Fermat principle in Finsler spacetimes

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variational principle can be applied (i) to the vacuum light rays in an alternative spacetime theory, based on Finsler geometry, and (ii) to light rays in an anisotropic non-dispersive medium with a general-relativistic spacetime as background.     

The frequency of light propagating in gravitational wave spacetimes

We study the propagation of light signals in two exact solutions of vacuum Einstein's equations, in the geometric optics approximation. The gravitational wave affects the frequency of light propagating in it (a known effect) even if the metric componentsg _tt andg _ti (i=1, 2, 3) are zero. Moreover we find that red-/blue-shift depends on the relative spatial position of the light source and the observer, even if the wavefront is perfectly uniform, leading to a characteristic redshift pattern.     

The speed of light and the speed of neutrinos

The approximate equality in the arrival times of the neutrino and light signals from SN 1987A allows an accurate check of the hypothesis of special relativity that the limiting velocity for all forms of radiation is the same.     

Note on varying speed of light cosmologies

The various requirements on a consistent varying speed of light (‘VSL’) theory are surveyed, giving a short check-list that needs to be satisfied by such theories.     

The measurement of the speed of light

In order that a measurement of one item against another item is significant it must be verified that these items ARE INDEPENDENT of each other. It can readily be shown that the unit of m/s is proportional to the speed of light and hence measurements of the speed of light in units of m/s are basically flawed. Some aspects of the speed of light not being a constant are discussed.     

Note on the completeness of spacetimes

Three formally different definitions of completeness for normal hyperbolic manifolds are discussed and shown to be inequivalent.     

Note on Kantowski-Sachs spacetimes

It is shown that a portion of de Sitter space can be expressed in the formds ²=dt ²–A ² (t)dr ²–B ²(t)(d ²+sin ² d ²). It follows that it is a Kantowski-Sachs spacetime, according to the usual definition. This disproves the statement sometimes seen in the literature that all Kantowski-Sachs spacetimes are anisotropic.     

光拍法测光速实验中的几个误解

利用光拍法测光速的实验中主要存在3个误解.笔者结合实验教学,从光拍频波的原理、光拍频波的形成和传播以及光拍频波的接收和光路调节3个方面,对光拍法测光速实验中易产生误解的内容进行了剖析并给予澄清.     

Beyond the classical Rayleigh limit with twisted light

It is shown that twisted stochastic light can serve as illumination that may produce images with a resolution overcoming the Rayleigh limit by an order of magnitude. This finding is illustrated for an isoplanatic axially symmetric system with low angular aperture and twisted scalar Gaussian Schell-model illumination.     

Laser wavelength measurements and the speed of light

Early determinations of the speed of light, based on astronomical observations or terrestrial time-of-flight experiments, were largely superseded in the 1940's by measurements of the frequency and wavelength of microwave radiation. The results were limited by the uncertainty in the wavelength measurements, and it was apparent that greater accuracy could be achieved by using radiation of shorter wavelength. It was, however, not until the development of lasers, and the nonlinear optical techniques made possible by their high output intensities, that frequency measurements could be extended towards the visible region of the spectrum.Stimulated by a demand for a more precise knowledge of the speed of light for application in space research, geodesy, and metrology, a new series of determinations has recently taken place. The measurements were made upon the radiations from a number of different stabilized-laser systems operating in the near infrared and visible spectral regions. Several different interferometric techniques were developed for the wavelength measurements. The results have led to a new recommended value for the speed of light, 299 792 458±1.2 m s^–1, and to the possibility of re-defining the unit of length.     

Effective traveling-wave excitation below the speed of light

We demonstrate that effective traveling-wave excitation of high-gain amplifiers requires velocities that are remarkably slower than the velocity of light. Experiments with a femtosecond-laser-pumped molecular hydrogen laser exhibit pronounced enhancement of the intensity if an excitation velocity that is slower than the velocity of light is employed. These results are directly scalable to shorter wavelengths, paving the way for a more effective pump setup for x-ray lasers.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

Limits of spacetimes

The limits of a one-parameter family of spacetimes are defined, and the properties of such limits discussed. The definition is applied to an investigation of the Schwarzschild solution as a limit of the Reissner-Nordström solution as the charge parameter goes to zero. Two new techniques — rigidity of a geometrical structure and Killing transport — are introduced. Several applications of these two subjects, both to limits and to certain other questions in differential geometry, are discussed.     

Progressing waves on spherical spacetimes

A family of spherically symmetrical spacetimes that are transparent to minimally coupled scalar multipole waves is investigated. The concept of transparency is reformulated in terms of the established concept of progressing waves. The set of spherically symmetric spacetimes and the family of wave equations for which the transparency condition can be shown to hold is generalized.     

锁定放大器在光速测量中的应用

结合声光调制原理和锁定放大器的工作原理,设计了基于调制法的测量光速实验.通过测量和计算得出光速为2.993×108 m/s和3.000×108 m/s,与光在空气中的速度值2.997×108 m/s相比,误差分别为0.13%和0.10%.此方法的优点是光速经过调制后,光的频率被调制为60～100 MHz,使得光波长调制为3～5 m,便于在实验室里进行光速测量.     

利用脉冲激光进行光速测定

介绍了利用溴化亚铜激光器输出的脉冲激光通过光纤延时的方法测出光波波包中心所通过的光程及所需时间，从而实现测定光速的实验开设及其设计思想。     

Predicted effects of a speed bump on light vehicle noise

A speed bump reduces traffic noise levels during the deceleration phase and increases them during the acceleration phase. The net effect of a speed bump on noise from a light vehicle is assessed by means of the concept of noise energy density, S. This is a function of the instantaneous distance between the vehicle and the bump, S(x). To determine the function S(x) explicitly, five measurements of the sound exposure level, for each vehicle, are needed. It is assumed that the noise from each vehicle is generated by a single non-directional point source and propagates without vertical-surface reflections. An example prediction is presented based on measurements of sound exposure levels due to passenger cars.     

Classification of multidimensional spacetimes

We classify all eleven-dimensional spatially homogeneous spacetimes, which contain a seven-dimensional compact subspace and admit a simple-transitive group of isometry, by enumerating the real ten-dimensional Lie algebras which contain an n-dimensional (n⩾7) compact Lie subalgebra. The main result of this paper consists in giving a complete list of the distinct real ten-dimensional algebras which admit a non-trivial Levi decomposition. It is hoped that this investigation may be of some help in studying eleven-dimensional and ten-dimensional cosmologies which are considered in the context of Kaluza-Klein, supergravity and superstring theories.