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

Lorentz group theory and polarization of the light

Some facts of the theory of the Lorentz group are specified for looking at the problems of light polarization optics in the frames of vector Stokes-Mueller and spinor Jones formalism. In view of great differences between properties of isotropic and time-like vectors in Special Relativity we should expect principal differences in describing completely polarized and partly polarized light. In particular, substantial differences are revealed when turning to spinor techniques in the context of the polarized light. Because Jones complex formalism has close relation to spinor objects of the Lorentz group, within the field of the light polarization we could have physical realizations on the optical desk of some subtle topological distinctions between orthogonal L_{+}^{\uparrow} =SO_{0}(3.1) and spinor SL(2.C) groups. These topological differences of the groups find their corollaries in the problem of the so-called spinor structure of physical space-time, some new points are considered.Comment: 17 pages. Talk given at 16 International Seminar: NCPS, May 19-22, 2009, Minsk. A shorter vertion published as a journal pape

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

The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of Statistical Mechanics

In 1916 Einstein introduced the first rules for a quantum theory of electromagnetic radiation, and he applied them to a model of matter in thermal equilibrium with radiation to derive Planck's black-body formula. Einstein's treatment is extended here to time-dependent stochastic variables, which leads to a master equation for the probability distribution that describes the irreversible approach of Einstein's model towards thermal equilibrium, and elucidates aspects of the foundation of statistical mechanics. An analytic solution of this equation is obtained in the Fokker-Planck approximation which is in excellent agreement with numerical results. At equilibrium, it is shown that the probability distribution is proportional to the total number of microstates for a given configuration, in accordance with Boltzmann's fundamental postulate of equal a priori probabilities for these states. While the counting of these configurations depends on particle statistics- Boltzmann, Bose-Einstein, or Fermi-Dirac - the corresponding probability is determined here by the dynamics which are embodied in the form of Einstein's quantum transition probabilities for the emission and absorption of radiation. In a special limit, it is shown that the photons in Einstein's model can act as a thermal bath for the evolution of the atoms towards the canonical equilibrium distribution of Gibbs. In this limit, the present model is mathematically equivalent to an extended version of the Ehrenfests' ``dog-flea'' model, which has been discussed recently by Ambegaokar and Clerk

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

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

Noncommutative General Relativity

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be a noncommutative extension of the unimodular theory of gravitation. We compute the leading order noncommutative correction to the action and derive the noncommutative correction to the equations of motion of the weak gravitation field.Comment: v2: 10 pages, Discussion on noncommutative coordinate transformations has been changed. Corresponding changes have been made throughout the pape

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

Unimodular loop quantum gravity and the problems of time

We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not couple to terms in the expectation value of the energy-momentum tensor proportional to the metric tensor. The path integral takes the same form as is used to define spin foam models, with the additional constraint that the determinant of the four metric is constrained to be a constant by a gauge fixing term. We also review the proposal of Unruh, Wald and Sorkin- that the hamiltonian quantization yields quantum evolution in a physical time variable equal to elapsed four volume-and discuss how this may be carried out in loop quantum gravity. This then extends the results of arXiv:0904.4841 to the context of loop quantum gravity.Comment: 14 pages lagex, no figure

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