Electromagnetic Propagators in Hyperbolic Robertson-Walker Cosmologies

Green functions (retarded, advanced, Feynman and Dyson propagators) are calculated for the electromagnetic field in Robertson-Walker cosmologies with hyperbolic 3-manifolds as spacelike slices. The starting point is the Proca equation, i.e., the Maxwell field with a finite photon mass for infrared regularization, in a static cosmology with simply connected hyperbolic 3-sections. The time and space components of the resolvent kernel are scalar and vectorial point-pair invariants, respectively, and this symmetry allows for an explicit evaluation in the spectral representation. It is found that the quantum propagators have a logarithmic infrared singularity, which drops out in the zero curvature limit. Retarded and advanced Green functions remain well defined in the limit of zero photon mass, and they admit a simple generalization, by conformal scaling, to expanding 3-spaces. In cosmologies with multiply connected hyperbolic 3-manifolds as spacelike sections, the four enumerated propagators are constructed by means of Poincare series. The spectral decomposition of the Green functions is given in terms of Eisenstein series for a certain class of open hyperbolic 3-spaces, including those with Schottky covering groups corresponding to solid handle-bodies as spacelike slices

Tachyons, Lamb Shifts and Superluminal Chaos

An elementary account on the origins of cosmic chaos in an open and multiply connected universe is given; there is a finite region in the open 3-space in which the world-lines of galaxies are chaotic, and the mixing taking place in this chaotic nucleus of the universe provides a mechanism to create equidistribution. The galaxy background defines a distinguished frame of reference and a unique cosmic time order; in this context superluminal signal transfer is studied. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Estimates on tachyon mixing in the geometric optics limit are derived. The potential of a static point source in this field theory is a damped periodic function. We treat this tachyon potential as a perturbation of the Coulomb potential, and study its effects on energy levels in hydrogenic systems. By comparing the induced level shifts to high-precision Lamb shift measurements and QED calculations, we suggest a tachyon mass of 2.1 keV and estimate the tachyonic coupling strength to subluminal matter. The impact of the tachyon field on ground state hyperfine transitions in hydrogen and muonium is investigated. Bounds on atomic transition rates effected by tachyon radiation as well as estimates on the spectral energy density of a possible cosmic tachyon background radiation are derived

Ether, Luminosity and Galactic Source Counts

An interpretation of the cosmological redshift in terms of a cosmic ether is given. We study a Robertson-Walker cosmology in which the ether is phenomenologically defined by a homogeneous and isotropic permeability tensor. The speed of light becomes so a function of cosmic time like in a dielectric medium. However, the cosmic ether is dispersion free, it does not lead to a broadening of spectral lines. Locally, in Euclidean frames, the scale factors of the permeability tensor get absorbed in the fundamental constants. Mass and charge scale with cosmic time, and so do atomic energy levels. This substantially changes the interpretation of the cosmological redshift as a Doppler shift. Photon frequencies are independent of the expansion factor; their time scaling is determined by the permeability tensor. The impact of the ether on the luminosity-distance, on the distance-redshift relation, and on galactic number counts is discussed. The Hubble constant is related to the scale factors of the metric and the permeability tensor. We study the effects of the ether at first in comoving Robertson-Walker coordinates, and then, in the context of a flat but expanding space-time, in the globally geodesic rest frames of galactic observers

Tachyons in Robertson-Walker Cosmology

Superluminal signal transfer is studied in the context of a preferred cosmic frame of reference provided by the galactic background. The receding galaxies constitute a frame of absolute rest, in which the energy of tachyons (faster-than-light particles) is unambiguously defined as a positive quantity. The causality violation which arises in relativistic tachyonic theories is avoided. We define interactions of particles and tachyons in terms of elastic head-on collisions and energy-momentum conservation. To compare the theory developed with existing relativistic theories, tachyons are studied at first in a Minkowski universe, and the causality of a superluminal communication process is analyzed. Then we discuss the dynamics of tachyons in a Robertson-Walker universe with linear expansion factor and negatively curved three-space. We point out the consequences that the space expansion has on tachyons, like a finite life-time in the frame of absolute rest, and multiple images in the rest frames of moving observers

Cosmic Time Variation of the Gravitational Constant

A pre-relativistic cosmological approach to electromagnetism and gravitation is explored that leads to a cosmic time variation of the fundamental constants. Space itself is supposed to have physical substance, which manifests by its permeability. The scale factors of the permeability tensor induce a time variation of the fundamental constants. Atomic radii, periods, and energy levels scale in cosmic time, which results in dispersionless redshifts without invoking a space expansion. Hubble constant and deceleration parameter are reviewed in this context. The time variation of the gravitational constant at the present epoch can be expressed in terms of these quantities. This provides a completely new way to restrain the deceleration parameter from laboratory bounds on the time variation of the gravitational constant. This variation also affects the redshift dependence of angular diameters and the surface brightness, and we study in some detail the redshift scaling of the linear sizes of radio sources. The effect of the varying constants on source counts is discussed, and an estimate on the curvature radius of the hyperbolic 3-space is inferred from the peak in the quasar distribution. The background radiation in this dispersionless, permeable space-time stays perfectly Planckian. Cosmic time is discussed in terms of atomic and gravitational clocks, as well as cosmological age dating, in particular how the age of the Universe relates to the age of the Galaxy in a permeable space-time

Cosmic Ether

A prerelativistic approach to particle dynamics is explored in an expanding Robertson-Walker cosmology. The receding galactic background provides a distinguished frame of reference and a unique cosmic time. In this context the relativistic, purely geometric space-time concept is criticized. Physical space is regarded as a permeable medium, the cosmic ether, which effects the world-lines of particles and rays. We study in detail a Robertson-Walker universe with linear expansion factor and negatively curved, open three-space; we choose the permeability tensor of the ether in such a way that the semiclassical approximation is exact. Galactic red-shifts depend on the refractive index of the ether. In the local Minkowskian limit the ether causes a time variation of mass, which scales inversely proportional to cosmic time. In the globally geodesic rest frames of galactic observers the ether manifests itself in an unbounded speed of signal transfer, in bifurcations of world-lines, and in time inversion effects

Conformal Tachyons

We study tachyons conformally coupled to the background geometry of a Milne universe. The causality of superluminal signal transfer is scrutinized in this context. The cosmic time of the comoving frame determines a distinguished time order for events connected by superluminal signals. An observer can relate his rest frame to the galaxy frame, and compare so the time order of events in his proper time to the cosmic time order. All observers can in this way arrive at identical conclusions on the causality of events connected by superluminal signals. An unambiguous energy concept for tachyonic rays is defined by means of the cosmic time of the comoving reference frame, without resorting to an antiparticle interpretation. On that basis we give an explicit proof that no signals can be sent into the past of observers. Causality violating signals are energetically forbidden, as they would have negative energy in the rest frame of the emitting observer. If an observer emits a superluminal signal, the tachyonic response of a second observer cannot reach him prior to the emission, i.e. no predetermination can occur

Interaction of Tachyons with Matter

A new interaction mechanism of superluminal particles with matter is suggested. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. The potential of a static point source in this field theory is a damped periodic function with 1/r-decay. We treat this potential as a perturbation of the Coulomb potential, and study its effects on cross-sections and energy levels. In the limit of large impact parameter, the periodicity of the potential has a pronounced effect on the classical cross-section, which gets singular at the accumulating extrema of the scattering angle. In this limit we define the cross-section wave mechanically, by semiclassical rainbow scattering. The impact of the tachyon potential on the energy levels of hydrogen and hydrogenic ions is calculated by means of Bohr-Sommerfeld quantization. Estimates for the tachyon mass (3 keV) and the coupling constant of the tachyon potential are derived on the basis of high-precision Lamb shift measurements

Einstein Coefficients and Equilibrium Formalism for Tachyon Radiation

The spectral energy density of an ideal Bose gas of superluminal particles (tachyons) is derived. To this end, we consider atoms in equilibrium with tachyon radiation, study spontaneous and induced transitions effected by tachyons, calculate the Einstein coefficients, all semiclassically, and obtain, by detailed balancing, the equilibrium distribution of the tachyon gas. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Atomic transitions induced by tachyons are compared to photonic ones, and the tachyonic analog to the photoelectric effect is discussed. The cosmic tachyon background is scrutinized in detail; high- and low-temperature expansions of the internal energy, the entropy, the heat capacities, and the number density are compared with the corresponding quantities of the photon background. The negative mass square in the wave equation changes the frequency scaling in the Rayleigh-Jeans law, and there are also significant changes in the low-temperature regime, in particular in the caloric and thermal equations of state. Quantitative estimates on the tachyon background and on Rydberg transitions induced by tachyon radiation are derived. Keywords: Superluminal black-body radiation; Tachyonic background radiation; Ether; Aether; Proca equation; Rydberg atoms

Nonlinear Non-Relativistic Gravity

A phenomenological theory of gravitation is proposed, based on a pre-relativistic approach to electromagnetism. The general relativistic, purely geometric, spacetime conception is criticized. Space itself is assumed to have physical substance. This substance, the ether, manifests by its permeability. Gravitational fields do not curve space, but rather distort the ether, and so affect its permeability. The permeability determines the speed of light, which is varying as in a dielectric medium. The theory is only in certain limits Lorentz invariant; the concept of a uniformly moving observer is likewise only approximate, and so is the principle of equivalence. Nonlinear field equations for the scalar gravitational field as well as the permeability tensor of the ether are constructed in a way to fit the classical experiments on gravitation. Estimates on the variation of the speed of light in our solar system are given