Calculation of the mean of an observable in quantum mechanics is typically assumed to require that the state vector be in the domain of the corresponding self-adjoint operator or for a mixed state that the operator times the density matrix be in the trace class. We remind the reader that these assumptions are unnecessary. We state what is actually needed to calculate the mean of an observable as well as its variance.

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical (...) ensemble after measurement. Quantum in-variance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics. (shrink)

A nonstandard viewpoint to quantum gravity is discussed. General relativity and quantum mechanics are to be related as two descriptions of the same, e.g. as Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics merged in the contemporary quantum mechanics. From the viewpoint of general relativity one can search for that generalization of relativity implying the in-variance “within – out of” of the same system.

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of (...) Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a (...) wave function describing a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken (...) seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM. -/- The following sketches how QFT describes fundamental physics and what the status of QFT is among other theories of physics. Since there is a strong emphasis on those aspects of the theory that are particularly important for interpretive inquiries, it does not replace an introduction to QFT as such. One main group of target readers are philosophers who want to get a first impression of some issues that may be of interest for their own work, another target group are physicists who are interested in a philosophical view upon QFT. (shrink)

The goal of the dissertation is, first, to develop in the tradition of conventional quantum mechanics what I call a propensity view of quantum properties, and to examine its coherence. Conventional quantum mechanics assumes the completeness of quantum mechanics. Taking the ontic version of the completeness assumption, which says that a state vector completely describes an individual quantum system as it is, I argue that the propensity view of quantum properties, i.e., the attribution of (...) certain irreducible propensities to a quantum system, is not only demanded but also can be coherently maintained. ;Second, I evaluate the relation between a propensity view of quantum properties and the demands of Einstein's program of realism, the backbone of which is the requirement that physical systems, as described by a theory, have properties independently of measurement. In doing so, I argue for a non-relational version of the quantum propensity view, which amounts to attributions propensities to individual quantum systems, and claim that conventional quantum mechanics together with the non-relational propensity view of quantum properties realizes physical realism, which is a particular version of Einstein's realist thesis and which reads that a physical system, as described by a theory, has at least some of its extrinsic properties independently of measurement. ;Third, quantum mechanics, in spite of its empirical success, has suffered from certain well-known conceptual puzzles, viz., the measurement problem and the problem of nonlocality as it arises in the Einstein-Podolsky-Rosen paradox. So we ask whether the propensity view of quantum properties can help us the resolve these problems. I argue that the so-called reduction of the wave packet is the source of both problems and suggest that there is a sense in which the propensity view of quantum properties explains the reduction of the wave packet and its nonlocal nature. On the other hand, the propensity view by itself fails to resolve the question of when or in what circumstances the reduction of the wave packet occurs, indicating that we do not as yet possess a complete understanding of quantum propensities. (shrink)

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic - compatible with realism about quantum mechanics - can be (...) maintained, albeit at the price of truth-functionality. Finally, the paper improves on Hellman (1980)'s argument that this lack of truth-functionality entails a change of meaning between classical and quantum logical connectives. (shrink)

Weak values are average quantities, therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as possible, building primarily on material from Moyal and Sonego :1135, 1991) . The weak variance is defined in terms of the Wigner function, using a standard construction from probability theory. We show this corresponds to a measurable quantity, which is not itself a weak (...) value. It also leads naturally to a connection between the imaginary part of the weak value of momentum and the quantum potential. We study how the negativity of the Wigner function causes negative weak variances, and the implications this has on a class of ‘subquantum’ theories. We also discuss the role of weak variances in studying determinism, deriving the classical limit from a variational principle. (shrink)

A century after the advent of quantum mechanics and general relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell’s inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava–Lifshitz gravity. Here, we explore a recent proposal for a “real ensemble” non-local description of quantum mechanics, (...) in which “particles” can copy each others’ observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as \ time)\, where \. Interestingly, this convergence is controlled by the absolute value of energy, suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem. (shrink)

Contemporary physicists, in creating theories adequate to nature's patterns of movement and development, speak the language of dialectics whether willingly or unwillingly. Even those whose personal outlook is at variance with dialectical philosophy acknowledge this in their own way. Thus Heisenberg states that inquiry into the foundations of the quantum theory, especially as carried out by Bohr, has features reminiscent of Hegelian philosophy. And, to quote Pauli, "dialectics is that mutual game of two opponents which is typical of (...) the Copenhagen interpretation of quantum mechanics." Bohr himself, while discussing the quantum theory, speaks of "profoundly true statements the opposites of which likewise contain deep verities.". (shrink)

The aim of this paper is to show that the argument put forth by Bell and Hallett against Putnam's thesis regarding the invariance of meaning for quantum logical connectives is insufficient to establish their conclusion. By using an example from the causal theory of time, the paper shows how the condition they specify as relevant in cases of meaning variance in fact fails. As a result, the conclusion that negation undergoes a change of meaning in the quantum (...) logical case is left in doubt. The paper proceeds in three stages. First, a summary of Putnam's argument for the invariance of meaning in the case of quantum logical connectives is provided; this is followed by a review of the criticisms advanced against it by Bell and Hallett. Finally, it is shown how the main claim upon which their major criticism rests is unfounded. (shrink)

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral “in finite limits”). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this (...) variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is δS≳ℏ, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is |∫ ′ t″ (δS[q]/δq(t))Δq(t)dt|≃ℏ, where the paths [q] and [Δq] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as Δ(Equation) Δ(Path) ≃ ℏ. This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement. (shrink)

In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the (...) general form of the state operators of ME packets is obtained with its help. The diagonal representation of the operators is found. A general way of calculating averages that can replace the partition function method is described. Classical mechanics is reinterpreted as a statistical theory. Classical trajectories are replaced by classical ME packets. Quantum states approximate classical ones if the product of the coordinate and momentum variances is much larger than Planck constant. Thus, ME packets with large variances follow their classical counterparts better than Gaussian wave packets. (shrink)

We present a new approach on the interpretation of the quantum mechanism. The derivation is phenomenological and incorporates an energetic vacuum which interacts with elementary particles. We consider a classical ensemble average for the square of 4-velocities of identical elementary particles with the same initial conditions in Minkowski space. The relativistic extension of a result in Brownian motion allows the variance to be identified with Bohm's quantum potential. A simple relation between 4-velocities and 4-momenta at a specific (...) 4-position with given proper time leads to one of two statistical equations that constitute our quantum theory, the other being the continuity equation. The Klein-Gordon equation is a consequence of these two statistical equations. (shrink)

The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities (...) for the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities “out there”. (shrink)

In quantum field theory, coherent states can be created that have negative energy density, meaning it is below that of empty space, the free quantum vacuum. If no restrictions existed regarding the concentration and permanence of negative energy regions, it might, for example, be possible to produce exotic phenomena such as Lorentzian traversable wormholes, warp drives, time machines, violations of the second law of thermodynamics, and naked singularities. Quantum Inequalities have been proposed that restrict the size and (...) duration of the regions of negative quantum vacuum energy that can be accessed by observers. However, QIs generally are derived for situations in cosmology and are very difficult to test. Direct measurement of vacuum energy is difficult and to date no QI has been tested experimentally. We test a proposed QI for squeezed light by a meta-analysis of published data obtained from experiments with optical parametric amplifiers and balanced homodyne detection. Over the last three decades, researchers in quantum optics have been trying to maximize the squeezing of the quantum vacuum and have succeeded in reducing the variance in the quantum vacuum fluctuations to \ dB. To apply the QI, a time sampling function is required. In our meta-analysis different time sampling functions for the QI were examined, but in all physically reasonable cases the QI is violated by much or all of the measured data. This brings into question the basis for QI. Possible explanations are given for this surprising result. (shrink)

(1) The idea that diffraction of matter particles can only be understood in terms of a temporary wave transformation or 'double manifestation' is an uneconomical ad hoc hypothesis, shattered already in 1923 by the unitary quantum theory of diffraction of Duane which in 1926 became part of the quantum mechanics, with a statistical interpretation of wave-like appearances. (2) Bohr's re-interpretation of Heisenberg's uncertainty of prediction as an indeterminacy of existence rests on an illegitimate literal translation of a wave (...) result into particle language which is at variance with experience as well as with the statistical interpretation. (3) The fact that one can transform the simple and unitary particle mechanics into a complicated wavelike form is only a weak substitute for genuine dualism -- as if one would see dualism in the transformability from the geo- to the heliocentric reference system. (4) The strongest argument against a symmetry of the particle and the wave theory of matter is the explainability of the former in terms of simple postulates of invariance, leaving the wave formalism as a purely ad hoc construction. (shrink)

We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase space. The total space of this fiber bundle consists of geometric quantum states, products of convex bodies carried by Lagrangian planes by their polar duals with respect to a second transversal Lagrangian plane. Using the theory of the John ellipsoid (...) we relate these geometric quantum states to the notion of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle. We show that the set of equivalence classes of unitarily related geometric quantum states is in a one-to-one correspondence with the set of all Gaussian wavepackets. We emphasize that the uncertainty principle appears in this paper as geometric property of the states we define, and is not expressed in terms of variances and covariances, the use of which was criticized by Hilgevoord and Uffink. (shrink)

This interdisciplinary volume of essays explores how the notion of time varies across disciplines by examining variance as a defining feature of temporalities in cultural, creative, and scholarly contexts. Featuring a President's Address by philosopher David Wood, it begins with critical reassessments of J.T. Fraser's hierarchical theory of time through the lens of Anthropocene studies, philosophy, ecological theory, and ecological literature; proceeds to variant narratives in fiction, video games, film, and graphic novels; and concludes by measuring time's variance (...) with tools as different as incense clocks and computers, and by marking variance in music, film, and performance art. (shrink)

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} on an additional time variable, named intrinsic time (...) at variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative g˙μν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{g}}_{\mu \nu }$$\end{document} of the metric field with respect to intrinsic time, corresponding to the conjugated momentum πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document}. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional A[gμν,πμν]=K[gμν,πμν]-S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }] = {\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }] - S[g_{\mu \nu }]$$\end{document}, playing formally the role of a Hamilton function, where S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} is the standard Einstein–Hilbert action while K[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action A[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} and not of energy. Since the Einstein–Hilbert action S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document}. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document} gives rise to a cosmological constant term in the path-integral approach. (shrink)

This Introduction to a Journal of Consciousness Studies Special Issue on Monist Alternatives to Physicalism summarises some of the basic problems of Physicalism and common fallacies in arguments for its defence that are found in the philosophical and scientific literature. It then introduces six monist alternatives: 1) a form of emergent panpsychism developed by William Seager; 2) a novel introduction to the process philosophy of A.N. Whitehead by Anderson Weekes; 3) a review of current developments in Russellian Monism by Torin (...) Alter and Yujin Nagasawa; 4) an analysis of dual-aspect monism and its relation to quantum mechanics originally proposed developed by Pauli and Jung and given a modern interpretation by Harald Atmanspacher; 5) a form of processing monism that might help to resolve ontological differences in Indian philosophy and psychology between dualist Samkya Yoga and nondualist Advaita Vedanta by K. Ramakrisna Rao; and 6) an account of Reflexive Monism, which, viewed as a global system, can incorporate many of the seemingly opposed “isms” that currently populate Consciousness Studies by Max Velmans. Whatever the fundamental nature of Nature might be, it must have the power to give rise to its observable manifestations. Consequently, all the papers in this issue are concerned to give a “natural” account of the relationships among consciousness, mind, and the material world that is entirely consistent with the findings of science, and they all accept that for a unified understanding, mind, consciousness and the material world must have a common base. The aim of the Special Issue is to contribute to a deeper understanding of that base, and to stimulate novel thinking about its nature. (shrink)

The basic theme of Popper's philosophy--that something can come from nothing--is related to the present situation in physical theory. Popper carries his investigation right to the center of current debate in quantum physics. He proposes an interpretation of physics--and indeed an entire cosmology--which is realist, conjectural, deductivist and objectivist, anti-positivist, and anti-instrumentalist. He stresses understanding, reminding us that our ignorance grows faster than our conjectural knowledge.

Econophysics is a branch of economics that applies concepts and methods from physics to the financial markets. This article focuses on the approaches to quantum finance developed by Kirill Ilinski and Belal E. Baaquie to deal with the uncertainty characterizing financial time series. Allegedly, their models rest on a formal analogy between quantum mechanics and finance. In order to evaluate them, we raise the question what is really quantum in quantum econophysics. We then argue that the (...) supposed analogy breaks in an important manner, which is relevant to explain the empirical success of the proposed models. (shrink)

It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schrödinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden variables. We consider instead a grand canonical ensemble of neural networks, by allowing an exchange of neurons with an auxiliary subsystem, to show that the free energy must also be multivalued. By imposing the multivaluedness condition on the free energy we (...) derive the Schrödinger equation with “Planck’s constant” determined by the chemical potential of hidden variables. This shows that quantum mechanics provides a correct statistical description of the dynamics of the grand canonical ensemble of neural networks at the learning equilibrium. We also discuss implications of the results for machine learning, fundamental physics and, in a more speculative way, evolutionary biology. (shrink)

Ballard et al.'s principle of deictic coding as exemplified in the analysis of fixation patterns relies on a functional dichotomy between foveal and extrafoveal vision based on the well-known dependency of spatial resolution on eccentricity. Experimental evidence suggests that for processes of pattern learning and recognition such a dichotomy may be less warranted because its manifestation depends on the learning state of the observer. This finding calls for an explicit consideration of learning mechanisms within deictic coding schemes.

The robustness of the classical tests on means (Z, t, and F) and variances (chi square and F) was investigated by obtaining 30,000 (or, sometimes, 10,000 or 150,000) values of the test statistic under assumption-violating conditions and comparing the actual proportion of Type I errors with the proportion expected when all assumptions are met. The sampling and testing conditions investigated were: population shape (L-shape or bell-shape), relative population variance (1 or 4), sample size (8, 16, or 24), nominal significance (...) level (.05,.01, or.001), and location of rejection region (left-tailed, right-tailed, or two-tailed). All tests on means were nonrobust under most of the investigated conditions, and one was nonrobust under all of them. Both tests on variances were extremely nonrobust under virtually all conditions. The worst nonrobustness of the one- and two-independent-sample Z and t tests rivaled or exceeded that of the notoriously nonrobust chi-square and F tests on variances. (shrink)

Newton's use of mathematics in mechanics was justified by him from his neo-platonician conception of the physical world that was going along with his «absolute, true and mathematical concepts» such as space, time, motion, force, etc. But physics, afterwards, although it was based on newtonian dynamics, meant differently the legitimacy of being mathematized, and this difference can be seen already in the works of eighteenth century «Geometers» such as Euler, Clairaut and d'Alembert (and later on Lagrange, Laplace and others). Despite (...) their inheritance of Newton's achievements, they understood differently the meaning and use of mathematical quantities for physics, in a way that was more neutral to metaphysics. The continental reception and assimilation of Newton's Principia had indeed occured as its budding onto Leibniz' calculus and a cartesian conception of rationality (spread in particular by the malebranchist disciples of Leibniz). This new thought of the legitimacy of mathematization is clearly at variance with Descartes' identification of physics with geometry, but it nevertheless can be traced back to Descartes' conception of magnitudes, as it was developed and analyzed from the notion of dimension in his Regulæ ad directionem ingenii (in particular, rule 14). This idea can be followed afterwards with further philosophical or mathematical specifications through authors such as Kant, Riemann and others. This inquiry into the original thought of magnitudes, and of physical magnitudes conceived through mathematization, leads us to suggest an extension of meaning for the concept of physical magnitude that puts emphasis on its relational and structural aspects rather than restraining it to a simple «numerically valued» acception. Such a broadening would have immediate implications on our comprehension of «non classical» aspects of contemporary physics in the quantum area and in dynamical systems. (shrink)

An astrophysicist offers an introduction to the theoretical principles, practical applications, and far-reaching implications of quantum physics and quantum mechanics.

This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our (...) current understanding of the profound nature of quantum concepts. First edition Hb (1987): 0-521-33495-0 First edition Pb (1988): 0-521-36869-3. (shrink)

In medieval writers we find a distinction between body as a substance – corpus-substantia – and body as a quantity – corpus-quantitas (or quantum). One of the earliest uses of this distinction is in works written by Robert Grosseteste in the 1220s. In this paper I explore his use and understanding of this distinction. I argue that he understands corpus-substantia as such as a dimensionless composite of a first corporeal form, corporeity, and prime matter. Corporeity itself is an active (...) power for three dimensions. Through its infinite and necessary self-multiplication corporeity extends the prime matter it informs into three dimensions, thereby resulting in corpus-quantum. I explore how Grosseteste’s conception of corporeity, though probably based on ideas found in Avicenna, diverges from different understandings of Avicenna’s conception of corporeity proposed by medieval and modern commentators. (shrink)

This paper investigated the variation in the multidimensional competencies and professional development needs of kindergarten teachers using a cross-sectional research design. It involved 54 purposively selected kindergarten teachers and collected the data using the self-assessment tool adopted by the Department of Education from the National Research Center for Teacher Quality in the Philippines. These data were analyzed using both descriptive and inferential statistics. As found, kindergarten teachers have a high level of competencies across dimensions. Also, they have a very high (...) extent of professional development needs in content knowledge and pedagogy and the learning environment and diversity of learners. Moreover, they have a high extent of professional needs in two dimensions. The reported high priorities for training imply more emphasis on providing them professional development activities. Results found no significant difference in the competencies of kindergarten teachers in terms of age, position, civil status, degree, and years of teaching. On the contrary, significant differences revealed in their competencies in content knowledge and pedagogy, learning environment and learners’ diversity, and curriculum and planning between those with masters and without a master’s degree. Lastly, results show no significant difference in their professional development needs. These results have implications for future research and planning for a more responsive and cost-effective professional development initiatives in the locale. (shrink)

We propose a new quantum ontology, in which properties are the fundamental building blocks. In this property ontology physical systems are defined as bundles of type-properties. Not all elements of such bundles are associated with definite case-properties, and this accommodates the Kochen and Specker theorem and contextuality. Moreover, we do not attribute an identity to the type-properties, which gives rise to a novel form of the bundle theory. There are no “particles” in the sense of classical individuals in this (...) ontology, although the behavior of such individuals is mimicked in some circumstances. This picture leads in a natural way to the symmetrization postulates for systems of many “identical particles”. (shrink)

Lifeworld realism and quantum-physical realism are taken as experience-dependent conceptions of the world that become objects of explicit reflection when confronted with context-external discourses. After a brief sketch of the two contexts of experience—lifeworld and quantum physics—and their realist interpretations, I will discuss the quantum world from the perspective of lifeworld realism. From this perspective, the quantum world—roughly speaking—has to be either unreal or else constitute a different reality. Then, I invert the perspective and examine the (...) lifeworld from the standpoint of quantumphysical realism. This conception of the lifeworld has gained momentum from new research results in recent decades. Despite its experiential basis, quantum-physical realism bears an ambiguity akin to that of lifeworld realism. While the perspectival inversion serves to highlight the problem, it also contributes to an improved understanding of lifeworld-realism. (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast (...) to Wave Function Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)