Variability of fundamental constants

If the fine structure constant is not really constant, is this due to a variation of $e$, $\hbar$, or $c$? It is argued that the only reasonable conclusion is a variable speed of light.Comment: preliminary draft, comments welcom

Doubly Special Relativity with a minimum speed and the Uncertainty Principle

The present work aims to search for an implementation of a new symmetry in the space-time by introducing the idea of an invariant minimum speed scale ($V$). Such a lowest limit $V$, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the space-time at the subatomic level for very low energies close to the background frame ($v\approx V$), providing a fundamental understanding for the uncertainty principle, i.e., the uncertainty relations should emerge from the space-time with an invariant minimum speed.Comment: 10 pages, 8 figures, Correlated paper in: http://www.worldscientific.com/worldscinet/ijmpd?journalTabs=read. arXiv admin note: substantial text overlap with arXiv:physics/0702095, arXiv:0705.4315, arXiv:0709.1727, arXiv:0805.120

Alternative derivation of the relativistic contribution to perihelic precession

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximately elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle, rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated relativistic contribution to perihelic precession agrees with established first-order results. The reduced radius for the circular orbit is in agreement to first-order with that calculated from the Schwarzschild effective potential. The method of solution is understandable by undergraduate students.Comment: 12 pages, 2 figures. Accepted for publication in the American Journal of Physic

The Maxwell Lagrangian in purely affine gravity

The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein-Maxwell equations in the metric-affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.Comment: 9 pages; published versio

Analytic Formulas for the Orientation Dependence of Step Stiffness and Line Tension: Key Ingredients for Numerical Modeling

We present explicit analytic, twice-differentiable expressions for the temperature-dependent anisotropic step line tension and step stiffness for the two principal surfaces of face-centered-cubic crystals, the square {001} and the hexagonal {111}. These expressions improve on simple expressions that are valid only for low temperatures and away from singular orientations. They are well suited for implementation into numerical methods such as finite-element simulation of step evolution.Comment: 10 pages; reformatted with revtex (with typos corrected) from version accepted by SIAM--Multiscale Modeling and Simulation on Nov. 21, 2006; greatly expanded introduction, several minor fixes (mostly stylistic

Can Solar System observations tell us something about the cosmological constant?

In this note we show that the latest determinations of the residual Mercury's perihelion advance, obtained by accounting for almost all known Newtonian and post-Newtonian orbital effects, yields only very broad constraints on the cosmological constant. Indeed, from \delta\dot\omega=-0.0036 + - 0.0050 arcseconds per century one gets -2 10^-34 km^-2 < Lambda < 4 10^-35 km^-2. The currently accepted value for Lambda, obtained from many independent cosmological and large-scale measurements, amounts to almost 10^-46 km^-2.Comment: Latex2e, 4 pages, 2 table, no figures, 11 references. Table 2 added, typos in the units of Lambda correcte

Action Principle for the Generalized Harmonic Formulation of General Relativity

An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona--Casas and Palenzuela (BBP). The relationship between the generalized harmonic action and the BBP action is discussed in detail.Comment: This version is contains more thorough presentations and discussions of the key results. To be published in PRD. (8 pages, no figures

On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity

The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.Comment: Substantial changes from v1 including added author, change of title and emphasis of the paper although all original results of v1. remai

The mystery of the cosmic vacuum energy density and the accelerated expansion of the Universe

After a short history of the $\Lambda$-term it is explained why the (effective) cosmological constant is expected to obtain contributions from short-distance-physics, corresponding to an energy scale of at least 100 GeV. The actual tiny value of the cosmological constant in any natural scale of units represents, therefore, one of the deepest mysteries of present day fundamental physics. We also briefly discuss recent astronomical evidence for a cosmologically significant vacuum energy density causing an accelerating expansion of the universe. This arises mainly from the Hubble diagram of type Ia supernovae and from the observed temperature fluctuations of the cosmic microwave background radiation. If this should become an established fact, we are also confronted with a disturbing {\it cosmic coincidence} problem.Comment: 12 pages, 2 figures, iopart macros include

The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)

Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest and next-nearest neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, non pairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two high-symmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).Comment: 8 pages, 3 figures, submitted to Phys. Rev.