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.     

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.     

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.     

Zur unitarisierten Gravitationstheorie mit lang- und kurzrechweitigen Termen (mit ruhmasselosen und schweren Gravitonen)

In our papers, TREDER [1, 2] we have formulated a unified electrodynamics of the fourth order with bi-wave equations for the vector potential A. In this electrodynamics EINSTEIN ian photon and heavy W-mesons are the field quanta. In correspondence to this field theory we are able to formulate a unified theory of gravitation, too. The field equations for the gravitational metrics grr in this theory are corresponding with the EINSTEIN equations of General Relativity in the same way like the electromagnetic bi-wave equations are corresponding with the MAXWELL equations. The metric g_μν is a linear functional of an EINSTEIN ian long-range potential g_μν and of a subatomic short-range potential definierte Materie-Tensor die gemeinsame Quelle für alle drei Felder ist. Dann ist g1_μν, g2_μν und g_μν und es gelten die Funktional-Bedingungen wobei hier g2_μν Feldgleichungen vom “kosmologischen Typ” befriedigt. By these conditions, the short-range interaction becomes a repulsive force and the action of the NEWTON -EINSTEIN ian attraction and of the subatomic repulsion makes the matter point-like (as in the E.-I.-H.-method) but self-consistent. The gravitational metrics g2_μν become regulary. P. e., in the EINSTEIN approximation the field of a point-like mass M is given by a SCHWARZSCHILD     

Einfluß des Randes auf das effektive Verhalten heterogener Körper - Anwendung auf Rayleighwellen

Effective Elastic Properties of Finite Heterogeneous Media - Application to Rayleigh-waves Rayleigh waves in a heterogeneous material (multiphase mixtures, composite materials, polycrystals) are governed by integrodifferential equations derived by the aid of known methods for infinite heterogeneous media. According to this wave equation the velocity depends on the frequency, and the waves are damped. After some simplifications (isotropy, nonrandom elastic constants) the following is obtained: if the fluctuations of the mass density are restricted to the vicinity of the boundary, the frequency dependent part of the velocity behaves like \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^3}}{{{\mathop c\limits^\circ} _t^3}} $\end{document} and the damping is proportional to \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^4 \omega ^5}}{{{\mathop c\limits^\circ} _t^5}} $\end{document}, whereas \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^2 \omega ^2}}{{{\mathop c\limits^\circ} _t^2}} $\end{document} respectively \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^4}}{{{\mathop c\limits^\circ} _t^4}} $\end{document} is found if the fluctuations are present in the whole half-space. From this it is seen, what assumptions are necessary to describe the waves by differential equations with frequenc y-dependent mass density.     

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: .     

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. .     

The metal‐insulator transitions of VO2: A band theoretical approach

The results of first principles electronic structure calculations for the metallic rutile and the insulating monoclinic phase of vanadium dioxide are presented. In addition, the insulating phase is investigated for the first time. The density functional calculations allow for a consistent understanding of all three phases. In the rutile phase metallic conductivity is carried by metal orbitals, which fall into the one‐dimensional band, and the isotropically dispersing bands. Hybridization of both types of bands is weak. In the phase splitting of the band due to metal‐metal dimerization and upshift of the bands due to increased p‐d overlap lead to an effective separation of both types of bands. Despite incomplete opening of the optical band gap due to the shortcomings of the local density approximation, the metal‐insulator transition can be understood as a Peierls‐like instability of the band in an embedding background of electrons. In the phase, the metal‐insulator transition arises as a combined embedded Peierls‐like and antiferromagnetic instability. The results for VO₂ fit into the general scenario of an instability of the rutile‐type transition‐metal dioxides at the beginning of the d series towards dimerization or antiferromagnetic ordering within the characteristic metal chains. This scenario was successfully applied before to MoO₂ and NbO₂. In the compounds, the and bands can be completely separated, which leads to the observed metal‐insulator transitions.     

Electrons with alternating on-site and correlated hopping interactions

The 1 D one-band Hubbard model with different repulsive on-site interactions on even (U+V > 0) and odd (U-V > 0) sites, supplemented by the correlated-hopping term (t* > 0), describing the modification of the electron hopping by the presence of other particles on the sites, is considered as a 1 D model for CuO systems. The ground state phase diagram is studied within the framework of the bosonization technique and renormalization group analysis valid for weak coupling. Depending on the choice of model parameters, the following sequences of phase transitions with increasing bandfilling occur: 1) metal-insulator-metal (for t* ? U/4); 2) metal-insulator-metal-superconductor $ ({\rm for}U/4 < t * \le U/\sqrt 8);3) $metal-superconductor-metal-insulator-metal-superconductor $ ({\rm for}U/\sqrt 8 \le t * < (U + V)/\sqrt 8){\rm and}4) $metal-superconductor $ ({\rm for}(U + V)/\sqrt 8 \le t*) $.     

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.     

Einsteins Feldtheorie mit Fernparallelismus und Diracs Elektrodynamik (Unitäre Feldtheorie mit dem Vektorpotential als Bezugstetrade)

Einstein's Field Theory with Tele-Parallelism and Dirac's Classical Theory of Electrons (Unified Field Theory with the Vector-Potential as a Reference-Tetrad) The Einstein-Maxwell theory of gravitation and electro-magnetism with Dirac-gauge AⁱA_i = m²c⁴/e² of the vector-potential A_i can be written as a purely geometrical field theory. The geometry of this field theory is Einstein's “Riemannian geometry with teleparallelism” and the vectorpotential is given by the time-like component of the tetrads h which define this tele-parallelism; we have -Physically, this unified field theory implies a generalization of the Einstein-Maxwell equations by introduction of a “current without current” describing Faraday's “gravoelectrical induction” corresponding with Dirac's electronic current λA_i.     

Gravitationskollaps und Lichtgeschwindigkeit im Gravitationsfeld

An elementary criterion of the stability of a matter sphere against gravitational collapse is given by the circular velocity condition of POINCARÉ : In a space with a spherically symmetric gravitation potential ? (r) and with a spherically symmetric metric gik (e.g., a SCHWARZSCHILD space time) the circular velocity V^* of a particle on the surface r = R of the matter-sphere must be (This condition is a consequence of the virial theorem and of the POINCARÉ theorem.) - However, EINSTEIN 's axiom of causality implies that this velocity V^* must be smaller than the local velocity of light v: V^*2 < v². And this local velocity v is a function of the gravitation potential ?, too: v = v [?]. In the case of NEWTON 's or EINSTEIN 's theory the spherically symmetric gravitation potential is given by the NEWTON ian function ? = fM/r. In the special theory of relativity, we would have v = c (c = EINSTEIN 's fundamental velocity) and grr = 1. Therefore, the specialrelativistic stability condition is R > fMc^?2. - But in the NEWTON ian theory v is depending of the gravitation potential and depends of the boundary condition for the light propagation, also. According to the ansatz of LAPLACE (1799) we have: (emanation-theory of light). But, according to SOLDNER (1801), we have Therefore, we are finding in the case of LAPLACE the same condition R > fMc^?2 as in the SRT. But, in the case of SOLDER 's ansatz non condition for stability is resulting. - In the general relativistic theories the local velocity of light is given by EINSTEIN 's expression According to EINSTEIN 's theory of “static gravitation” (1911/12) we have grr = 1 and therefore the formula and according to the GRT (with - g_ω = grr^?1) we have the formula Therefore, the Hilbert-Laue condition r= R > 3fMc^?2 results as stability condition. From the gravo-optical point of view, in GRT and for the classical ansatz of LAPLACE “black-holes” with bounding states of light result for R ≤ 2fM^?2. But, no “black-holes” are existing according to SOLDNER 's ansatz. However, in GRT each black-hole must be a “collapsar”. But according to the classical theory of LAPLACE we have uncollapsed “black- holes” for the domain .     

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.     

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}.     

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).     

Kinetic Study of the Emission of the First Negative System in an Argon-Nitrogen Plasma at Atmospheric Pressure

Quantitative optical spectroscopy measurements of the emission spectra of the N(B²∑_u,)ν′→X²∑_gν″ transition (first negative system) in an Ar-N₂ microwave discharge at atmospheric pressure have allowed determination of the rate coefficient of the production of N molecules in the B² ∑_u, state with vibrational level ν′ = 0. The N(B²∑_u, ν′) molecules are produced by the reaction in a surface-wave-induced microwave discharge (2450 MHz) sustained in an open-ended dielectric tube. The rate coefficient K (T) has been obtained for ν′ν″ = 0 for different gas temperatures by varying the incident microwave power. The K₀₀(T) values are between 7.10^?10 and 4.10^?10 cm³ s^?1 for the temperature range 2500 to 3450K.     

Aspects of stability and phenomenology in type IIA orientifolds with intersecting D6‐branes

Intersecting branes have been the subject of an elaborate string model building for several years. After a general introduction into string theory, this work introduces in detail the toroidal and $\mathbb{Z}_N$‐orientifolds. The picture involving D9‐branes with B‐fluxes is shortly reviewed, but the main discussion employs the T‐dual picture of intersecting D6‐branes. The derivation of the R‐R and NS‐NS tadpole cancellation conditions in the conformal field theory is shown in great detail. Various aspects of the open and closed chiral and non‐chiral massless spectrum are discussed, involving spacetime anomalies and the generalized Green‐Schwarz mechanism. An introduction into possible gauge breaking mechanisms is given, too. Afterwards, both 𝒩 = 1 supersymmetric and non‐supersymmetric approaches to low energy model building are treated. Firstly, the problem of complex structure instabilities in toroidal ΩR‐orientifolds is approached by a $\mathbb{Z}_3$‐orbifolded model. In particular, a stable non‐supersymmetric standard‐like model with three fermion generations is discussed. This model features the standard model gauge groups at the same time as having a massless hypercharge, but possessing an additional global B‐L symmetry. The electroweak Higgs mechanism and the Yukawa couplings are not realized in the usual way. It is shown that this model descends naturally from a flipped SU(5) GUT model, where the string scale has to be at least of the order of the GUT scale. Secondly, supersymmetric models on the $\mathbb{Z}_4$‐orbifold are discussed, involving exceptional 3‐cycles and the explicit construction of fractional D‐branes. A three generation Pati‐Salam model is constructed as a particular example, where several brane recombination mechanisms are used, yielding non‐flat and non‐factorizable branes. This model even can be broken down to a MSSM‐like model with a massless hypercharge. Finally, the possibility that unstable closed and open string moduli could have played the role of the inflaton in the evolution of the universe is being explored. In the closed string sector, the important slow‐rolling requirement can only be fulfilled for very specific cases, where some moduli are frozen and a special choice of coordinates is taken. In the open string sector, inflation does not seem to be possible at all.     

Comments on the Pressure Dissociation of Deuterium as Related to the Nova Laser Hugoniot

The recent Nova laser experimental Hugoniot for deuterium can be justified by a simple model which involves only very general properties of this material and which highlights the role of the molecular dissociation. The region of maximal compression along the principal Hugoniot is characterized by , , , where E_B is the binding energy of a molecule, and ρ_o is the initial density.     

Über ein weiteres Variationsprinzip im Zusammenhang mit kraftfreien Magnetfeldern

Im Anschluß an ein von Woltjer [1] diskutiertes Variationsproblem wird gezeigt: Die Euler-Lagrange-Gleichungen des Variationsproblems mit der Nebenbedingung wo H = rot A gesetzt ist, sind die Differentialgleichungen der kraftfreien Magnetfelder mit variablem α. Die Nebenbedingung läßt sich für alle Felder H erfüllen, die keinen singulären Punkt mit H = 0 in dem betrachteten Volumen V haben. In persuance of a variational principle discussed by Woltjer [1] it is shown that the Euler-Lagrange-equations of the variational problem with the secondary condition where H = rot A are the differential equations of the force-free magnetic fields with a variable scalar α. The secondary condition can be accomplished for all magnetic fields which do not contain singular points with H = 0 in the volume V under consideration.