Velocity Of Light In Vacuum Research Articles

Bayesian Nonparametric Inference of the Neutron Star Equation of State via a Neural Network

Abstract We develop a new nonparametric method to reconstruct the equation of state (EoS) of a neutron star with multimessenger data. As a universal function approximator, the feed-forward neural network (FFNN) with one hidden layer and a sigmoidal activation function can approximately fit any continuous function. Thus, we are able to implement the nonparametric FFNN representation of the EoSs. This new representation is validated by its capability of fitting the theoretical EoSs and recovering the injected parameters. Then, we adopt this nonparametric method to analyze the real data, including the mass–tidal deformability measurement from the binary neutron star merger gravitational-wave event GW170817 and mass–radius measurement of PSR J0030+0451 by NICER. We take the publicly available samples to construct the likelihood and use the nested sampling to obtain the posteriors of the parameters of the FFNN according to the Bayesian theorem, which in turn can be translated to the posteriors of the EoS parameters. Combining all of these data for a canonical 1.4 M ⊙ neutron star, we get a radius R 1.4 = 11.83 − 1.08 + 1.25 km and tidal deformability Λ 1.4 = 323 − 165 + 334 (90% confidence interval). Furthermore, we find that in the high-density region (≥3ρ sat), the 90% lower limits of c s 2 / c 2 (where c s is the sound speed and c is the velocity of light in vacuum) are above 1/3, which means that the so-called conformal limit (i.e., c s 2 / c 2 < 1 / 3 ) is not always valid in the neutron stars.

Multipole analysis on gyroscopic precession in f(R) gravity with irreducible Cartesian tensors

In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/{c}^{3}$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of general relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a pointlike or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of gravitoelectric-type precession, gravitomagnetic-type precession, $f(R)$ precession, and Thomas precession are all derived. The first two types of precession are collectively called general relativity-like precession, and the $f(R)$ precession is the correction in $f(R)$ gravity. At the leading pole order, these expansions can recover the results for the gyroscope moving around a pointlike or ball-like source. If the gyroscope has a nonzero four-acceleration, its spin's total angular velocity of precession up to $1/{c}^{3}$ order in $f(R)$ gravity is the same as that in general relativity.

All waves have a zero tunneling time

Abstract Zero tunneling time and thereby a faster than light traversal velocity was calculated nearly a hundred years ago and has been observed recently. We report about experimental results and estimations, which confirm the zero time tunneling for elastic as well as for electromagnetic and Schrödinger waves. Zero time tunneling was first observed with microwaves 1992 (H. Aichmann and G. Nimtz, Found. Phys., vol. 44, p. 678, 2014; A. Enders and G. Nimtz, J. Phys. I, vol. 2, p. 169, 1992). In 2008, zero time was also observed for tunneling electrons (P. Eckle, A. N. Pfeiffer, C. Cirelli, et al., Science, vol. 322, p. 1525, 2008). Presumably, this effect took place with atoms quite recently (R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, Nature, vol. 583, p. 529, 2020). The Einstein relation E 2 = (ħk)2 c 2 is not satisfied in the tunneling process, since the wave number k is imaginary (E is the total energy, ħ the Planck constant, and c the vacuum velocity of light), Zero time tunneling is described by virtual photons (A. Stahlhofen and G. Nimtz, Europhys. Lett., vol. 76, p. 189, 2006). The tunneling process itself violates the Special Theory of Relativity. Remarkably, Brillouin conjectured that wave mechanics is valid for all waves independent of their field (L. Brillouin, Wave Propagation in Periodic Structures, Chap. VIII, New York, Dover Publications, 1953).

Role of time in implementation of innovative technologies

Time is considered as production resource, which determines the need for its effective use in connection with other production resources. The problem consists in the inconsistency of the results of the existing forecasting system of production which are founded on modern concepts of space and time. The theoretical positions of Galilean, A. Lorentz and G. Minkowski were analyzed. A. Einstein’s explanations regarding the use of the velocity of light in vacuum as a constant in the well-known dependency for the generalized four-dimensional space were studied. An attempt is made to solve the applied problem in space and time, taking as a constant, for example, standard or maximum possible, (calculated) productivity.

Gyro-devices – natural sources of high-power high-order angular momentum millimeter-wave beams

The Orbital Angular Momentum (OAM) carried by light beams with helical phasefront (vortex beams) has been widely employed in many applications such as optical tweezers, optical drives of micro-machines, atom trapping, and optical communication. OAM provides an additional dimension (diversity) to multiplexing techniques, which can be utilized in addition to conventional multiplexing methods to achieve higher data rates in wireless communication. OAM beams have been thoroughly studied and used in the optical regime but in the mm-wave and THz-wave region, they are still under investigation. In these frequency bands, there are difficulties associated with beam-splitting and beam-combining processes as well as with the use of spiral phase plates and other methods for OAM generation, since the wavelength is much larger compared to those at optical frequencies, leading to higher diffraction losses. The present paper describes the natural generation of high-power OAM modes by gyro-type vacuum electron devices with cylindrical interaction circuit and axial output of the generated rotating higher-order transverse electric mode TEm,n, where m > 1 and n are the azimuthal and radial mode index, respectively. The ratio between the total angular momentum (TAM) JN and total energy WN of N photons is given by m/ω, where ω is the angular frequency of the operating mode, which in a gyrotron oscillator is close to the TEm,n-mode cutoff frequency in the cavity. Therefore, m/ω = Rc/c, where Rc is the caustic radius and c the velocity of light in vacuum. This means that the OAM is proportional to the caustic radius and at a given frequency the same for all modes with the same azimuthal index m. Right-hand rotation (co-rotation with the electrons) corresponds to a positive value of m and left-hand rotation to negative m. The corresponding OAM mode number (topological charge) is l = m – 1. Circularly polarized TE1n modes only possess a Spin Angular Momentum (SAM: s = ±1). TE0n modes have neither SAM nor OAM. This is the result of the photonic (quasi-optical) approach to derive the TAM of modes generated in gyrotrons. The same result follows from the electromagnetic (EM) wave approach for the TAM within a given waveguide volume per total energy of the EM wave in the same volume. Such high-power output beams with very pure higher-order OAM, generated by gyrotron oscillators or amplifiers (broadband) could be used for multiplexing in long-range wireless communications. The corresponding mode and helical wavefront sensitive detectors for selective OAM-mode sorting are available and described in the present paper.

Postsaturation dynamics and superluminal propagation of a superradiant spike in a free-electron laser amplifier

We study the dynamics of an isolated spike of radiation in superradiant regime. We show that conditions exist where the pulse moves with a group velocity larger than the velocity of light in vacuum and is followed by a pedestal resulting from a complex postsaturation dynamics. The tail is constituted by a train of subpulses with both transverse and longitudinal coherence and decaying amplitudes. We analyze the dynamical conditions leading to the formation of the main pulse and the tail. We study the correlation of the tail structure with the longitudinal phase space of the electrons, and provide a recipe to partially suppress this tail.

Vector Potential of Electromagnetic Wave above Strongly Inductive Two-Layer Earth Surface

Vertical components of the vector potential of electromagnetic wave above two-layer strongly inductive impedance medium are determined. The solution is represented as a Sommerfeld integral. Singularities of such an integral are determined using effective parameters. The phase velocity of the surface electromagnetic wave is considered. It is shown that such a velocity is always less than the velocity of light in vacuum, so that the surface electromagnetic waves cannot be classified as the Zenneck waves for which the phase velocity is greater than the velocity of light (similarly to electromagnetic waves in waveguides).

Spectral Particularities of Femtosecond Optical Pulses Propagating in Dispersive Medium

We have proposed a refined solution of the wave equation for a dispersive medium without restriction on the duration of an optical pulse. We apply a series of elementary wave packages (EWP) to the representation of superwideband signals (fs pulse). We investigate peculiarities of the propagation of waves with low and high frequencies through the one-resonance medium. We show the existence of a “precursor” for fs optical pulses. We propose a formula for the optical signal velocity (OSV). Its value does not exceed the light velocity in vacuum. We have designed a method of adaptation of EWP-pulses to time-domain spectroscopy.

Optical transmission characteristics of multi-band triangular-lattice photonic crystal coupling cavity waveguide based on annular microcavity

The light localization characteristics of the near-infrared triangular-lattice photonic crystal annular microcavity are studied theoretically in this paper. The photonic crystal has a lattice constant of <i>a</i>=540 and it is composed of silicon rods each with a radius of <i>r</i>=135 immersed in air background. The two kinds of annular microcavities are obtained by removing 12 silicon rods which are located respectively at a distance of 2a and at a distance of √<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i> to the central rod. Five resonant wavelengths and the corresponding eigen mode profiles of the microcavity are studied. A coupled resonant optical waveguide is formed by integrating the microcavities with a periodic length of 7<i>a</i> in space. The group velocity of light beam propagation within multiple guiding bands are analyzed by the tight-binding approximation method. The maximum and minimum velocity of 0.0028<i>c</i> and 0.00082<i>c</i> are obtained, where <i>c</i> is the light velocity in vacuum. The light transmittance values and spatial steady distributions of the electric field's amplitude through the structure at several wavelengths within the guiding bands are studied by the finite-difference time-domain method. The results are consistent with that calculated by the plane wave expand method. Interleaving circular microcavities perpendicular to the direction of optical transmission at a lateral distance of 2√<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i>, the coupling region between the adjacent microcavities is changed, the difference in group velocity between guiding bands apparently decreases and the transmittance values of two frequency bands are enhanced.<br/>Keeping the size of silicon rods unchanged, two kinds of microcavities are constructed by removing the six rods with the distances of 2<i>a</i> and √<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i> from the center of the central silicon rod, respectively. The resonant wavelengths supported by the above two microcavities are studied. Two coupled-resonant optical waveguides with a periodic length of 7<i>a</i> are proposed. Connecting these two coupled cavity optical waveguides with the W1-typed input/output waveguides, the selecting and sharing function of guiding band are finally achieved for wavelengths within different frequency bands. Keeping the group velocity slowing down, a maximum value of one guiding band reaches 0.00047<i>c</i>.

Piercing the veil of modern physics: part 2 & philosophy

Based on Aristotle's definition, all the knowledge was able to be divided into three parts: natural science, metaphysics and mathematics. Among them, we can distinguish between natural science and metaphysics according to whether there exists in reality. And the principle of the limit in mathematics helps us to break the bondage of finite thought. From the quantitative changes of real space to have gone deep into a qualitative difference of ideal realm, it has accomplished the unity of opposites of all knowledge. Take the postulation as an example. This concept corresponds to limiting value, and is a hypothesis that humans can only be continually to modify the one-sided view to approach the truth but can't use empirical methods to prove or disprove it. Newton's First Law is such a postulation, which has invariance or absoluteness, can be called the absolute truth, and belonged to the metaphysical category. According to the above philosophical principles we have found that in Einstein's special relativity there is a paradoxes, which is to use an absolute truth (the principle of constant light velocity in vacuum) to overthrow another absolute truth (the absoluteness of simultaneity) but one of them can't be proved to be false. And his mistake to be found out, which is to confuse the light speed in reality with the c. So, starting from the perspective of all knowledge, all the inertial systems are redefined, Galileo's coordinate transformations once again enabled; and in order to eliminate the false and retain the true, Einstein's two postulations in special relativity are reshaped, which can make them reasonably to return to the framework of absolute space-time. Finally to point out, it has been identified that so-called Nonbeing in Lao-tzu is the metaphysics, which will certainly have great significance to unify the Eastern and Western philosophy.

The derivation of the general form of kinematics with the universal reference system

Abstract In the article, the whole class of time and position transformations was derived. These transformations were derived based on the analysis of the Michelson-Morley experiment and its improved version, that is the Kennedy-Thorndike experiment. It is possible to derive a different kinematics of bodies based on each of these transformations. In this way, we demonstrated that the Special Theory of Relativity is not the only theory explaining the results of experiments with light. There is the whole continuum of the theories of kinematics of bodies which correctly explain the Michelson-Morley experiment and other experiments in which the velocity of light is measured. Based on the derived transformations, we derive the general formula for the velocity of light in vacuum measured in any inertial reference system. We explain why the Michelson-Morley and Kennedy-Thorndike experiments could not detect the ether. We present and discuss three examples of specific transformations. Finally, we explain the phenomenon of anisotropy of the cosmic microwave background radiation by means of the presented theory. The theory derived in this work is called the Special Theory of Ether – with any transverse contraction. The entire article contains only original research conducted by its authors.

Actively controllable terahertz switches with graphene-based nongroove gratings

We systematically investigated the tunable dynamic characteristics of a broadband surface plasmon polariton (SPP) wave on a silicon-graded grating structure in the range of 10–40 THz with the aid of single-layer graphene. The theoretical and numerical simulated results demonstrate that the SPPs at different frequencies within a broadband range can be trapped at different positions on the graphene surface, which can be used as a broadband spectrometer and optical switch. Meanwhile, the group velocity of the SPPs can be modulated to be several hundred times smaller than light velocity in vacuum. Based on the theoretical analyses, we have predicted the trapping positions and corresponding group velocities of the SPP waves with different frequencies. By appropriately tuning the gate voltages, the trapped SPP waves can be released to propagate along the surface of graphene or out of the graded grating zone. Thus, we have also investigated the switching characteristics of the slow light system, where the optical switching can be controlled as an “off” or “on” mode by actively adjusting the gate voltage. The slow light system offers advantages, including broadband operation, ultracompact footprint, and tunable ability simultaneously, which holds great promise for applications in optical switches.

Electrodynamics and spacetime geometry: Astrophysical applications

After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Amp\`{e}re laws where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena such as: the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.

Derivation of Transformation and One-Way Speed of Light in Kinematics of Special Theory of Ether

At present, it is believed that the Special Theory of Relativity (STR) is the only theory explaining the Michelson-Morley and Kennedy-Thorndike experiments. This article proved that another theory in accordance with these experiments is possible. In this article, we derive the new theory of kinematics of bodies from the universal frame of reference (UFR, ether), which we called the Special Theory of Ether (STE). The article explains why Michelson-Morley and Kennedy-Thorndike experiments could not detect the universal frame of reference. In article, a different transformation of time and position than the Lorentz transformation is derived on the basis of the geometric analysis of the Michelson-Morley and Kennedy-Thorndike experiments. The formula for summation of speeds for absolute speed has been derived. Based on the derived transformation, we derive the formula for the velocity of light in vacuum measured in any inertial reference system. The entire article contains only original research conducted by its authors.

The Explanation of the Michelson-Morley Experiment Results by Means Universal Frame of Reference

It is commonly thought that the Michelson-Morley experiment from 1887 and Kennedy-Thorndike experiment from 1932 demonstrated that the universal frame of reference (ether) does not exist and that the velocity of light in vacuum is absolutely constant. The analysis of this experiment led to the creation of the Special Theory of Relativity (STR). The article explains why Michelson-Morley and Kennedy-Thorndike experiments could not detect the universal frame of reference. In this article, a different transformation of time and position than the Lorentz transformation is derived on the basis of the geometric analysis of the Michelson-Morley and Kennedy-Thorndike experiments. The transformation is derived based on the assumption that the universal frame of reference (UFR) exists. UFR is a frame of reference in which the velocity of light is constant in every direction. In inertial frames of reference moving in the UFR, the velocity of light may be different. The article has derived the formula for relative speed and patterns for the maximum and minimum speed of light that can be measured in the inertial system. Finally, the anisotropy of the microwave background radiation has been explained by using the presented theory. According to the body kinematics model presented in this article, anisotropy of cosmic microwave background is the Doppler effect for observer moving in the UFR.

The Geometric Derivation of the Transformation of Time and Position Coordinates in STE

It is commonly thought that the Michelson-Morley experiment from 1887 (1) and Kennedy-Thorndike experiment from 1932 (2) demonstrated that the ether does not exist and that the velocity of light in vacuum is absolutely constant. The analysis of this experiment led to the creation of the special theory of relativity (STR). In this article, a different transformation of time and position than the Lorentz transformation is derived on the basis of the geometric analysis of the Michelson-Morley experiment. The transformation is derived based on the assumption that the universal frame of reference, called the ether, exists. Our concept states that the ether is not a substance with physical properties, as it was understood in the past, but a frame of reference in which the velocity of light is constant in every direction. In inertial frames of reference moving in the ether, the velocity of light may be different. The obtained transformations are transformations from the ether to the inertial frame and from the inertial frame to the ether. Based on the new transformation, the Special Theory of Ether (STE) was created (4), (5).

Mössbauer experiments in a rotating system: Recent errors and novel interpretation

We consider the energy shift between emission and absorption lines in the Mossbauer experiments in a rotating system in the view of a recently reported extra component of such a shift, in addition to the usual relativistic time dilation effect, expressed by the inequality k > 0.5 in the expression for the relative energy shift ΔE/E = −ku2/c2 (u is the orbital velocity, and c the light velocity in vacuum). We consider the recent attempts of re-interpretation of the Mossbauer rotor experiments, showing their incorrectness, and analyze the proposed explanations of the physical origin of this extra energy shift. This way we stress that the energy of nuclei located in crystal cells should be determined via relativistic quantum mechanics, involving the geometry of a rotating disc. We show that the standard theory yields k = 1/2; applying the YARK gravitational theory, we obtain k = 2/3 in a perfect agreement with experimental data.

Interpretation of Mössbauer experiment in a rotating system: A new proof for general relativity

A historical experiment by Kündig on the transverse Doppler shift in a rotating system measured with the Mössbauer effect (Mössbauer rotor experiment) has been recently first re-analyzed and then replied by an experimental research group. The results of re-analyzing the experiment have shown that a correct re-processing of Kündig’s experimental data gives an interesting deviation of a relative redshift between emission and absorption resonant lines from the standard prediction based on the relativistic dilatation of time. That prediction gives a redshift ∇EE≃−12v2c2 where v is the tangential velocity of the absorber of resonant radiation, c is the velocity of light in vacuum and the result is given to the accuracy of first-order in v2c2. Data re-processing gave ∇EE≃−kv2c2 with k=0.596±0.006. Subsequent new experimental results by the reply of Kündig experiment have shown a redshift with k=0.68±0.03 instead.By using Einstein Equivalence Principle, which states the equivalence between the gravitational “force” and the pseudo-force experienced by an observer in a non-inertial frame of reference (included a rotating frame of reference) here we re-analyze the theoretical framework of Mössbauer rotor experiments directly in the rotating frame of reference by using a general relativistic treatment. It will be shown that previous analyses missed an important effect of clock synchronization and that the correct general relativistic prevision in the rotating frame gives k≃23 in perfect agreement with the new experimental results. Such an effect of clock synchronization has been missed in various papers in the literature with some subsequent claim of invalidity of relativity theory and/or some attempts to explain the experimental results through “exotic” effects. Our general relativistic interpretation shows, instead, that the new experimental results of the Mössbauer rotor experiment are a new, strong and independent, proof of Einstein general relativity.In the final section of the paper we discuss an analogy with the use of General Relativity in Global Positioning Systems.

Sound velocity bound and neutron stars.

It has been conjectured that the velocity of sound in any medium is smaller than the velocity of light in vacuum divided by sqrt[3]. Simple arguments support this bound in nonrelativistic and/or weakly coupled theories. The bound has been demonstrated in several classes of strongly coupled theories with gravity duals and is saturated only in conformal theories. We point out that the existence of neutron stars with masses around two solar masses combined with the knowledge of the equation of state of hadronic matter at "low" densities is in strong tension with this bound.

Structured relativistic particle, helix-type Minkowski diagram, and “more general” relativity

A model of a 3D classical particle built up of micro-scale spinor fragments, hence structured, is proved sufficient (demands no additional postulates) to generate a theory of relativistic motion, provided the velocity of light in vacuum is the speed limit. In this case, the particle’s structure endows a mechanical action with a clear geometric sense and allows for derivation of a Lagrangian function of the same form as in special relativity. But the graphic image of motion becomes a 3D helix instead of a 4D space-time world line. A forced distortion of the helix line (curved and compressed) results in emerging of variable metric components thus leading to an equation of particle motion under the influence of a geometric potential, an equation identical to that of 4D geodesic. The logical line of the theory is traced in detail.