SOCIAL LASER THEORY: A QUANTUM-LIKE FRAMEWORK FOR COLLECTIVE SOCIAL DYNAMICS

Growing empirical evidence reveals that traditional set-theoretic structures cannot in general be applied to cognitive phenomena. This has raised several problems, as illustrated, for example, by probability judgement errors and decision-making (DM) errors. We propose here a unified theoretical perspective which applies the mathematical formalism of quantum theory in Hilbert space to cognitive domains. In this perspective, judgements and decisions are described as intrinsically non-deterministic processes which involve a contextual interaction between a conceptual entity and the cognitive context surrounding it. When a given phenomenon is considered, the quantum-theoretic framework identifies entities, states, contexts, properties and outcome statistics, and applies the mathematical formalism of quantum theory to model the considered phenomenon. We explain how the quantum-theoretic framework works in a variety of judgement and decision situations where systematic and significant deviations from classicality occur.

Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing that an analysis of an interactive situation involving a mating competition between certain lizard morphs allows to identify a quantum theoretic structure. More in particular, we show that when this lizard competition is analyzed structurally in the light of a compound entity consisting of subentities, the contextuality provided by the presence of an underlying rock-paper-scissors cyclic dynamics leads to a violation of Bell's inequality, which means it is of a non-classical type. We work out an explicit quantum-mechanical representation in Hilbert space for the lizard situation and show that it faithfully models a set of experimental data collected on three throat-colored morphs of a specific lizard species. Furthermore, we investigate the Hilbert space modeling, and show that the states describing the lizard competitions contain entanglement for each one of the considered confrontations of lizards with different competing strategies, which renders it no longer possible to interpret these states of the competing lizards as compositions of states of the individual lizards.

The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems or, to be more precise, to information processing in them. Quantum-like modeling has its basis in quantum information theory, and it can be considered one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on the theory of open systems in its most general form-the theory of open quantum systems. In this review, we explain its applications to biology and cognition, especially theory of quantum instruments and the quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest given to QBism, as it may be the most useful interpretation.

Einstein’s program of classical field theory for physics has not been proven unrealizable. However, Bell has shown that a theory of this type could not be consistent with all of the predictions of quantum mechanics. It is reasonable to assume that fields in a theory of the Einstein type could be described as classical dynamical systems. We begin by formulating conditions for an operator representation in Hilbert space of the phase functions of a finite classical system. It is proved that such a representation cannot be commutative. The Weyl representation fulfills the required conditions: in Appendix A it is shown to map the quadratically integrable phase functions isometrically into the Hilbert-Schmidt operators. It follows that the image 77 of the phase probability density is a statistical operator in the sense of von Neumann, though not generally nonnegative definite. The Weyl representation is then formally extended to infinite classical systems and applied to interacting relativistic tensor wave fields (spinor fields, not being single valued, present difficulties). With the choiceħ =π−1, this representation satisfies the requirements of canonical quantization. The Hamiltonian operator and operators for the usual field quantities are the same as in quantum field theory. However, an additional field interaction term appears, modifying von Neumann’s equation for the time dependence ofU. Essential divergence difficulties should not arise, since no divergences occur in classical field theory. This representation of classical field theory is amenable, in just the same way as quantum field theory, to a configuration space representation and a corresponding particle interpretation. These aspects will be discussed in a later publication.

Quantum cognition is a scientific approach to cognitive phenomena which makes use of the mathematical formalism of quantum theory. Quantum interference effect constitutes one of this theory’s main tenets and has been repeatedly demonstrated experimentally, in the last decade, in adult subjects. In the present paper, we aim to demonstrate, for the first time, the existence of thequantum interference effect on children during an experiment involving an integration of cognition and emotion. Our positive results consolidate the presuppositions of quantum cognition, enlarging its field of application to children’s mental apparatus and evidence the important question to consider the quantum model in the current investigated question of the interaction of cognition and emotion in children at neurological and psychological levels.

The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a theoretical framework for the representation of concepts and their conjunctions and disjunctions that uses the quantum formalism. This framework provides a unified solution to the 'conceptual combinations problem' of cognitive psychology, explaining the observed deviations from classical (Boolean, fuzzy set and Kolmogorovian) structures in terms of genuine quantum effects. In particular, natural concepts 'interfere' when they combine to form more complex conceptual entities, and they also exhibit a 'quantum-type context-dependence', which are responsible of the 'over- and under-extension' that are systematically observed in experiments on membership judgments.

ABSTRACTThis paper describes an attempt to formulate quantum field theory, in particular quantum electrodynamics, in terms of Hilbert space theory. The work of Cook (1) is extended to give a precise description of non-interacting electrons and positrons. The hole interpretation is not required in this extension, and no subtraction formalism is required. It is shown that the formalism can never reduce to that of intuitive quantum field theory except by an abuse of language associated with the δ-function. Interaction cannot be introduced in a simple manner into the rigorous formalism, so it seems extremely difficult to develop the Hilbert space formalism for quantum field theory in any useful manner.These difficulties indicate that an investigation of the Hilbert space basis of simple quantum theory is necessary before a rigorous mathematical formalism for intuitive quantum field theory can be developed.

The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition paradigm' was recently challenged by its proven impossibility to simultaneously model 'question order effects' and 'response replicability'. In Part I of this paper we describe sequential dichotomic measurements within an operational and realistic framework for human cognition elaborated by ourselves, and represent them in a quantum-like 'extended Bloch representation' where the Born rule of quantum probability does not necessarily hold. In Part II we apply this mathematical framework to successfully model question order effects, response replicability and unpacking effects, thus opening the way toward quantum cognition beyond Hilbert space.

The Hilbert space formalism is a powerful language to express many cognitive phenomena. Here, relevant concepts from signal detection theory are recast in that language, allowing an empirically testable extension of the quantum probability formalism to psychophysical measures, such as detectability and discriminability.

An experimental test of quantum effects in gravity has recently been proposed, where the ability of the gravitational field to entangle two masses is used as a witness of its quantum nature. The key idea is that if gravity can generate entanglement between two masses then it must have at least some quantum features (i.e., two non-commuting observables). Here we discuss what existing models for coupled matter and gravity predict for this experiment. Collapse-type models, and also quantum field theory in curved spacetime, as well as various induced gravities, do not predict entanglement generation; they would therefore be ruled out by observing entanglement in the experiment. Instead, local linearised quantum gravity models predict that the masses can become entangled. We analyse the mechanism by which entanglement is established in such models, modelling a gravity-assisted two-qubit gate.

In the heuristic Feynman integral we integrate with respect to the Gaussian factor determined by the Lagrangian of a free particle. This is not a proper framework for quantum field theory where we expand around the free field (oscillator Lagrangian). In this chapter we further develop such an approach (initiated in Chap. 6 ) to functional integration with paths resulting from arbitrary Gaussian states. The Gaussian states are solutions of the Schrödinger equation for quadratic Hamiltonians. They are distinguished in quantum theory as the only states which have positively definite probability distribution in the phase space (the Wigner distribution). First, we discuss an expansion around paths of a particular solution of the Schrödinger equation. Then, we apply the method to QFT showing that paths in imaginary time can be identified with the Euclidean fields. The method of a construction of the stochastic process corresponding to a Gaussian solution of the Schrödinger equation is applied to quantum field theory on a manifold. We define the Schrödinger representation in Hilbert space for quantum fields on an expanding manifold on the basis of Gaussian solutions of the functional Schrödinger equation.

In this paper we establish the existence of the non‐perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the algebra, which is an algebra generated by holonomy‐diffeomorphisms and by translation operators on an underlying configuration space of connections, exist. We construct operators, which correspond to the Hamiltonian of general relativity and the Dirac Hamiltonian, and show that they give rise to their classical counterparts in a classical limit. We also find that the structure of an almost‐commutative spectral triple emerge in the same limit. The Hilbert space representation, that we find, is non‐local, which appears to rule out spacial singularities such as the big bang and black hole singularities. Finally, the framework also permits an interpretation in terms of non‐perturbative Yang‐Mills theory as well as other non‐perturbative quantum field theories. This paper is the first of two, where the second paper contains mathematical details and proofs.

According to a regnant criterion of physical equivalence for quantum theories, a quantum field theory (QFT) typically admits continuously many physically inequivalent realizations. This, the second of a two‐part introduction to topics in the philosophy of QFT, continues the investigation of this alarming circumstance. It begins with a brief catalog of quantum field theoretic examples of this non‐uniqueness, then presents the basics of the algebraic approach to quantum theories, which discloses a structure common even to ‘physically inequivalent’ realizations of a QFT. Finally, it introduces and evaluates a handful of strategies for interpreting quantum theories in the face of the non‐uniqueness of their Hilbert space representations.

The current economic crisis has provoked an active response from the interdisciplinary scientific community. As a result many papers suggesting what can be improved in understanding of the complex socio-economics systems were published. Some of the most prominent papers on the topic include (Bouchaud, 2009; Farmer and Foley, 2009; Farmer et al, 2012; Helbing, 2010; Pietronero, 2008). These papers share the idea that agent-based modeling is essential for the better understanding of the complex socio-economic systems and consequently better policy making. Yet in order for an agent-based model to be useful it should also be analytically tractable, possess a macroscopic treatment (Cristelli et al, 2012). In this work we shed a new light on our research group's contributions towards understanding of the correspondence between the inter-individual interactions and collective behavior. We also provide some new insights into the implications of the global and local interactions, the leadership and the predator-prey interactions in the complex socio-economic systems.

The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.