Finite Speed Of Light Research Articles

Radiative transfer of 21-cm line through ionised cavities in an expanding universe

Abstract The optical depth parameterisation is typically used to study the 21-cm signals associated with the properties of the neutral hydrogen (H i) gas and the ionisation morphology during the Epoch of Reionisation (EoR), without solving the radiative transfer equation. To assess the uncertainties resulting from this simplification, we conduct explicit radiative transfer calculations using the cosmological 21-cm radiative transfer (C21LRT) code and examine the imprints of ionisation structures on the 21-cm spectrum. We consider a globally averaged reionisation history and implement fully ionised cavities (H ii bubbles) of diameters d ranging from 0.01 Mpc to 10 Mpc at epochs within the emission and the absorption regimes of the 21-cm global signal. The single-ray C21LRT calculations show that the shape of the imprinted spectral features are primarily determined by d and the 21-cm line profile, which is parametrised by the turbulent velocity of the H i gas. It reveals the spectral features tied to the transition from ionised to neutral regions that calculations based on the optical depth parametrisation were unable to capture. We also present analytical approximations of the calculated spectral features of the H ii bubbles. The multiple-ray calculations show that the apparent shape of a H ii bubble (of d = 5 Mpc at z = 8), because of the finite speed of light, differs depending on whether the bubble’s ionisation front is stationary or expanding. Our study shows the necessity of properly accounting for the effects of line-continuum interaction, line broadening and cosmological expansion to correctly predict the EoR 21-cm signals.

High-frequency magnetohydrodynamics

We consider the case that the displacement current is not neglected in the classical MHD equations, as it is usually done. This amounts to cast them in the relativistic framework of a finite speed of light. We show some consequences in describing magnetic reconnection phenomena and for hydromagnetic waves. In the first case, the equation for the magnetic induction is changed from (formally) parabolic to (formally) hyperbolic, in the second case both, the perturbed magnetic field and the particle velocity, obey to a certain third-order in time partial differential equation, rather than to the classical wave equation. We stress the role of two typically small but nonzero parameters, the magnetic diffusivity, η (corresponding to large values of the Lundquist number), and ε:=c−2.

Coulomb’s Law in Electrostatic, Gravitational and Inertial Forces and Emission of Radiation

Electric fields, from charges in bodies, in accordance with Coulomb’s law, occupying a vacuum, constitute an elastic medium called aether. Electrostatic, gravitational, and inertial forces are explained by considering the aether as an electric-field medium, supporting transmission of radiation at the speed of light. A partice of charge Q is supposed to be an impregnable hollow sphere, with radial force pulling the surface outwards, to maintain a stable structure of radius a and mass m, as the smallest quantities. Lines of force from stationary adjacent charges, are curled, in positive potential energy, for repulsion or negative for attraction. A charge Q, moving at constant velocity, carries its straight lines of radial fields, with increase forwards, to account for the kinetic energy. Force of gravity is by virtue of bodies displacing volumes of the aether, one in the shadow of another, to make for a pushings force of attraction, in accordance with Newton’s law. Due to finite speed of light, acceleration of charge Q moving at time t with velocity v, is not simultaneously passed to all the fields, resulting in curling of lateral field lines and creation of reactive field E and inertial force QE = -m(dv/dt), as inertia. Coulomb’s law is modified, with a velocity term, in view of aberration of electric field, for radiation from accelerated charges. Curving of space-time continuum is replaced with curling of electric field lines of force. Materials for teaching electromagnetic fields and radiation, in space, are well provided.

Light and Radio Radiations from a Moving Charged Particle

Two types of electromagnetic radiation are identified: light radiation and radio radiation. Light radiation is due to aberration of electric field in the motion of a charged particle in an external electric field, where energy radiated, proportional to the square of amplitude of velocity, is the difference between change in potential energy and change in kinetic energy. This is so with electrons revolving in the electric field of the nucleus of an atom. Radio radiation, due to finite speed of light, whereby an oscillating charged particle generates a magnetic field in phase with an electric field, at a point in space, resulting in generation of energy, proportional to the square of amplitude of acceleration, as from a radio antenna. The electric field in the Poynting vector is the sum of external accelerating field and internal induction field due to acceleration of a charged particle, in accordance with Faraday’s law. The induction field also acts on the same charge creating it, to produce the inertial force, equal and opposite to the accelerating force, thereby explaining the cause of inertia. Radio radiation explains the presence of Cosmic Microwave Background Radiation as a local phenomenon from within the atoms of a body

Adaptive optics LEO uplink pre-compensation with finite spatial modes.

Adaptive optics pre-compensation of free-space optical communications uplink from ground to space is complicated by the "point ahead angle" due to spacecraft velocity and the finite speed of light, as well as anisoplanatism of the uplink beam and the wavefront beacon. This Letter explores how pre-compensation varies with the number of spatial modes applied and how it varies with a beacon at the point-ahead angle versus a downlink beacon. Using a w0 = 16cm Gaussian beam propagating through a modified Hufnagel-Valley model as an example, we find pre-compensation performance plateaus beyond ∼100 applied modes regardless of integrated turbulence strength, and that a point ahead beacon provides a 1-4 dB gain in median received power and an order-of-magnitude reduction in scintillation over a downlink beacon at wavelengths typical of optical communications. Modeling tailored to specific scenarios should be conducted to determine whether implementing a resource-intensive point ahead beacon is the optimum path to meeting link requirements.

Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications

In this paper, we discuss the design and feasibility of a multifunctional laser instrument capable of precision ranging, time transfer, and wideband communications over interplanetary distances throughout our solar system. To simplify the communications discussion, On-Off Keying (OOK) is assumed for the high bandwidth (MHz to GHz) modulation format, and the required laser powers and transmit and receive apertures are determined for each Earth–planet link as a function of data rate. Optimization of the transmitter and receiver antenna gains is reviewed. It is further assumed that the spacecraft is in orbit about the planet of interest in order to justify the need for large data downloads rates and that single-photon sensitive detector arrays can be utilized to aid in the acquisition, detection, and tracking of the opposite terminal. Satellite acquisition and tracking is complicated by the long one-way propagation distances (up to 40 AU), the finite speed of light, the orbital and rotational velocities of the two planets, and, if applicable, the spacecraft orbital speed about the planet. Taking advantage of the highly circular and coplanar planetary orbits within our solar system, point ahead angles are estimated for all combinations of possible Earth–planet positions revealing solar orbital geometries where planetary motion does not introduce a need for point ahead angles. Finally, possible methods for simplifying the initial mutual acquisition of the planetary and Earth terminals and maintaining the coalignment of their respective optical systems is discussed.

Photometric IGM tomography: Efficiently mapping quasar light echoes with deep narrow-band imaging

ABSTRACT In the standard picture, episodes of luminous quasar activity are directly related to supermassive black hole (SMBH) growth. The ionizing radiation emitted over a quasar’s lifetime alters the ionization state of the surrounding intergalactic medium (IGM), enhancing the Lyα forest transmission – so-called proximity effect – which can be observed in absorption spectra of background sources. Owing to the finite speed of light, the transverse direction of the proximity effect is sensitive to the quasar’s radiative history, resulting in ‘light echoes’ that encode the growth history of the SMBH on Myr time-scales. In this paper, we introduce a new technique to photometrically map this quasar light echoes using Lyα forest tomography by using a carefully selected pair of narrow-band filters. A foreground narrow-band filter is used to measure Lyα forest transmission along background galaxies selected as Lyα emitters by a background narrow-band filter. This novel double narrow-band tomographic technique utilizes the higher throughput and wider field of view of imaging over spectroscopy to efficiently reconstruct a two-dimensional map of Lyα forest transmission around a quasar. We present a fully Bayesian framework to measure the luminous quasar lifetime of a SMBH from photometric IGM tomography, and examine the observational requirements. This new technique provides an efficient strategy to map a large area of the sky with a modest observing time and to identify interesting regions to be examined by further deep 3D follow-up spectroscopic Lyα forest tomography.

Jupiter’s Satellites, from Cassini to Today’s Icy Worlds: 350 Years of Observation and Study of the Galilean Satellites of Jupiter at Paris Observatory

The satellites of Jupiter discovered by Galileo in 1610 are among the most interesting and difficult objects to study. These are complex worlds whose size is close to that of Mars. The four satellites are similar to a small solar system, their motions bringing together all the difficulties of celestial mechanics. These satellites, known as the Galilean satellites also have the peculiarity of being regularly eclipsed by the planet Jupiter, a phenomenon easily observed from Earth. As soon as the Paris Observatory was created, it soon became clear that these satellites were not only objects of study for astronomers, but also valuable auxiliaries for geographers and explorers, helping to define a universal time. Thus, they were used to perfect the cartography of France as desired by Louis XIV during the creation of the observatory. They also helped demonstrate the finite speed of light. The greatest astronomers were interested by these satellites, especially Laplace, who first, understood and described the dynamics of the Jovian system. Delambre undertook to observe and collect many observations of the eclipses of these satellites which are still useful today. More recently, space exploration revived these studies; the Voyager probe sent us unprecedented images revealing their icy surface. The continuous gain in accuracy of astrometric observations allowed to refine their dynamics, modeling and constraining their internal structure: the tidal effects of Jupiter on its satellites are now observable from Earth. These satellites remain a chosen field of study at Paris Observatory; where 350 years later their story continues to be told.

An Homage to Heinrich Hertz [Around the Globe

In 1861 and in 1865, Clerk Maxwell predicted theoretically that electromagnetic waves should exist in nature and that visible light was an electromagnetic wave (the finite speed of light being, by then, well known). In 1873, in his famous <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A Treatise on Electricity and Magnetism</i> , Maxwell titled one of the chapters “Electromagnetic Theory of Light.”

Nondipole effects on the double-slit interference in molecular ionization by xuv pulses.

The double-slit interference in single-photon ionization of the diatomic molecular ion H2 + is theoretically studied beyond the dipole approximation. Via simulating and comparing the interactions of the prealigned H2 + and the hydrogen atom with the xuv pulses propagating in different directions, we illustrate two kinds of effects that are encoded in the interference patterns of the photoelectrons from H2 +: the single-atom nondipole effect and the two-center-interference one, both associated with the finite speed of light. While the two effects could modify the maxima of the interference fringes, we show that the former one hardly affects the interference minima. Our results and analysis show that the interference minima rule out the influences of the photon-momentum transfer and, potentially, the multielectron effect, thus performing a better role in decoding the zeptosecond time delay for the pulse hitting one and the other atomic centers of the molecule.

Effect of the finite speed of light in ionization of extended molecular systems

We study propagation effects due to the finite speed of light in ionization of extended molecular systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shrödinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the hbox {H}_{2}^{+} molecular ion and the hbox {Ne}_2 dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily accessible than the ground breaking synchrotron measurement by Grundmann et al. (Science 370:339, 2020).

Rhazes’ Contributions to Alchemy and Pharmacy

Context: Persia has been the cradle of science across human history. Many of today’s concepts in science, such as the finite speed of light and alcohol distillation, were first proposed by Persian scientists. Mohammad ibn Zakariya Razi (Rhazes) is undoubtedly one of the greatest Persian scientists over human history. Evidence Acquisition: In this paper, in addition to a brief review of the history of pharmacy and chemistry sciences in Persia, Rhazes’ valuable books in the fields of pharmacy and chemistry, along with a brief description of them, were introduced. Data were extracted from different historical and bibliography books and also the citation databases of PubMed, Scopus, and Google Scholar. Results: Rhazes’ books and treatises in the fields of pharmacy and chemistry have been classified into three categories: (1) the books and treatises containing some sections on pharmacy like Al-Hawi fi al-Tibb (Liber Continens) and Al-Mansouri fi al-Tibb, (2) those written merely on pharmacy, like Qarabadin (pharmacopeia), and (3) the books focusing on alchemy (kimia), like Sirr al-Asrar (Secret of secrets) and Al Asrar (Liber Secretorum). Three volumes of Al Hawi fi al-Tibb were applied as a reference in pharmacology in Western universities for many years. Sirr al-Asrar is his most important book on alchemy, describing raw materials used in alchemy, experimental apparatus necessary for alchemical investigations, and detailed procedures for the chemical manipulation of arsenic and sulfur. Conclusions: These valuable manuscripts demonstrate the ancient heritage of Persians and the great roles and contributions of Persian scientists in the history of science.

On apparent faster-than-light behavior of moving electric fields

For every observer, however distant, the electric field of a uniformly moving charge is always directed away from, or points towards, the instantaneous present position of the charge and not away from, or towards, the retarded position at which the observer sees it (due to the finite speed of light). This fact is a well-established consequence of, among others, the application of the Li\'enard-Wiechert potentials, and its significance for fundamental physics is probably not fully appreciated. Here we show how and why this property has non-negligible consequences for what we take for granted about the relativity of simultaneity and faster-than-light communication. In particular, if we consider two opposite electric charges whose distance shrinks to zero at a constant velocity (shrinking electric dipole), then the cancellation of the total field seems to be instantaneous everywhere in space and in every inertial reference frame. A simple variant of the shrinking electric dipole setup appears to allow a sort of faster-than-light communication of information. Our results provide simple theoretical support to the conclusions of recent experiments on the propagation speed of Coulomb and magnetic fields. It would also be interesting to explore any possible connection between our findings and quantum non-locality.

Collective radiation from distant emitters

Waveguides allow for direct coupling of emitters separated by large distances, offering a path to connect remote quantum systems. However, when facing the distances needed for practical applications, retardation effects due to the finite speed of light are often overlooked. Previous works studied the non-Markovian dynamics of emitters with retardation, but the properties of the radiated field remain mostly unexplored. By considering a toy model of two distant two-level atoms coupled through a waveguide, we study the spectrum of the radiated field that exhibits non-Markovian features such as linewidth broadening beyond standard superradiance, or narrow Fano-resonance-like peaks. We also observe modifications to the energy-exchange dynamics in the presence of retardation. We discuss a proof-of-concept implementation of our results in a superconducting circuit platform.

On special relativistic effects via classical physics.

We present an analytic study of light propagation in a simple Michelson-Morley interferometer as observed by inertial observers to understand any connections among classical physics, optical physics, and special relativity. To that end, we develop coordinate transformations of wave propagation as observed in inertial frames (i.e., non-accelerating reference frames). We find that relativistic and other effects appear naturally as a result of finite light speed. Such effects include wavefront tilt relative to the normal of energy flow with the wavefront normal tilting relative to the Poynting vector.

Declare your motivations

Declare your motivations

Sensitivity and accuracy of Casimir force measurements in air

Quantum electrodynamic fluctuations cause an attractive force between metallic surfaces. At separations where the finite speed of light affects the interaction, it is called the Casimir force. Thermal motion determines the fundamental sensitivity limits of its measurement at room temperature, but several other systematic errors contribute uncertainty as well and become more significant in air relative to vacuum. Here we discuss the viability of several measurement techniques in air (force modulation, frequency modulation, and quasi-static deflection), characterize their sensitivity and accuracy by identifying several dominant sources of uncertainty, and compare the results to the fundamental sensitivity limits dictated by thermal motion and to the uncertainty inherent to calculations of the Casimir force. Finally, we explore prospects for mitigating the sources of uncertainty to enhance the range and accuracy of Casimir force measurements.

Energy-conserving Relativistic Corrections to Strong-shock Propagation

Abstract Astrophysical explosions are accompanied by the propagation of a shockwave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity V can be nonrelativistic (V ≪ c, where c is the speed of light), ultrarelativistic (V ≃ c), or moderately relativistic (V ∼ few × 0.1c). While self-similar energy-conserving solutions to the fluid equations that describe the shock propagation are known in the nonrelativistic (the Sedov–Taylor blastwave) and ultrarelativistic (the Blandford–McKee blastwave) regimes, the finite speed of light violates scale invariance and self-similarity when the flow is only mildly relativistic. By treating relativistic terms as perturbations to the fluid equations, here we derive the , energy-conserving corrections to the nonrelativistic Sedov–Taylor solution for the propagation of a strong shock. We show that relativistic terms modify the post-shock fluid velocity, density, pressure, and the shock speed itself, the latter being constrained by global energy conservation. We derive these corrections for a range of post-shock adiabatic indices γ (which we set as a fixed number for the post-shock gas) and ambient power-law indices n, where the density of the ambient medium ρ a into which the shock advances declines with spherical radius r as ρ a ∝ r −n . For Sedov–Taylor blastwaves that terminate in a contact discontinuity with diverging density, we find that there is no relativistic correction to the Sedov–Taylor solution that simultaneously satisfies the fluid equations and conserves energy. These solutions have implications for relativistic supernovae, the transition from ultra- to subrelativistic velocities in gamma-ray bursts, and other high-energy phenomena.

The influence of retardation and dielectric environments on interatomic Coulombic decay

Interatomic Coulombic decay (ICD) is a very efficient process by which high-energy radiation is redistributed between molecular systems, often producing a slow electron, which can be damaging to biological tissue. During ICD, an initially-ionised and highly-excited donor species undergoes a transition where an outer-valence electron moves to a lower-lying vacancy, transmitting a photon with sufficient energy to ionise an acceptor species placed close by. Traditionally the ICD process has been described via ab initio quantum chemistry based on electrostatics in free space, which cannot include the effects of retardation stemming from the finite speed of light, nor the influence of a dispersive, absorbing, discontinuous environment. Here we develop a theoretical description of ICD based on macroscopic quantum electrodynamics in dielectrics, which fully incorporates all these effects, enabling the established power and broad applicability of macroscopic quantum electrodynamics to be unleashed across the fast-developing field of ICD.

Relativistic quantum chemistry involving heavy atoms

Quantum chemistry is nowadays a term referring to a wide set of theoretical frameworks and models mainly relying on non-relativistic quantum mechanics. While, in most cases, the picture of the molecular structure and of the chemical reality provided by non-relativistic quantum chemistry is appropriate, we live in a universe with a finite speed of light. While neglecting variation of mass and velocity in the interaction of electrons and atomic nuclei is often safe, this is no more the case when heavy atoms are involved. In the present paper, we will briefly review the most rigorous way to include relativity in the modeling of molecular systems, that is to use the full 4-component (4c) formalism derived from the Dirac equation. Specifically, we will review the implementation that has been carried out in an effective 4c code called BERTHA. A recently developed method to gain deep insights into chemical bond is also presented and discussed in the 4c Dirac–Kohn–Sham context, the so-called natural orbitals for chemical valence/charge-displacement analysis.