This causes the total failure of FCS as a candidate semantics. Then we turn to the other option, which is a variant of SCS, since it uses again choice functions for pairs of sentences only. This semantics however presupposes that the applicability of the connective | is restricted to quantifier-free sentences, and thus the class of well-formed formulas and sentences of the language is restricted too. Granted these syntactic restrictions, the usual axiomatizations of FOLS turn out to be sound and conditionally complete with respect to this second semantics, just like the corresponding systems of PLS. (shrink)

The bare theory is a no-collapse version of quantum mechanics which predicts certain puzzling results for the introspective beliefs of human observers of superpositions. The bare theory can be interpreted to claim that an observer can form false beliefs about the outcome of an experiment which produces a superpositional result. It is argued that, when careful consideration is given to the observer’s belief states and their evolution, the observer does not end up with the beliefs claimed. This result leads to (...) questions about whether there can be any allure for no-collapse theories as austere as the bare theory. (shrink)

Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space-like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel “Macro-Macro” paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N≈105 particles. Crucial experimental issues as the violation of Bell’s inequalities by the Macro-Macro system are considered.