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)

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.

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.

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)

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.

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)

In the 1890s Ludwig Mach employed photography for visualizing streamlines in the emerging field of aerodynamic research. Étienne-Jules Marey developed a similar approach at the turn of the century. The two projects can be related to a number of current discussions on the history of scientific photography. The case of Ludwig Mach demonstrates how the collection of numerical data became both the subject and the challenge of a line of research intimately linked to the capacities of photography. At the end (...) of the nineteenth century, the particular potential of scientific photography is very often defined by comparison with the limited power of the human eye. In contrast, the example of streamline photography underlines that the requirements of the research context are critical for successfully employing photography. Marey’s studies point to a tension between his characterization of chronophotography as a method for analyzing the elementary units of processes in nature on the one hand and the necessary summation of single moments in time in his recordings of streamlines on the other. What Marey usually qualified as a cumbersome confusion was here the prerequisite of observation. The ’philosophy in machines’ ultimately limited the success of streamline photography; it aided in debates about qualitative matters, but could hardly provide what most interested scientists and engineers: reliable numbers. (shrink)

Semantic composition in language must be closely related to semantic composition in thought. But the way the two processes are explained differs considerably. Focusing primarily on propositional content, language theorists generally take semantic composition to be a truth-conditional process. Focusing more on extensional content, cognitive theorists take it to be a form of concept combination. But though deep, this disconnect is not irreconcilable. Both areas of theory assume that extensional (i.e., denotational) meanings must play a role. As this article demonstrates, (...) they also have the potential to fulfill a mediative function. What is shown is that extensional meanings are themselves inherently compositional. On this basis, it becomes possible to model semantic composition without assuming the existence of any specifically linguistic/conceptual apparatus. Examples are presented to demonstrate this direct style of modeling. Abstract connections between composition in thought and language can then be made, raising the prospect of a more unified, theoretical account of semantic composition. (shrink)

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 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)

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.

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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.

The Schrodinger's Cat and Wigner's Friend thought experiments, which logically follow from the universality of quantum mechanics at all scales, have been repeatedly characterized as possible in principle, if perhaps difficult or impossible for all practical purposes. I show in this paper why these experiments, and interesting macroscopic superpositions in general, are actually impossible in principle. First, no macroscopic superposition can be created via the slow process of natural quantum packet dispersion because all macroscopic objects are inundated with decohering (...) interactions that constantly localize them. Second, the SC/WF thought experiments depend on von Neumann-style amplification to achieve quickly what quantum dispersion achieves slowly. Finally, I show why such amplification cannot produce a macroscopic quantum superposition of an object relative to an external observer, no matter how well isolated the object from the observer, because: the object and observer are already well correlated to each other; and reducing their correlations to allow the object to achieve a macroscopic superposition relative to the observer is equally impossible, in principle, as creating a macroscopic superposition via the process of natural quantum dispersion. (shrink)

By deriving the Lorentz transformation from the absolute speed of light, Einstein demonstrated the relativistic variability of space and time, enabling him to explain length contraction and time dilation without recourse to a "luminiferous ether" or preferred frame of reference. He also showed that clocks synchronized at a distance via light signals are not synchronized in a frame of reference differing from that of the clocks. However, by mislabeling the relativity of synchrony the "relativity of simultaneity," Einstein implied that this (...) effect concerns an actual difference in times from one frame to another rather than merely a failure of clock synchronization across frames. As a theory of length contraction and time dilation on the basis of relative motion in the context of the absolute speed of light, special relativity is the definitive interpretation of the Lorentz transformation and the correct explanation of relativistic phenomena. The relativity of simultaneity, as I demonstrate, plays no role in this explanation but instead provides apparent justification for a view of time in which the present moment is frame-dependent. In contrast to its legitimate application, special relativity fails as a theory of time on the basis of the relativity of simultaneity. (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)

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)