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.     

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.     

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.     

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.     

Probing signals of the littlest Higgs model via the WW fusion processes at the high energy e + e- collider

In the framework of the littlest Higgs (LH) model, we consider the processes and , and we calculate the contributions of new particles to the cross sections of these processes in the future high energy e ⁺ e^- collider (ILC) with TeV. We find that, with reasonable values of the free parameters, the deviations of the cross sections for the processes from their SM values might be comparable to the future ILC measurement precision. The contributions of the light Higgs boson H⁰ to the process are significantly large in all of the parameter space preferred by the electroweak precision data, which might be detected in the future ILC experiments. However, the contributions of the new gauge bosons B_H and Z_H to this process are very small.Received: 22 February 2005, Revised: 27 April 2005, Published online: 6 July 2005PACS: 12.60.Cn, 14.70.Pw, 14.80.Cp     

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.     

Strongly positive semigroups and faithful invariant states

Let (?, τ, ω) denote aW*-algebra ?, a semigroupt>0?τ _t of linear maps of ? into ?, and a faithful τ-invariant normal state ω over ?. We assume that τ is strongly positive in the sense that $$\tau _t (A^ * A) \geqq \tau _t (A)^ * \tau _t (A)$$ for allA∈? andt>0. Therefore one can define a contraction semigroupT on ?= \(\overline {\mathcal{M}\Omega } \) by $$T_t A\Omega = \tau _t (A)\Omega ,{\rm A} \in \mathcal{M},$$ where Ω is the cyclic and separating vector associated with ω. We prove 1. the fixed points ?(τ) of τ are given by ?(τ)=?∩T′=?∩E′, whereE is the orthogonal projection onto the subspace ofT-invariant vectors, 2. the state ω has a unique decomposition into τ-ergodic states if, and only if, ?(τ) or {?υE}′ is abelian or, equivalently, if (?, τ, ω) is ?-abelian, 3. the state ω is τ-ergodic if, and only if, ?υE is irreducible or if $$\mathop {\inf }\limits_{\omega '' \in Co\omega 'o\tau } \left\| {\omega '' - \omega '} \right\| = 0$$ for all normal states ω′ where Coω′°τ denotes the convex hull of {ω′°τ _t } _t>0. Subsequently we assume that τ is 2-positive,T is normal, andT* _t ?₊Ω \( \subseteqq \overline {\mathcal{M}_ + \Omega } \) , and then prove 4. there exists a strongly positive semigroup |τ| which commutes with τ and is determined by $$\left| \tau \right|_t \left( A \right)\Omega = \left| {T_t } \right|A\Omega ,$$ 5. results similar to 1 and 2 apply to |τ| but the τ-invariant state ω is |τ|-ergodic if, and only if, $$\mathop {\lim }\limits_{t \to \infty } \left\| {\omega 'o\tau _t - \omega } \right\| = 0$$ for all normal states ω′.     

Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

The photoassociative spectroscopy, photoassociative molecule formation, and trapping of ultracold \mathsf{^{39}K^{85}Rb}

We have observed the photoassociative spectra of colliding ultracold ³⁹K and ⁸⁵Rb atoms to produce KRb* in all eight bound electronic states correlating with the ³⁹K (4s) + ⁸⁵Rb(5p _1/2 and 5p _3/2) asymptotes. These electronically excited KRb* ultracold molecules are detected after their radiative decay to the metastable triplet (a state and (in some cases) the singlet (X ground state. The triplet (a ultracold molecules are detected by two-photon ionization at 602.5 nm to form KRb ⁺ , followed by time-of-flight mass spectroscopy. We are able to assign a majority of the spectrum to three states (2(0 ⁺ ), 2(0^-), 2(1)) in a lower triad of states with similar C ₆ values correlating to the K(4s) + Rb (5p _1/2) asymptote; and to five states in an upper triad of three states (3(0 ⁺ ), 3(0^-), 3(1)) and a dyad of two states (4(1), 1(2)), with one set of similar C ₆ values within the upper triad and a different set of similar C ₆ values within the dyad. We are also able to make connection with the short-range spectra of Kasahara et al. [J. Chem. Phys. 111, 8857 (1999)], identifying three of our levels as v = 61, 62 and 63 of the 1 4(1) state they observed. We also argue that ultracold photoassociation to levels between the K(4s) + Rb (5p _3/2) and K(4s) + Rb (5p _1/2) asymptotes may be weakly or strongly predissociated and therefore difficult to observe by ionization of a (or X molecules; we do know from Kasahara et al. that levels of the 1 4(1) and 2 5(1) states in the intra-asymptote region are predissociated. A small fraction ( 1/3) of the triplet (a ultracold molecules formed are trapped in the weak magnetic field of our magneto-optical trap (MOT).Received: 22 September 2004, Published online: 23 November 2004PACS: 33.20.Fb Raman and Rayleigh spectra (including optical scattering) - 34.20.Cf Interatomic potentials and forces - 33.80.Ps Optical cooling of molecules; trapping     

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.     

A measurement of semileptonic B decaysto narrow orbitally-excited charm mesons

The decay chain is identified in a sample of 3.9 million hadronic Z decays collected with the OPAL detector at LEP. The branching ratio BR is measured to be for the J ^P =1⁺ (D⁰ ₁) state. For decays into the J ^P =2⁺ (D₂ ^*0) state, an upper limit of 1.4 x 10^-3 is placed on the branching ratio at the 95% confidence level.Received: 20 December 2002, Revised: 15 April 2003, Published online: 12 September 2003     

Isospin mixing \bar{K}N\hbox{-}{\pi}{\Sigma} interaction and \bar{K}NN\hbox{-}{\pi} {\Sigma}N quasi-bound state

A phenomenological isospin-dependent $\bar{K}N\hbox{-}\pi\Sigma$ potential reproducing a medium KEK value of 1s kaonic hydrogen level shift instead of a K ^? p scattering length is constructed. The corresponding three-body $\bar{K}NN\hbox{-}\pi\Sigma N$ calculation using the obtained potential is performed.     

Lifetime vibrational interference during the NO 1s-1π* resonant excitation studied by the NO+(A 1Π → X 1Σ+) fluorescence

Dispersed fluorescence from fragments formed after the de-excitation of the 1s^-1π^* resonances of N^*O and NO^* has been measured in the spectral range of 118–142 nm. This range is dominated by lines of atomic nitrogen and oxygen fragments and by the bands in the NO⁺ ion which result from the participator Auger decay of the 1s^-1π^* resonances. Ab-initio calculations of the transition probabilities between vibrational levels during the reaction NO N^*O ⇒ NO were used to explain the observed intensity dependence for the fluorescence bands on the exciting-photon energy across the resonances and on both v^′ and v^′′ vibrational quantum numbers. The multiplet structure of the 1s^-1π^* resonance and lifetime vibrational interference explain the observed exciting-photon energy dependence of the fluorescence intensity. A strong spin-orbit coupling between singlet and triplet states of NO⁺ is proposed to reduce additional cascade population of the state via radiative transitions from the and states and to explain remaining differences between measured and calculated integral fluorescence intensities.     

Probing spin-orbit quenching in Cl (2P) + H2 via crossed molecular beam scattering

In our previous work we investigated electronically non-adiabatic effects in using crossed molecular beam scattering coupled with velocity mapped ion imaging. The prior experiments placed limits on the cross-section for electronically non-adiabatic spin-orbit excitation and electronically non-adiabatic spin-orbit quenching . In the present work, we investigate electronically non-adiabatic spin-orbit quenching for which is the required first step for the reaction of Cl^* to produce ground state HCl+H products. In these experiments we collide Cl (²P) with H₂ at a series of fixed collision energies using a crossed molecular beam machine with velocity mapped ion imaging detection. Through an analysis of our ion images, we determine the fraction of electronically adiabatic scattering in Cl^* +H₂, which allows us to place limits on the cross-section for electronically non-adiabatic scattering or quenching. We determine the following quenching cross-sections σ _quench(2.1 kcal/mol) = 26 ± 21 ?², σ _quench(4.0 kcal/mol) = 21 ± 49 ?², and σ _quench(5.6 kcal/mol) = 14 ± 41 ?².     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

ω- πγtransition form factor in proton-proton collisions

Dalitz decays of ω and ρ mesons, and , produced in pp collisions are calculated within a covariant effective meson-nucleon theory. We argue that the ω transition form factor is experimentally accessible in a fairly model-independent way in the reaction pp → ppπ⁰ e ⁺ e ^- for invariant masses of the π⁰ e ⁺ e ^- subsystem near the ω pole. Numerical results are presented for the intermediate-energy kinematics of envisaged HADES experiments.     

Absorption of solar radiation by solar neutrinos

We calculate the absorption probability of photons radiated from the surface of the Sun by a left-handed neutrino with definite mass and a typical momentum for which we choose |p₁| = 0.2 MeV, producing a heavier right-handed antineutrino. Considering the two transitions and we obtain the two oscillation lengths L₁₂ = 4960.8 m, L₂₃ = 198.4 m, the two absorption probabilities P₁₂^abs. = 2.5 x 10^-67, P₂₃^abs. = 1.2 x 10^-58 and the two absorption ranges au, au, using a neutrino mass differences of meV, meV and associated transition dipole moments. We collect all necessary theoretical ingredients, i.e. neutrino mass and mixing scheme, induced electromagnetic transition dipole moments, quadratic charged lepton mass asymmetries and their interdependence.Received: 4 November 2003, Revised: 23 March 2004, Published online: 5 May 2004