Journal articles on the topic 'Relativistic Velocity Transformation'
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1
Bachman, R. A. "Relativistic phase velocity transformation." American Journal of Physics 57, no. 7 (July 1989): 628–30. http://dx.doi.org/10.1119/1.15958.
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Ungar, Abraham. "THE RELATIVISTIC PROPER-VELOCITY TRANSFORMATION GROUP." Progress In Electromagnetics Research 60 (2006): 85–94. http://dx.doi.org/10.2528/pier05121501.
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Lin, De-Hone. "The 2+1-Dimensional Special Relativity." Symmetry 14, no. 11 (November 14, 2022): 2403. http://dx.doi.org/10.3390/sym14112403.
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In the new mathematical description of special relativity in terms of the relativistic velocity space, many physical aspects acquire new geometric meanings. Performing conformal deformations upon the 2-dimensional relativistic velocity space for the (2+1)-dimensional special relativity, we find that these conformal deformations correspond to the generalized Lorentz transformations, which are akin to the ordinary Lorentz transformation, but are morphed by a global rescaling of the polar angle and correspondingly characterized by a topological integral index. The generalized Lorentz transformations keep the two fundamental principles of special relativity intact, suggesting that the indexed generalization may be related to the Bondi–Metzner–Sachs (BMS) group of the asymptotic symmetries of the spacetime metric. Furthermore, we investigate the Doppler effect of light, the Planck photon rocket, and the Thomas precession, affirming that they all remain in the same forms of the standard special relativity under the generalized Lorentz transformation. Additionally, we obtain the general formula of the Thomas precession, which gives a clear geometric meaning from the perspective of the gauge field theory in the relativistic velocity space.
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Stedman, G. E. "Relativistic transformation of group velocity via spatial filtering." American Journal of Physics 60, no. 12 (December 1992): 1117–22. http://dx.doi.org/10.1119/1.16957.
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Choi, Yang-Ho. "Multiple velocity composition in the standard synchronization." Open Physics 20, no. 1 (January 1, 2022): 155–64. http://dx.doi.org/10.1515/phys-2022-0017.
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Abstract Mansouri and Sexl (MS) presented a general framework for coordinate transformations between inertial frames, presupposing a preferred reference frame the space-time of which is isotropic. The relative velocity between inertial frames in the standard synchronization is shown to be determined by the first row of the transformation matrix based on the MS framework. Utilizing this fact, we investigate the relativistic velocity addition. To effectively deal with it, we employ a diagram of velocity that consists of nodes and arrows. Nodes, which are connected to each other by arrows with relative velocities, represent inertial frames. The velocity composition law of special relativity has been known to be inconsistent with the reciprocity principle of velocity, through the investigation of a simple case where the inertial frames of interest are connected via a single node. When they are connected through more than one node, many inconsistencies including the violation of the reciprocity principle are found, as the successive coordinate transformation is not reduced to a Lorentz transformation. These inconsistencies can be cured by introducing a reference node such that the velocity composition is made in conjunction with it. The reference node corresponds to the preferred frame. The relativistic velocity composition law has no inconsistencies under the uniqueness of the isotropic frame.
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Salosin, Evgeny Georgievich. "LORENTZ TRANSFORMATION CHANGE." Globus 8, no. 1(66) (February 4, 2022): 36–40. http://dx.doi.org/10.52013/2658-5197-66-1-9.
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For relativistic velocities, Galileo’s principle of addition of four-dimensional velocities is valid, and not the Lorentz transformation. In this case, it is impossible to write down the law of conservation of energy with Newton’s potential using the Lorentz transformation. And with the proposed transformation it is possible. In addition, the invariance of the wave equation with respect to the Galilean transformation with four-dimensional velocity is obtained. The GR equation is also invariant under the Galileo transformations of the four-vector. This transformation is a more general case of invariance than the Lorentz transformation. Moreover, the Lorentz transformation is contradictory. For a single massive body in general relativity, the Lorentz transformation is not valid, since the metric tensor is not Galilean. Although in the case of SRT such a transformation is possible. Those. the properties of inertial coordinate systems are violated. For a Galilean transformation of a four-vector for a massive body, a Galilean transformation is possible. Moreover, from the Galilean transformations of the four-vector, one can obtain the Lorentz transformation, but with the use of three-dimensional velocity. Three-dimensional speed is limited by the speed of light in real space, where all tricks with its use come from. The 4D speed is unlimited, and there are no coordinate transformation tricks. If you use the transformation between inertial coordinate systems using a limited threedimensional velocity, then tricks arise with the transformation of space and time. If you use unlimited four-dimensional speed, then there are no tricks with a change in space-time. Four-dimensional speed is a more general concept than three-dimensional, and you need to measure the parameters at four-dimensional speed, then there will be no tricks. Thus, measuring time with the help of four-dimensional velocity, we will not get an increase in the muon lifetime.
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Lyra, Alexandre, and Marcelo Carvalho. "Unifying the Galilei Relativity and the Special Relativity." ISRN Mathematical Physics 2013 (June 11, 2013): 1–17. http://dx.doi.org/10.1155/2013/156857.
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We present two models combining some aspects of the Galilei and the Special relativities that lead to a unification of both relativities. This unification is founded on a reinterpretation of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low velocity. In the first model, the Galilei relativity plays a prominent role in the sense that the basic kinematical laws of Special relativity, for example, the Lorentz transformation and the velocity law, follow from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a second model that leads to a generalization of the Lorentz transformation, which includes, as particular cases, the standard Lorentz transformation and transformations that apply to the case of superluminal frames.
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Alsing, P. M., and G. Milburn. "Lorentz Invariance of Entanglement." Quantum Information and Computation 2, no. 6 (October 2002): 487–512. http://dx.doi.org/10.26421/qic2.6-4.
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We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin $1/2$ particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.
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Putra, Fima Ardianto. "De Broglie Wave Analysis of the Heisenberg Uncertainty Minimum Limit under the Lorentz Transformation." Jurnal Teras Fisika 1, no. 2 (September 20, 2018): 1. http://dx.doi.org/10.20884/1.jtf.2018.1.2.1008.
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A simple analysis using differential calculus has been done to consider the minimum limit of the Heisenberg uncertainty principle in the relativistic domain. An analysis is made by expressing the form of and based on the Lorentz transformation, and their corresponding relation according to the de Broglie wave packet modification. The result shows that in the relativistic domain, the minimum limit of the Heisenberg uncertainty is p x ?/2 and/or E t ?/2, with is the Lorentz factor which depend on the average/group velocity of relativistic de Broglie wave packet. While, the minimum limit according to p x ?/2 or E t ?/2, is the special case, which is consistent with Galilean transformation. The existence of the correction factor signifies the difference in the minimum limit of the Heisenberg uncertainty between relativistic and non-relativistic quantum. It is also shown in this work that the Heisenberg uncertainty principle is not invariant under the Lorentz transformation. The form p x ?/2 and/or E t ?/2 are properly obeyed by the Klein-Gordon and the Dirac solution.
Key words: De Broglie wave packet, Heisenberg uncertainty, Lorentz transformation, and minimum limit.
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Lavenda, B. H. "Special Relativity via Modified Bessel Functions." Zeitschrift für Naturforschung A 55, no. 9-10 (October 1, 2000): 745–53. http://dx.doi.org/10.1515/zna-2000-9-1001.
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The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the 'k calculus' which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle's position are Gaussian and Poisson, respectively.
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Bates, Neil. "A Paradox of Energy Conservation due to the Relativistic Velocity-Transformation Law." Physics Essays 1, no. 4 (December 1, 1988): 244–46. http://dx.doi.org/10.4006/1.3033418.
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Lavenda, B. H. "Is Relativistic Quantum Mechanics Compatible with Special Relativity?" Zeitschrift für Naturforschung A 56, no. 5 (May 1, 2001): 347–65. http://dx.doi.org/10.1515/zna-2001-0503.
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Abstract The transformation from a time-dependent random walk to quantum mechanics converts a modified Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel function of an imaginary argument is the solution of the finite difference differential Schrödinger equation whereas the same function of a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition of the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of 7r/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components of a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms of ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms of a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral of the modified Bessel function and determines the paths of steepest descent in the classical limit. If the definitions of frequency and wave number in terms of the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation of causality. In order to get surfaces of constant phase to move at the group velocity, an integrating factor is required which determines how the intensity decays in time. The phase correlation between neighboring sites in quantum mechanics is given by the phase factor for the electron to reverse its direction, whereas, in special relativity, it is given by the Doppler shift.
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Yang, Zhigen, and Ming Zhao. "VLBI Relativistic Time Delay Model with Picosecond Precision." Symposium - International Astronomical Union 156 (1993): 211. http://dx.doi.org/10.1017/s007418090017322x.
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The VLBI relativistic time delay model of transformation is reformuled with a precision of better than 1 ps, which is given as followswhere is geocentric newtonial potential, and are the barycentric velocity vector in B-frame and the geocentric velocity vector of antenna i. Ŝ is the unit vector of the direction from the barycenter of solar system to the source. c is the speed of light in vacuum. , where is the geocentric baseline vector. δtv can be expressed as in which and where Δtatm, Δtion and Δtaxo are the tropospheric, the ionospheric and the axio offset refraction delays respectively, and Δtgrav is called the gravitational time delay. A straightforward differentation of expression (1), the equation of d(dτ)/dt can be obtained. The included in the can be expressed as The orders of magnitude of the various correction terms in expression (4) and (5) are estimated respectively. Conclusion: expression (4) and (5) should be taken into account in the VLBI relativistic model of transformation for the 1 ps precision. Equation (1) and the expression of its differentation differ from all the models which have been published earlier.
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Giona, Massimiliano. "Covariance and Spinorial Statistical Description of Simple Relativistic Stochastic Kinematics." Fluctuation and Noise Letters 19, no. 04 (July 17, 2020): 2050042. http://dx.doi.org/10.1142/s021947752050042x.
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It is shown that Generalized Poisson–Kac processes are closed with respect to Lorentz transformations, providing a class of covariant kinematic processes. The transformation properties of the associated partial probability densities (waves) display spinorial character in a probability space, and their spinorial character is intrinsically related to the parametrization of the internal degrees of freedom of the process. Parity function analysis associated with the bias induced in the partial-wave recombination process by a Lorentz boost, indicates a symmetry breaking in the recombination dynamics. In an inertial reference frame moving with constant velocity [Formula: see text] with respect to the rest frame of the process, stochastic fluctuations are progressively damped out till complete suppression in the limit for [Formula: see text].
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Paul, SN. "Nonlinear Instability of Circularly Polarised Waves in a Magnetised Relativistic Plasma." Australian Journal of Physics 43, no. 3 (1990): 311. http://dx.doi.org/10.1071/ph900311.
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An intensity dependent nonlinear dispersion relation of a circularly polarised wave in a magnetised relativistic plasma is derived using a special Lorentz transformation and then the stability criteria of the wave are investigated. From numerical estimations it is observed that electromagnetic waves, having powers much below that for the occurrence of nonlinear phenomena due to self-action effects, are unstable in a magnetised relativistic dense plasma. The effects of a strong magnetic field on the group velocity and cut-off frequency in a dense plasma are also discussed.
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Javanshiry, Mohammad. "The Mechanical Behavior of a Multispring System Revealing Absurdity in the Relativistic Force Transformation." International Journal of Mathematics and Mathematical Sciences 2021 (December 11, 2021): 1–8. http://dx.doi.org/10.1155/2021/2706705.
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The mechanical motion of a system consisting of simple springs is investigated from the viewpoint of two inertial observers with a relativistic relative velocity. It is shown that the final displacement of the springs is not measured the same by the observers. Indeed, it is demonstrated that there is an incompatibility between kinematics and dynamics in Einstein’s relativity regarding the force transformation.
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Nguyen, D. B. "The relativistic transformations of velocity, acceleration, and higher derivatives as differentials of nonlinear extensions of the Lorentz transformation." American Journal of Physics 59, no. 8 (August 1991): 748–51. http://dx.doi.org/10.1119/1.16755.
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Drake, Samuel Picton, and Geoff Pointer. "Comment on “Relativistic phase velocity transformation” [Am. J. Phys. 57(7), 628–630 (1989)]." American Journal of Physics 87, no. 5 (May 2019): 403–4. http://dx.doi.org/10.1119/1.5096624.
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Hu, Ben Yu-Kuang. "Relativistic transformation of perpendicular velocity components from the constancy of the speed of light." American Journal of Physics 76, no. 7 (July 2008): 691. http://dx.doi.org/10.1119/1.2919744.
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Unlu, Hilmi. "Special Relativity in Six Dimensions." Journal of Asian Scientific Research 12, no. 4 (November 4, 2022): 188–217. http://dx.doi.org/10.55493/5003.v12i4.4646.
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In the four-dimensional spacetime theory of special relativity, the space coordinate is time contracted along the motion, while perpendicular coordinates are invariant and time varies with position. This leads to a velocity transformation valid at speed of light and used in showing invariance electric and magnetic fields which are invariant along x-axis but change occur along y, and z-axes, contrary to the classical electrodynamics. In this work we introduce a new six-dimensional spacetime theory which allows time (position) change of position (time) in three coordinate axes and still satisfy the Lorentz invariance conditions of metric and Maxwell’s wave equations between two frames. We derive a new velocity transformation rule which is valid at any relative speed of massive frames moving with respect to each other. We derived expressions for relativistic mass, energy, Doppler shift, time dilation, length contraction, photon rest mass, and used the conservation of relativistic power to prove that the electric and magnetic fields and consequently, Maxwell wave equations are Lorentz invariant between two massive frames with and without nonzero photon mass in vacuum and materials medium. Calculated photon mass is in excellent agreement with the measured and observed upper bounds of 1.24x10-54 kg and1.75x 10-53 kg, respectively.
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Sheng, Xin-Li, Yang Li, Shi Pu, and Qun Wang. "Lorentz Transformation in Maxwell Equations for Slowly Moving Media." Symmetry 14, no. 8 (August 9, 2022): 1641. http://dx.doi.org/10.3390/sym14081641.
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We use the method of field decomposition, a widely used technique in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The “deformed” Maxwell equations derived using SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium’s co-moving frame. Our results show that the Lorentz transformation in the SVA of up to O(v/c) (v is the speed of the medium and c is the speed of light in a vacuum) is essential to derive these equations: the time and charge density must also change when transforming to a different frame, even in the SVA, not just the position and current density, as in the Galilean transformation. This marks the essential difference between the Lorentz transformation and the Galilean one. We show that the integral forms of Faraday and Ampere equations for slowly moving surfaces are consistent with Maxwell equations. We also present Faraday equation in the covariant integral form, in which the electromotive force can be defined as a Lorentz scalar that is independent of the observer’s frame. No evidence exists to support an extension or modification of Maxwell equations.
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Treumann, Rudolf A., and Wolfgang Baumjohann. "The usefulness of Poynting's theorem in magnetic turbulence." Annales Geophysicae 35, no. 6 (December 15, 2017): 1353–60. http://dx.doi.org/10.5194/angeo-35-1353-2017.
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Abstract. We rewrite Poynting's theorem, already used in a previous publication Treumann and Baumjohann (2017a) to derive relations between the turbulent magnetic and electric power spectral densities, to make explicit where the mechanical contributions enter. We then make explicit use of the relativistic transformation of the turbulent electric fluctuations to obtain expressions which depend only on the magnetic and velocity fluctuations. Any electric fluctuations play just an intermediate role. Equations are constructed for the turbulent conductivity spectrum in Alfvénic and non-Alfvénic turbulence in extension of the results in the above citation. An observation-based discussion of their use in application to solar wind turbulence is given. The inertial range solar wind turbulence exhibits signs of chaos and self-organization.
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Moradpour, Hooman, and Afshin Montakhab. "Relativistic three-partite non-locality." International Journal of Quantum Information 14, no. 02 (March 2016): 1650008. http://dx.doi.org/10.1142/s0219749916500088.
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Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation (LT) has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and Greenberger–Horne–Zeilinger (GHZ) states which exhibit distinctly different types of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Czachor’s relativistic spin operator and Svetlichny’s inequality as the main measure of non-locality and uses the same angles in the rest frame (S) as well as the moving frame ([Formula: see text]), then maximally violated inequality in S will decrease in the moving frame, and will eventually lead to lack of non-locality (i.e. satisfaction of inequality) in the [Formula: see text] limit. This is shown for both the GHZ and W states and in two different configurations which are commonly studied (Cases 1 and 2). Our results are in line with a more familiar case of two particle case. We also show that the satisfaction of Svetlichny’s inequality in the [Formula: see text] limit is independent of initial particles’ velocity. Our study shows that whenever we use Czachor’s relativistic spin operator, results draws a clear picture of three-particle non-locality making its general properties consistent with previous studies on two-particle systems regardless of the W state or the GHZ state is involved. Throughout the paper, we also address the results of using Pauli’s operator in investigating the behavior of [Formula: see text] under LT for both of the GHZ and W states and two cases (Cases 1 and 2). Our investigation shows that the violation of [Formula: see text] in moving frame depends on the particle’s energy in the lab frame, which is in agreement with some previous works on two and three-particle systems. Our work may also help us to classify the results of using Czachor’s and Pauli’s operators to describe the spin entanglement and thus the system spin in relativistic information theory.
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Ivanov, Sergei, Vladimir Kuptsov, Vladimir Badenko, and Alexander Fedotov. "An Elaborated Signal Model for Simultaneous Range and Vector Velocity Estimation in FMCW Radar." Sensors 20, no. 20 (October 16, 2020): 5860. http://dx.doi.org/10.3390/s20205860.
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A rigorous mathematical description of the signal reflected from a moving object for radar monitoring tasks using linear frequency modulated continuous wave (LFMCW) microwave radars is proposed. The mathematical model is based on the quasi-relativistic vector transformation of coordinates and Lorentz time. The spatio-temporal structure of the echo signal was obtained taking into account the transverse component of the radar target speed, which made it possible to expand the boundaries of the range of measuring the range and speed of vehicles using LFMCW radars. An algorithm for the simultaneous estimation of the range, radial and transverse components of the velocity vector of an object from the observation data of the time series during one frame of the probing signal is proposed. For an automobile 77 GHz microwave LFMCW radar, a computer experiment was carried out to measure the range and velocity vector of a radar target using the developed mathematical model of the echo signal and an algorithm for estimating the motion parameters. The boundaries of the range for measuring the range and speed of the target are determined. The results of the performed computer experiment are in good agreement with the results of theoretical analysis.
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Sosenko†, Petro P. "Quasi-particles in magnetized plasmas: second-order approximation." Journal of Plasma Physics 53, no. 2 (April 1995): 223–34. http://dx.doi.org/10.1017/s0022377800018134.
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A second-order approximation is formulated and studied within the context of the quasi-particle description of magnetized plasmas. The general case of relativistic particles in non-uniform but stationary magnetic fields, and in additional force fields that are strongly non-uniform but slowly evolving in time compared with particle gyrations with the cyclotron frequency, is considered. In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle velocity is calculated up to second order, when polarization particle drift as well as the renormalization of the lower-order result become equally significant. A general expression for the velocity of particle polarization drift is obtained in terms of quasi-particle properties, and with account taken of finite-Larmor-radius effects and non-uniformity of magnetic fields. A guiding-centre transformation is found that makes it possible to achieve equal mean velocities of particle, guiding centre and quasi-particle up to second order. Then polarization drifts enter the particle, guiding-centre and quasi-particle equations of motion.
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Abbas, Ummi, Beatrice Bucciarelli, and Mario G. Lattanzi. "Differential astrometric framework for the Jupiter relativistic experiment with Gaia." Monthly Notices of the Royal Astronomical Society 485, no. 1 (February 14, 2019): 1147–56. http://dx.doi.org/10.1093/mnras/stz452.
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Abstract We employ differential astrometric methods to establish a small field reference frame stable at the microarcsecond (μas) level on short time-scales using high-cadence simulated observations taken by Gaia in 2017 February of a bright star close to the limb of Jupiter, as part of the relativistic experiment on Jupiter’s quadrupole. We achieve subμas-level precision along scan through a suitable transformation of the field angles into a small-field tangent plane and a least-squares fit over several overlapping frames for estimating the plate and geometric calibration parameters with tens of reference stars that lie within ∼0.5 deg from the target star, assuming perfect knowledge of stellar proper motions and parallaxes. Furthermore, we study the effects of unmodelled astrometric parameters on the residuals and find that proper motions have a stronger effect than unmodelled parallaxes, e.g. unmodelled Gaia DR2 proper motions introduce extra residuals of ∼23 μas (AL) and 69 μas (AC) versus the ∼5 μas (AL) and 17 μas (AC) due to unmodelled parallaxes. On the other hand, assuming catalogue errors in the proper motions and parallaxes such as those from Gaia DR2 has a minimal impact on the stability introducing subμas and μas level residuals in the along and across scanning direction, respectively. Finally, the effect of a coarse knowledge in the satellite velocity components (with time-dependent errors of 10 μas s−1) is capable of enlarging the size of the residuals to roughly 0.2 mas.
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BANACH, ZBIGNIEW, and WIESLAW LARECKI. "EVOLUTION OF CENTRAL MOMENTS FOR A GENERAL-RELATIVISTIC BOLTZMANN EQUATION: THE CLOSURE BY ENTROPY MAXIMIZATION." Reviews in Mathematical Physics 14, no. 05 (May 2002): 469–510. http://dx.doi.org/10.1142/s0129055x02001223.
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Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY)150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau–Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.
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KOPEIKIN, SERGEI M. "GRAVITOMAGNETISM AND THE SPEED OF GRAVITY." International Journal of Modern Physics D 15, no. 03 (March 2006): 305–20. http://dx.doi.org/10.1142/s0218271806007663.
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Experimental discovery of the gravitomagnetic fields generated by translational and/or rotational currents of matter is one of primary goals of modern gravitational physics. The rotational (intrinsic) gravitomagnetic field of the Earth is currently measured by the Gravity Probe B. The present paper makes use of a parametrized post-Newtonian (PN) expansion of the Einstein equations to demonstrate how the extrinsic gravitomagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay caused by a moving gravitational lens. We prove that measuring the extrinsic gravitomagnetic field is equivalent to testing the relativistic effect of the aberration of gravity caused by the Lorentz transformation of the gravitational field. We show that the recent Jovian deflection experiment is a null-type experiment testing the Lorentz invariance of the gravitational field (aberration of gravity), thus, confirming existence of the extrinsic gravitomagnetic field associated with the orbital motion of Jupiter with accuracy 20%. We comment on physically inadequate interpretations of the Jovian deflection experiment given by a number of researchers who are not experts in modern VLBI techniques and the subtleties of JPL ephemeris. We propose to measure the aberration of gravity effect more accurately by observing the gravitational deflection of light by the Sun and processing VLBI observations in the geocentric frame with respect to which the Sun is moving with velocity ~30 km/s.
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PIWNICKI, P. "GEOMETRICAL APPROACH TO LIGHT IN INHOMOGENEOUS MEDIA." International Journal of Modern Physics A 17, no. 11 (April 30, 2002): 1543–58. http://dx.doi.org/10.1142/s0217751x02009746.
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Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only. The introduction of an appropriately chosen three-dimensional metric leads to a significant simplification of the description of light propagation in an inhomogeneous medium: light rays become geodesics of the metric and the field vectors are parallel transported along the rays. The new metric is connected to the usual flat space metric diag[1,1,1] via a conformal transformation leading to new, effective values of the medium parameters [Formula: see text] and [Formula: see text] with [Formula: see text]. The corresponding index of refraction is thus constant and so is the effective velocity of light. Space becomes effectively empty but curved. All deviations from straight-line propagation are now due to curvature. The approach is finally used for a discussion of the Riemann–Silberstein vector, an alternative, complex formulation of the electromagnetic fields.
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Kholmetskii, Alexander L., and Tolga Yarman. "Thomas–Wigner rotation and Thomas precession in covariant ether theories: novel approach to experimental verification of special relativity." Canadian Journal of Physics 93, no. 5 (May 2015): 503–18. http://dx.doi.org/10.1139/cjp-2014-0340.
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We continue the analysis of Thomas–Wigner rotation (TWR) and Thomas precession (TP) initiated in (Kholmetskii and Yarman. Can. J. Phys. 92, 1232 (2014). doi:10.1139/cjp-2014-0015 ; Kholmetskii et al. Can. J. Phys. 92, 1380 (2014). doi:10.1139/cjp-2014-0140 ), where a number of points of serious inconsistency have been found in the relativistic explanation of these effects. These findings motivated us to address covariant ether theories (CET), as suggested by the first author (Kholmetskii. Phys. Scr. 67, 381 (2003)) and to show that both TWR and TP find a perfect explanation in CET. We briefly reproduce the main points of CET, which are constructed on the basis of general symmetries of empty space–time, general relativity principles, and classical causality, instead of Einstein’s postulates of the special theory of relativity (STR). We demonstrate that with respect to all known relativistic experiments performed to date in all areas of physics, both theories, STR and CET, yield identical results. We further show that the only effect that differentiates STR and CET is the measurement of time-dependent TWR of two inertial frames, K1 and K2, related by the rotation-free Lorentz transformation with a third inertial frame, K0, in the situation, where the relative velocity between K1 and K2 remains fixed. We discuss the results obtained and suggest a novel experiment, which can be classified as a new crucial test of STR.
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DUMITRESCU, Horia, Vladimir CARDOS, Radu BOGATEANU, and Alexandru DUMITRACHE. "The Structured Wall-Turbulence, a Galilean Relativistic Phenomenon." INCAS BULLETIN 12, no. 2 (June 5, 2020): 47–61. http://dx.doi.org/10.13111/2066-8201.2020.12.2.5.
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The relationship between heavenly bodies and earthly behavior along with its importance took many centuries before the rigor scientific understanding enabled the true influences on Earth, such as its complicated motion and perceived other regularities in the behavior of earthly objects. One of these was the tendency for all things in one vicinity to move in the same downward direction according to the influence that is known as gravity property. Moreover, matter was observed to transform, sometimes, from one form into another, such as with melting of ice or vaporizing/cavitation of water, but the total quantity of that matter never seemed to change, which reflects the law at which we now refer to as the conservation/ integrity of mass, including its latent energy. Much latter it is noticed that planet Earth forms a self-regulating complex system, i.e. the Earth’s surface is alive, that is known as the Gaia hypothesis, reflected in the Newton-Galilei dynamics through the law of equal action and reaction for stress vector and tensor, respectively. In addition, at was noticed that there are many material bodies with the important property that they retain their shapes, excepting the flowing fluids, whence the idea of rigid spatial motion arose, and it becomes possible to understood spatial relationships in terms a precise, well-defined geometry, the Euclidian three-dimensional geometry. Though the heavenly bodies are permanently moving in a self-built on universe like a timeless perpetuum mobile, the time remains an important property for the behaviors/motions of an Earth-bound object due to their relativity as against the diurnal rotation depending on the velocities of the impacted object. In contrast to the constant inertia condition where for small starting velocities and accelerations the Newton’s determinist principle is applied, the onset of a motion of the Earth-bound material bodies, at higher velocities and accelerations (O(g)), involves changes of moving matter/inertia under influence of gravitational field via some intrinsic latent motions/processes. They achieve the kinetic-gravitational mutual energy transfer obeying the Galilei’s law of inertia for self-equilibrating impact forces. The intrinsic motions, at the cellular scale (10-6 m), are responsible for the kinetic trinity of the momentum, kinetic energy and power, and they represent what it is called structured turbulence, i.e. a Galilean space-time structure according to the mathematical idea of a bundle (or fibre bundle) and its gauge connection. The bundle and gauge connection are a kind of Galilean transformation to a system moving with constant velocity carrying its relativistic non-inertial fraction as a blend of structure less turbulence and non-rigorously defined intermittency of a non-inertial motion.
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CASTRO, CARLOS. "ON THE VARIABLE FINE STRUCTURE CONSTANT, STRINGS AND MAXIMAL-ACCELERATION PHASE SPACE RELATIVITY." International Journal of Modern Physics A 18, no. 29 (November 20, 2003): 5445–73. http://dx.doi.org/10.1142/s0217751x0301646x.
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We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration relativity principle in the space–time tangent bundle and in phase spaces (cotangent bundle). The maximal proper-acceleration bound is a = c2/Λ in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. The group transformation laws of this maximal-acceleration phase space relativity theory under velocity and acceleration boosts are analyzed in full detail. For pure acceleration boosts it is shown why the minimal Planck-areas (maximal string tension) are universal invariant quantities in any frame of reference. Inspired by the maximal-acceleration corrections to the Lamb shifts of one-electron atoms by Lambiase, Papini and Scarpetta, we derive the exact integral equation that governs the renormalization-group-like scaling dependence of the fractional change of the fine structure constant as a function of the cosmological redshift factor and a cutoff scale Lc, where the maximal acceleration relativistic effects are dominant. A particular physical model exists dominated entirely by the vacuum energy, when the cutoff scale is the Planck scale, with ΩΛ = 1. The cosmological implications of this extreme case scenario are studied.
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James, Hugh. "Accounting for the expansion of the universe using an energy/momentum model to construct the space-time metric." F1000Research 11 (March 21, 2022): 344. http://dx.doi.org/10.12688/f1000research.108648.1.
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Background: The success of the theories of special and general relativity in describing localised phenomena, such as objects undergoing high speed motion or located in gravitational fields, needs no further elaboration. However, when applied to the evolution of the universe several problems arise which can require an additional model, e.g., inflation during the early expansion, and adjustments to parameters to account for phenomena such as the late-time acceleration of the universe. Methods: Focusing on the difference between the ways in which space and time are measured, this paper shows that there are two paths which allow the equations of special relativity to be produced from the same basic postulates. Results: While the standard theory assumes a fundamental existence of a coordinate framework which incorporates both space and time, an alternate path is possible which uses an energy/momentum, or dynamic model to derive a new metric equivalent to the standard space-time framework. When utilising the dynamic metric, the relativistic equations are unchanged for local phenomena such as the Lorentz coordinate transformation and the energy/momentum equation for high-velocity objects. Conclusions: However, the derived metric alters the perceived overall structure of the universe in a manner that, for the simplest model under this system, allows the reproduction of observed cosmological features, such as the intrinsic flatness of the universe and the apparent late-time acceleration of its expansion, without the need of additional models or changes in parameter values.
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Mathews, W. N. "Relativistic velocity and acceleration transformations from thought experiments." American Journal of Physics 73, no. 1 (January 2005): 45–51. http://dx.doi.org/10.1119/1.1806482.
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Chen, Mu Yi, and Su-Long Nyeo. "The field equations in a three-dimensional commutative space." International Journal of Modern Physics A 34, no. 15 (May 30, 2019): 1950078. http://dx.doi.org/10.1142/s0217751x19500787.
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The field equations in a three-dimensional commutative space based on a set of commutation relations are derived. In this space, the commutation relation of the position and kinematic momentum of a particle is generalized to include a metric tensor field in addition to a vector field. The introduction of a metric tensor is a generalization of the commutation relation for Feynman’s proof of the Maxwell equations. In this paper, as the equations of motion and the field equations are classical, the Poisson bracket and not the commutation relation is used in the calculations. As the commutative space is defined by the Poisson bracket, the equations of motion for the particle and the field equations for the metric tensor and vector are derived from the Poisson bracket in Hamiltonian mechanics. The Helmholtz conditions, which express the existence of a Lagrangian for a particle in the space, are also derived from the Poisson bracket. Then the field equations are calculated explicitly by two approaches. One is to calculate the Helmholtz conditions using the equations of motion. The other is to calculate the Jacobi identity for the kinematic momentum or velocity of the particle. In addition to the homogeneous Maxwell equations, the generalized field equations are obtained to define the generalized electric and magnetic fields of the tensor field. Just like the usual electric and magnetic fields, the generalized fields are invariant under a local gauge transformation and should play significant roles in physics. Finally, the homogeneous Maxwell equations of the vector field are seen to exhibit similarities with the generalized field equations for the tensor field. This similarity provides a useful theoretical framework for constructing gravitoelectromagnetism, which is based on analogies between the equations for electromagnetism and relativistic gravitation. It remains to establish the usefulness of the theoretical framework with applications of the field equations.
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Ziefle, Reiner Georg. "Einstein’s special relativity violates the constancy of the velocity c of light under one-way conditions and thus contradicts the behavior of electromagnetic radiation." Physics Essays 34, no. 3 (September 1, 2021): 274–78. http://dx.doi.org/10.4006/0836-1398-34.3.274.
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On Earth, we always measure the constant velocity c of electromagnetic radiation. Einstein assumed the velocity c of light to be constant in all inertial frames and developed his theory of special relativity by considering a light beam that moves back and forth, whereby he derived transformations between the coordinates of two reference frames: A moving reference frame represented by the coordinate system k and the coordinate system k that is at rest with respect to k. However, by applying Einstein’s theory of relativity, with its postulates of relativistic time dilation and length contraction, to electromagnetic radiation that moves only in one direction, either in the direction of or in the opposite direction to a moving inertial frame, it is demonstrated that the constancy of the velocity c of light is not compatible with Einstein’s theory of special relativity. It becomes obvious that Einstein’s relativistic physics must be an unrealistic theory, and consequently, we need an alternative, nonrelativistic, explanation of the constancy of the velocity c of electromagnetic radiation measured on Earth, and for the special and general “relativistic” phenomena.
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Al-Tamimi, Mohammad. "Problematic of Lorentz -Einstein’s Transformations." Advances in Social Sciences Research Journal 8, no. 6 (July 4, 2021): 423–30. http://dx.doi.org/10.14738/assrj.86.10399.
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When I tried to derive which was used by Lorentz in his transformations, I found it has a different value. Also the same problem happened with was used by Einstein in equations of the special theory of relativity (STR).
To explain this problematic, I tried to apply these transformations to a perfect and real relativistic experiment where I proved this real problematic, that confused physical society for decades.
Indeed, I strongly believe that, this problematic is coming as a reflection of the conception of the velocity law on STR where, we can’t build this conception on the bending of the dimensions of the spacetime.
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AMELINO-CAMELIA, GIOVANNI. "DOUBLY-SPECIAL RELATIVITY: FIRST RESULTS AND KEY OPEN PROBLEMS." International Journal of Modern Physics D 11, no. 10 (December 2002): 1643–69. http://dx.doi.org/10.1142/s021827180200302x.
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I examine the results obtained so far in exploring the recent proposal of theories of the relativistic transformations between inertial observers that involve both an observer-independent velocity scale and an observer-independent length/momentum scale. I also discuss what appear to be the key open issues for this research line.
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Brumberg, V. A. "Earth Rotation Velocity in Relation with Different Reference Frames." Symposium - International Astronomical Union 166 (1995): 293. http://dx.doi.org/10.1017/s0074180900228222.
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The high precision of present observations makes it reasonable to clear up a question about GRT (general relativity theory) corrections in the problem of Earth's rotation. The answer is that one may almost forget about GRT corrections when dealing in an adequate reference system (RS). The problem of Earth's rotation may be related to the relativistic hierarchy of RS started in (Brumberg and Kopejkin, 1989) and completed in (Klioner, 1993). Let letters B, G and T be related to barycentric, geocentric and topocentric RS, respectively. Let DRS and KRS be dynamically nonrotating or kinematically nonrotating RS, respectively. From the dynamical equations of rotation it follows that the most adequate system for studying the Earth's rotation is DGRS. Apart from the geophysical factors the rotation of the Earth in this system is fairly well approximated by the rigid-body rotation with some angular velocity . The same rotation of the Earth as considered in BRS and DTRS may be also approximated by the rigid-body rotation but with some additive relativistic corrections and with other angular velocities ωi and , respectively. Substituting these three rotation relations into four-dimensional BRS-DGRS and DGRS-DTRS transformations one may express ωi and in terms of and determine the additive relativistic corrections in BRS and BTRS. These corrections are of importance for treating kinematics problems in various coordinate systems and for obtaining physically meaningful solutions of the dynamical equations of rotation in the barycentric reference system.The complete text will be published in Journal of Geodynamics.
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Hassani, Mohamed Elmansour. "Foundations of Superluminal Relativistic Mechanics." Communications in Physics 24, no. 4 (March 9, 2015): 313. http://dx.doi.org/10.15625/0868-3166/24/4/4850.
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The paper provides an elementary derivation of new superluminal spatio-temporal transformations based on the idea that, conceptually and kinematically, each subluminal, luminal and/or superluminal inertial reference frame has, in addition to its relative velocity, its proper specific kinematical parameter, which having the physical dimensions of a constant speed. Consequently, the relativity principle and causality principle both are coherently extended to superluminal velocities and, more importantly, this original approach constitutes the first basic step toward the formulation of superluminal relativistic mechanics, which is in fact a pure superluminalization of special relativity theory.
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BENOVA, E., S. T. IVANOV, and A. A. RUKHADZE. "Surface waves in a plasma flow." Journal of Plasma Physics 63, no. 5 (June 2000): 489–93. http://dx.doi.org/10.1017/s0022377800008357.
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Dispersion characteristics of surface waves in a semibounded plasma flow with relativistic velocity u0 parallel to the plasma–vacuum interface are presented. The plasma is considered to be cold and collisionless, which allows us to take into account only the electron motion. It is shown that – in contrast to the bulk waves, which are invariant with respect to Lorentz transformations and whose spectrum is independent of the flow velocity – the surface waves are not invariant, which leads to a dependence of their spectrum on the flow velocity and, correspondingly, to non-reciprocity. The latter peculiarity is due to the fact that the boundary conditions are not invariant.
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JAFARIZADEH, M. A., and M. MAHDIAN. "SPIN–MOMENTUM CORRELATION IN RELATIVISTIC SINGLE-PARTICLE QUANTUM STATES." International Journal of Quantum Information 08, no. 03 (April 2010): 517–28. http://dx.doi.org/10.1142/s0219749910006125.
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This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.
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de la Cruz-Hernández, Manuel E., and Sergio Mendoza. "Full analytical ultrarelativistic 1D solutions of a planar working surface." Monthly Notices of the Royal Astronomical Society 507, no. 2 (July 30, 2021): 1827–35. http://dx.doi.org/10.1093/mnras/stab2158.
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ABSTRACT We show that the 1D planar ultrarelativistic shock tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the hydrodynamical quantities of the problem form two shock waves separating from a contact discontinuity. The procedure is based on the extensive use of the Taub jump conditions for relativistic shock waves, the Taub adiabatic, and performing Lorentz transformations to present the solution in a system of reference adequate for an external observer at rest. The solutions are found using a set of very useful theorems related to the Lorentz factors when transforming between systems of reference. The energy dissipated inside the working surface is relevant for studies of light curves observed in relativistic astrophysical jets and so, we provide a full analytical solution for this phenomenon assuming an ultrarelativistic periodic velocity injected at the base of the jet.
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Cooperstock, F. I. "Weak-field general relativistic dynamics and the Newtonian limit." Modern Physics Letters A 31, no. 05 (February 5, 2016): 1650037. http://dx.doi.org/10.1142/s0217732316500371.
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We show that the generally held view that the gravity of weak-field nonrelativistic-velocity sources being invariably almost equivalent to Newtonian gravity (NG) (the “Newtonian limit” approach) is in some instances misleading and in other cases incorrect. A particularly transparent example is provided by comparing the Newtonian and general relativistic analyses of a simple variant of van Stockum’s infinite rotating dust cylinder. We show that some very recent criticisms of our work that had been motivated by the Newtonian limit approach were incorrect and note that no specific errors in our work were found in the critique. In the process, we underline some problems that arise from inappropriate coordinate transformations. As further support for our methodology, we note that our weak-field general relativistic treatment of a model galaxy was vindicated recently by the observations of Xu et al. regarding our prediction that the Milky Way was 19–21 kpc in radius as opposed to the commonly held view that the radius was 15 kpc.
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Friedman, Yaakov, and Tzvi Scarr. "Symmetry and Special Relativity." Symmetry 11, no. 10 (October 3, 2019): 1235. http://dx.doi.org/10.3390/sym11101235.
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We explore the role of symmetry in the theory of Special Relativity. Using the symmetry of the principle of relativity and eliminating the Galilean transformations, we obtain a universally preserved speed and an invariant metric, without assuming the constancy of the speed of light. We also obtain the spacetime transformations between inertial frames depending on this speed. From experimental evidence, this universally preserved speed is c, the speed of light, and the transformations are the usual Lorentz transformations. The ball of relativistically admissible velocities is a bounded symmetric domain with respect to the group of affine automorphisms. The generators of velocity addition lead to a relativistic dynamics equation. To obtain explicit solutions for the important case of the motion of a charged particle in constant, uniform, and perpendicular electric and magnetic fields, one can take advantage of an additional symmetry—the symmetric velocities. The corresponding bounded domain is symmetric with respect to the conformal maps. This leads to explicit analytic solutions for the motion of the charged particle.
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Trübenbacher, E. "A Lorentz Invariant Schrödinger Equation for Spin 0." Zeitschrift für Naturforschung A 44, no. 9 (September 1, 1989): 801–10. http://dx.doi.org/10.1515/zna-1989-0905.
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Abstract Using the concept of distributions, the square root of the operator - Δ + m2 is taken in a mathematically well defined way for one component wave functions. A new representation of proper Lorentz transformations for one component wave functions makes it possible to construct a relativistic quantum mechanics for spin 0, comprising a Lorentz invariant wave equation, a scalar product, and a positive definite density satisfying, together with a current, a continuity equation, and coupling of scalar and vector potentials. Some interesting consequences of the theory concerning the concept of particle trajectory and velocity of propagation of the probability amplitude are discussed in detail. As an example of practical application a perturbation theory for discrete states is set up.
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Rubin, Jacques. "Applications of a Particular Four-Dimensional Projective Geometry to Galactic Dynamics." Galaxies 6, no. 3 (August 3, 2018): 83. http://dx.doi.org/10.3390/galaxies6030083.
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Relativistic localizing systems that extend relativistic positioning systems show that pseudo-Riemannian space-time geometry is somehow encompassed in a particular four-dimensional projective geometry. The resulting geometric structure is then that of a generalized Cartan space (also called Cartan connection space) with projective connection. The result is that locally non-linear actions of projective groups via homographies systematically induce the existence of a particular space-time foliation independent of any space-time dynamics or solutions of Einstein’s equations for example. In this article, we present the consequences of these projective group actions and this foliation. In particular, it is shown that the particular geometric structure due to this foliation is similar from a certain point of view to that of a black hole but not necessarily based on the existence of singularities. We also present a modified Newton’s laws invariant with respect to the homographic transformations induced by this projective geometry. Consequences on galactic dynamics are discussed and fits of galactic rotational velocity curves based on these modifications which are independent of any Modified Newtonian Dynamics (MOND) or dark matter theories are presented.
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Moradi, Shahpoor. "Relativity of mixed entangled states." Quantum Information and Computation 11, no. 11&12 (November 2011): 957–67. http://dx.doi.org/10.26421/qic11.11-12-6.
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We obtain the necessary and sufficient separability and distillability conditions of mixtures of a maximally entangled state and the completely separable state in relativistic setting. In an inertial frame we study the entanglement under Wigner rotations induced by Lorentz transformations. We also investigate the mixed state entanglement of scalar and Dirac fields as seen by two relatively accelerated observers. For scalar field we show that in infinite acceleration limit the state has no longer distillable entanglement. For dirac field the entanglement in the infinite acceleration limit is finite. In both cases we show that there are states that will change from entangled into separable for a certain value of velocity or acceleration. We conclude that distillability is a relative concept, depending on the frame in which it is observed.
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Consoli, Maurizio, and Alessandro Pluchino. "The CMB, Preferred Reference System, and Dragging of Light in the Earth Frame." Universe 7, no. 8 (August 23, 2021): 311. http://dx.doi.org/10.3390/universe7080311.
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The dominant CMB dipole anisotropy is a Doppler effect due to a particular motion of the solar system with a velocity of 370 km/s. Since this derives from peculiar motions and local inhomogeneities, one could meaningfully consider a fundamental frame of rest Σ associated with the Universe as a whole. From the group properties of Lorentz transformations, two observers, individually moving within Σ, would still be connected by the relativistic composition rules. However, the ultimate implications could be substantial. Physical interpretation is thus traditionally demanded in order to correlate some of the dragging of light observed in the laboratory with the direct CMB observations. Today, the small residuals—from those of Michelson–Morley to present experiments with optical resonators—are just considered instrumental artifacts. However, if the velocity of light in the interferometers is not the same parameter “c” of Lorentz transformations, nothing would prevent a non-zero dragging. Furthermore, the observable effects would be much smaller than what is classically expected and would most likely be of an irregular nature. We review an alternative reading of experiments that leads to remarkable correlations with the CMB observations. Notably, we explain the irregular 10−15 fractional frequency shift presently measured with optical resonators operating in vacuum and solid dielectrics. For integration times of about 1 s and a typical Central European latitude, we also predict daily variations of the Allan variance in the range (5÷12)·10−16.
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Munera, H. A. "Einstein’s dream to unify all forces finally materializes: a revived de Broglie’s pilot-wave theory with novel solutions." Journal of Physics: Conference Series 2197, no. 1 (March 1, 2022): 012021. http://dx.doi.org/10.1088/1742-6596/2197/1/012021.
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Abstract Starting from Louis de Broglie’s pilot wave-theory, this paper unifies gravity and quantum mechanics under a single mathematical field theory for all forces in Nature. Two families of potentials coexist as mathematical solutions for the homogeneous Klein-Gordon equation which is the same homogeneous classical wave equation: (a) Neo-Laplacian local time-independent background potentials, and (b) Novel time-distance entangled Q(q) potentials which are isomorph to distance-time-velocity transformations based on any of the competing relativistic theories (Lorentz, Poincaré or Einstein), or on the pre-relativistic Galilean invariant Doppler equations. This remarkable property makes present theory compatible with all previous empirical evidence, including experiments conventionally interpreted as supporting Einstein’s special relativity. We report explicit closed solutions for potentials solving the one-dimensional and three-dimensional classical wave equations, and describe in detail how to calculate time-independent neo-Laplacian background forces and relativistically isomorph time-dependent entangled forces. The scale of the problem appears as a required parameter, thus making our theory applicable to all scales of Nature from quarks to cosmos. A usually overlooked neo-Laplacian logarithmic potential predicts the observed high values of non-Keplerian tangential speeds at the galactic scale. At the human scale, calculations relative to hurricanes and tornadoes may be facilitated by the closed form of our unified forces. A novel torsion component of gravity automatically appears from our new solutions.