On a scale function for testing the conformality of a Finsler manifold to a Berwald manifold

In this paper, we are going to discuss the problem whether how we can check the conformality of a Finsler manifold to a Berwald manifold. The method is based on a differential 1-form constructing on the underlying manifold by the help of integral formulas such that its exterior derivative is conformally invariant. If the Finsler manifold is conformal to a Berwald manifold, then the exterior derivative vanishes. This gives the following necessary condition: the differential form is closed and, at least locally, it is exact as the exterior derivative of a scale function for testing the conformality. A necessary and sufficient condition is also given in terms of a distinguished linear connection on the underlying manifold – it is expressed by the help of canonical data. In order to illustrate how we can simplify the process in special cases Randers manifolds are considered with some explicit calculations.     

Modified Newton's gravity in Finsler space as a possible alternative to dark matter hypothesis

A modified Newton's gravity is obtained as the weak field approximation of the Einstein's equation in Finsler space. It is found that a specified Finsler structure makes the modified Newton's gravity equivalent to the modified Newtonian dynamics (MOND). In the framework of Finsler geometry, the flat rotation curves of spiral galaxies can be deduced naturally without invoking dark matter.     

Quantum General Relativity and the Meaning of (R + R2) Theories

It is argued that, due to the cut-off lengths arising in Quantum General Relativity, R2 corrections of Einstein's theory cannot be interpreted as quantum corrections.     

An Analytical Treatment of the Clock Paradox in the Framework of the Special and General Theories of Relativity

No Heading In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear (in space). No inertial motion steps are considered. The rest clock is denoted as (1), the to and fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: (1) What is the effect of the finite force acting on (2) on the proper time interval ⁽²⁾ measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The special theory of relativity is used in order to describe the hyperbolic (in spacetime) motion of (2) in the frame I. (II) Is this effect an absolute one, i.e., does the accelerated observer A comoving with (2) obtain the same results as that obtained by the observer in I, both qualitatively and quantitatively, as it is expected? We use the general theory of relativity in order to answer this question. It turns out that _I = _A for both the clocks, ⁽²⁾ does depend on g = F/m, and = ⁽²⁾/⁽¹⁾ = (1 – ²atanhj)/ < 1. In it ; = V/c and V is the velocity acquired by (2) when the force is inverted.     

The Redshift Periodicity of Galaxies as a Probe of the Correctness of General Relativity

Recent theoretical work determines the correct coupling constant of a scalar field to the Ricci curvature of spacetime in general relativity. The periodicity in the redshift distribution of galaxies observed by Broadhurst et al., if genuine, determines the coupling constant in the proposed scalar field models. As a result, these observations contain important information on the problem of whether general relativity is the correct theory of gravity in the region of the universe at redshifts z < 0.5.     

Context Independence as a Statistical Property of Hidden Variable Theories

The context dependence of Bell local hiddenvariable theory is reconsidered both in its mathematicaland physical justification. The compatibility of thecontext dependence of individual measurement results with the context independence of the statisticsof measurement results is shown to warrant theconsistency of the Bell framework with respect to theGleason no-hidden-variables theorem. Finally, a sharp distinction between context dependence and (anyform of) nonlocal dependence is defended on thebackground of some recent algebraic proofs ofnonlocality.     

Approaches to the Physical Mechanisms and Theories of Low-Concentration Effects in Aqueous Solutions

The influence of optical, plasma, and mechanical effects on the macroscopic properties of aqueous solutions is discussed. An important role of the nano-objects that are spontaneously formed in a liquid or generated by external perturbation sources in the formation of these properties is stated. It is suggested that the presence of nano-objects in aqueous solutions determines the behavior of most various processes: from the formation of shock waves to the change in the ion composition and regulation of biological activity. Nonmonotonic dependences of the absorption and luminescence efficiency on the concentration of ion impurity centers in crystals are demonstrated. One of the causes of nonmonotonicity is the aggregation of active centers from neighboring lattice cells. Active aggregates are identified based on a thermodynamic calculation, in agreement with the spectral and relaxation experimental data. Particular analytical models of the thermodynamic state of water and aqueous solutions and the kinetics of chemical reactions occurring in them are reviewed. Here, a key point is the consideration of short-lived hydrogen bonds between water and solute molecules The formalism of the theory of dichotomous noise is used to describe these twinkling hydrogen bonds. Its application indicates, in particular, the possibility of forming a low-concentration droplet phase in solutions. A scheme of successive unification of particular models of thermodynamics and kinetics of aqueous solutions, based on an analogy with the theory of luminescence effects in ion impurity centers, is proposed.

     

Determination of the Effective Energy due to a Constant Modification in General Relativity

In this letter, we firstly discuss the geometric consequences of the resultant field equations in a specified f(R) theory of gravity. Afterwards, keeping the so called field equations separated, we investigate the analytical behavior of the effective energy, corresponding to our peculiar modification.     

On the Appeal to a Pre-Established Harmony Between Pure Mathematics and Relativity Physics

Soon after its appearance in 1905, the Einsteinian relativity with its relativistically admissible 3-velocities was recognized by Vladimir Variak in 1908 as the realization in physics of the hyperbolic geometry of Bolyai and Lobachevski. At the same time, however, during the years 1907–1909 Minkowski reformulated the Einsteinian relativity in terms of a space of 4-velocities that now bears his name. As a result, the special theory of relativity that we find in the mainstream literature is not the one originally formulated by Einstein but, rather, the one reformulated by Minkowski. Thus, in particular, one of the most powerful ideas of Einstein in 1905, the Einstein addition of relativistically admissible 3-velocities that need not be parallel, is unheard of in most texts on relativity physics. Following our recently published book, Beyond the Einstein Addition, Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces [1], the aim of this article is to employ the principle of pre-established harmony between mathematics and physics to demonstrate that the original Einsteinian relativity, as opposed to the Minkowskian relativity, is the legitimate formulation of special relativity whose time has returned.     

Turbulent Helium Gas Cell as a New Paradigm of Daily Meteorological Fluctuations?

We compare the spectral properties of long meteorological temperature records with laboratory measurements in small convection cells. Surprisingly, the atmospheric boundary layer sampled on a daily scale shares the statistical properties of temperature fluctuations in small-scale experiments. This fact can be explained by the hydrodynamical similarity between these seemingly very different systems. The results suggest that the dynamics of daily temperature fluctuations is determined by the soft turbulent state of the atmospheric boundary layer in the continental climate.     

A Solution to Einstein's Equations for the Mixmaster Universe in Complex General Relativity

Starting from Einstein's equations of the Classical General Relativity, new kinds of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions.     

External-Internal Group Quotient Structure for the Standard Model in Analogy to General Relativity

In analogy to the class structure for generalrelativity with a local Lorentz group as stabilizer anda basic tetrad field for the parametrization, acorresponding class structure is investigated for the standard model with alocal hyperisospin group U(2). The lepton, quark,Higgs, and gauge fields used in the standard modelcannot be basic in a coset interpretation; they may to be taken as first-order terms in a flatspacetime, particle-oriented expansion of a basic field(as the analogue to the tetrad) and itsproducts.     

The Evolution of Interfacial Strength as a Way to Characterize a Low-Temperature Limit of the Surface Glass Transition of an Amorphous Polymer

The evolution of autoadhesive strength, σ, with healing temperature, T _h, at the symmetric amorphous polystyrene (PS)?PS interfaces of the samples with vitrified bulk has been used to characterize a low-temperature limit of the surface glass transition temperature T _g ^surface(low). The existence of a linear relationship between the square root of σ and T _h has been found for both polydisperse and monodisperse polymers. By the extrapolation of straight lines σ ^1/2 ? T _h to σ ^1/2 = 0, the values of T _g ^surface(low) have been determined and compared with those of a high-temperature limit of T _g ^surface, T _g ^surface(high), measured earlier. The differences between T _g ^surface(low) and T _g ^surface(high) have been found to be insignificant, 10–20°C. Using an average value of the shift of T _g ^surface(low) with healing time, t _h, the quasi-equilibrium value of the surface glass transition temperature of amorphous PS T _∞ ^surface has been estimated to be 10–15°C.     

One-Dimensional World as a Tool to Study Chiral Effects

JETP Letters - An analog of the chiral separation effect and the chiral magnetic effect has been studied for fermions in one spatial dimension. The relation of these effects to axial anomaly in the...     

A Theorem Relating Solutions of a Fourth-Order Theory of Gravity to General Relativity

Within a fourth-order theory of gravity we give,for a static asymptotically flat spacetime, anexpression of the active mass (gravitational mass), infirst order in the coupling constant, , of the curvature squared term in the Lagrangiandensity, a generalization of the Tolman expression forthe energy, which establishes a relationship between theactive mass and the source structure in a static spacetime. Within this approximation, we canprove that the fourth-order theory shares with Generalrelativity (GR) the property that, for sources ofcompact support, the active mass is independent of any two-dimensional surface which encloses thesupport of the matter distribution. Finally, we provethat only for conformally invariant sources thefourth-order theory and GR share the same static andasymptotically flat solutions.     

Equivalence Between an Extension of Teleparallelism to a Weyl Geometry and General Relativity

Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and “geometrize” electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the Schwarzschild solution to a particular class of this extension. In addition, I obtain the field equations of some models based on this extension, including the one which is equivalent to Einstein’s field equations with a massless scalar field.     

Reflections on the Application of the Geometric Approach to Quantum Mechanics to General Relativity

This article is a series of remarks on theapplication of the geometric approach to quantummechanics to gravitation. Bianchi Type I cosmologies areused as minisuperspace models in order to give concrete examples of the problems one expects toencounter.