Über die Schwere des Lichtes in der Newtonschen und in der Einsteinschen Gravitationstheorie

The gravity theories of Newton and Einstein are giving opposite sentences about the velocity of light in gravitational field. According to the Newtonian theory the velocity v in gravitational field is greater than the velocity c in a field-free space: v > c. According to general relativity theory we have a smaller velocity: v < c. For a spherical symmetric gravitational field Newton's theory gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 + \frac{{fM}}{{c^2 r}}} \right) $\end{document} but Einstein's theory of 1911 gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - \frac{{fM}}{{c^2 r}}} \right) $\end{document} and general relativity gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - 2\frac{{fM}}{{rc^2 }}} \right) $\end{document}. Therefore, the radarecho-measurations of Shapiro are the experimentum crucis for Einstein's against Newton's theory.     

Die Lorentz-Transformation als Ausdruck der Superposition gegenläufiger Raum-Zeit-Beziehungen,Preisgabe des Relativitätsprinzips

The Lorentz Transformation as an Expression of Opposite Spacetime Relations. Abandonment of the Principle of Relativity Any increase of the characteristic energy of any body endowed with a clock, ΔE = E — E₀ (E₀ being the rest energy), is connected with an increase of its time lapse, t/t₀ = E/E₀ (EINSTEIN 1907). Effective observation of this accelerating influence on the speed of any clock is restricted on the increase of the potential energy only. Increase of the kinetic energy \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{E}{{E_0 }}\, = \,\frac{1}{{\sqrt{1 - \frac{v}{{c^2 }}} }}} \right) $\end{document} is, on the contrary, connected with a decrease of the time lapse, a decrease of exactly the same but inverse (reciprocal) amount to the increase of the energy: \documentclass{article}\pagestyle{empty}\begin{document}$ t/t_0{\rm = }E_0 /E{\rm = }\sqrt {1 - \frac{{v^2 }}{{c^2 }}.} $\end{document}. Moreover this amount is that one postulated by the Lorentz Transformation. This effect is the well-known “time dilatation” of the Special Theory of Relativity, the “transversal Doppler effect”. The Lorentztransformation is of exclusively kinematical meaning and therefore takes no account of the energy increase connected with any motion. There is no reason, why the time accelerating effect of any energy rises should be absent in the case of kinetic energy, paying regard to is seem indispensable. Therefore the actual effect \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {1 - \frac{{v^2 }}{{c^2 }}} $\end{document} has to be given as a superposition of the time accelerating energy effect \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt {1 - \frac{{v^2 }}{{c^2 }}} $\end{document} and a decelerating kinematic effect of “double” (inverse square) amount: 1 – v²/c². Modified transformation equations are derived which pay regard to this subdivision of the actual relations concerning times and local scales, and whose interated form is nevertheless identical with the classical Lorentz Transformation, if kinetic energy is the sole one being present. Of course this new subdivision of the content of meaning in the transformations is in contradiction with the ?principle of relativity”?, it presumes the existence of an inertial frame absolutely at rest related to the universe, A series of arguments is asserted which let appear the existence of such an absolute frame more fascinating than the equivalence of the variety of all inertial frames.     

Nonlinear Interaction of S-Polarized Incident Radiation and Surface Waves in Magnetoactive Plasma

The effect of an external magnetic field on the nonlinear interaction of S-polarized electromagnetic radiation incident on a S-polarized surface wave in a plasma layer was studied analytically. We have calculated the amplitudes of generated waves at combination frequencies. The generated waves are of P-polarization and can be either electromagnetic or surface waves, depending on the signal of the value=\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\chi '^2 = \frac{{k'^2 }}{{\varepsilon '}} - \frac{{\omega '^2 }}{{c^2 }} + k'\frac{\partial }{{\partial x}}\frac{{\varepsilon '_2 }}{{\varepsilon '\varepsilon '_1 }}} $\end{document}.     

A Remark about the Point Interaction in one Dimension

The zero range limit of one dimensional Schrödinger operator is studied by scaling technique and new results are obtained for potentials V with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \smallint \limits_{\rm R} $\end{document} V(x)dx = 0.     

Intensity Effects in Scattering of Electromagnetic Waves by Electrons Moving in External Magnetic Field

In this paper we consider the emission processes of a relativistic electron moving in the field of a plane electromagnetic wave and in a homogeneous magnetic field. A detailed analysis of the most important characteristics of the radiation properties for arbitrary values of the magnetic field, compared with \documentclass{article}\pagestyle{empty}\begin{document}$ [H_0 = \frac{{m^2 c^3}}{{e\hbar}}]$\end{document} = 4.41.10¹³ gauss, is presented.     

Paketimpulse in der magnetischen Kernresonanz

Composite Pulses in Nuclear Magnetic Resonance For the compensation of spatial inhomogeneity of the radiofrequency field and a resonance offset in NMR experiments, composite pulses are used instead of the conventional single pulses. In the present work the effect of a resonance offset on composite pulses is treated quantitatively. It will be shown also experimentally that the various constructions for \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{\pi }{2} $\end{document} composite pulses (contrary to π composite pulses) lead to only two different degrees of compensation depending on the choice of the phase of the pulses or the sign of the resonance offset.     

The Scattering on the Bound State and the Two-Particle Resonances

In the given paper the scattering of a spinless particle by another spinless particle bound in the external field is considered in the three-dimensional case. The external field is represented by the rectangular well and the two-particle interaction is parametric. The influence of the single-particle basis and of the strength of the two-particle interaction on the resonance structure of the cross-section is investigated in the limit of weak coupling between channels. It is shown that the dependence of the number of resonances N_r on the number of single-particle levels N is given by the following formula: \documentclass{article}\pagestyle{empty}\begin{document}$ N_r = \frac{{N^2 + (N - 4)^2 }}{2}. $\end{document}. The scattering of a particle by another particle bound in the field of a core is considered.     

Electrodynamic Model of Initiation and Extinction of Emitting Sites Interacting Together in Cold Cathode Spots (Type A) in Air

From an electrodynamic and simple quantum-mechanical point of view a model is proposed which explains the phenomena of minimum arc current as well as the formation and extinction of tiny emitting sites interacting together in cold cathode spots (called type A) on the base of a specific coupling between the tunnelling “average” electrons and the metal bulk phonon field. The model seems to be especially applicable to such experimental conditions where typical trumpetlike microcraters with pronounced rims with diameters in the range 0.5—1 μm are left by microspot ensembles on the cathode surface. The model yields emitting-site lifetimes, currents, current densities and radii in the order of τ_p^s ? \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {3M/m} $\end{document} τ₀ ? 10^?11 sec, I_min = 4π ? \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {n/\mu _0 m} $\end{document}? 0.4 A, j = nev_s ? 4 · 10¹³ A/m² and r_a ? 2c/ω_Pl ? 30 nm (τ_p^s…lifetime of short wave phonons, M … atom mass, m … electron mass, τ₀ … mean free collision time of Fermi electrons at room temperature, n … conduction electron density in the metal bulk, v_s … metal bulk sound velocity, c … light velocity, ω_Pl … metal bulk plasma frequency (values for copper). The lifetime and the interaction diameter of an emitting site (event) ensemble are derived to τ_p^l ?(M/m) τ_p ? 3 nsec and Λ_p^l = ν_sτ_p^l ? 10 μ (τ_pΛ_p^l … lifetime and mean free path of long wave phonons).     

Calibration of the electrical aerosol analyzer at subambient pressures

A commercial Electrical Aerosol Analyzer (EAA, TSI Inc. model 3030) was calibrated experimentally at three subambient pressures (i. e., 0.901, 0.878, and 0.853 atm). Each calibration resulted in a 19 × 11 response matrix and a size dependent sensitivity curve $ \left({\frac{{pA}}{{{\# \mathord{\left/ {\vphantom {\# {cm^3}}} \right. \kern-\nulldelimiterspace} {cm^3}}}}} \right) $. The results of the calibration were incorporated into a data reduction computer program for size distribution inversion. The accuracy of the calibration was tested by measuring the size distribution of a NaCl polydisperse aerosol at the three subambient pressures. All the tests gave good agreement in the inverted mean geometric diameter and geometric standard deviation of the aerosol number size distribution.     

Einsteins hermitesche Relativitätstheorie als Unifikation von Gravo- und Chromodynamik

Einstein's Hermitian Theory of Relativity as Unification of Gravo- and Chromodynamics Einstein's Hermitian unified field theory is the continuation of the Riemannian GRG to complexe values with a Hermitian fundamental tensor gμ_v = g_v*μ This complexe continuation of GRG implies the possibility of matter and anti matter with a sort of CPT theorem. — Einstein himself has interpreted his theory as a unification and generalization of the Einstein and Maxwell theory, th. i. of gravodynamics and of electrodynamics. However — according the EIH approximation —, from Einstein's equations no Coulomb-like forces between the charges are resulting (INFELD, 1950). But, the forces between two charges ?_A and ?_B have the form (Treder 1957) It is interesting that such forces are postulated in the classical models of the chromodynamics of the interactions between quarks (for the confinement of their motions. If we interprete the purely imaginary part gμ_v of the hermitian metrics gμ_v=gμ_v+gμ_v as the dual of the field of gluons then, all peculiarities of Einstein's theory become physically meaningful. — Einstein's own interpretation suggests that the both long-range fields, gravitation and electromagnetism, must be unified in a geometrical field theory. However, the potential α/r + ε/2 has a “longer range” than the Coulomb potential ～1, and such an asymptotical potential ～ ε/2 is resulting from Einstein's equations (TREDER 1957). In Einstein's theory there are no free charges with \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_A^n {\varepsilon A} $\end{document}. (Wyman 1950) because the field mass of a charged particle becomes infinite asymptotically: That means, in a chromodynamics we dont's have free quarks. The same divergence are resulting from one-particle systems with non-vanishing total charges: M～ε²r. However, if the total charges vanish because in a domain ～L³ the positive sources are compensated by negative sources, the field masses of the n-charge systems become finite. From the gravitational part of Einstein's equations we get field masses which are the masses measured by observers in distances r ? L. That means, the masses of quark systems with the colour condition \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_A^n {\varepsilon A} $\end{document} are proportional to the linear dimension L of the system.     

Die teleskopischen Prinzipien der Gravitationstheorie. (Machsches Prinzip,Mach-Einsteinsche Relativität der Trägheit und die Hertzsche Mechanik)

The Telescopical Principles in the Theory of Gravitation. (Machs Principle, Relativity of Inertia According to Mach and Einstein and Hertz' Mechanics) We give an explication and analytical formulation of Mach's principle of the “relativity of inertia” and of the Mach-Einstein doctrine on the determination of inertia by gravitation. These principles are whether “philosophical” nor “epistemological” postulates but well defined physical axioms with exactly analytical expressions. - The fundamental principle is the Galileian “reciprocity of motions”. According to this “generalized Galilei invariance” the principal functions of analytical dynamics (Lagrangian L and Hamiltonian H) are depending upon the differences ??_AB of the coordinate vectors ??_A and ??_B of the velocity differences ??_AB = ??_A-??_B, only. The Galileian reciprocity of motions means that whether the vectors ??_A and ??_A nor the accelerations ??_A of one particle have a physical significance. A mechanics obtaining this generalized Gailei-invariance cannot depend upon a kinematical Term \documentclass{article}\pagestyle{empty}\begin{document}$ T = \frac{1}{2}\mathop {\Sigma m_A \mathop r\nolimits_A^2}\limits_A $\end{document} in the Lagrangian. Therefore, the inertial masses of the particles must be homogeneous function of interaction potentials Φ_A,B. According to the Einsteinian equivalence of inertia and gravity these interactions have to be the Newtonian gravitation. In a universe with N mass points the Mach-Einsteinian Lagrangian for our “gravodynamics without inertia” is In such a Mach-Einstein universe the celestical dynamics becomes in the first approximation the Newtonian dynamics, in the second (the “post-Newtonian”) approximation the general relativistic Einstein effects are resulting.-However, our gravodynamics gives new effects for large masses (no gravitational collapses) and in cosmology (secular accelerations a.o.). Generally, the space of our gravodynamics is whether the Newtonian “absolute space” V₃ nor the relativistic Einstein-Minkowski world V₄ but the Hertzian configuration space V_3N of the N particles. According to the relativity of inertia the Hertzian metrics become Riemannian metrics which are homogenous functions of the Newtonian gravitational potentials. .     

Boundaries Immersed in a Scalar Quantum Field

We study the interaction between a scalar quantum field $\hat \phi (x)$, and many different boundary configurations constructed from (parallel and orthogonal) thin planar surfaces on which $\hat \phi (x)$ is constrained to vanish, or to satisfy Neumann conditions. For most of these boundaries the Casimir problem has not previously been investigated. We calculate the canonical and improved vacuum stress tensors $ \langle \hat T_{\mu \nu } (x)\rangle\$ and $ \langle \Theta _{\mu \nu (x)} \rangle\$ of $\hat \phi (x)$; for each example. From these we obtain the local Casimir forces on all boundary planes. For massless fields, both vacuum stress tensors yield identical attractive local Casimir forces in all Dirichlet examples considered. This desirable outcome is not a priori obvious, given the quite different features of $ \langle \hat T_{\mu \nu } (x)\rangle\$ and $ \langle \Theta _{\mu \nu (x)} \rangle\$. For Neumann conditions. $ \langle \hat T_{\mu \nu } (x)\rangle\$ and $ \langle \Theta _{\mu \nu (x)} \rangle\$ lead to attractive Casimir stresses which are not always the same. We also consider Dirichlet and Neumann boundaries immersed in a common scalar quantum field, and find that these repel. The extensive catalogue of worked examples presented here belongs to a large class of completely solvable Casimir problems. Casimir forces previously unknown are predicted, among them ones which might be measurable.     

Adsorption,Desorption, Dissoziation und Rekombination von SO2 an einer Palladium(111)-Oberfläche

Adsorption, Desorption, Dissociation and Recombination of SO₂ on a Palladium (111) Surface The adsorption, desorption as well as decomposition- and recombination-reactions of SO₂ on Pd(1 1 1) were studied for temperatures T = 160-1200 K using LEED, AES, thermal desorption-mass-spectrometry and molecular beam techniques. At 160 K SO₂ adsorption with an initial sticking coefficient s₀ = 1 is molecular and non-ordered; it is characterized by a precursor state and leads to a saturation coverage Θ ≈ 0,3. Heating up the adlayer SO₂ is the only desorption product, namely directly from (SO₂)_ad in the α-peak (T_max = 240 K) and as the product of recombination of (SO)_ad and O_ad in the β-peak (T_max = 330-370 K). A great part of the oxygen originating from SO₂-dissociation is incorporated into the subsurface region, resulting in an atomic S-adlayer with Θ_S = 1/7 which exhibits a (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 7 {\rm x}\sqrt 7 $\end{document}) R ± 19,1°-superstructure. This structure is also observed, if a 320 K-SO₂-exposure induced (2 × 2)-SO saturation layer with Θ_SO = 0,5 is heated up or if SO, is exposed at T > 500 K, where it corresponds to Θ_S, values of 3/7 and 2/7, respectively. Furthermore the poisoning effect of adsorbed sulfur on the dissociative O₂,-adsorption and the oxidation of sulfur by heating up an O? S-coadsorption layer were studied. As a result the following kinetic parameters (activation energies and frequency factors) were determined: .     

A shortcut to general tree‐level scattering amplitudes in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} = 4$\end{document} SYM via integrability

We combine recent applications of the two‐dimensional quantum inverse scattering method to the scattering amplitude problem in four‐dimensional $ \mathcal{N} = 4$ Super Yang‐Mills theory. Integrability allows us to obtain a general, explicit method for the derivation of the Yangian invariants relevant for tree‐level scattering amplitudes in the $ \mathcal{N} = 4$model.     

Na‐site energy of P2‐type NaxM O2 (M = Mn and Co)

P2‐type Na_xM O₂ (M = Mn and Co) is a promising cathode material for low‐cost sodium ion secondary batteries. In this structure, there are two different crystallographic Nai (i = 1 and 2) sites with different Coulomb potential $ (\varphi _i)$ provided by M^4–x and O^2–. Here, we experimentally determine a difference ${(\rm \Delta }\varepsilon \equiv \varepsilon _1 - \varepsilon _2)$ of Na‐site energies ${(}\varepsilon _i \equiv e\varphi {\kern 1pt} _i)$ based on the temperature dependence of the site occupancies. We find that ${\rm \Delta }\varepsilon \;{=}\;56\;{K}$ for Na_0.52MnO₂ is significantly smaller than 190 K for Na_0.59CoO₂. We interpret the suppressed ${\rm \Delta }\varepsilon $ in Na_0.52MnO₂ in terms of the screening effect of the Na⁺ charge. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Editorial

The production of charmed mesons ,D ^± , andD ^*± is studied in a sample of 478,000 hadronicZ decays. The production rates are measured to be

The integrated density of states for the difference Laplacian on the modified Koch graph

We consider the integrated density of statesN(λ) of the difference Laplacian ?Δ on the modified Koch graph. We show thatN(λ) increases only with jumps and a set of jump points ofN(λ) is the set of eigenvalues of ?Δ with the infinite multiplicity. We establish also that $$0< C_1 \leqslant \mathop {\lim }\limits_{\lambda \to 0} \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }}< \overline {\mathop {\lim }\limits_{\lambda \to 0} } \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }} \leqslant C_2< \infty$$ whered _s =2log5/log(40/3) is the spectral dimension of MKG.     

More corrections to the sixth-order anomalous magnetic moment of the muon

The contribution to the sixth-order muon anomaly from second-order electron vacuum polarization is determined analytically to orderm _e/m _μ. The result, including the contributions from graphs containing proper and improper fourth-order electron vacuum polarization subgraphs, is $$\begin{gathered} \left( {\frac{\alpha }{\pi }} \right)^3 \left\{ {\frac{2}{9}\log ^2 } \right.\frac{{m_\mu }}{{m_e }} + \left[ {\frac{{31}}{{27}}} \right. + \frac{{\pi ^2 }}{9} - \frac{2}{3}\pi ^2 \log 2 \hfill \\ \left. { + \zeta \left( 3 \right)} \right]\log \frac{{m_\mu }}{{m_e }} + \left[ {\frac{{1075}}{{216}}} \right. - \frac{{25}}{{18}}\pi ^2 + \frac{{5\pi ^2 }}{3}\log 2 \hfill \\ \left. { - 3\zeta \left( 3 \right) + \frac{{11}}{{216}}\pi ^4 - \frac{2}{9}\pi ^2 \log ^2 2 - \frac{1}{9}log^4 2 - \frac{8}{3}a_4 } \right] \hfill \\ + \left[ {\frac{{3199}}{{1080}}\pi ^2 - \frac{{16}}{9}\pi ^2 \log 2 - \frac{{13}}{8}\pi ^3 } \right]\left. {\frac{{m_e }}{{m_\mu }}} \right\} \hfill \\ \end{gathered} $$ . To obtain the total sixth-order contribution toa _μ?a _e, one must add the light-by-light contribution to the above expression.