On the gravitational redshift

The study of the gravitational redshift\,---\,a relative wavelength increase of $\approx 2 \times 10^{-6}$ was predicted for solar radiation by Einstein in 1908\,---\,is still an important subject in modern physics. In a dispute whether or not atom interferometry experiments can be employed for gravitational redshift measurements, two research teams have recently disagreed on the physical cause of the shift. Regardless of any discussion on the interferometer aspect\,---\,we find that both groups of authors miss the important point that the ratio of gravitational to the electrostatic forces is generally very small. For instance, the gravitational force acting on an electron in a hydrogen atom situated in the Sun's photosphere to the electrostatic force between the proton and the electron is approximately $3 \times 10^{-21}$. A comparison of this ratio with the predicted and observed solar redshift indicates a discrepancy of many orders of magnitude. Here we show, with Einstein's early assumption of the frequency of spectral lines depending only on the generating ion itself as starting point, that a solution can be formulated based on a two-step process in analogy with Fermi's treatment of the Doppler effect. It provides a sequence of physical processes in line with the conservation of energy and momentum resulting in the observed shift and does not employ a geometric description. The gravitational field affects the release of the photon and not the atomic transition. The control parameter is the speed of light. The atomic emission is then contrasted with the gravitational redshift of matter-antimatter annihilation events.Comment: 19 Pages; 2 Table

National economic impacts of an EU environmental policy: an applied general equilibrium analysis

The objective of this paper is to quantify the economic effects of the introduction of a system of tradable permits in the European Union (EU). For this purpose we use linked applied general equilibrium models (AGE) for eleven EU member countries. This method enables us to measure the change in competitiveness for domestic industries, the impact on growth, employment and inflation in member countries, and the cost and benefits of a cooperative approach to adhere to a EU target of emissions of air pollutants. The results we will present are first results from the SOLVGE/GEM-E3 Projekt. GEM-E3 stands for General Equilibrium Modeling for Energy - Economy - Environment, a joint undertaking of NTUA-Athens (P. Capros, P. Georgakopoulos), CESKULeuven (S. Proost and D. Van Regemorter), Univ. Mannheim and ZEW (K. Conrad and T. Schmidt), GEMME-CEA (N. Ladoux), Univ. Strathclyde (P. MacGregor), CORE-UCL (Y. Smeers), With respect to a policy on greenhouse gases we will quantify the economic impact for the, EU by introducing a EU-wide tradable permit system, free of charge and based on the present energy intensity and energy mix. Under growth there will be a positive market price for permits with demand by countries where the cost of substitution are high and supply by those countries where the cost of substitution are low. We will measure economic performance and trade flows under a noncoordinated CO2 policy where each country limits the emission of CO2 by 10% and will compare the result with a cooperative outcome where the European Union as a decision maker aims at reducing CO2 by 10%. --