Velocity of Light

According to the commonly accepted view, Galileo Galilei promoted in 1638 an experiment that seemed able to show that the speed of light is finite. An analysis of archival material shows that two decades later the members of Florence scientific society Accademia del Cimento followed Galileo guidelines by actually attempting measures of the speed of light and suggesting improvements. This analysis also reveals that a fundamental difference exists between Galileo's and Florence academy's methodologies and that Galileo's experiment was, in some respect, a pioneering work belonging also to the history of the psychology of perception.

It is argued that there is a connection between the fundamental forces of electromagnetism and gravitation. This connection occurs because of: 1) the fundamental significance of the finite and invariant velocity of light in inertial reference frames in the special theory, and 2) the reliance of the general theory of relativity upon the special theory of relativity locally in spacetime. The connection between the fundamental forces of electromagnetism and gravitation follows immediately from these two points. Because this connection has not been acknowledged, a brief review is provided of: 1) the role of the finite and invariant velocity of light in inertial reference frames in the special theory, and 2) certain fundamental concepts of the general theory, including its reliance on the special theory locally.

All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined like it happens for Fermi coordinates both in special and general relativity. As a consequence, it is not known how non-inertial observers can build {\it equal-time surfaces} which a) correspond to a conventional observer-dependent definition of synchronization of distant clocks; b) are good Cauchy surfaces for Maxwell equations. Another type of coordinate singularities are those connected to the relativistic rotating coordinate systems (the rotating disk).We show that the use of Hamiltonian methods based on 3+1 splittings of space-time allows to define as many observer-dependent globally defined radar 4-coordinate systems as nice foliations of space-time with space-like hyper-surfaces admissible according to M$\o$ller (for instance only differentially rotating relativistic coordinate system are allowed). All these conventional notions of an {\it instantaneous 3-space} for an arbitrary observer can be empirically defined by introducing generalizations of Einstein ${1\over 2}$ convention for clock synchronization in inertial frames. Each admissible 3+1 splitting corresponds to a non-rigid non-inertial frame centered on the observer. When there is a Lagrangian description of an isolated relativistic system, its reformulation as a parametrized Minkowski theory allows to show that all the admissible synchronization conventions are {\it gauge equivalent}, as it also happens in canonical metric and tetrad gravity, where, however, the chrono-geometrical structure of space-time is dynamically determined.

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly reexamined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of 'theories' that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri-Sexl synchronization gauge and, finally, to the even more general Anderson-Vetharaniam-Stedman's synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light on inertial and rotating reference frames, the GPS's working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams.

The Earth’s ionosphere plays a crucial role in Global Positioning System (GPS) accuracy because this layer
represents the largest source of positioning error for the users of the GPS after the turn-off of Selective Availability
(SA). This paper studies the ionospheric effect on transionospheric signal propagation for the Earth-satellite path using
3D Jones Ray-Tracing utilizing Nelder-Mead optimisation algorithm. The ionospheric delay or advance is obtained
from the difference between the distance of the ray path from the satellite to the receiver determined from the raytracing
and the distance for propagation over the line of sight (LOS) at the velocity of light in vacuum. The difference
between the standard dual-frequency models corrected range and LOS, known as Residual Range Error (RRE) is
calculated. Results show that the RRE of group delay value is different from RRE of phase advance. On the other
hand, the group and phase path is longer when considering the geomagnetic field effect on both GPS frequencies L1
and L2. The higher order term in total electron content (TEC) calculation that relates to the refractive index is normally
neglected due to its small value, but it is clearly shown that it does have some effects in ray-tracing. This analysis
needs to be considered for more accurate GPS range finding

After recalling the rigorous mathematical representations in Relativity Theory (RT ) of (i): observers, (ii): reference frames fields, (iii): their classifications, (iv) naturally adapted coordinate systems (nacs) to a given reference frame, (v): synchronization procedure and some other key concepts, we analyze three problems concerning experiments on rotating frames which even now (after almost a century from the birth of RT ) are sources of misunderstandings and misconceptions. The first problem, which serves to illustrate the power of rigorous mathematical methods in RT is the explanation of the Sagnac effect (SE ). This presentation is opportune because recently there are many non sequitur claims in the literature stating that the SE cannot be explained by SRT, even disproving this theory or that the explanation of the effect requires a new theory of electrodynamics. The second example has to do with the measurement of the one way velocity of light in rotating reference frames, a problem for which many wrong statements appear in recent literature. The third problem has to do with claims that only Lorentz like type transformations can be used between the nacs associated to a reference frame mathematically moddeling of a rotating platform and the nacs associated with a inertial frame (the laboratory). Whe show that these claims are equivocated.

The Radioactive Beam Experiment at ISOLDE (REX-ISOLDE-Experiment) which presently is being developed and under construction at CERN serves to investigate exotic, very neutron rich, radioactive nuclei [1] (Radioactive beam EXperiment at ISOLDE: Coloumb Excitation and Neutron Transfer Reactions of Exotic Nuclei, Proposal to the ISOLDE commitee, CERNSIC94-25). A linear accelerator delivers radioactive ions which are produced by the isotope separator ISOLDE with energies between 0.85 and 2.2 MeV/u. The Linac will consist of a RFQ-accelerator, an interdigital H-Structure (IH) and three 7-gap-resonators with variable energy. While the LMU Munich is responsible for the frontpart of the accelerator, the backpart is being built by the MPI [2] (H. Podlech, Master Thesis, MPI-H- V21-1997V21- , Heidelburg, 1997. After estimation of the voltage of one resonator to 1.75 MV at 90 kW, the design velocities were ®xed to 5.4%, 6.0% and 6.6% of the velocity of light. Three downscaled models (1:2.5) were built in order to optimize the shuntimpedance and the ®eld-distribution at the operation frequency of the ampli®ers of 101.28 MHz. The optimization of all low power resonators is now successfully ®nished. Extensive beam dynamic calculations were made in order to optimize the transmission of the beam up to the target. It turned out that ®nal energies between 0.85 and 2.2 MeV/u with nearly 100% transmission can be achieved. The acceptance in the x-plane is 1.2p mm mrad (norm.) and in the y-plane 3.0p mm mrad (norm.). The bunchlength of the fully accelerated beam (2.2 MeV/u) is 2.4 ns at the target. The development of the resonators was accompanied by extensive MAFIA calculations. It could be demonstrated that spiral-resonators like 7-gap-resonators can be calculated with MAFIA with an accuracy of 1% in comparison with experimental results. Presently, the tanks and the half shells of the power type resonators are manufactured in the workshops of the MPI. Ó 1998 Elsevier Science B.V.

We consider the possibility that Lorentz violation can generate differences between the limiting velocities of light and charged matter. Such effects would lead to efficient vacuum Cherenkov radiation or rapid photon decay. The absence of such effects for 104.5 GeV electrons at the Large Electron Positron collider and for 300 GeV photons at the Tevatron therefore constrains this type of Lorentz breakdown. Within the context of the standard-model extension, these ideas imply an experimental bound at the level of −5.8 × 10 −12 ≤κtr − (4/3)c 00 e ≤ 1.2 × 10 −11 tightening existing laboratory measurements by 3-4 orders of magnitude. Prospects for further improvements with terrestrial and astrophysical methods are discussed.

It is suggested that a moving canonical particle interacts with a vacuum regarded as a "soft" cellular space. The interaction results into the emergence of elementary excitations of spaceinertons -surrounding the particle. It is assumed that such a motion leads not only to the spatial oscillation of the particle along a path but to the oscillation of the particle centre-of-mass as well. This phenomenon culminating in the anisotropic pulsation of the particle is associated with the notion of spin. The particle-space interaction is treated as the origin of the matter waves which are identified with the particle inertia and inertons surrounding the moving particle are considered as carriers of its inert properties. Inertons are also identified with real carriers of the gravitational interaction and the range of the particle gravitational potential is evaluated by the inerton cloud amplitude Λ = λc/v 0 , where λ is the de Broglie wavelength, c and v 0 are the velocity of light...

First-order tests of special relativity are based on a comparison of clocks synchronized with the help of slow clock transport with those synchronized by the Einstein procedure. This comparison enables the measurement of the one-way velocity of light and is equivalent to a measurement of the time dilatation factor. The accuracy of present measurements is of the order 10−7, yielding an upper limit of 3 cm/sec for the ether drift.

The theory of photodetection and quantum-optical coherence is formulated in the Heisenberg picture and in such a way that the causal propagation of fields at the velocity of light is manifest. Objections to the standard theory, based on a putative violation of causality, are shown to be unfounded, as is the notion that normal ordering is essential for the elimination of an infinite contribution from the vacuum field. In a similar vein we revisit the Fermi two-atom problem and explicitly demonstrate the causal nature of the interaction without invoking simplifying approximations that have recently been called into question.

The electromagnetic wave equations in a moving medium may be approximated by a form similar to that of the Schrödinger equation for a particle in an electromagnetic field, with the velocity v of the medium and the vorticity ∇×v playing the roles of the vector potential and magnetic field, re- spectively. A purely classical optical analogue of the Aharonov-Bohm effect follows by consider- ation of the interference pattern produced by two beams, each of which propagates in a region with zero vorticity, but such that the flux of the vorticity through the closed loop defined by the optical paths does not vanish. Fizeau's experiment (1851) on the velocity of light in moving media may be regarded as an example of such a situation.

The present work is devoted to massive gauge fields in special relativity with two fundamental constants-the velocity of light, and the Planck length, so called doubly special relativity (DSR). The two invariant scales are accounted for by properly modified boost parameters. Within above framework we construct the vector potential as the (1/2, 0) ⊗ (0, 1/2) direct product, build the associated field strength tensor together with the Dirac spinors and use them to calculate various observables as functions of the Planck length.

According to the commonly accepted view, Galileo Galilei devised in 1638 an experiment that seemed able to show that the velocity of light is finite. An analysis of archival material shows that two decades later members of the Florence scientific society Accademia del Cimento followed Galileo guidelines by actually attempting to measure the velocity of light and suggesting improvements. This analysis also reveals a fundamental difference between Galileo's and Florence academy's methodologies and that Galileo's experiment was, in some respects, a pioneering work affecting also the history of the psychology of perception.

Observed variations concerning the brightness distributions in four extragalactic radio sources were so rapid that the apparent transverse velocity of expansion is greater than the velocity of light. The term superluminal is used to describe this phenomenon. A review is provided of the observations of superluminal expansions. Attention is given to four sources including three quasars (3C345, 3C273, and 3C279) and one radio galaxy (3C120). The significance of the observations is evaluated. The fact that the superluminal effect has been seen in a galaxy as well as in three quasars suggests that it cannot be used as evidence against a cosmological origin for the redshifts.

We present an exact formula for the computation of the interference rate of radi-ation in the case of two charges revolving with constant angular velocity at opposite ends of a diameter in a fixed circle. The formula is valid for arbitrary velocities of the charges, and can be easily studied ...

When the electrons stored in the ring of the European Synchrotron Radiation Facility (ESRF, Grenoble) scatter on a laser beam (Compton scattering in flight) the lower energy of the scattered electron spectra, the Compton Edge (CE), is given by the two body photon-electron relativistic kinematics and depends on the velocity of light. A precision measurement of the position of this CE as a function of the daily variations of the direction of the electron beam in an absolute reference frame provides a oneway test of Relativistic Kinematics and the isotropy of the velocity of light. The results of GRAAL-ESRF measurements improve the previously existing one-way limits, thus showing the efficiency of this method and the interest of further studies in this direction.

It is well known that very high axial -or longitudinal -electric fields can be obtained in vacuo using very intense focused laser beams. If these fields are in the transverse magnetic TM 01 mode, very high gains in energy (exceeding 1 GeV) can be obtained if sufficiently energetic ultra-relativistic electrons (say 1 GeV) are injected on-axis and near the optimum phase. This energy gain is obtained even though the phase velocity of the axial component of the TM 01 laser beam is greater than the vacuum velocity of light. The result is apparently related to the Gouy phase shift at focus.

A new method to study the one-way velocity of electromagnetic (e.m.) radiation is proposed which uses interferometric detection of microwaves. Time intervals of a fraction of the wave period (down to 10-14s) can thus be measured. A set of generalised space-time transformations between inertial systems (GT) is used, defined by: a) the two-way velocity of e.m. radiation is c in

It is suggested that a moving canonical particle interacts with a vacuum regarded as a "soft" cellular space. The interaction results into the emergence of elementary excitations of space - inertons - surrounding the particle. It is assumed that such a motion leads not only to the spatial oscillation of the particle along a path but to the oscillation of the particle centre-of-mass as well. This phenomenon culminating in the anisotropic pulsation of the particle is associated with the notion of spin. The particle-space interaction is treated as the origin of the matter waves, which are identified with the particle inertia and inertons surrounding the moving particle are considered as carriers of its inert properties. Inertons are also identified with real carriers of the gravitational interaction and the range of the particle gravitational potential is evaluated by the inerton cloud amplitude $\Lambda=\lambda c/v$, where $\lambda$ is the de Broglie wavelength, $c$ and $v$ ...

In the present paper, we have made an analysis to observe the effect of introduction of defect on dispersion relation, group velocity, and effective group index in a conventional photonic band gap (PBG) structure. The study shows that inside the PBG materials group velocity and effective group index becomes negative in both types (conventional as well as defect PBG structure) of structure at a certain range of frequencies. Also, near the edges of the bands it attains very high values of index of refraction. A defect PBG structure gives a very unique feature that group velocity becomes exactly zero at a particular value of frequency and also becomes several hundred times greater than the velocity of light which is not attainable with the conventional PBG structure. Defect PBG structures with such peculiar characteristics are seen in lasing without inversion, in construction of perfect lens, in trapping of photon and other optical devices.

The Novello-DeLorenci-Luciane (NDL) field theory of gravitation predicts that gravitational waves (GWs) follow geodesics of a modified (effective) geometry with a speed lower than the velocity of light. The theory also demonstrates that GWs exhibit the phenomenon of birefringence, formerly believed to be exclusive of electromagnetic waves. Here prospective astrophysical tests of these predictions are proposed. I point out that future measurements of gravitational waves in coincidence with a non-gravitational process such as {\it a neutrino burst} (and likely a burst of gamma-rays) may prove useful to discriminate among all the existing theories of gravity. It is also stressed that microlensing of gravitational waves emitted by known galactic sources (i.e., pulsars) in the bulge, lensed by either the Galaxy's central black hole (Sgr A$^\ast$) or a MACHO object adrift among the Milky Way's stars, may provide a clean test of the birefringence phenomenon implied by the NDL gra...

If one analyzes the stochastic behaviour of classical Weyssenhoff particles imbedded in a relativistic thermostat one obtains (for random jumps at the velocity of light) a probability distribution corresponding to Proca's equations for nonzeromass spin-one particles.

In 1907 Einstein discussed with Wilhelm Wien the occurrences of superluminal velocities in dispersive and absorptive media. Einstein tried to present to Wien an expression for the group velocity in dispersive media that was based on his 1905 relativistic addition theorem for velocities, which he claimed to be valid for absorptive media, and to demonstrate the impossibility of superluminal velocities. However, he recognized that his expression needed an amendment and correction. Einstein did not convince Wien, and was finally confused, because he did not have the correct expression for the group velocity in dispersive media. However, he wrote Wien, "it is beyond doubt that our electromagnetic theories of dispersion can never yield superluminal velocity for the propagation of an optical signal".

Fermi co-ordinates are proper co-ordinates of a local observer determined by his trajectory in space-time. Two observers at different positions belong to different Fermi frames even if there is no relative motion between them. Use of Fermi co-ordinates leads to several physical conclusions related to relativistic effects seen by observers in arbitrary motion. In flat space-time, the relativistic length seen by an observer depends only on his instantaneous velocity, not on his acceleration or rotation. In arbitrary space-time, for any observer the velocity of light is isotropic and equal to $c$, provided that it is measured by propagating a light beam in a small neighbourhood of the observer. The value of a covariant field measured at the position of the observer depends only on his instantaneous position and velocity, not on his acceleration. The notion of radiation is observer independent. A "freely" falling charge in curved space-time does not move along a geodesic and t...

With the physical hypothesis of the existence of a covariant subquantum vacuum, Dirac's aether, we show that: (i) the idea that subquantum random jumps occur at the velocity of light is a consequence of the introduction of stochastic fluctuations into the g, , field of general relativity and (ii) the Klein-Gordon equation can be deduced, in a new simple way, from a stochastic process on the set of the four possible space-time directions of the velocity of light.

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.

A theoretical study of Al(1-x)Ga(x)N, based on full-potential linearized augmented plane wave method, is used to investigate the variations in the bandgap, optical properties and non-linear behavior of the compound with the variation of Ga concentration. It is found that the bandgap decreases with the increase of Ga in Al(1-x)Ga(x)N. A maximum value of 5.5 eV is determined for the bandgap of pure AlN which reaches to minimum value of 3.0 eV when Al is completely replaced by Ga. The static index of refraction and dielectric constant decreases with the increase in bandgap of the material, assigning a high index of refraction to pure GaN when compared to pure AlN. The refractive index drops below 1 for photon energies larger than 14 eV results group velocity of the incident radiation higher than the vacuum velocity of light. This astonishing result shows that at higher energies the optical properties of the material shifts from linear to non-linear. Furthermore, frequency dependent reflectivity and absorption coefficients show that peak value of the absorption coefficient and reflectivity shifts towards lower energy in the UV spectrum with the increase in Ga concentration. This comprehensive theoretical study of the optoelectronic properties of the alloys is presented for the first time which predicts that the material can be effectively used in the optical devices working in the visible and UV spectrum.

Self-similar deformation of three-wave stimulated Brillouin scattering (SBS) dissipative structures ("Brillouin quasi-solitons") yields superluminous behaviors. The authors discuss the relevancy of the various velocities involved in the nonlinear propagation of such complex structures, both in the ideal semi-infinite case and in a real-world Brillouin fiber ring laser experiment. Optical and acoustical group velocities greater than are shown to occur during pulse propagation in SBS soliton lasers. Index Terms-Solitons, Sommerfeld & Brillouin, stimulated Brillouin scattering (SBS), superluminal propagation, superluminous propagation, velocity of light.

The Earth's ionosphere plays a crucial role in Global Positioning System (GPS) accuracy because his layer represents the largest source of positioning error for the users of the GPS after the turn-off of Selective Availability (SA). This paper studies the ionospheric effect on ...

We present an optical characterization of photonic glasses, composed of randomly arranged, monodisperse dielectric spheres packed at high filling fractions. We provide a detailed optical study of the resonant behavior of diffuse light transport through such systems. By means of independent static and dynamic measurements, we show resonances in the transport mean free path, diffusion constant, and also energy velocity of light. We also show that the main transport parameters can be controlled by varying the sphere diameter.

After recalling the rigorous mathematical representations in Relativity Theory (RT) of (i) observers, (ii) reference frames fields, (iii) their classifications, (iv) naturally adapted coordinate systems (nacs) to a given reference frame, (v) synchronization procedure and some other key concepts, we analyze three problems concerning experiments on rotating frames which even now (after almost a century after the birth of RT) are sources of misunderstandings and misconceptions. The first problem, which serves to illustrate the power of rigorous mathematical methods in RT, is the explanation of the Sagnac effect (SE). This presentation is opportune because recently there have appeared many non sequitur claims in the literature stating that the SE cannot be explained by SRT, even disproving this theory or claiming that the explanation of the effect requires a new theory of electrodynamics. The second example has to do with the measurement of the one-way velocity of light in rotating reference frames, a problem about which many wrong statements appear in recent literature. The third problem has to do with claims that only Lorentz-like type transformations can be used between the nacs associated with a reference frame mathematically modeling of a rotating platform and the nacs associated with a inertial frame (the laboratory). We show that these claims are equivocal.

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity v (including a velocity more than c) . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.

In this paper, it is shown, using a geometrical approach, the isotropy of the velocity of light measured in a rotating frame in the Minkowski space-time, and it is verified that this result is compatible with the Sagnac effect. Furthermore, we find that this problem can be reduced to the solution of geodesic triangles in a Minkowskian cylinder. A relationship between the problems established on the cylinder and on the Minkowskian plane is obtained through a local isometry.

We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincart invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light.

In this work we revisit the process of constructing wave equations for the scalar and vector potentials of an electromagnetic field, and show that a wave equation with an arbitrary velocity (including a velocity higher than the velocity of light in vacuum) for the scalar potential exists in the framework of classical electrodynamics. Some consequences of this fact are considered. It is shown (in the Appendix) at what point this work differs from works concerned of the problem of the gauge invariance in the classical electrodynamics.