Disproving Einstein’s light speed invariance postulate

The value for the speed of light ‘c’ = 299792458 m/s is widely known and used in theoretical physics, experimental physics, astronomy and astrophysics. However, this is the roundtrip speed from the source to the detector and back. The roundtrip speed of light has been verified thoroughly by several experiments to be a constant. Still, the equality of the one-way speed of light with the roundtrip speed of light, or the isotropy of the one-way speed of light, has never been verified. It is impossible to measure the one-way speed of light unless an absolute (standard) simultaneity is to be found. Yet, testing the isotropy of the one-way speed of light using a mathematical structure that resembles an isosceles triangle is still possible. Since the roundtrip speed of light has already proven to be isotropic, there are values only with which the one-way speed of light can travel in a path, maintaining the roundtrip speed of light to be isotropic. These values serve as limits to the maximum speed that the one-way speed of light can have in its direction of propagation in its path, from which two light pulses from both ends of its path send to the same clock, thereby evading the need for synchronization and allowing the possibility to test the constancy of the one-way speed of light.

Further to previous work by the author which claimed an infinite speed of light in vacuum in a problem of electromagnetism, in this paper the same result of an infinite speed of light in vacuum is reported in a lumped element electric circuit. A circuit consisting of resistors, capacitors and an independent voltage source with specific initial conditions is considered in a laboratory frame $K$ where the circuit is at rest. The relativistic transformation of the circuit is obtained when it is observed from an inertial frame $K^{\prime}$ . The circuit is analyzed by the Laplace transform technique. The fact that the electric charge on a capacitor has continuous time derivatives at the origin of the time axis leads to the conclusion that the Lorentz factor $\gamma=1/\sqrt{1-v^{2}/c^{2}}$ equals 1 for any value of $v$ , the speed of $K^{\prime}$ with respect to $K$ . This means that $c$ , the speed of light in vacuum, is infinite. A heuristic argument is exploited to claim that the circuit can be considered lumped when observed from both $K$ and $K^{\prime}$ . Also it is shown that the convection current densities due to charges on capacitor plates observed from $K^{\prime}$ have no influence on the Kirchhoff's voltage and current law equations so that the infinite speed of light in vacuum result remains applicable. The result of this paper implies that the instantaneous action-at-a-distance effect can be observed for the system under study, i.e. even though currents and voltages of the circuit in frame $K$ are functions of time, these functions can instantaneously be measured from $K^{\prime}$ , because $t=t^{\prime}$ .

Recent research has established that it is possible to exercise extraordinary control of the velocity of propagation of light pulses through a material system. Both extremely slow propagation (much slower than the velocity of light in vacuum) and fast propagation (exceeding the velocity of light in vacuum) have been observed. This article summarizes this recent research, placing special emphasis on the description of the underlying physical processes leading to the modification of the velocity of light. To understand these new results, it is crucial to recall the distinction between the phase velocity and the group velocity of a light field. These concepts will be defined more precisely below; for the present we note that the group velocity gives the velocity with which a pulse of light propagates through a material system. One thus speaks of “fast” or “slow” light depending on the value of the group velocity vg in comparison to the velocity of light c in vacuum.

The propagation of ultrashort light pulses in optical media is one of the most interesting problems of optics. The group velocity is generally used as a quantity which gives the speed of a wave packet. In dispersive media the group velocity can behave abnormally exceeding c, the velocity of light in vacuum, or even become negative1. Superluminous pulse propagation has also been observed upon propagation of pulses in deeply saturated amplifiers2, in a resonant medium with inverted population3–4 and in quantum-mechanical tunneling of single photons through dielectric mirrors5. It should be noted that the effect discussed below has a completely different origin.

Having established in previous articles that the principle of the constancy of speed of light of Special Relativity Theory is false in general, we examine some consequences of the non-constancy of speed of light in vacuum for different Galilean reference systems. We consider the modified Lorentz transformation incorporating different speeds of light for different inertial frames and which is a result of the non-constancy of speed of light in vacuum for different Galilean reference systems, i.e., reference systems in uniform rectilinear motion with respect to each other. Some consequences of this transform including the limit speed concept, transformation of lengths, summation and transformation of velocities are considered. Results of the transformation of the electromagnetic field are given. Also discussed are some consequences of the relativity of the electromagnetic field, all under the modified Lorentz transformation. These include variance of the electric charge, transformation of the potentials, transformation of the force. Some of the highlights of these consequences are as follows. The transformation of lengths abide by the same rule as in Special Relativity Theory, at least in form. Transformation of time intervals and velocities now involve the speeds of light in vacuum for both inertial frames in distinction from Special Relativity Theory. The invariance of charge no longer applies and charge measured depends on the reference frame the measurement is made from. Force acting on a charge q in an external electromagnetic field has the same form as in Special Relativity Theory, but now because charge is no longer invariant, the force transformation also has to be modified accordingly.

Techniques on slow and fast lights are of fundamental interest because they are targeted toward the understanding of physical laws for light-pulse propagation [1] as well as nonlinear optics at the level of single photon [2, 3]. They are also promising for many applications such as controllable optical delay/accelerant lines, optical memories, and devices for quantum information processing [4, 5, 6]. Traditionally slow and fast lights occur when the lights propagate in a dispersive amplifying/absorbing medium [7]. Early works on the demonstration of slow and fast lights were blurred by the pulse deformation due to the amplification or the attenuation of light pulses during propagation [8, 9, 10]. A breakthrough on slow lights was realized by Hau’s group at Harvard University [2], who decelerated a light pulse to as slow as 17 m s−1 based on the electromagnetically induced transparency (EIT) effect [11] in an ultracold gas of sodium atoms, while that on fast lights was followed by the work of Wang et al. [12], who reported the observation of distortionless superluminal light pulses. It is worthy of note that no signal propagates at a velocity faster than the speed of light in vacuum [12, 13]. The photorefractive effect is a versatile nonlinear effect and is able to occur in photorefractive materials even at very low light intensities. The photorefractive wave coupling is inherently a highly dispersive process because it takes time to redistribute the photoexcited charge carriers among different donors and acceptors. Such a photorefractive wave coupling would result in dispersive changes in both the intensity and the phase of the light during the propagation. The dispersive properties of the intensity coupling effect were well discussed in the literature [14, 15, 16, 17, 18] and in the books [19] and [20]. We will pay special attention on the dispersive photorefractive phase-coupling effect and its application to the generation of slow and fast lights.

I n 1998, laser pulses were slowed [1] in a Bose-Einstein condensate (BEe) [2] ofsodium to only 17 m/s, more than seven orders of magnitude lower than the speed of light in vacuum. Associated with the dramatic reduction factor for the light speed was a spatial compression of the pulses by the same large factor. A light pulse, which was more than 1 km long in vacuum, was compressed to a size of -50 flm, and at that point was completely contained within the condensate [1]. This allowed the light-slowing experiments to be brought to their ultimate extreme [3]: in the summer of 2000, light pulses were completely stopped, stored, and subsequently revived in an atomic medium, with millisecond storage times [4]. The initial ultra-slow light experiments spurred a flurry of slow light investigations, and slow or partially stopped light has now been observed in limited geometries in warm rubidium vapours [5-7], liquid-nitrogen cooled crystals [8], and recently in room temperature crystals [9]. Here, we begin with a discussion ofultra-slow and stopped light. We describe how cold atoms and Bose-Einstein condensates have been manipulated to generate media with extreme optical properties. While the initial experiments concentrated on the light propagation, we have recently begun a number of investigations of the effects that slow light has on the medium in which it propagates. Effects are profound because both the velocity and length scales associated with propagating light pulses have been brought down to match the characteristic velocity and length scales of the medium. With the most recent extension, the light roadblock [10], we have compressed light pulses to a length ofonly 2 f!ill. Here, we describe the use of ultra-compressed light pulses to probe superfluidity and the creation of quantized vortices in BEes through formation of'superfluid shock. waves'. We also present the observation of an ultra-slow-light-based, pulsed atom laser. Furthermore, we demonstrate the use of slow and stopped light for manipulation of optical information, in particular in Bose-Einstein condensates that allow for phase coherent processing of three-dimensional, compressed patterns of stored optical information.

Further to two previous works by the author which claimed an infinite speed of light in vacuum in a problem of electromagnetics and in the case of a lumped electric circuit, in this paper the same infinite speed of light in vacuum result is proved in the case of various linear and nonlinear systems. Linear and nonlinear systems in state-space formalism and a single-input, single-output (SISO) nonlinear system represented in the form of a differential equation are considered. All of the systems are at rest in the laboratory frame $K$ . The inertial frame $K^{\prime}$ starts its motion abruptly at $t=t^{\prime}=0$ . The time derivative of the state variable vector or the highest order time derivative of the output function of the SISO system in $K$ is Lorentz transformed to frame $K^{\prime}$ and the continuity of the transformed vector or the SISO system function in $K^{\prime}$ is exploited to infer that $c$ , the speed of light in vacuum has to be infinite. The emergence of a Dirac delta function in case this continuity condition is not satisfied, causes a mismatch of delta functions in the system equations which paves the way to the infinite $c$ finding. Because in order to transform the space and time coordinates between inertial frames the Lorentz transformation is used and one postulate that the Lorentz transform is based on is the relativity principle of special relativity theory, it must be watched that the system equations taken up obey the relativity principle.

A world system is composed of the world lines of the rest observers in the system. We present a relativistic coordinate transformation, termed the transformation under constant light speed with the same angle (TCL-SA), between a rotating world system and the isotropic system. In TCL-SA, the constancy of the two-way speed of light holds, and the angles of rotation before and after the transformation are the same. Additionally a transformation for inertial world systems is derived from it through the limit operation of circular motion to linear motion. The generalized Sagnac effect involves linear motion, as well as circular motion. We deal with the generalized effect via TCL-SA and via the framework of Mansouri and Sexl (MS), analyzing the speeds of light. Their analysis results correspond to each other and are in agreement with the experimental results. Within the framework of special and general relativity (SGR), traditionally the Sagnac effect has been dealt with by using the Galilean transformation (GT) in cylindrical coordinates together with the invariant line element. Applying the same traditional methods to an inertial frame in place of the rotating one, we show that the speed of light with respect to proper time is anisotropic in the inertial frame, even if the Lorentz transformation, instead of GT, is employed. The local speeds of light obtained via the traditional methods within SGR correspond to those derived from TCL-SA and from the MS framework.

The speed of light sets the maximum possible rate for transmission of information, in excess of 108 meters per second. Light pulses in optical fibers carry bits of data around the world in sub-second time frame, enabling interactive global communications. There is a constant demand for increasing the network performance in view of steadily growing information flows. It is envisioned that the presently required multiple conversions between optical pulses and electronic signals at network hubs may be eliminated in future when routing and switching of data flows is performed all-optically. This vision can be realized if the speed of light is dynamically controlled, allowing for synchronization and multiplexing of signals. Furthermore, by temporarily making the light slower it becomes possible to compress optical signals and perform their manipulation in compact photonic chips. Additionally, in the regime of slow light the photon-matter interactions are dramatically enhanced, enabling the active control of light and nonlinear transformations of signals. Slowing down the light is a challenging physical problem. In conventional dielectrics, the speed of light can only be reduced by a factor less than four which is limited by the optical refractive index of available materials. The most dramatic slowing down of light to a complete stop was reported in the regime of electromagnetically induced transparency [1]. This phenomenon is based on a resonant interaction of light with an atomic system and accordingly the speed of light is very sensitive to the frequency detuning. This restricts the effect to narrow frequency ranges limiting its applicability to communication networks with demands for data rates in excess of 100Gb per second. In contrast, dielectric photonic structures with a periodic modulation of the optical refractive index at a sub-micrometer scale can be engineered to operate at any frequency range. Periodic modulation results in resonant light scattering, and reduction of pulse speed by more than 100 times was registered experimentally in photonic crystals [2–4]. Ultra-slow light propagation can also be realized based on the coupling between high-Q optical cavities [5–10]. However, in all static structures the maximum usable delay decreases for shorter pulses which have larger bandwidth and exhibit stronger distortions due to the effect of frequency dispersion [11]. It was suggested that the restriction on the delay-bandwidth product, the key parameter characterizing the device capacity to store optical signals [12], can be overcome in dynamically tunable structures, with the exciting possibility to completely stop and then release light pulses all-optically [13, 14].KeywordsPhotonic CrystalGroup VelocityPhotonic StructureCoupling LengthSlow LightThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We show that the concept of the Lorentz-invariant mass of groups of particles can be applied to light pulses consisting of very large but finite numbers of noncollinear photons. Explicit expressions are found for the invariant mass of this manifold of photons for the case of diverging Gaussian light pulses propagating in vacuum. As the found invariant mass is finite, the light pulses propagate in vacuum with a speed somewhat smaller than the light speed. A small difference between the light speed and the beam-propagation velocity is found to be directly related to the invariant mass of a pulse. Focusing and/or defocusing light pulses is shown to strengthen the effect in which the pulse slows down while the pulse invariant mass increases. A scheme for measuring these quantities experimentally is proposed and discussed.

A combined analytical and numerical analysis of the propagation of a step-function light pulse in a resonant medium is presented. It is found that the light pulse evolves into a steady-state amplitude-modulated wave train very closely approximated by the Jacobian elliptic function $\mathcal{E}=1.25 {\mathcal{E}}_{0}dn[(\frac{1}{\ensuremath{\tau}})(t\ensuremath{-}\frac{z}{V}); \ensuremath{\lambda}]$, where the modulus of the elliptic function $\ensuremath{\lambda}$ is equal to $\frac{4}{5}$ and ${\mathcal{E}}_{0}$ is the amplitude of the input pulse. This result is consistent with an earlier analysis which showed that the elliptic $\mathrm{dn}$ function represented one of two classes of functions which satisfy the equations of resonant-pulse propagation and correspond to the distortionless propagation of an amplitude-modulated wave train through an inhomogeneously broadened medium. Expressions for the period, velocity, and parameter $\ensuremath{\tau}$ of the elliptic function are found as functions of the intensity of the input pulse. The form of the steady-state wave train is found to be the same in either an attenuating or amplifying medium. It is found that the velocity of the pulse train becomes significantly less than the speed of light when the density of energy that can be stored in the resonant atoms becomes an appreciable fraction of the energy density of the electromagnetic field. The conditions necessary for observing the amplitude-modulated pulse train in gaseous S${\mathrm{F}}_{6}$ and Na vapor are discussed.

There have been many recent theoretical and experimental reports on the propagation of light pulses at speeds exceeding the speed of light in vacuum $c$ within media with anomalous dispersion, either opaque or with gain. Superluminal propagation has also been reported within vacuum, in the case of inhomogeneous pulses. In this paper we show that the observations of superluminal and non-causal propagation of evanescent pulses under the conditions of frustrated internal reflection are only apparent, and that they can be simply explained employing an explicitly (sub)luminal causal theory. However, the usual one-dimensional approach to the analysis of pulse propagation has to be abandoned and the spatial extent of the incoming pulse along the directions normal to the propagation direction has to be accounted for to correctly interpret the propagation speed of these evanescent waves. We illustrate our theory with animations of the time development of a pulse built upon the Huygen's construction.

By analytical calculations it has been shown that in papers on the measurement of the velocity of light published in 2011 in the journals Uspekhi Fizicheskikh Nauk [Physics–Uspekhi] and Pis’ma v ZhETF [JRTP Letters], in actual fact the velocity of a light pulse from a relativistic clot of electrons was not measured. All that was done was to compare the velocity of light emitted by an ultrarelativistic source with the velocity of light from a fixed source, i.e., both in the first and second variants (one independent quantity was compared with another), in essence, it was simply postulated. In the first variant a glass plate was used as the fixed light source, and in the second variants, a synchrotron pulse was used as the reference signal. The velocity of light was calculated using a calculated time based on the postulate of the special theory of relativity (STR) on the invariance of the velocity of light. This, of course, contradicts the Newton–Ritz hypothesis on ballistic addition of velocities, but at the present time this idea is not taken seriously. Practically none of the serious contemporary critics of STR, apart, of course, from amateurs, holds this point of view. The result cannot be considered as a direct experimental confirmation of the second postulate of Einstein’s special theory of relativity, i.e., its main part, which speaks of the constancy of the velocity of light in all inertial reference frames, but only of that part which speaks of the independence of the velocity of light on motion of the source. Moreover, this same result stands as equal proof of the so-called theory of the luminiferous ether, which held sway up to the creation of the special theory of relativity and which has now been revived, i.e., it does not distinguish between these two theories. It is fundamentally impossible in principle to measure the velocity of light by the proposed method, it is only possible to postulate it.

PULSE SIGNALS IN OPEN CIRCULAR DIELECTRICWAVEGUIDEM. Legenkiy and A. ButrymDepartment of Theoretical RadiophysicsKarazin Kharkiv National University4 Svobody Square, Kharkiv 61077, UkraineAbstract|Excitation and propagation of a pulse electromagneticwave in an open circular dielectric waveguide is considered. Partition ofthe pulse fleld into radiated wave, surface wave, and guided wave hasbeen revealed and the corresponding physical efiects are interpreteddirectly in the time domain. Namely it was shown that there is aprecursor at the rod axis that propagates with speed of light in freespace. It originates from the pulse surface wave that propagates alongthe rod surface and radiates into the rod in a Cherenkov like manner.1. INTRODUCTIONOne of the main trends in communications recently consists inincreasing channel capacity by exploiting ultrawideband short pulses.Among transmission lines that are of high interest in communicationsare optical flbers (dielectric waveguides). Propagation of ultrashortelectromagnetic pulses in such lines has not been studied su–cientlyyet. So it is of interest to consider physical processes that occurwith excitation and propagation of pulse signals in open dielectricwaveguides. This problem is also met in analysis of pulse radiationfrom a rod antenna.Harmonic wave propagation in dielectric waveguides is wellstudied in the Frequency Domain (FD) [1]. In this case the soughtfleld in the structure is presented as a set of uncoupled modes. Thereare guided wave modes that have fleld localized within the rod, thespectrum being discrete. These modes are used for transmittinginformation. In describing flelds near the sources one also needs to