Pothos & Busemeyer's (P&B's) query about whether quantum probability can provide a foundation for the cognitive modeling embodies so many underlying implications that the subject is far from exhausted. In this brief commentary, however, I suggest that the conceptual thresholds of the meaningful learning give rise to a typical Boltzmann's weighting measure, which indicates astatistical verisimilitudeof quantum behavior in the human cognitive ensemble.

Ever since the early days of quantum mechanics it has been suggested that consciousness could be linked to the collapse of the wave function. However, no detailed account of such an interplay is usually provided. In this paper we present an objective collapse model where the collapse operator depends on integrated information, which has been argued to measure consciousness. By doing so, we construct an empirically adequate scheme in which superpositions of conscious states are dynamically suppressed. Unlike other proposals in (...) which “consciousness causes the collapse of the wave function,” our model is fully consistent with a materialistic view of the world and does not require the postulation of entities suspicious of laying outside of the quantum realm. (shrink)

The theoretical use of representation faces, among others, two types of inconsistencies, namely: a representation requires the figure of the agent to which it will be representative, which leads either to circularity or to infinite return; and the resulting one, which is the difficulty in reconciling a description, in representative terms, with other more fundamental scientific categories. The proposal of the present study for the solution of these problems was the identification of a referential process starting from the correlation between (...) states of a physical system. It will present an inference about how the superposition of causal history moments of a system can result in a self-referential structure. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

This work presents a novel formulation of quantum mechanics as the solution to an entropy maximization problem constrained by empirical measurement outcomes. By treating the complete set of possible measurement outcomes as an optimization constraint, our entropy maximization problem derives the axioms of quantum mechanics as theorems, demonstrating that the theory's mathematical structure is the least biased probability measure consistent with the observed data. This approach reduces the foundation of quantum mechanics to a single axiom, the measurement constraint, from which (...) the full theory emerges through entropy maximization. In contrast to the conventional axiomatic approach, the framework grounds the axioms directly in empirical data, substantially restricting the interpretational landscape ruling out interpretations inconsistent with this empirical foundation. (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)

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics. We will argue that—leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes—the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of the efficient cause or in terms of the final cause. We (...) will discuss and analyze why both, ‘final cause’ and ‘efficient cause’ models, face severe difficulties to solve the measurement problem. In contradistinction to these schemes we will present a new model based on the immanent cause which, we will argue, provides an intuitive understanding of the measurement process in QM. (shrink)

The validity of the conclusion to the nonlocality of quantum mechanics, accepted widely today as the only reasonable solution to the EPR and Bell issues, is questioned and criticized. Arguments are presented which remove the compelling character of this conclusion and make clear that it is not the most obvious solution. Alternative solutions are developed which are free of the contradictions related with the nonlocality conclusion. Firstly, the dependence on the adopted interpretation is shown, with the conclusion that the alleged (...) nonlocality property of the quantum formalism may have been reached on the basis of an interpretation that is unnecessarily restrictive. Secondly, by extending the conventional quantum formalism along the lines of Ludwig and Davies it is shown that the Bell problem may be related to complementarity rather than to nonlocality. Finally, the dependence on counterfactual reasoning is critically examined. It appears that locality on the quantum level may still be retained provided one accepts a newly proposed principle of nonreproducibility at the individual quantum level as an alternative of quantum nonlocality. It is concluded that the locality principle can retain its general validity, in full conformity with all experimental data. (shrink)

A Controlled Not variant of the standard quantum teleportation protocol affords a step-by-step analysis of what is, or can be said to be, achieved in the process in either location. Dominant interpretations of what quantum teleportation consists in and implies are reviewed in this light. Being mindful of the statistical significance of the terms and operations involved, as well as awareness of classical analogies, can help sort out what is specifically quantum-mechanical, and what is not, in so-called teleportation. What the (...) latter achieves appears to be the transmission, without the involvement of mysterious channels, of what a quantum state encapsulates: the multitiered probabilistic characterization of a given preparation, which might be all we can possibly know about a physical system in a given experimental situation. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave (...) functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2The Dirac Sea Model3Equilibrium States and the Vacuum4Excitations of the Vacuum and the Fock Space Formalism5The Appearance of Particle Creations and Annihilations6The Merits of the Bohmian Approach. (shrink)

A drastic resolution of the quantum paradoxes is proposed, combining (I) von Neumann's postulate that collapse of the state vector is due to the act of observation, and (II) my reinterpretation of von Neumann's quantal irreversibility as an equivalence between wave retardation and entropy increase, both being “factlike” rather than “lawlike” (Mehlberg). This entails a coupling of the two de jure symmetries between (I) retarded and (II) advanced waves, and between Aristotle's information as (I) learning and (II) willing awareness. Symmetric (...) acceptance of cognizance as a source of retarted waves, and of will as a sink of advanced waves, is submitted as a central “paradox” of the Copernican or Einsteinian sort, out of which new light is shed upon previously known paradoxes, such as the EPR paradox, Schrödinger's cat, and Wigner's friend. Parapsychology is thus found to creep into the picture. (shrink)

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B〉 〈B|. An exact “correspondence” exists between the Born-Jordan-Dirac “wavelike” algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations |B) (...) (B| were over “real hidden states.” While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes 〈A|C〉 = 〈C|A〉*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |〈A|C〉|2. CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is 〈Ψ| U |Φ〉 = 〈Ψ| UΦ〉 = 〈ΦU|Φ〉, with |Φ〉 denoting a preparation, |Ψ〉 a measurement, and U the evolution operator. The transformation |Ψ〉 = |UΦ〉 or |Φ〉 = |U−1Ψ〉 exchanges the “preparation representation” and the “measurement representation” of a system and is ancillary in the formalization of the quantum chance game by the “wavelike algebra” of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude 〈A|C〉 = Σ 〈A|B〉〈B|C〉 between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility 〈A|C〉 = 〈C|A〉* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of “blind statistical retrodiction”—that is, of “final cause.”. (shrink)

Joseph Bertrand's 1888 evidencing that assignment of a probability depends upon what one chooses to know or not and to control or not, congruent with Grad's 1961 evidencing that statistical entropy depends upon what one deems relevant or not in formalization and measurement, radically undermine common sense realism; mean values are symbols, but symbols of what? For that very reason, recent clever conceptualizations of the quantum measurement process via partial tracing do not restore realism: How could deliberate ignorance generate a (...) reality? Beyond this, Born's and Jordan's quantal wavelike probability calculus, entailing algebraic nonseparability and spacetime nonlocality, blurs “reality” still more radically. Thus information stands out as the master word, with its two reciprocal aspects: knowledge and organization. (shrink)

Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but can sometimes (...) be justified by considering some of the metaphysical issues surrounding the question of the applicability of mathematics to physical reality. 1 Introduction 2 Rejecting inferential permissiveness 3 The agreement problem 4 Independent objections to the liberal view. (shrink)

Attemts to explain causal paradoxes of Quantum Mechanics (QM) have tried to solve the problems within the framework of Quantum Electrodynamics (QED). We will show, that this is impossible. The original theory of QED by Dirac (Proc Roy Soc A117:610, 1928) formulated in its preamble four preliminary requirements that the new theory should meet. The first of these requirements was that the theory must be causal. Causality is not to be derived as a consequence of the theory since it was (...) a precondition for the formulation of the theory; it has been constructed so that it be causal. Therefore, causal paradoxes logically cannot be explained within the framework of QED. To transcend this problem we should consider the following points: Dirac himself stated in his original paper (1928) that his theory was only an approximation. When he returned to improve the theory later (Proc Roy Soc A209, 1951), he noted that the new theory “involves only the ratio e / m , not e and m separately”. This is a sign that although the electromagnetic effects (whose source is e ) are magnitudes stronger than the gravitational effects (whose source is m ), the two are coupled. Already in 1919, Einstein noted that “the elementary formations which go to make up the atom” are influenced by gravitational forces. Although in that form the statement proved not to be exactly correct, the effects of gravitation on QM phenomena have been established. The conclusion is that we should seek a resolution for the causal paradoxes in the framework of the General Theory of Relativity (GTR)—in contrast to QED, which involves only the Special Theory of Relativity (STR). We show that causality is necessarily violated in GTR. This follows from the curvature of the space-time. Although those effects are very small, one cannot ignore their influence in the case of the so-called “paradox phenomena”. (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)

A case study of the development of quantum field theory and of S-matrix theory, from their inceptions to the present, is presented. The descriptions of science given by Kuhn and by Lakatos are compared and contrasted as they apply to this case study. The episodes of the developments of these theories are then considered as candidates for competing research programs in Lakatos' methodology of scientific research programs. Lakatos' scheme provides a reasonable overall description and a plausible assessment of the relative (...) value of these two programs in terms of progressive and degenerating problem shifts. Also discussed are the roles of various types of models as they have been used in these areas of theoretical high-energy physics. (shrink)

In this paper the role of the mathematical probability models in the classical and quantum physics is shortly analyzed. In particular the formal structure of the quantum probability spaces (QPS) is contrasted with the usual Kolmogorovian models of probability by putting in evidence the connections between this structure and the fundamental principles of the quantum mechanics. The fact that there is no unique Kolmogorovian model reproducing a QPS is recognized as one of the main reasons of the paradoxical behaviors pointed (...) out in the quantum theory from its early days. (shrink)

Recently I published an article in this journal entitled “Less interpretation and more decoherence in quantum gravity and inflationary cosmology” :1019–1045, 2015). This article generated responses from three pairs of authors: Vassallo and Esfeld :1533–1536, 2015), Okon and Sudarsky :852–879, 2016) and Fortin and Lombardi. In what follows, I reply to the criticisms raised by these authors.

Indispensability arguments for realism about mathematical entities have come under serious attack in recent years. To my mind the most profound attack has come from Penelope Maddy, who argues that scientific/mathematical practice doesn't support the key premise of the indispensability argument, that is, that we ought to have ontological commitment to those entities that are indispensable to our best scientific theories. In this paper I defend the Quine/Putnam indispensability argument against Maddy's objections.

We examine, in the context of the Einstein-Podolsky-Rosen-Bohm gedankenexperiment, problems associated with state reduction and with nonlocal influences according to different interpretations of quantum mechanics, when attempts are made to apply these interpretations in the relativistic domain. We begin by considering the significance of retrodiction within four different interpretations of quantum mechanics, and show that three of these interpretations, if applied in a relativistic context, can lead to ambiguities in their description of a process. We consider ways of dealing with (...) these ambiguities, in particular focussing on the “preferred frame” hypothesis. We then re-examine an argument involving nonlocal measurements which claimed that the preferred frame hypothesis is not tenable, and show that this argument does not in fact necessitate a rejection of the preferred frame. We then suggest that, to avoid confusion, the preferred frame could be extended to cover unitary interactions as well as state reductions. We conclude with a brief examination of a proposal that state reduction should take effect across the backward light cone of a measurement event. (shrink)

In this paper we derive the Schrödinger equation by comparing quantum statistics with classical statistical mechanics, identifying similarities and differences, and developing an operator functional equation which is solved in a completely algebraic fashion with no appeal to spatial invariances or symmetries.

En este artículo, se introducirá el formalismo de cuantificación canónica denominado "cuantificación geométrica". Dado que dicho formalismo permite entender la mecánica cuántica como una extensión geométrica de la mecánica clásica, se identificarán las insuficiencias de esta última resueltas por dicha extensión. Se mostrará luego como la cuantificación geométrica permite explicar algunos de los rasgos distintivos de la mecánica cuántica, como, por ejemplo, la noconmutatividad de los operadores cuánticos y el carácter discreto de los espectros de ciertos operadores. In this article, (...) We shall introduce the formalism of canonical quantization called "geometric quantization". Since this formalism let us understand quantum mechanics as a geometric extension of classical mechanics, we shall identify the insufficiencies of the latter that are resolved by such an extension. We shall show that geometric quantization permits us to explain some fundamental features of quantum mechanics, such as the non-commutativity of quantum operators and the discrete spectrum of some operators describing physical quantities. (shrink)

We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that (...) the classical notion is overdetermined. (shrink)

The objective of the consistent-amplitude approach to quantum theory has been to justify the mathematical formalism on the basis of three main assumptions: the first defines the subject matter, the second introduces amplitudes as the tools for quantitative reasoning, and the third is an interpretative rule that provides the link to the prediction of experimental outcomes. In this work we introduce a natural and compelling fourth assumption: if there is no reason to prefer one region of the configuration space over (...) another, then they should be “weighted” equally. This is the last ingredient necessary to introduce a unique inner product in the linear space of wave functions. Thus, a form of the principle of insufficient reason is implicit in the Hilbert inner product. Armed with the inner product we obtain two results. First, we elaborate on an earlier proof of the Born probability rule. The implicit appeal to insufficient reason shows that quantum probabilities are not more objective than classical probabilities. Previously we had argued that the consistent manipulation of amplitudes leads to a linear time evolution; our second result is that time evolution must also be unitary. The argument is straightforward and hinges on the conservation of entropy. The only subtlety consists of defining the correct entropy; it is the array entropy, not von Neumann's. After unitary evolution has been established we proceed to introduce the useful notion of observables and we explore how von Neumann's entropy can be linked to Shannon's information theory. Finally, we discuss how various connections among the postulates of quantum theory are made explicit within this approach. (shrink)

The relevance of symmetry to today's physics is a widely acknowledged fact. A significant part of recent physical inquiry – especially the physics concerned with investigating the fundamentalbuilding blocks of nature – is grounded on symmetry principles andtheir many and far-reaching consequences. But where these symmetries come from and what their real meaning is are open questions, at the center of a developing debate among physicists and philosophers of science. To tackle the problems arising in considering the symmetry issue is (...) the main purpose of this paper. Starting with briefly recalling the bases for the discussion – how symmetry enters and operates in physics, its special effectiveness in the quantum domain and the many relevant functions it performs (Sections 1–3), the paper then focus on the general interpretative questions that arise and the sorts of answers that have been given (Section 4). (shrink)

In this paper I contend that standard quantum theory has a minimal interpretation, on which all physicists agree. That interpretation is sufficient for every application of quantum theory and it has been confirmed by a countless number of experiments. However, it provides neither an overall picture of the quantum world nor an intended ontology for quantum theory. For those reasons, several full interpretations have been proposed in order to complete the minimal interpretation. I then argue that those interpretations –which are (...) empirically equivalent, but mutually incompatible- are metaphysical ventures that cannot be confirmed by any conceivable experience. Moreover, I claim that the program of finding the ontology for quantum theory rests on the false assumption that there is a unique ontology compatible with each physical theory. I conclude that there is no direct path either from the formalism of quantum theory to its intended ontology, or from determinate metaphysical assumptions to the quantum formalism. (shrink)

In Calosi and Wilson (Phil Studies 2019/2018), we argue that on many interpretations of quantum mechanics (QM), there is quantum mechanical indeterminacy (QMI), and that a determinable-based account of metaphysical indeterminacy (MI), as per Wilson 2013 and 2016, properly accommodates the full range of cases of QMI. Here we argue that this approach is superior to other treatments of QMI on offer, both realistic and deflationary, in providing the basis for an intelligible explanation of the interference patterns in the double-slit (...) experiment. We start with a brief overview of the motivations for QMI and for a determinable-based account of MI (§1). We then apply a developed 'glutty' implementation of determinable-based QMI to the superposition-based QMI present in the double-slit experiment, and positively compare the associated explanation of double-slit interference with that available on a metaphysical supervaluationist account of QMI (§2). We then present and respond to objections, due to Glick (2017) and Torza (2017), either to QMI (§3) or to our specific account of QMI (§4); in these sections we also positively compare our treatment of double-slit interference to that available on Glick's deflationary treatment of QMI. We conclude with some dialectical observations (§5). (shrink)

On many currently live interpretations, quantum mechanics violates the classical supposition of value definiteness, according to which the properties of a given particle or system have precise values at all times. Here we consider whether either metaphysical supervaluationist or determinable-based approaches to metaphysical indeterminacy can accommodate quantum metaphysical indeterminacy (QMI). We start by discussing the standard theoretical indicator of QMI, and distinguishing three seemingly different sources of QMI (S1). We then show that previous arguments for the conclusion that metaphysical supervaluationism (...) cannot accommodate QMI, due to Darby 2010 and Skow 2010, are unsuccessful, in leaving open several supervaluationist responses. We go on to provide more comprehensive argumentation for the negative conclusion. Here, among other results, we establish that the problems for supervaluationism extend far beyond the concern that is the focus of Darby's and Skow's discussions (according to which a supervaluationist approach is incompatible with the orthodox interpretation, in light of the Kochen-Specker theorem) to also attach to common understandings of other interpretations on which there is QMI (S2). We then argue that a determinable-based account can successfully accommodate all three varieties of QMI (S3). We close by observing the positive mutual bearing of our results on the coherence and intelligibility of both quantum mechanics and metaphysical indeterminacy (S4). (shrink)

Starting from a set of assumptions mainly of an “operational” or experimentally based nature, a derivation of quantum mechanics is presented, with the aim of clarifying the essential features of the theory and their interpretation. Various properties of quantum mechanics such as the addition of amplitudes, the calculation of probabilities, de Broglie's equations, and energy-momentum conservation are derived from first principles. It is investigated whether quantum amplitudes may be constructed from quantities of higher order than complex numbers. Measurable physical quantitics, (...) as traditionally understood, are seen to play a role distinct from and supplementary to the behavior of the quantum amplitudes themselves. This is related to two distinct aspects of the nature of time in the context of quantum mechanics. (shrink)

We present three different derivations of the transition probabilities to the continuum. It is shown that calculations, performed as a direct application of the postulates of orthodox quantum mechanics (OQM), do not yield results consistent with experiments. Traditional treatments are summarized and criticized. The relation of the transitions to the continuum with the traditional quantum measurement problem is pointed out; we sum up and comment some contributions concerning this issue. It is shown that an approach based on the notion of (...) spontaneous projections yields expressions of the transition probabilities similar to those obtained in the traditional way and new predictions which could be submitted to experimental tests. (shrink)

A new interpretation of quantum theory is proposed. It coincides in a number of points with the orthodox interpretation, the main difference being that the projection of the state vector can occur without the intervention of any observer.

The design, maintenance and use of all measuring instruments involve indicators of the thing, property, or event they are expected to detect or measure. And every quantitative indicator is a functional relation between imperceptible and perceptible facts—for example, the “flow” of time and the rotation of a watch’s hands. The empirical test of any quantitative hypothesis involves the translation of the unobservable variables occurring in it into the observable variable(s) in the indicator hypothesis. Yet, indicators have escaped the notice of (...) nearly all philosophers of science—a fact that may indicate unfamiliarity with laboratory work. (shrink)

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as (...) in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

This paper describes a long-standing, though little-known, debate between Paul Dirac and Werner Heisenberg over the nature of scientific methodology, theory change, and intertheoretic relations. Following Heisenberg’s terminology, their disagreements can be summarized as a debate over whether the classical and quantum theories are “open” or “closed.” A close examination of this debate sheds new light on the philosophical views of two of the great founders of quantum theory.

The study of the motion of the magnetic top—a classical spherical top which carries magnetic moment proportional to its angular momentum, is motivated and inspired by the quantum mechanical relation between spin angular momentum and spin magnetic moment. Inversely, the magnetic top, taken to be the classical model of quantum spin, implies the description of spin states by probability amplitudes of the top orientation angles, instead of by Pauli spinors. This opens new possibilities for the interpretation of many interesting spin (...) experiments which serve as tests of basic principles of quantum mechanics and of the postulates of the quantum theory of measurement. (shrink)

The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is (...) developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed. (shrink)

Kramers's equation specialized to the Coulomb field is factored using a rotationally invariant, angular momentum based, algebra of three anticommuting operators. Comparing the explicit chiral two-component solutions for the factored equation to the two-component solutions defined by the Foldy-Wouthuysen series for the Dirac-Coulomb Hamiltonian, it is concluded that this series cannot converge.

Using the diffusion model associated by the author with the wave equations, a part of current quantum radiation theory is reformulated so that the characteristic divergences in the associated calculations no longer arise. The reformulation does this by stipulating, on purely physical grounds, that a transition involving a “virtual” quantum must include a high frequency “cutoff” factor in its interaction Hamiltonian. For a transition involving a “real” quantum, the stipulation is that the “cutoff” factor is not to be included.

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.

This paper examines the epistemological significance of the present situation of underdetermination in quantum mechanics. After analyzing this underdetermination at three levels---formal, ontological, and methodological---the paper considers implications for a number of variants of the thesis of scientific realism in fundamental physics and reassesses Lakatos‘ characterization of progress in physical theory in light of the present situation. Next, this paper considers the implications of underdetermination for Weinberg’s ‘‘dream of a final theory.’’ Finally, the paper concludes by suggesting how one might (...) still think of realism and progress in fundamental physics despite the possibility of persistent underdetermination in quantum mechanics. (shrink)

In this paper we construct the ortholattices arising in quantum logic starting from the phenomenologically plausible idea of a collection of ensembles subject to passing or failing various “tests.” A collection of ensembles forms a certain kind of preordered set with extra structure called anorthospace; we show that complete ortholattices arise as canonical completions of orthospaces in much the same way as arbitrary complete lattices arise as canonical completions of partially ordered sets. We also show that the canonical completion of (...) an orthospace of ensembles is naturally identifiable as the complete lattice of properties of the ensembles, thereby revealing exactlywhy ortholattices arise in the analysis of “tests” or experimental propositions. Finally, we axiomatize the hitherto implicit concept of “test” and show how they may be correlated with properties of ensembles. (shrink)

The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of (...) Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account. (shrink)

The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, (...) but to a set of sub-problems. (shrink)