Quantum MV algebras

We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.I should like to thank Prof. M.L. Dalla Chiara and Dr. P. Minari for many interesting comments and remarks. Daniele Mundici     

Divine Action and Quantum Theory

Recent articles by Nicholas Saunders, Carl Helrich, and Jeffrey Koperski raise important questions about attempts to make use of quantum mechanics in giving an account of particular divine action in the world. In response, I make two principal points. First, some of the most pointed theological criticisms lose their force if we attend with sufficient care to the limited aims of proposals about divine action at points of quantum indetermination. Second, given the current state of knowledge, it remains an open option to make theological use of an indeterministic interpretation of quantum mechanics. Any such proposal, however, will be an exploratory hypothesis offered in the face of deep uncertainties regarding the measurement problem and the presence in natural systems of amplifiers for quantum effects.     

God, Chaos, and the Quantum Dice

A recent noninterventionist account of divine agency has been proposed that marries the probabilistic nature of quantum mechanics to the instability of chaos theory. On this account, God is able to bring about observable effects in the macroscopic world by determining the outcome of quantum events. When this determination occurs in the presence of chaos, the ability to influence large systems is multiplied. This paper argues that, although the proposal is highly intuitive, current research in dynamics shows that it is far less plausible than previously thought. Chaos coupled to quantum mechanics proves to be a shaky foundation for models of divine agency.     

An Axiomatic Theory of Law

This paper presents in outline Luigi Ferrajoli’s axiomatic and general theory of law, as developed in his lifelong work Principia Iuris. The first section focuses on the three main aspects of the theory: the methodological, the theoretical and the pragmatic, which respectively represent the theory’s syntax, semantics and its pragmatics. Ferrajoli identifies three deontic gaps of norms: firstly, the one between their validity and efficacy; secondly, the one between their justice and validity; and finally, and most importantly, the one between validity and existence (i.e. normative force). The presence of such gaps is, according to Ferrajoli, the extraordinary innovation that entrenched constitutions have brought into modern legal systems, by establishing norms that are superior to statutes and case law. In this sense, all normative phenomena (except for the constitution itself) can be conceived both as norms and as facts. In the second section the role of juridical science is briefly discussed.     

God's Action in the World: The Relevance of Quantum Mechanics

It has been suggested that God can act on the world by operating within the limits set by Heisenberg's uncertainty principle (HUP) without violating the laws of nature. This requires nature to be intrinsically indeterministic. However, according to the statistical interpretation the quantum mechanical wavefunction represents the average behavior of an ensemble of similar systems and not that of a single system. The HUP thus refers to a relation between the spreads of possible values of position and momentum and so is consistent with a fully deterministic world. This statistical interpretation of quantum mechanics is supported by reference to actual measurements, resolves the quantum paradoxes, and stimulates further research. If this interpretation is accepted, quantum mechanics is irrelevant to the question of God's action in the world.     

Quantum Theory and the Resurrection of Jesus

Abstract :  Ever since the time of Hume it has been a truism that the worldview of empirical science, and Christian assertion of the resurrection of Jesus, are antithetical to each other. Yet post‐Newtonian science, and especially quantum theory, suggests the need for a reappraisal of this truism. This reappraisal will first examine the implications of the indeterminism of the quantum world, to consider the physical possibility of Jesus' resurrection. Second, an appraisal of the historical evidence will suggest the likelihood of Jesus' resurrection. Finally, I will consider some implications of all this for contemporary Christian thought.     

Axiomatic foundations of the Marxian Theory of Value

The aim of the present paper is to provide a logical reconstruction of the Marxian Theory of Value. This reconstruction is based upon the concept of abstract as opposed to that of homogeneous labor. Abstract labour is a social relation that holds in a market economy, (at least) whenever the profit rate is uniform; it consists in a comparison of the different labors through the exchange relationship. The author proved in a different place (see García de la Sienra, 1987) that there exists a mathematical representation of abstract labor which is unique up to similarity transformations. The existence of this function — which is none other than the value function — is the basis of the present axiomatization, which includes detailed reconstructions of two of the most important models of the theory.     

The RNA World and Divine Action in and Through Quantum Mechanics

ABSTRACT

Life emerged on Earth approximately 4.1 billion years ago. Current scholarship on the origin of life supports the RNA world scenario, although controversy still goes on. This article examines the origin issue in light of a divine action theory proposed by Robert J. Russell. Although the author himself has not much considered the issue in light of the divine action, the article is still fruitful in the sense that the origin of life issue is now incorporated into the dialogue with divine action, and also that Russell’s divine action theory can be reconsidered in a new context.     

Quantum Theory and the Boundary between Science and Spirit: Some Remarks from a Friend of Kabbalah

Physicists and philosophers argue whether quantum theory has spiritual implications. The vast majority of opinions are at two extremes: Some contend that quantum theory has absolutely no spiritual implications whatsoever, whereas others assert that it forms the very basis of a modern spirituality and can be directly applied to the human condition. It is this article's contention that neither extreme is correct. Quantum theory does have spiritual implications—a fact that its founders intuited and its enemies, Einstein preeminent among them, considered prima facie evidence of its as yet undiscovered flaws. Quantum theory has proven itself against all challenges more successfully than any other scientific theory, but its spiritual implications are extremely subtle. It provides a boundary to the materialistic, deterministic worldview and shows that there must be more to reality than that, but is inherently incapable of providing evidence as to the nature of what lies beyond that boundary.     

Schrödinger's Cat and Divine Action: Some Comments on the Use of Quantum Uncertainty to Allow for God's Action in the World

I present results of recent work in the field of quantum optics and relate this work to discussions about the theory of quantum mechanics and God's divine action in the world. Experiments involving atomic decay, relevant to event uncertainty in quantum mechanics, as well as experiments aimed at elucidating the so–called Schrödinger's–cat paradox, help clarify apparent ambiguities or paradoxes that I believe are at the heart of renewed attempts to locate God within our constructed physical theories and tend to narrow the gaps proposed as an opening for divine action. Some problems arise because of imprecise use of nonmathematical language to force quantum mechanics into an intuitive "classical" framework.     

Extended Quantum Logic

The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.     

MV-Algebras and Quantum Computation

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers. Presented by Heinrich Wansing     

Figuring Matter: Quantum Physics as a New Age Rhetoric

The language through which scientific advancements are relayed reflects specific social, political, and cultural needs and expectations, as well as specific constellations of hopes and anxieties. Constructions and applications of atomic discourse provide a material touchstone that is no less tangible than any other aspect of scientific enquiry. The 1970s New Age movement saw the deployment of quantum concepts with the publication of Fritjov Capra's (1975) widely popular The Tao of Physics and Gary Zukav's (1979) The Dancing Wu Li Masters, and from these publications the notions of quantum consciousness and quantum mysticism were born. In the late twentieth and early twenty-first century, the post-New Age concept of quantum healing began to structure a cluster of self-help programs, while at the same time quantum ‘get-rich’ schemes developed a presence on the internet. In these reconfigurations of the quantum, atomic particles have been transformed into vivified ‘agents’ whose unique movements and interactions promise to secure health, happiness, and wealth to self-directed and depoliticized consumers. The commodification inherent in this process extends increasingly to encompass areas of subjectivity—for example, spirituality—that historically have been considered immune to overt commercialization. This extension of the commodification process is evidenced in the way that quantum methodologies are commercialized and then sold to people as a means of advancing, not just their financial interests, but their spiritual well-being as well. The new economy of the atom also emerges from the late-twentieth and early twenty-first century retreat from the public sphere and the attendant atrophy of the public sphere as a site of interpersonal engagement. At the same time, the invocation and application of quantum rhetoric touches on a deep contemporary sense of being unmoored and the need for structured guidance as a means toward a renewed sense of control over one's life. The nomadic quality of quantum language and concepts ensures that, no matter what an individual's complaint or desire, there exists a quantum strategy to ameliorate or realize it. This remarkable adaptability marks twenty-first century quantum language as unique, not only within the discipline of physics, but also relative to all fields of scientific inquiry.     

Quantum information in an evolutionary perspective

An approach to quantum phenomena is reviewed that deals with the possibility of their realistic interpretation in the sense that they represent manifestations of hermeneutic circles between quantum “objects” and their experimental boundary conditions. Quantum cybernetics provides an evolutionary perspective in that all higher‐level organizations like molecules, cells, living systems, etc., can be discussed under one and the same systemic viewpoint: a hermeneutic circularity between a “core” (or “nucleus") and a relevant “periphery” (or “environment") which constitutes the systems’ organization and information potential.

Generally, in realistic theories, an individual quantum system is analyzable into a local “particle‐like” nonlinearity of a generally nonlocal “wave‐like” mode of some sub‐quantum structure of the vacuum ("Dirac ether"). In this view, a “particle” can be considered as being “guided” along one specific route by the (generally nonlocal) configurations of superimposed waves, which spread along all possible paths of an experimental setup. Moreover, in the approach of Quantum Cybernetics, an additional focus is given on the fact that the energy and momentum of a particle also determine the wave behavior. Thus, “waves” and “particles” are mutually and self‐consistently defined, and Quantum Cybernetics puts particular emphasis on the circular relationship—mediated by plane waves—between a quantum system and its macroscopically defined boundary conditions.     

一种新决策模型——量子决策模型

近10年以来, 一些学者基于量子理论研究思想与方法探索出了量子决策模型。由于该模型独特的理论结构, 它可被用于解释传统决策理论所难以解释的问题, 尤其是个体在不确定情况下的决策行为。该模型解释了诸如分离效应、分类决策的干涉效应以及合取谬误等传统决策模型很难解释的问题, 研究者已经证实其中一种称为量子问题等式的决策模型可以精确地预测决策中的顺序效应。作为一个有助于分析心理学中决策现象的新研究领域, 量子决策模型具有深入研究的理论意义和实践意义。     

SCIENCE'S CONCEPTION OF HUMAN BEINGS AS A BASIS FOR MORAL THEORY

Abstract. Niels Bohr stated, and Werner Heisenberg reiterated, that “in the great drama of existence we ourselves are both actors and spectators.” Their emphasis stems from the fact that the entry of human beings into physics as actors constitutes the most fundamental philosophical departure of twentieth‐century basic physics from its eighteenth‐ and nineteenth‐century forerunners. Those earlier theories claimed that our human conscious thoughts are mere witnesses to, or by‐products of, essentially mechanically determined brain processes. In stark contrast, certain conscious decisions that are made by human beings, but that are not determined by any known law, statistical or otherwise, enter irreducibly into orthodox contemporary physical theory. These actions are required to counteract effects of Heisenberg's Uncertainty Principle, which ordains that the physically described process of nature, acting alone, produces not a physical world of the kind we experience but rather a continuous smear of potential possible worlds of the kind we know. This contradiction between theory and experience is resolved in orthodox contemporary physical theory by bringing certain effects of our conscious human choices into the dynamics in essentially the way that we intuitively feel that our conscious intentions affect the physical world, namely, via the effects of our intentional efforts on our physically described bodies. The moral implications of this profound change in physics are discussed.