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Experiments with the transverse Doppler effect have demonstrated that the wavelength of light increases with the speed of the source relative to the observer. The relativity principle implies that such a change cannot be detected by in situ measurements and this prediction has been verified by wavelength determinations carried out with a cavity resonator over an extended period of time during which the orbital speed of the Earth changes significantly. On this basis it can be concluded that the dimensions of the cavity resonator increase in direct proportion to the Doppler wavelength, and thus that isotropic length expansion occurs with relativistic time dilation, not the anisotropic Fitzgerald-Lorentz length contraction predicted by the special theory of relativity. The failure of the Lorentz space-time transformation to anticipate the length expansion effect is discussed and an alternative set of equations is introduced to eliminate the experimental contradiction in the existing theory.

In the framework of Special Relativity and in agreement with the electromagnetic approach used to connect Quantum and Relativistic effects in Bridge Theory, a first order wave-equation able to emulate the wave-particle duality in terms of local electromagnetic interactions is proposed. The equation is able to describe the propagation of a fermion as a de Broglie's wave and simultaneously to characterise the wave in motion with a mass energy as a particle. The solution of the wave-equation proposed is compatible with the de Broglie's idea of an empty pilot wave, carrying information about the dynamical properties of a particle materialising during each local interaction with the observers.

We present an in depth analysis and a new derivation of the Doppler factor in the Lienard-Wiechert potentials, based on geometrical considerations in Minkowski space. We argue that, contrary to a common assumption, the methods used for deriving the Doppler factor in the case of an electrically charged extended particle are not applicable in the case of a point particle. A geometrical interpretation of the Doppler factor is nonetheless found in the later case, based on the electromagnetic interaction model of Fokker. In this model the interaction takes place between infinitesimal worldline segments with end points connected by light signals, just like the points where light pulses are emitted and detected in general. This analogy reveals that the relativistic Doppler effect is the missing link between the classical Doppler effect and the Doppler factor in the Lienard-Wiechert potentials., one typo corrected, and more consistent notation for the source charge at point C (previously also labeled 1), and for the field point P (previously also labeled 2 or A)

The scattering of time-harmonic plane waves by a perfectly electrically conducting (PEC) half-plane (H-P) in relativistic uniform motion is discussed. The problem is formulated using the special theory of relativity by means of the Lorentz transformation applied to the classic Sommerfeld solution. Exact fields are obtained for the 3-D vector problem of scattering of an obliquely incident and arbitrarily polarized plane wave by a PEC H-P in relativistic translational motion. The total fields are then presented as the relativistic analog of their motionless counterparts and an association with the uniform asymptotic theory of diffraction framework is inferred. In addition to recovering known features such as the relativistic Doppler effect and shadow boundary shifts, it is herein depicted a polarization coupling effect due to motion that can give rise to a 3-D scattered field with all components present even for a linearly polarized incident wave. Validating results and illustrative examples are also presented.

This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invariance and to the Lorentz transformations are presented. The general invariance of Maxwell equations is discussed. Different theoretical expectations for possible results of Michelson-Morley experiment and some physical consequences are considered. Some critical remarks to the notion of the light speed and its constancy are given. The relativistic law for velocity addition, including strangeness of a noncollinear addition and a superluminal motion, is discussed. Critical analysis of two works which proof the need for existence of an invariant velocity is consequentially made.

Laser cooling and precision laser spectroscopy of highly charged ions are considered as frontiers of atomic physics research at heavy ion storage rings. A brief overview of the fundamentals of these powerful methods, applied to relativistic stored ion beams, is given. Preliminary results from laser cooling of lithium-like 16O5+ ion beams at a relativistic energy of 275.7 MeV/u at the heavy-ion storage ring CSRe are presented and prospects for upcoming experiments at the future facility HIAF are discussed.

Numerous experiments have been carried out to validate the Lorentz transformation or to find possible violations of Lorentz invariance, based on test theories to test special relativity. The test theory of Mansouri and Sexl (MS) provides a general framework for the transformation of inertial frames, presuming a preferred system of reference. Based on the MS framework, this paper systematically approaches the relativistic Doppler effect such that its dependency on transformation coefficients and parameters can be investigated. The Doppler effect is formulated in a complex Euclidean space where time is represented with imaginary numbers. Two formulae of the Doppler effect, which have been derived in an arbitrary transformation within the MS framework, are presented: one between an inertial frame and the preferred one and the other between arbitrary inertial frames. It is shown from the former formulation that the Doppler effect is independent of the synchronization of clocks, which implies that the Doppler-shifted frequency in the absolute synchronization is the same as that in the standard synchronization. The latter formula can allow us to find Doppler shifts without information on the velocities of inertial frames relative to the preferred frame. Exploiting these theoretical results, we examine the transverse and the longitudinal Doppler effects in detail.

Till now was known only one Doppler effect. In the article, we have named it classical. By the exact solution of correct mathematical problems with initial and boundary conditions which in mathematics are named as Cauchy’s problems adequate to physical processes which are described by Maxwell’s equations forming system of the partial differential equations of hyperbolic type of the problems of mathematical physics, existence of two Doppler effect was discovered. They differ from each other quantitatively and on physical sense. Classical Doppler effect, according to its physical sense, we have named radiated Doppler effect. Other effect, earlier completely unknown, according to physical sense, we have named reflected Doppler effect. The second new physical phenomenon derived as a result of research in this article, we have named deviation of radiated (classical) Doppler effect. The sense of opening is that the quantitative value of radiated Doppler effect measured by the receiver depends on an angle betwee...

Relativity theory formulation is proposed, based not on the axiomatic postulation of its main principles but on their inference out of a thought experiment. With this approach, the experimentally observed independence of the speed of light from the motion of source and observer is a necessary consequence of the finiteness of propagation speed of all kinds of information. The mechanism of relativistic effects origination is described; the formulas of Lorentz transformations, Doppler quadratic effect, electromagnetic interaction and centrifugal force of inertia are derived.

In this paper the authors show that the ‘mechanism’ of mass increase is simple and can be explained by the wave feature of body micro-comps. From this point of view, the mass increase with speed perceived by a fixed observer is a Doppler relativistic effect.

We reveal relations between superluminal and subluminal spatiotemporally localized optical pulses and the phenomena of the relativistic aberration of a wavevector and the Doppler shift. It turns out that such waves are Lorentz-transformed versions of simple optical waves generated in another reference frame. The requirement of a null Doppler shift is shown to give rise to a speed associated with the relativistic velocity addition law of a double (two-step) Lorentz transformation. The effects of such a transformation are examined both in terms of four-coordinates and in the spectral domain. It is established that a subluminal pulse reverses its direction. In addition to a change in direction, the propagation term of a superluminal pulse becomes negative. The aberration due to a double Lorentz transformation is examined in detail for propagation invariant superluminal waves (X wave, Bessel X wave), as well as intensity-invariant superluminal and subluminal waves. Detailed symmetry considerations are provided for the superluminal focus X wave and the subluminal MacKinnon wavepacket.

A generalization of the Hubble law in the framework of the special theory of relativity received. The relativistic Doppler effect allows you to find a nonlinear relationship between redshift and distance.

Supermassive black hole binaries (SMBHBs) should be common in galactic nuclei as a result of frequent galaxy mergers. Recently, a large sample of sub-parsec SMBHB candidates was identified as bright periodically variable quasars in optical surveys. If the observed periodicity corresponds to the redshifted binary orbital period, the inferred orbital velocities are relativistic (v/c~0.1). The optical and UV luminosities are expected to arise from gas bound to the individual BHs, and would be modulated by the relativistic Doppler effect. The optical and UV light curves should vary in tandem with relative amplitudes which depend on the respective spectral slopes. We constructed a control sample of 42 quasars with aperiodic variability, to test whether this Doppler colour signature can be distinguished from intrinsic chromatic variability. We found that the Doppler signature can arise by chance in ~20% (~37%) of quasars in the nUV (fUV) band. These probabilities reflect the limited quality of the control sample and represent upper limits on how frequently quasars mimic the Doppler brightness+colour variations. We performed separate tests on the periodic quasar candidates, and found that for the majority, the Doppler boost hypothesis requires an unusually steep UV spectrum or an unexpectedly large BH mass and orbital velocity. We conclude that at most ~1/3rd of these periodic candidates can harbor Doppler-modulated SMBHBs., Comment: submitted in MNRAS

We use the Lorentz transformation equations to derive a unified equation for the Doppler effect–that can be used for any one-dimensional (sound, water, EM, etc.) wave in any medium. This unified equation includes the effects of motion, if present, of the medium relative to the observer as well as the relative velocity between the observer and the source. This master equation can be applied to both relativistic and nonrelativistic situations to recover the more familiar Doppler effect expressions and it clarifies that the Doppler equations given in standard textbooks for both sound and EM waves, are basically the same. The advantage of this unified equation is that it reduces the effort in solving complex problems. Basic knowledge of Lorentz transformations and their physical effects is enough to understand this derivation.

We report on complementary tests and measurements regarding our recent determination of the Boltzmann constant, kB, by means of Doppler broadening thermometry, also providing additional information as compared to previous articles. A revised uncertainty budget is illustrated, including some new components that were ignored in previous spectroscopic experiments, and better quantifying other components that were estimated to be negligible. In particular, we consider the relativistic Doppler effect, the perturbation caused by the finite bandwidth of the detection system and the influence of the spontaneous emission content of the probe laser. These new components do not increase the global uncertainty which still amounts to 24 ppm. Our value for the Boltzmann constant is 1.380 631 (33) × 10−23 J K−1, which is the best determination reported so far by using an optical method.

In the past few years, the perturbation due to the finite speed of light was among the most inconsistent in corner-cube absolute gravimeters. For the relativistic treatment of the perturbation based on Lorentz transformation, the relation between Doppler shift in special relativity and time delay in classical domain is easily misunderstood, leading to spurious conclusions. To avoid these issues, we apply a 'relativistic geometrical method' based on the motion of photons to calculate the frequency shift in corner-cube absolute gravimeters, where the misunderstood relation has been corrected. Additionally, we find that the modern corner-cube absolute gravimeters cannot sense effects of the special relativity.

The properties of the platonic quadridimensional space, the modeling of De Broglie waves and the resulting concept of mass (see hal-01165196, v1 ; hal-01207447, v1 ; hal-01213447, v1) seem to allow a quantum approach to the laws of gravitation by a postulate of quantified declination. The main idea of this article is that the guiding angle of the trajectory of a massive body in gravitational interaction with others is modified by a quantum, independent of the chosen observation frame, at each perception of an occurrence of the De Broglie waves generated by one of these other massive bodies. This elementary quantized hypothesis, associated with the conservation of three absolute physical quantities, leads surprisingly rapidly to the results expected by the classical laws of gravitation., Les propriétés de l’espace quadridimensionnel platonicien, la modélisation de l’onde de phase et le concept de masse qui en découlent (cf. les documents hal-01081576, v1; hal-01205805, v1; hal-01213062, v1) semblent permettre une approche quantique des lois de la gravitation par un postulat de déclinaison quantifiée. L’idée directrice de cet article est que l’angle directeur de la trajectoire d’un corps massif en interaction gravitationnelle avec d’autres est modifié d’un quantum indépendant du référentiel d’observation choisi, à chaque perception d’une occurrence de l’onde de phase de De Broglie générée par l’un de ces autres corps massifs. Cette hypothèse quantifiée élémentaire, associée à la conservation de trois quantités physiques absolues, conduit rapidement, de façon surprenante, aux résultats attendus par les lois classiques de la gravitation.

Chapter 6 starts the more advanced part of the book. The concept of 4-vectors and their dot product are introduced and used to define the general Lorentz transformation using matrices. With the help of Appendix B , the chapter extends the two-dimensional Lorentz transformations to the full four-dimensional Lorentz boosts. The general transformation of the coordinates of a four-dimensional event (its time and the three coordinates of its location) is derived as the building block of other 4-vectors. The general relativistic law of addition of velocities is an immediate consequence of this transformation. Aberration of light is introduced in a new light by deriving the formulas from the general relativistic law of addition of velocities. General Doppler formula and global positioning systems are discussed. The notions of 4-velocity and 4-momentum are introduced next and the general Lorentz transformation of energy and momentum 3-vector is derived. The invariant length of the 4-momentum is identified as (mc 2 ) 2 ( m c 2 ) 2 and the idea of independence of mass from velocity is reiterated. Four-acceleration is defined as the derivative of 4-velocity with respect to proper time and used to introduce 4-force and the second law of motion.

we pointed out the idea of Einstein, light speed is independent of the observer i.e. The principle of light speed invariance is incorrect. Instead of Lorentz Transformation we suggested a new time-space transformation, this revision of the Relativity will deeply effect the development of Science and Technology.

The Global Positioning System (GPS) measures distances by determining the elapsed time for light to pass between the corresponding endpoints and multiplying this value with the speed of light c. An example is considered in which a metal rod and a clock are carried onboard a satellite. It is shown that Einstein’s light-speed postulate is only consistent with the deduction that the rod has increased in length at the same time that the clock has slowed down because of time dilation. Both results are independent of the orientation of the metal rod to an observer on the earth’s surface, so the above conclusion indicates that isotropic length expansion accompanies time dilation (clock riddle) on the satellite, contrary to expectations from the Fitzgerald-Lorentz length contraction (FLC) prediction of the Special Theory of Relativity (STR). This logical argument thus shows that the Lorentz transformation (LT) is selfcontradictory and therefore invalid. It is also shown that the experimental results of the transverse Doppler effect are only consistent with isotropic length expansion accompanying time dilation. A GPS-compatible space-time transformation (GPSLT) is then derived that removes the contradiction of the LT while still satisfying Einstein’s two postulates of relativity.

The influence of light source on the receiver as electromagnetic interaction is considered. The mechanical influence of the moving charged body on a motionless one is defined in the experimental laws of electrodynamics. These laws determine the changes of parameters of the light source that moves relatively the receiver. The laws of change of light frequency and its direction of the moving source are derived from the laws of electromagnetism. At small velocity of source movement they coincide with classical results: the Doppler effect and phenomenon of aberration. The interaction of the source and receiver depends only on their velocity of movement relatively each other. There is no world medium, the relative movement to which would influence the characteristics of light source.

The frequency conversion under the parametric Doppler effect, which occurs when weak probe radiation reflects off from a refractive index inhomogeneity induced in a nonlinear medium by intense pumping, has been analyzed. Under these conditions, the frequency dispersion of the medium is assumed to correspond to the single Lorentz oscillator model. It is shown that the presence of resonance and a spectral range forbidden for propagation may lead to a complex Doppler effect, where the incident radiation is single-frequency but the reflected radiation consists of two or three monochromatic waves, one of which has a phaseconjugated wavefront.

Advanced civilizations capable of interstellar travel, if they exist, are likely to have advanced propulsion methods. Spaceships moving at high speeds would leave a particular signature which could be detected from Earth. We propose a search based on the properties of light reflecting from objects travelling at relativistic speeds. Based on the same principles, we also propose a simple interstellar beacon with a solar sail.

The Lo rentz transformation is well known. In this paper, we have presented various types of applications of different Lorenz Transformat ions according to the nature of movement of one inertial frame relat ive to the other inertial frame such as relativistic aberration, relativ istic Doppler's effect and reflection of light ray by a moving mirro r. When one frame moves along X- axis with respect to the rest frame then we can find these applications for special Lo rentz transformation. When the motion o f the mov ing frame is not along X-axis relat ive to the rest frame but the mot ion is along any arbitrary direction then we can find these formulae for most general Lorentz transformation. We can generate these formulae fo r d ifferent types of most general Lorentz transformations using mixed number, quaternion and geometric product.

Dan je povijesni pregled sustava mjerenja brzine s početkom na kraju 19. stoljeća. Opisani su mehanički brzinomjer i dva najčešća načina elektroničkog mjerenja brzine: Reedov prekidač i Hallove sonde. Uvod u satelitsku navigaciju i GPS. Mjerenje brzine pomoću GPS-a i Dopplerov efekt GPS signala. Radi dodatnog pojašnjenja relativističkog Dopplerovog efekta objašnjeni su osnovni principi specijalne i opće teorije relativnosti. GPS sustav nadopunjen je INS sustavom navigacije i opisan je fizikalni princip funkcioniranja akcelerometra i žiroskopa. Integracija satelitske navigacije i inercijalnih osjetila izvedena je pomoću Kalmanovog filtra. Navedeni su matematički modeli za estimaciju nagiba i brzine vozila. U zadnjem poglavlju prikazan je postav mjerenja i snimljeni valni oblici: uporedba mjerenja brzine GPS signalima frekvencije 1Hz, 10Hz i 20Hz, mjerenje brzine akcelerometrom i estimacija brzine Kalmanovim filtrom. Komentirane su razlike, ograničenja i mogućnosti nadogradnje korištenih estimacijskih modela. Historical review of speed measurement systems starting in late 19th century is given. Mechanical speedometer and two most common electronic speed measurement techniques are described: Reed switch and Hall effect sensors. Introduction to satellite navigation and GPS. Speed measurement using GPS and Doppler effect of GPS signal. To present better explanation of relativistic Doppler effect, basic principles of special and general theory of relativity are clarified. GPS is extended with INS and physical principles of accelerometer and gyroscope are described. Satellite navigation and inertial sensors integration is done with Kalman filter. Mathematical models for incline and speed estimation are suggested. In last chapter there is shown sensor placement and recorded waveforms: comparation of speed measurements conducted with 1Hz, 10Hz and 20Hz GPS signals, accelerometer speed measurement and Kalman filter speed estimation. Differences between waveforms are discussed as well as limitations and improvement possibilities of used estimation models.

Generalized Doppler shift for light is derived by considering both velocity and acceleration, and is used to calculate time dilation ratio. A circular mirror used to measure time is transformed to the elliptical mirror in a reference frame when it is in motion. The special relativistic Doppler shift is calculated in any propagation direction of light for a constant velocity of motion. Furthermore, the generalized Doppler shift is derived by considering both the velocity and the acceleration effect. The ratio of the frequency shifts are shown as a function of velocity, acceleration, and detection angle.