This study shows how precise simple analytical solutions for the generalized Dirac equation with repulsive vector and attractive energy-dependent Lorentz scalar potentials, position-dependent mass potential, and a tensor interaction term can be obtained within the framework of both similarity transformation and the asymptotic iteration methods. These methods yield a significant improvement over existing approaches and provide more plausible and applicable ways in explaining the pseudospin symmetry’s breaking mechanism in nuclei.

A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state ψ is coupled to the metric tensor g, and the effect of the “quantum potential” is absorbed in the geometry. At the same time, ψ satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 (...) unknowns: ψ and the components of the metric tensor gµv. The states of stable localized particles are identified, and vacuum-state solutions for both the Euclidean and the Lorentzian case are explicitly presented. (shrink)

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace (...) zero. In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality. (shrink)

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the (...) Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on (...) the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation.The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about “God’s particle” and its mass generation for all the other particles. (shrink)

In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{0,1}$\end{document}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be (...) completely characterised by algebraic invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum, the quantum potential and the relativistic time evolution of its spin for the first time. (shrink)

A massless Weyl-invariant dynamics of a scalar, a Dirac spinor, and electromagnetic fields is formulated in a Weyl space, W4, allowing for conformal rescalings of the metric and of all fields with nontrivial Weyl weight together with the associated transformations of the Weyl vector fields κμ, representing the D(1) gauge fields, with D(1) denoting the dilatation group. To study the appearance of nonzero masses in the theory the Weyl symmetry is broken explicitly and the corresponding reduction of the Weyl space (...) W4 to a pseudo-Riemannian space V4 is investigated assuming the breaking to be determined by an expression involving the curvature scalar R of the W4 and the mass of the scalar, selfinteracting field. Thereby also the spinor field acquires a mass proportional to the modulus Φ of the scalar field in a Higgs-type mechanism formulated here in a Weyl-geometric setting with Φ providing a potential for the Weyl vector fields κμ. After the Weyl-symmetry breaking, one obtains generally covariant and U(1) gauge covariant field equations coupled to the metric of the underlying V4. This metric is determined by Einstein's equations, with a gravitational coupling constant depending on Φ, coupled to the energy momentum tensors of the now massive fields involved together with the (massless) radiation fields. (shrink)

In this work, we reconstruct the cosmological unified dark fluid model proposed previously by Elkhateeb (Astrophys Space Sci 363(1):7, 2018) in the framework of _f_(_R_) gravity. Utilizing the equivalence between the scalar-tensor theory and the _f_(_R_) gravity theory, the scalar field for the dark fluid is obtained, whence the _f_(_R_) function is extracted and its viability is discussed. The _f_(_R_) functions and the scalar field potentials have then been extracted in the early and late times of asymptotically de Sitter (...) spacetime. The ability of our function to describe early time inflation is also tested. The early time scalar field potential is used to derive the slow roll inflation parameters. Our results of the tensor-to-scalar ratio _r_ and the scalar spectral index \(n_s\) are in good agreement with results from Planck-2018 TT+TE+EE+lowE data for the model parameter \(n > 2\). (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)

There are well-known problems associated with the idea of gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation. We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized theory without introducing further structure. We then address a potential response by showing (...) that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation. (shrink)

The generalized thermodynamic potential analysis of nonlinear irreversible processes precludes the analysis of rotational processes. The nonexistence of scalar potential functions necessitates a thermodynamic analysis of the system forces. A field analysis in the phase space of the generalized displacements and velocities treats the force components as tensors of second order that tend to deform and rotate the irreversible process, which is viewed as an elastic material. The analysis of chemical oscillatory processes involves the introduction of the thermodynamic (...) vector potential, which is subsequently used in the formulation of a variational principle and to define an energy flux vector. The direction of energy flow elucidates the mechanism by which steady motion is maintained and it is a characteristic property of open systems. Field analyses of systems that are described by half and single degrees of freedom are contrasted. (shrink)

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical (...) equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, and by Knox (2011) that general relativity is equivalent to teleparallel gravity, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity. (shrink)

The paper investigates the status of gravitational energy in Newtonian Gravity, developing upon recent work by Dewar and Weatherall. The latter suggest that gravitational energy is a gauge quantity. This is potentially misleading: its gauge status crucially depends on the spacetime setting one adopts. In line with Møller-Nielsen’s plea for a motivational approach to symmetries, we supplement Dewar and Weatherall’s work by discussing gravitational energy–stress in Newtonian spacetime, Galilean spacetime, Maxwell-Huygens spacetime, and Newton–Cartan Theory. Although we ultimately concur with Dewar (...) and Weatherall that the notion of gravitational energy is problematic in NCT, our analysis goes beyond their work. The absence of an explicit definition of gravitational energy–stress in NCT somewhat detracts from the force of Dewar and Weatherall’s argument. We fill this gap by examining the supposed gauge status of prima facie plausible candidates—NCT analogues of gravitational energy–stress pseudotensors, the Komar mass, and the Bel-Robinson tensor. Our paper further strengthens Dewar and Weatherall’s results. In addition, it sheds more light upon the subtle link between sufficiently rich inertial structure and the definability of gravitational energy in NG. (shrink)

Neurite orientation dispersion and density imaging is a diffusion model specifically designed for brain magnetic resonance imaging. Despite recent studies suggesting that NODDI modeling might be more sensitive to brain development than diffusion tensor imaging, these studies were limited to a relatively small age range and mainly based on the manually operated region of interest analysis. Therefore, this study applied NODDI to investigate brain development in a large sample size of 214 subjects ranging in ages from 0 to 14. (...) The whole brain was automatically segmented into 122 regions. The maturation trajectory of each region was characterized by the time course of diffusion metrics and further quantified using nonlinear regression. The NODDI-derived metrics, neurite density index and orientation dispersion index, increased with age. And these two metrics were superior to the DTI-derived metrics in SVM regression models of age. The NDI in white matter exhibited a more rapid growth than that in gray matter. These diffusion indicators experienced conspicuous increases during early childhood and the growth speed slowed down in adolescence. Region-specific maturation patterns were described throughout the brain, including white matter, cortical and deep gray matter. These development patterns were evaluated and discussed on the basis of NODDI’s model assumptions. To summarize, this study verified the high sensitivity of NODDI to age over a crucial developmental period from newborn to adolescence. Moreover, the existing knowledge of brain development has been complemented, suggesting that NODDI has a potential capability in the investigation of brain development. (shrink)

Gravitomagnetic equations result from applying quaternionic differential operators to the energy–momentum tensor. These equations are similar to the Maxwell’s EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; the Hamilton–Jacobi equation loaded by the quantum potential. (...) This equation in pair with the continuity equation leads to getting the Schrödinger equation describing a state of the superfluid quantum medium ; gravitomagnetic wave equations loaded by forces acting on the outer space. These waves obey to the Planck’s law of radiation. (shrink)

The right inferior frontal gyrus has most strongly, although not exclusively, been associated with response inhibition, not least based on covariations of behavioral performance measures and local gray matter characteristics. However, the white matter microstructure of the rIFG as well as its connectivity has been less in focus, especially when it comes to the consideration of potential subdivisions within this area. The present study reconstructed the structural connections of the three main subregions of the rIFG using diffusion tensor (...) imaging, and further assessed their associations with behavioral measures of inhibitory control. The results revealed a marked heterogeneity of the three subregions with respect to the pattern and extent of their connections, with the pars orbitalis showing the most widespread inter-regional connectivity, while the pars opercularis showed the lowest number of interconnected regions. When relating behavioral performance measures of a stop signal task to brain structure, the data indicated an association between the dorsal opercular connectivity and the go reaction time and the stopping accuracy. (shrink)

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each (...) non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories. (shrink)

In order to get to a geometrically based theory of gravitation and electromagnetism, a gauge covariant bimetric tetrad space-time is introduced. The Weylian connection vector is derived from the tetrads and it is identified with the electromagnetic potential vector. The formalism is simplified by the use of gauge-invariant quantities. The theory contains a contorsion tensor that is connected with spinning properties of matter. The electromagnetic field may be induced by conventional sources and by spinning matter. In absence of (...) spinning matter, the equations are identical with those of the gauge-covariant bimetric theory.(23). (shrink)

In the United States, approximately 2.53 million people sustain a concussion each year. Relative to adults, youth show greater cognitive deficits following concussion and a longer recovery. An accurate and reliable imaging method is needed to determine injury severity and symptom resolution. The primary objective of this study was to characterize concussions with diffusion tensor imaging. This was performed through a normative Z-scoring analysis of DTI metrics, fractional anisotropy, axial diffusivity, and radial diffusivity, to quantify patient-specific injuries and identify (...) commonly damaged brain regions in paediatric concussion patients relative to healthy controls. It was hypothesized that personalizing the detection analysis through normative Z-scoring would provide an understanding of trauma-induced microstructural damage. Concussion patients were volunteers recruited from the Emergency Department of the McMaster Children’s Hospital with a recent concussion, 9 males and 17 females, mean age 14.22 ± 2.64, while healthy paediatric brain DTI datasets were obtained from an MRI data repository. Significant abnormalities were commonly found in the longitudinal fasciculus, fronto-occipital fasciculus, and corticospinal tract, while unique abnormalities were localized in a number of other areas reflecting the individuality of each child’s injury. Total injury burden, determined by the number of regions containing outliers per DTI metric per patient, was used as the metric to quantify the overall injury severity of each patient. The primary outcome of this analysis found that younger patients experienced a significantly greater injury burden when measured using fractional anisotropy. These results show that DTI was able to detect microstructural changes caused by concussion, on a per-person basis, and has the potential to be a useful tool for improving diagnostic accuracy and prognosis of a concussion. (shrink)

Fibre suspension has garnered considerable attention in turbulent flows that are used in many industries. Solid particles, such as dust particles, notably affect the turbulent flow field in a rotational frame. In assessing their impacts, the dusty turbulent flow for fibre suspensions needs to be studied in a frame of rotation that can be substantially applied in many industries. This study, therefore, aims to build a theoretical model for the energy motion of dusty turbulent flow of fibre suspensions in a (...) rotational frame. The turbulence momentum equation was considered to formulate the model in presence of dusty fluid rotating flow of fibre suspensions. The newly derived equation was derived in second-order correlation tensors Fi,j, Wi,j, Gi,j, Si,j, Xi,j, Yi,j, Qi,j, and Ri,j at any two points in the flow domain, where the tensors were expressed as space, time, and distance functions. The developed model is a considerable improvement because it takes into account all of the potential influential parameters that could affect the motion of turbulent energy, such as dust particles, suspending particles, and rotating frame. However, the impact of these parameters on turbulence energy motion must be evaluated in order to assess the performance of turbulence systems utilized in a variety of industries, such as paper manufacturing. The present theoretical development will contribute to open up experimental and numerical research opportunities for the advancement of the industry, science, and technology. (shrink)

The significance of the de Broglie/Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the single-particle Newton–Wigner position. The effect of non-positive excursions of the ensemble density for extreme cases of positive-energy waves is easily computed using an integral of the equations of motion developed here for free spin-0 particles in 1 + 1 dimensions and is interpreted in terms of virtual-like pair creation and annihilation beneath the Compton wavelength. A Bohm-theoretic description of the acausal explosion of (...) a specific Newton–Wigner-localized state is presented in detail. The presence of virtual pairs found is interpreted as the Bohm picture of the spatial extension beyond single point particles proposed in the 1960s as to why space-like hyperplane dependence of the Newton–Wigner wavefunctions may be needed to achieve Lorentz covariance. For spin-1/2 particles the convective current is speculatively utilized for achieving parity with the spin-0 theory. The spin-0 improper quantum potential is generalized to an improper stress tensor for spin-1/2 particles. (shrink)

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rotating body. This implies the corresponding improvements in equations of motion. Using the Liouville’s theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of (...) a second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector. (shrink)

A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and (...) vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, our reformulation retains the potentially important antisymmetric contribution. (shrink)

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of the causal interpretation. It is shown how an osculating Finslerian metric tensor, a torsion tensor, and a tetrad field define respectively the strain, the dislocation density, and the Burgers vector in the “natural state” of the wave, which is a non-Riemannian space of distant parallelism. A quantum torque determined (...) by the quantum potential is introduced and the example of a screw dislocated wave is discussed. (shrink)

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in “six-vector” form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's four equations expressed as (...) one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated. (shrink)

By means of a Clebsch representation which differs from that previously applied to electromagnetic field theory it is shown that Maxwell's equations are derivable from a variational principle. In contrast to the standard approach, the Hamiltonian complex associated with this principle is identical with the generally accepted energy-momentum tensor of the fields. In addition, the Clebsch representation of a contravariant vector field makes it possible to consistently construct a field theory based upon a direction-dependent Lagrangian density (it is this (...) kind of Lagrangian density that may arise when developing the Finslerian extension of general relativity). The corresponding field equations are proved to be independent of any gauge of Clebsch potentials. The law of energy-momentum conservation of the field appears to be covariant and integrable in a rather wide class of direction-dependent Lagrangian densities. (shrink)

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary charge), (...) the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge. (shrink)

Newtonian and Machian aspects of the stationary gravitational field are brought into formal analogy with a stationary electromagnetic field. The electromagnetic vector potential equals (up to a factor) the timelike Killing vector field. The current density is given by the contraction of the Killing vector with the Ricci tensor. A coordinate-dependent split in electric and magnetic field vectors is given, and some results of classical electrodynamics are used to illustrate the analogy. In the linearized theory, the usual Maxwell (...) equations are obtained. The analogy also holds from the point of view of particle motion. The geodesic equation is brought into a special form that exhibits an analog to the Lorentz force. Two examples (which have played an important role in the theoretical discovery of Machian effects) are considered. (shrink)

It is shown that in every gauge the potential of the electromagnetic field in the presence of sources is resolved by an extension of the Helmholtz theorem into a solenoidal component and an irrotational component irrelevant for description of the field. Only irrotational components are affected by gauge transformations; in Coulomb gauge the irrotational component vanishes: the potential is solenoidal. The method of solution of the wave equation by use of positive- and negative-frequency parts is extended to solutions (...) of D'Alembert's equation, and applied to equations satisfied by the potential in Coulomb gauge and the electric and magnetic vectors. Fourier transforms of potentials specifying destruction/creation operators become time dependent in the presence of sources. Our central equation states this time dependence. Frequency parts of Maxwell's equations are obtained. When the retarded potential in Coulomb gauge is resolved into kinetic and dissipative components, the latter is shown to be in radiation gauge. Correspondingly, the energy/stress tensor is resolved into three components; the power/force density, into two: a kinetic and a dissipative component. Work done by the latter component is negative: energy and momentum are dissipated from matter to radiation. Boson quantization conditions are satisfied by the kinetic component of the retarded potential, but commutators of the dissipative component are determined by the current sources. The energy/stress tensor and Hamiltonian of the field in the presence of sources are derived from the classical Lagrangian density. The relation between the Hamiltonian and the energy is shown to agree with the time dependence of the destruction/creation operators in Heisenberg picture. (shrink)

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, (...) e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)

It is shown how to identify potential signatures of noncommutative geometry within the decay spectrum of a muon in orbit near the event horizon of a microscopic Schwarzschild black hole. This possibility follows from a re-interpretation of Moffat’s nonsymmetric theory of gravity, first published in Phys. Rev. D 19:3554, 1979, where the antisymmetric part of the metric tensor manifests the hypothesized noncommutative geometric structure throughout the manifold. It is further shown that for a given sign convention, the predicted (...) signatures counteract the effects of curvature-induced muon stabilization predicted by Singh and Mobed in Phys. Rev. D 79:024026, 2009. While it is unclear whether evidence for noncommutative geometry may become observable anytime soon, this approach at least provides a useful direction for future quantum gravity research based on the ideas presented here. (shrink)

In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons.The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus (...) by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent.A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms. (shrink)

Family income is associated with gray matter morphometry in children, but little is known about the relationship between family income and white matter structure. In this paper, using Tract-Based Spatial Statistics (TBSS), a whole brain, voxel-wise approach, we examined the relationship between family income (assessed by income-to-needs ratio) and white matter organization in middle childhood (N = 27, M = 8.66 years). Results from a nonparametric, voxel-wise, multiple regression (threshold-free cluster enhancement, p < 0.05, FWE corrected) indicated that lower family (...) income was associated with lower white matter organization (assessed by fractional anisotropy) for several clusters in white matter tracts involved in cognitive and emotional functions including fronto-limbic circuitry (uncinate fasciculus and cingulum bundle), association fibers (inferior longitudinal fasciculus, superior longitudinal fasciculus), and corticospinal tracts. Further, we examined the possibility that cumulative risk exposure might function as one of the potential pathways by which family income influences neural outcomes. Using multiple regressions, we found lower fractional anisotropy in portions of these tracts, including those found in the left cingulum bundle and left superior longitudinal fasciculus, was significantly related to greater exposure to cumulative risk (β = -0.47, p < 0.05 and β = -0.45, p < 0.05). (shrink)

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, (...) gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics. (shrink)

The purpose of this special issue and the conference that inspired it was to address the issue of conceptual integration in a science of consciousness. We felt this to be important, for while current efforts to scientifically investigate consciousness are taking place in an interdisciplinary context, it often seems as though the very terms being used to sustain a sense of interdisciplinary cooperation are working against it. This is because it is this very array of common concepts that generates a (...) sense of unity among consciousness researchers, despite the fact the concepts mean different things in different disciplines. These Concepts of Consciousness include the following: realism, representation, intentionality, information, control, memory and self. Given this list, we believed we could best approach the issue of potential conceptual integration by addressing each concept from different perspectives and asking the following: how do uses of the concept differ, must these meanings be synthesized in order for there to be a unified science of consciousness, is a unified conceptual scheme necessary to establish an independent science of consciousness, is a unified conceptual scheme possible, if it is not possible, why not, and if it is possible, what might it look like? To this end we invited, for each concept, two scholars who made extensive use of the identified concept in their work. The papers entailed in this special issue constitute the outcome of this effort, and in what follows we offer a brief examination of possible forms of integration the papers seem to collectively suggest. (shrink)

Microbes in the gastrointestinal tract are under selective pressure to manipulate host eating behavior to increase their fitness, sometimes at the expense of host fitness. Microbes may do this through two potential strategies: (i) generating cravings for foods that they specialize on or foods that suppress their competitors, or (ii) inducing dysphoria until we eat foods that enhance their fitness. We review several potential mechanisms for microbial control over eating behavior including microbial influence on reward and satiety pathways, (...) production of toxins that alter mood, changes to receptors including taste receptors, and hijacking of the vagus nerve, the neural axis between the gut and the brain. We also review the evidence for alternative explanations for cravings and unhealthy eating behavior. Because microbiota are easily manipulatable by prebiotics, probiotics, antibiotics, fecal transplants, and dietary changes, altering our microbiota offers a tractable approach to otherwise intractable problems of obesity and unhealthy eating. (shrink)

There has been a growing interest in research concerning memory modification technologies (MMTs) in recent years. Neuroscientists and psychologists are beginning to explore the prospect of controllable and intentional modification of human memory. One of the technologies with the greatest potential to this end is optogenetics—an invasive neuromodulation technique involving the use of light to control the activity of individual brain cells. It has recently shown the potential to modify specific long-term memories in animal models in ways not (...) yet possible with other MMTs. As the therapeutic potential of optogenetics has already prompted approval of the first human trials, it is especially important and timely to consider the opportunities and dangers this technology may entail. In this article, we focus on possible consequences of optogenetics as an MMT by analyzing fundamental threats potentially associated with memory modifications: the potential disruption of personality and authenticity. (shrink)

O presente artigo tangencia o conceito de tensor esgueirando-se pelos platôs linguísticos de Mil platôs, agenciando o que Deleuze e Guattari potencializam em o que passou?, e que buscamos atualizar em o que passa? Nesse sentido, buscamos a articulação entre o que ambos os conceitos movimentam: isso, que acontece na relação entre dois ou mais estratos. Percebemos que o tensor transversa a obra de Deleuze e Guattari e, mesmo que não exerça um relevo, está lá, estrategicamente em funcionamento. (...) Destarte, desejamos articular com esses conceitos de partida, uma possibilidade para poder inventariar os deslocamentos imanentes de escrileitura, como forma de aproximar procedimentos didático-tradutórios, que possam vir a ser envolvidos em uma pesquisa, que deseja experimentarse em momentos de invenção. Para tanto, problematizamos uma tríade conceitual – tensor, o que passa?, e escrileitura, de modo a possibilitar perspectivas de composição e de funcionamentode uma máquina abstrata escrileitora de invenções. Com o Método Maquinatório de Pesquisa, afirmamos a busca por dar vez e voz a um processo de maquinações, que possam vir tensionar uma crítica sintomatológica, duplamente articulada a uma clínica maquinatória; um Plano de Organização tensionado por um Plano de Invenção; e, no intermezzo desses encontros, algo passa, algo pode passar; e, assim, persistem os rastros de uma escrileitura, envolta e revolta em um contínuo recursivo: escrever-ler-escrever. Nesse percurso, jogamos os dados em um tabuleiro desejante; procuramos abrir um caminho para a passagem de procedimentos escrileitores de invenção, e ensaiamos uma aposta: poder tensionar a transitividade atual-potencial do fazer linguístico, literário e escritureiro. Palavras-chave: Educação. Filosofia da diferença. Método Maquinatório de Pesquisa. Escrileitura. Tensor. (shrink)

The vav proto‐oncogene encodes a 95 kDa protein which is expressed exclusively in hematopoietic cells. Analysis of the deduced amino acid sequence has revealed the presence of a src‐homology 2 (SH2) domain, 2 SH3 domains, a cysteine‐rich region with similarity to protein kinase C, and a region highly similar to proteins with guanine nucleotide exchange activity on ras‐like GTPases. Recent work has shown that vav is tyrosine phosphorylated in response to stimulation of surface membrane receptors in a variety of hematopoietic (...) cell lines. Vav may play a role in hematopoietic cell signaling by coupling tyrosine kinase pathways to ras‐like GTPases through the regulation of guanine nucleotide exchange. (shrink)

We argue that the de-extinction of the mammoth cannot be ethically grounded by duties to the extinct mammoth, to ecosystem health or to individual organisms in ecosystems missing the mammoth. However, the action can be shown to be morally permissible via the goods it will afford humans, including advances in scientific knowledge, valuable experiences of awe and pleasure, and perhaps improvements to our moral character or behaviour—if and only if suffering is minimal. Finally, we call for empirical research into how (...) the possibility of the technology affects our behaviour or our character to help the debate transcend duelling intuitions. (shrink)

Board composition, insider participation on compensation committees, and director compensation practices can potentially cause conflicts of interest between directors and shareholders. If these corporate governance structures result in situations where actions beneficial to directors do not also benefit shareholders, then shareholders may suffer.Corporate ethics programs usually address conflicts of interest that may arise in the firm''s activities. Some boards of directors take active roles in their firms'' ethics programs by actively overseeing the programs. This paper empirically examines the relationship between (...) ethics programs and potential conflicts of interest and the relationship between board involvement in a firm''s ethics program and potential conflicts of interest. (shrink)

ABSTRACT:The profound influence of Thomas Donaldson and Thomas Dunfee’s integrative social contracts theory on the field of business ethics has been challenged by Andreas Scherer and Guido Palazzo’s Habermasian approach, which has achieved prominence of late with articles that expressly question the defensibility of ISCT’s hypernorms. This article builds on recent efforts by Donaldson and Scherer to bridge their accounts by providing discursive foundations to the hypernorms at the heart of the ISCT framework. Extending prior literature, we propose an ISCT* (...) framework designed to retain ISCT’s practical virtue of managerial guidance while answering the demands of Scherer and Palazzo’s discursive account. By subscribing to a suitable portfolio of discursively justified hypernorms, we argue, companies unlock the valuable moral guidance of ISCT*, which says to treat these hypernorms as unequivocal outer bounds to the pursuit of business and as a starting point to tailor local norms through discursive stakeholder engagement. (shrink)

This study uses a rational ethical decision-making framework to examine the influence of moral intensity (potential harm and social pressure) on whistleblowing intention and behaviour using organisational commitment as a moderator. A scenario was developed, and an online questionnaire was used to conduct an empirical analysis on the responses of 533 participants. The mean age and years of work experience of the respondents were 31 and 8.2 years, respectively. The results show, first, that while moral intensity is correlated with (...) whistleblowing intention, only the potential harm is positively correlated with such intention. Second, potential harm and social pressure differentially affect whistleblower choice of using an internal or external channel. Third, organisational commitment has a moderated mediation effect among moral intensity, whistleblowing intention and behaviour. Fourth, whistleblowers may be grouped into four conceptual types: indifferent, rebel, mature and spoil. Finally, theoretical and managerial implications of the findings are discussed. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); (...) Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)