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

Cosmological gravitomagnetism and Mach's principle

The spin axes of gyroscopes experimentally define local non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? We consider linear perturbations of Friedmann-Robertson-Walker cosmologies with k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin axes of gyroscopes relative to the directions of geodesics to quasars in the asymptotic unperturbed FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of linear cosmological gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state for cosmological matter, are: 1) The dragging of a gyroscope axis by rotational perturbations of matter beyond the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot is the derivative with respect to cosmic time. 2) If the perturbation of matter is a homogeneous rotation inside some radius around a gyroscope, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For the most general linear cosmological perturbations the time-evolution of all gyroscope spin axes exactly follow a weighted average of the energy currents of cosmological matter. The weight function is the same as in Ampere's law except that the inverse square law is replaced by the Yukawa force with the Hubble-dot cutoff. Our results demonstrate (in first order perturbation theory for FRW cosmologies with k = 0) the validity of Mach's hypothesis that axes of local non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde

On the interaction of a single-photon wave packet with an excited atom

The interaction of a single-photon wave packet with an initially excited two-level atom in free space is studied in semiclassical and quantum approaches. It is shown that the final state of the field does not contain doubly occupied modes. The process of the atom's transition to the ground state may be accelerated, decelerated or even reversed by the incoming photon, depending on parameters. The spectrum of emitted radiation is close to the sum of the spectrum of the incoming single-photon wave packet and the natural line shape, with small and complicated deviations.Comment: 17 pages, 5 figure

New two-sided bound on the isotropic Lorentz-violating parameter of modified Maxwell theory

There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin-one-half Dirac particle p^\pm with minimal coupling to the nonstandard photon \widetilde{\gamma}, the resulting modified-quantum-electrodynamics model involves a single dimensionless "deformation parameter," \widetilde{\kappa}_{tr}. The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation p^\pm \to p^\pm \widetilde{\gamma} for the case of positive \widetilde{\kappa}_{tr} and photon decay \widetilde{\gamma} \to p^+ p^- for the case of negative \widetilde{\kappa}_{tr}. From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and an excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on \widetilde{\kappa}_{tr} is obtained, which improves by eight orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed.Comment: 18 pages, v5: published version in preprint styl

Gravitation, electromagnetism and the cosmological constant in purely affine gravity

The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein-Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid only for weak electromagnetic fields. Therefore the purely affine formulation that combines gravitation, electromagnetism and the cosmological constant cannot be a simple sum of terms corresponding to separate fields. Consequently, this formulation of electromagnetism seems to be unphysical, unlike the purely metric and metric-affine pictures, unless the electromagnetic field couples to the cosmological constant.Comment: 14 pages, extended and combined with gr-qc/0701176; published versio

On the nonsymmetric purely affine gravity

We review the vacuum purely affine gravity with the nonsymmetric connection and metric. We also examine dynamical effects of the second Ricci tensor and covariant second-rank tensors constructed from the torsion tensor in the gravitational Lagrangian.Comment: 15 pages; published versio

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

Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it Planck variable) whose distribution is just the Bose distribution yielding the Planck law of black-body radiation. The fractional part is the dark part (we call is dark variable) with a continuous distribution, which is, of course, not observed in the experiments. It is proved that the Bose distribution is infinitely divisible, and the irreducible decomposition of it is given. The Planck variable can be decomposed into an infinite sum of independent binary random variables representing the binary photons (more accurately photo-molecules or photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons follow the Fermi statistics. Consequently, the black-body radiation can be viewed as a mixture of statistically and thermodynamically independent fermion gases consisting of binary photons. The binary photons give a natural tool for the dyadic expansion of arbitrary (but not coherent) ordinary photon excitations. It is shown that the binary photons have wave-particle fluctuations of fermions. These fluctuations combine to give the wave-particle fluctuations of the original bosonic photons expressed by the Einstein fluctuation formula.Comment: 29 page

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page

Quantum Mechanical Carrier of the Imprints of Gravitation

We exhibit a purely quantum mechanical carrier of the imprints of gravitation by identifying for a relativistic system a property which (i) is independent of its mass and (ii) expresses the Poincare invariance of spacetime in the absence of gravitation. This carrier consists of the phase and amplitude correlations of waves in oppositely accelerating frames. These correlations are expressed as a Klein-Gordon-equation-determined vector field whose components are the ``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. The imprints themselves are deviations away from this vector field.Comment: 8 pages, RevTex. Html version of this and related papers on accelerated frames available at http://www.math.ohio-state.edu/~gerlac