Marginal structural models can be used to estimate the causal effect of a potentially time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting can be sensitive to model misspecification and lead to high-variance estimates due to extreme weights. Various methods have been proposed to partially address this, including covariate balancing propensity score to mitigate treatment model misspecification, and truncation and stabilized-IPTW to temper extreme weights. In this article, (...) we present kernel optimal weighting, a convex-optimization-based approach that finds weights for fitting the MSMs that flexibly balance time-dependent confounders while simultaneously penalizing extreme weights, directly addressing the above limitations. We further extend KOW to control for informative censoring. We evaluate the performance of KOW in a simulation study, comparing it with IPTW, sIPTW, and CBPS. We demonstrate the use of KOW in studying the effect of treatment initiation on time-to-death among people living with human immunodeficiency virus and the effect of negative advertising on elections in the United States. (shrink)

In order to reduce the dimensionality of parameter space and enhance out-of-sample forecasting performance, this research compares regularization techniques with Autometrics in time-series modeling. We mainly focus on comparing weighted lag adaptive LASSO with Autometrics, but as a benchmark, we estimate other popular regularization methods LASSO, AdaLASSO, SCAD, and MCP. For analytical comparison, we implement Monte Carlo simulation and assess the performance of these techniques in terms of out-of-sample Root Mean Square Error, Gauge, and Potency. The comparison is assessed with (...) varying autocorrelation coefficients and sample sizes. The simulation experiment indicates that, compared to Autometrics and other regularization approaches, the WLAdaLASSO outperforms the others in covariate selection and forecasting, especially when there is a greater linear dependency between predictors. In contrast, the computational efficiency of Autometrics decreases with a strong linear dependency between predictors. However, under the large sample and weak linear dependency between predictors, the Autometrics potency ⟶ 1 and gauge ⟶ α. In contrast, LASSO, AdaLASSO, SCAD, and MCP select more covariates and possess higher RMSE than Autometrics and WLAdaLASSO. To compare the considered techniques, we made the Generalized Unidentified Model for covariate selection and out-of-sample forecasting for the trade balance of Pakistan. We train the model on 1985–2015 observations and 2016–2020 observations as test data for the out-of-sample forecast. (shrink)

Multiple sensory signals from visual, somatosensory and vestibular systems are used for human postural control. To maintain postural stability, the central nervous system keeps the center of mass (CoM) within the base of support. The influence of the stomatognathic motor system on postural control has been established under static conditions, but it has not yet been investigated during dynamic steady-state balance. The purpose of the study was to investigate the effects of controlled stomatognathic motor activity on the control and (...) stability of the CoM during dynamic steady-state balance. A total of 48 physically active and healthy adults were assigned to three groups with different stomatognathic motor conditions: jaw clenching, tongue pressing and habitual stomatognathic behavior. Dynamic steady-state balance was assessed using an oscillating platform and the kinematic data were collected with a 3D motion capturing system. The path length (PL) of the 3D CoM trajectory was used for quantifying CoM sway. Temporal dynamics of the CoM movement was assessed with a detrended fluctuation analysis (DFA). An uncontrolled manifold (UCM) analysis was applied to assess the stability and control of the CoM with a subject-specific anthropometric 3D model. The statistical analysis revealed that the groups did not differ significantly in PL, DFA scaling exponents or UCM parameters. The results indicated that deliberate jaw clenching or tongue pressing did not seem to affect the sway, control or stability of the CoM on an oscillating platform significantly. Because of the task-specificity of balance, further research investigating the effects of stomatognathic motor activities on dynamic steady-state balance with different movement tasks are needed. Additionally, further analysis by use of muscle synergies or co-contractions may reveal effects on the level of muscles, which were not visible on the level of kinematics. This study can contribute to the understanding of postural control mechanisms, particularly in relation to stomatognathic motor activities and under dynamic conditions. (shrink)

Introduction: Falls are the leading cause of fatal and nonfatal injuries among older adults. Studies showed that older adults can reduce the risk of falls after participation in an unexpected perturbation-based balance training, a relatively novel approach that challenged reactive balance control. This study aims to investigate the effect of the practice schedule on reactive balance function and its transfer to proactive balance function. Our primary hypothesis is that improvements in reactive balance control following block (...) PBBT will be not inferior to the improvements following random PBBT.Methods and Analysis: This is a double-blind randomized controlled trial. Fifty community-dwelling older adults will be recruited and randomly allocated to a random PBBT group or a block PBBT group. The random PBBT group will receive eight training sessions over 4 weeks that include unexpected machine-induced perturbations of balance during hands-free treadmill walking. The block PBBT group will be trained by the same perturbation treadmill system, but only one direction will be trained in each training session, and the direction of the external perturbations will be announced. Both PBBT groups will receive a similar perturbation intensity during training, the same training period, and the same concurrent cognitive tasks during training. The generalization and transfer of learning effects will be measured by assessing the reactive and proactive balance control during standing and walking before and after 1 month of PBBT, for example, step and multiple steps and fall thresholds, Berg balance test, and fear of falls. The dependent variable will be rank transformed prior to conducting the analysis of covariance to allow for nonparametric analysis.Discussion: This research will explore which of the balance retraining paradigms is more effective to improve reactive balance and proactive balance control in older adults over 1 month. The research will address key issues concerning balance retraining: older adults’ neuromotor capacities to optimize training responses and their applicability to real-life challenges.Clinical Trial Registration: Helsinki research ethics approval has been received. (shrink)

The injunction to “analyze the way you randomize” is well known to statisticians since Fisher advocated for randomization as the basis of inference. Yet even those convinced by the merits of randomization-based inference seldom follow this injunction to the letter. Bernoulli randomized experiments are often analyzed as completely randomized experiments, and completely randomized experiments are analyzed as if they had been stratified; more generally, it is not uncommon to analyze an experiment as if it had been randomized differently. This article (...) examines the theoretical foundation behind this practice within a randomization-based framework. Specifically, we ask when is it legitimate to analyze an experiment randomized according to one design as if it had been randomized according to some other design. We show that a sufficient condition for this type of analysis to be valid is that the design used for analysis should be derived from the original design by an appropriate form of conditioning. We use our theory to justify certain existing methods, question others, and finally suggest new methodological insights such as conditioning on approximate covariate balance. (shrink)

Randomized controlled trials in educational research tend to be small. Small trials can have large, chance, imbalances in important covariates. For studies with sample sizes greater than 50, chance imbalances can be corrected using analysis of covariance; for small trials, however, statistical power is maximized if the trial is balanced and analysis of covariance is used in the analysis. The aim of the present study was to discuss methods of improving covariate balance in trial design and to demonstrate (...) the method of minimization. Using an exemplar of a cluster or class‐randomized trial with 29 classes, we employed minimization to achieve covariate balance. Minimization achieved good balance on four prognostic variables. Many trialists in education use restricted forms of allocation, including pairing or stratified randomization. These approaches have disadvantages. Another approach rarely used in educational research is minimization. Minimization uses a simple arithmetic algorithm to produce balanced groups across a number of important covariates and should be more widely used in educational and psychological research. (shrink)

The monograph is an English, expanded and revised version of the book Cheshko, V. T., Ivanitskaya, L.V., & Glazko, V.I. (2018). Anthropocene. Philosophy of Biotechnology. Moscow, Course. The manuscript was completed by me on November 15, 2019. It is a study devoted to the development of the concept of a stable evolutionary human strategy as a unique phenomenon of global evolution. The name “An Evolutionary Metaphysics (Cheshko, 2012; Glazko et al., 2016). With equal rights, this study could be entitled “Biotechnology (...) as a result and factor of the evolutionary processˮ. The choice in favor of used “The Evolutionary Metaphysics of Human Enhancement Technologiesˮ was made in accordance with the basic principle of modern post-academician and human-sized science, a classic example of which is biotechnology. The “Metaphysics of Evolution” and “Evolutionary Metaphysics” concepts are used in several ways in modern philosophical discourse. In any case, the values contain a logical or associative reference to the teleological nature of the evolutionary process (Hull, 1967, 1989; Apel, 1995; Faye, 2016; Dupre, 2017; Rose, 2018, etc). In our study, the “evolutionary metaphysics” serves to denote the thesis of the rationalization and technologization of global evolution and anthropogenesis, in particular. At the same time, the postulate of an open future remains relevant in relation to the results of the evolutionary process. The theory of evolution of complex, including the humans system and algorithm for its constructing are а synthesis of evolutionary epistemology, philosophical anthropology and concrete scientific empirical basis in modern science. ln other words, natural philosophy is regaining the status bar element theoretical science in the era of technology-driven evolution. The co-evolutionary concept of 3-modal stable evolutionary strategy of Homo sapiens is developed. The concept based оn the principle of evolutionary complementarity of anthropogenesis: value of evolutionary risk and evolutionary path of human evolution are defined bу descriptive (evolutionary efficiency) and creative-teleological (evolutionary correctness) parameters simultaneously, that cannot bе instrumental reduced to others ones. Resulting volume of both parameters define the vectors of blological, social, cultural and techno-rationalistic human evolution Ьу two gear mechanism genetic and cultural co-evolution and techno-humanitarian balance. The resultant each of them сап estimated Ьу the ratio of socio-psychological predispositions of humanization / dehumanization in mentality. Explanatory model and methodology of evaluation of creatively teleological evolutionary risk component of NBIC technological complex is proposed. Integral part of the model is evolutionary semantics (time-varying semantic code, the compliance of the blological, socio-cultural and techno-rationalist adaptive modules of human stable evolutionary strategy). It is seem necessary to make three clarifications. First, logical construct, “evolutionary metaphysics” contains an internal contradiction, because it unites two alternative explanatory models. “Metaphysics”, as a subject, implies deducibility of the process from the initial general abstract principle, and, consequently, the outcome of the development of the object is uniquely determined by the initial conditions. Predicate, “evolutionary”, means stochastic mechanism of realizing the same principle by memorizing and replicating random choices in all variants of the post-Darwin paradigm. In philosophy, random choice corresponds to the category of “free will” of a reasonable agent. In evolutionary theory, the same phenomenon is reflected in the concept of “covariant replication”. Authors will attempt to synthesize both of these models in a single transdisciplinary theoretical framework. Secondly, the interpretation of the term “evolutionary (adaptive) strategyˮ is different from the classical definition. The difference is that the adaptive strategy in this context is equivalent to the survival, i.e. it includes the adaptation to the environment and the transformation (construction) of the medium in accordance with the objectives of survival. To emphasize this difference authors used verbal construction “adaptiveˮ (rather than “evolutionaryˮ) strategy as more adequate. In all other cases, the two terms may be regarded as synonymous. Thirdly, the initial two essays of this series were published in one book in 2012. Their main goal was the development of the logically consistent methodological concept of stable adaptive (evolutionary) strategy of hominines and the argumentation of its heuristic possibilities as a transdisciplinary scientific paradigm of modern anthropology. The task was to demonstrate the possibilities of the SESH concept in describing and explaining the evolutionary prospects for the interaction of social organization and technology (techno-humanitarian balance) and the associated biological and cultural mechanisms of the genesis of religion (gene-cultural co-evolution). In other words, it was related to the sphere of cultural and philosophical anthropology, i.e. to the axiological component of any theoretical constructions describing the behavior of self-organizing systems with human participation. In contrast, the present work is an attempt to introduce this concept into the sphere of biological anthropology and, consequently, its main goal is to demonstrate the possibility of verification of its main provisions by means of procedures developed by natural science, i.e. refers to the descriptive component of the same theoretical constructions. The result of this in the future should be methods for assessing, calculating and predicting the risk of loss of biological and cultural identity of a person, associated with a permanent and continuously deepening process of development of science and technology. (shrink)

Probability; Continuous probability distributions; Estimation; Tests of significance; Analysis of variance; Experimental design; Balanced incomplete randomized block designs and the analysis of covariance; Correlation and function fitting; The poisson process and couting problems; Distributions free tests.

In cooperative game theory with transferable utilities, there are two well-established ways of redistributing Shapley value payoffs: using egalitarian Shapley values, and using consensus values. We present parallel characterizations of these classes of solutions. Together with the axioms that characterize the original Shapley value, those that specify the redistribution methods characterize the two classes of values. For the class of egalitarian Shapley values, we focus on redistributions in one-person unanimity games from two perspectives: allowing the worth of coalitions to vary, (...) while keeping the player set fixed; and allowing the player set to change, while keeping the worth of coalitions fixed. This class of values is characterized by efficiency, the balanced contributions property for equal contributors, weak covariance, a proportionately decreasing redistribution in one-person unanimity games, desirability, and null players in unanimity games. For the class of consensus values, we concentrate on redistributions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}-person unanimity games from the same two perspectives. This class of values is characterized by efficiency, the balanced contributions property for equal contributors to social surplus, complement weak covariance, a proportionately decreasing redistribution in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}-person unanimity games, desirability, and null players in unanimity games. (shrink)

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be (...) more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments. (shrink)

Recently, there has been increasing interest in the use of heavily restricted randomization designs which enforce balance on observed covariates in randomized controlled trials. However, when restrictions are strict, there is a risk that the treatment effect estimator will have a very high mean squared error. In this article, we formalize this risk and propose a novel combinatoric-based approach to describe and address this issue. First, we validate our new approach by re-proving some known properties of complete randomization and (...) restricted randomization. Second, we propose a novel diagnostic measure for restricted designs that only use the information embedded in the combinatorics of the design. Third, we show that the variance of the MSE of the difference-in-means estimator in a randomized experiment is a linear function of this diagnostic measure. Finally, we identify situations in which restricted designs can lead to an increased risk of getting a high MSE and discuss how our diagnostic measure can be used to detect such designs. Our results have implications for any restricted randomization design and can be used to evaluate the trade-off between enforcing balance on observed covariates and avoiding too restrictive designs. (shrink)

Covariant Realism Hermeneutic phenomenology of science implies a particular version of realism. It approaches scientific entities in a twofold perspective: in their relation to other parts of the theory (as elements in a theoretical "language"), and in relation to the lifeworld as mediated by laboratory practices; as "fulfilled" in laboratory situations that "produce" worldly objects. The question then arises of the relation between the two perspectives; as Ginev has pointed out, there is danger of a theoretical essentialism which is implied (...) when the mathematical projection is conceived as operationalized by experiment. Ginev's proposal to avoid this involves the concept of "inscription." This paper proposes another approach, covariant realism, which draws from Heidegger's notion of formal indication and which makes explicit the temporality of theoretical objects in the flow of the research process. Formal indication does not so much describe phenomena as call them to our attention in a way that we can activate ourselves (as in laboratory contexts); it characterizes phenomena which are understood to be provisionally grasped, already interpreted, and anticipated as able to show themselves differently in different contexts. The value of this approach suggests deeper possibilities for hermeneutic phenomenology of science than have hitherto been explored. (shrink)

The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where 5-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum non-locality (...) into relativistic spacetimes. (shrink)

Analysis of Emmy Noether’s 1918 theorems provides an illuminating method for testing the consequences of “coordinate generality”, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether’s first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein (an apparent shift in Einstein’s thinking on the significance of general covariance between 1916 and 1918 is highlighted). (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of (...) classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

In this paper, the covariance control algorithm for nonlinear stochastic systems using covariance feedback is studied. Covariance control of nonlinear systems scenario involves the theory of covariance control based on the idea of the covariance feedback. Therefore, the proposed covariance control algorithm is derived for our case, firstly by applying the covariance control method and linear approximation of nonlinear systems, and then it is achieved by adopting this method for a class of nonlinear stochastic systems by using feedback linearization idea (...) and a covariance feedback controller. The effectiveness of the proposed covariance feedback algorithm is studied using numerous simulations concerning different nonlinear case studies. (shrink)

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein. (shrink)

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The (...) anomalies include neutrino oscillations, non-locality, and gravity.The two key QFT assumptions that are altered in PRD are the following: fields depend on space and time; and interactions between fields are local. Locality and non-locality refer to the correlation of particles with space-like separation. A local theory does not allow the existence of greater than light speed correlations, while a non-local theory does. PRD is a non-local theory that allows fields to depend on space, time and an invariant evolution parameter. A formulation of PRD is presented together with applications that can be directly compared to results from the conventional paradigm. (shrink)

John Earman's recent proposal that a substantive version of general covariance consists in the requirement that diffeomorphism invariance be a gauge symmetry is critically assessed. I argue that such a principle does not serve to differentiate general relativity from pre-relativistic theories. A model-theoretic characterization of two formulations of specially-relativistic theories is suggested. Diffeomorphisms are symmetries of only one such style of formulation and, I argue, Earman's proposal does not provide a reason to deny diffeomorphisms the status of gauge transformations relative (...) to this formulation. Carlo Rovelli's distinction between "passive" and "active" diffeomorphism invariance is also clarified. (shrink)

This paper represents an attempt to clarify a number of long-standing issues concerning the nature and status of the special and general principles of relativity in particular and symmetry or invariance principles in general. An analysis of the active and passive interpretations of symmetry operations is offered. This analysis yields an evaluation of the old covariance-invariance issue. It also demonstrates that the passive interpretation, insofar as it is not trivial, is parasitic on the active picture. Finally, the analysis shows that (...) grave difficulties lie in the way of any attempt to generalize the special principle of relativity in a manner like the one Einstein originally proposed. (shrink)

How can we reconcile two claims that are now both widely accepted: Kretschmann's claim that a requirement of general covariance is physically vacuous and the standard view that the general covariance of general relativity expresses the physically important diffeomorphism gauge freedom of general relativity? I urge that both claims can be held without contradiction if we attend to the context in which each is made.

The theory of scale-covariant gravity is extended to include charged matter and electromagnetism at the classical level. The possibility of charge creation exists and the creation rate of charge differs from the creation rate of matter. A variational principle for scale-covariant gravity and electromagnetism coupled to a charged perfect fluid is given.

The structure of covariant observables—normalized positive operator measures (POMs)—is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given.

iinstein oered the prin™iple of gener—l ™ov—ri—n™e —s the fund—ment—l physi™—l prin™iple of his gener—l theory of rel—tivityD —nd —s responsi˜le for extending the prin™iple of rel—tivity to —™™eler—ted motionF „his view w—s disputed —lmost immedi—tely with the ™ounterE™l—im th—t the prin™iple w—s no rel—tivity prin™iple —nd w—s physi™—lly v—™uousF „he dis—greeE ment persists tod—yF „his —rti™le reviews the development of iinstein9s thought on gener—l ™ov—ri—n™eD its rel—tion to the found—tions of gener—l rel—tivity —nd the evolution of the ™ontinuing de˜—te (...) over his viewpointF.. (shrink)

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

This book contains a cohesive overview of the most important theories and insights in the field of business ethics. At the same time, it further tailors these theories to the situation in which organizations function, presenting criteria that can be used to measure, assess, improve and report on corporate integrity.

In spite of a renewed interest in the relationship between spirituality and managerial thinking, the literature covering the link between Islam and management has been sparse – especially in the area of ethics. One potential reason may be the cultural diversity of nearly 1.3 billion Muslims globally. Yet, one common element binding Muslim individuals and countries is normative Islam. Using all four sources of this religion’s teachings, we outline the parameters of an Islamic model of normative business ethics. We explain (...) how this ethics model seeks to balance the needs of multiple stakeholders, and discuss its enforcement mechanisms. This Islamic approach to business ethics is centered around criteria that are in common with stakeholder theory such as justice and balance, and includes unique additional criteria such as trust and benevolence. (shrink)

We construct an explicit covariant Majorana formulation of Maxwell electromagnetism which does not make use of vector 4-potential. This allows us to write a “Dirac” equation for the photon containing all the known properties of it. In particular, the spin and (intrinsic) boost matrices are derived and the helicity properties of the photon are studied.

The Representational Theory of the Mind allows for psychological explanations couched in terms of the contents of propositional attitudes. Propositional attitudes themselves are taken to be relations to mental representations. These representations (partially) determine the contents of the attitudes in which they figure. Thus, Representationalism owes an explanation of the contents of mental representations. This essay constitutes an atomistic theory of the content of formally or syntactically simple mental representation, proposing that the content of such a representation is determined by (...) the intersection of the representation's correlational and control properties. The theory is distinguished from standard information-based accounts of mental content in allowing that the relevant correlations be contingent while insisting on an efferent aspect to mental content. The theory on offer allows for a natural explanation of misrepresentation, finds a niche for the notion of narrow content, welcomes radical first person fallibility with respect to questions of content, admits of mental ambiguity and recognizes that the future of a psychological agent is a factor in determining the content of the agent's present psychological states. (shrink)

The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on (...) wave-particle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory. (shrink)

Relativity Theory by Albert Einstein has been so far littleconsidered by cognitive scientists, notwithstanding its undisputedscientific and philosophical moment. Unfortunately, we don't have adiary or notebook as cognitively useful as Faraday's. But physicshistorians and philosophers have done a great job that is relevant bothfor the study of the scientist's reasoning and the philosophy ofscience. I will try here to highlight the fertility of a `triangulation'using cognitive psychology, history of science and philosophy of sciencein starting answering a clearly very complex question:why (...) did Einstein discover Relativity Theory? Here we arenot much concerned with the unending question of precisely whatEinstein discovered, that still remains unanswered, for we have noconsensus over the exact nature of the theory's foundations. We are mainly interested in starting to answer the`how question', and especially the following sub-question: what were his goals and strategies in hissearch? I will base my argument on fundamental publications ofEinstein, aiming at pointing out a theory-specific heuristic, settingboth a goal and a strategy: covariance/invariance.The result has significance in theory formation in science, especiallyin concept and model building. It also raises other questions that gobeyond the aim of this paper: why was he so confident in suchheuristic? Why didn't many other scientists use it? Where did he keep? such a heuristic? Do we have any other examples ofsimilar heuristic search in other scientific problemsolving? (shrink)

The traditional approach to the covariance problem in quantum mechanics is inverted and the space-time transformations are assumed as the basicunknowns, according to the prescription that the correspondence principle and the commutation rules must becovariant. It is shown that the only solutions are either Galilean or Lorentzian (including the possibility of an imaginary light-velocity c2<0). The Dirac formalism for the wave-equation and the condition c2>0 are obtained simoultaneously as theunique solution, provided that the Hamiltonian is Hermitean (in the usual sense), (...) and the internal degrees of freedom allow for afinite-dimensional representation. Infinite-dimensional representations are introduced in order to extend the Hamiltonian formalism to other spinors. (shrink)

New numerical solutions of 3+1D covariant kinetic theory are reported for nuclear collisions in the energy domain Ecm∼200 AGeV. They were obtained using the MPC 0.1.2 parton transport code employing high parton subdivision to retain Lorentz covariance. The solutions are compared to those of relativistic hydrodynamics employing Cooper–Frye isotherm freeze-out. The transport solutions follow a different dynamical path than hydrodynamics due to large dissipative effects when pQCD scattering rates and HIJING initial conditions are assumed. The transport freeze-out four-volume is sensitive (...) to the reaction rates. The final transverse momentum distributions are found to deviate by up to an order of magnitude from those of Cooper–Frye frozen hydrodynamics. (shrink)

A criterion is given for characterizing quantum mechanical joint distributions that have the same covariance of position and momentum.

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire (...) an imaginary part which is linear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter. (shrink)

We present a simple first step toward a relativistically covariant generalization of the Bohm-Bub hidden-variable theory. The model is applicable to spin measurement on a single Dirac particle and describes the collapse of the state vector to a spin-up or spin-down state. The essential postulate is that the hidden-variable vector transforms in the same way as the state vector under a Lorentz transformation. This yields a covariant collapse equation, which reduces to the ordinary Bohm-Bub equation for an observer stationary with (...) respect to the particle and shows a time dilated collapse for a moving observer. The model yields the correct quantum transition probabilities for all observers. (shrink)