Moving Observers in an Isotropic Universe

We show how the anisotropy resulting from the motion of an observer in an isotropic universe may be determined by measurements. This provides a means to identify inertial frames, yielding a simple resolution to the twins paradox of relativity theory. We propose that isotropy is a requirement for a frame to be inertial; this makes it possible to relate motion to the large scale structure of the universe.Comment: 8 pages, 1 figure, with minor typographical correctio

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

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

Localized mode interactions in 0-pi Josephson junctions

A long Josephson junction containing regions with a phase shift of pi is considered. By exploiting the defect modes due to the discontinuities present in the system, it is shown that Josephson junctions with phase-shift can be an ideal setting for studying localized mode interactions. A phase-shift configuration acting as a double-well potential is considered and shown to admit mode tunnelings between the wells. When the phase-shift configuration is periodic, it is shown that localized excitations forming bright and dark solitons can be created. Multi-mode approximations are derived confirming the numerical results.Comment: 4 pages, to appear in Phys. Rev.

Vacuum energy and Universe in special relativity

The problem of cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, the vacuum energy is important for the Universe even in the absence of gravity, i.e. in the case when the Newton constant G is exactly zero, G=0. We discuss the response of the vacuum energy to the perturbations of the quantum vacuum in special relativity, and find that as in general relativity the vacuum energy density is on the order of the energy density of matter. In general relativity, the dependence of the vacuum energy on the equation of state of matter does not contain G, and thus is valid in the limit when G tends to zero. However, the result obtained for the vacuum energy in the world without gravity, i.e. when G=0 exactly, is different.Comment: LaTeX file, 7 pages, no figures, to appear in JETP Letters, reference is adde

Vortices in fermion droplets with repulsive dipole-dipole interactions

Vortices are found in a fermion system with repulsive dipole-dipole interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator potential. Such systems have much in common with electrons in quantum dots, where rotation is induced via an external magnetic field. In contrast to the Coulomb interactions between electrons, the (externally tunable) anisotropy of the dipole-dipole interaction breaks the rotational symmetry of the Hamiltonian. This may cause the otherwise rotationally symmetric exact wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure

A Thousand Invisible Cords Binding Astronomy and High-Energy Physics

The traditional realm of astronomy is the observation and study of the largest objects in the Universe, while the traditional domain of high-energy physics is the study of the smallest things in nature. But these two sciences concerned with opposite ends of the size spectrum are, in Muir's words, bound fast by a thousand invisible cords that cannot be broken. In this essay I propose that collaborations of astronomers and high-energy physicists on common problems are beneficial for both fields, and that both astronomy and high-energy physics can advance by this close and still growing relationship. Dark matter and dark energy are two of the binding cords I will use to illustrate how collaborations of astronomers and high-energy physicists on large astronomical projects can be good for astronomy, and how discoveries in astronomy can guide high-energy physicists in their quest for understanding nature on the smallest scales. Of course, the fields have some different intellectual and collaborative traditions, neither of which is ideal. The cultures of the different fields cannot be judged to be right or wrong; they either work or they don't. When astronomers and high-energy physicists work together, the binding cords can either encourage or choke creativity. The challenge facing the astronomy and high-energy physics communities is to adopt the best traditions of both fields. It is up to us to choose wisely.Comment: Why "Fundamentalist" Physics Is Good for Astronomy (in response to the paper of Simon White, arXiv:0704.2291

Reply to "Can gravitational dynamics be obtained by diffeomorphism invariance of action?"

In a previous work we showed that, in a suitable setting, one can use diffeomorphism invariance in order to derive gravitational field equations from boundary terms of the gravitational action. Standing by our results we reply here to a recent comment questioning their validity.Comment: Accepted for publication in PR

The Electrostatics of Einstein's Unified Field Theory

When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by H\'ely. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when H\'ely's physically correct metric is adopted.Comment: 15 pages. Misprints corrected. To appear in General Relativity and Gravitatio

Nonequilibrium fluctuations in a resistor

In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation constant in the system, exploiting the Fluctuation-Dissipation Theorem (FDT). In non-equilibrium steady systems, Fluctuations Theorems (FT) additionally describe symmetry properties of the probability density functions (PDFs) of the fluctuations of injected and dissipated energies. We experimentally probe a model system: an electrical dipole driven out of equilibrium by a small constant current $I$, and show that FT are experimentally accessible and valid. Furthermore, we stress that FT can be used to measure the dissipated power $\bar{\cal P}=RI^2$ in the system by just studying the PDFs symmetries.Comment: Juillet 200