Academic literature on the topic 'Relativistic Velocity Transformation'
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Journal articles on the topic "Relativistic Velocity Transformation"
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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.
Book chapters on the topic "Relativistic Velocity Transformation"
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Freeman, Richard, James King, and Gregory Lafyatis. "Introduction to Special Relativity." In Electromagnetic Radiation, 113–83. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198726500.003.0005.
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The history of experiments and the development of the concepts of special relativity is presented with an emphasis on Einstein’s postulates of relativity and the relativity of simultaneity. The development of the Lorentz transformations follows Einstein’s work in enunciating the principles of covariance among inertial frames. The mathematics of the geometry of space-time is presented using Miniowski’s space-time diagrams. In developing Einstein’s argument for the reality of special relativity consequences, two examples of apparent paradoxes with their resolution are given: the twin and connected rocket problems. The mathematics of 4-vectors is developed with explicit presentation of the 4-vector gradient, 4-vector velocity, 4-vector momentum, 4-vector force, 4-wavevector, 4-current density, and 4-potential. This section sums up with the manifest covariance of Maxwell’s equations, and the presentation of the electromagnetic field and Einstein stress-energy tensor. Finally, simple examples of electromagnetic field transformation are given: static electric and magnetic fields parallel and transverse to the velocity relating two inertial frames; and the transformation of fields from a charge moving at relativistic velocities.
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d’Inverno, Ray, and James Vickers. "The key attributes of special relativity." In Introducing Einstein's Relativity, 31–48. 2nd ed. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198862024.003.0003.
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Abstract Chapter 3 adopts a more traditional approach to special relativity. Rather than using the k-calculus, it gives the standard derivation of the Lorentz transformations, working in non-relativistic units in which the speed of light is denoted by c, and restricting attention to two inertial observers S and S′ in standard configuration. As before, it shows that the Lorentz transformations follow from the two postulates, namely, the principle of special relativity and the constancy of the velocity of light. It then shows how these leave the distance between two ‘events’ in space-time invariant. This chapter also examines the key physical attributes of special relativity, namely length contraction and time dilation as well as the relativistic Doppler effect. The chapter also discusses uniform acceleration and the twin paradox.
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Dyall, Kenneth G., and Knut Faegri. "Basic Special Relativity." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0006.
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Special relativity is a fascinating and challenging branch of physics. It describes the physics of the high velocity/high energy regime, frequently turning up phenomena that appear paradoxical in view of our everyday experience. In this book we will be quite selective in our presentation of the theory of special relativity: we will concentrate on those features that we consider necessary for the later applications to relativistic quantum chemistry. We do this in good conscience, knowing that there is a vast literature on the subject, catering to a wide range of audiences—from the quite elementary to the very sophisticated. A few examples are listed in the reference list, but a visit to any nearby physics library will provide an ample selection of reading material for those wishing to delve deeper into the matter. In the present chapter we adopt a minimalist approach. We develop some of the basic concepts and formulas of special relativity, building on a rather elementary level of basic physics. The aim is to provide a sufficient foundation for those who want to proceed as quickly as possible to the more quantum chemical parts of the text. In later chapters we will introduce more advanced tools of physics and revisit some of the subjects treated here. The theory of special relativity deals with the description of physical phenomena in frames that move at constant velocity relative to each other. The classroom is one such frame, the car passing at constant speed outside the classroom is another. The trajectory of a ball being thrown up vertically in the car will look quite different whether we describe it relative to the interior of the car or relative to the interior of the classroom. In particular we will be concerned with inertial frames. We define an inertial frame as a frame where spatial relations are Euclidean and where there is a universal time such that free particles move with constant velocities. In classical Newtonian mechanics, relations between the spatial parameters and time in two inertial frames S and S’ are expressed in terms of the Galilean transformations.
Conference papers on the topic "Relativistic Velocity Transformation"
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Sharma, Kal Renganathan. "Critical Thickness of High Temperature Barrier Coatings of Magnesium Oxychloride Sorrel Cement." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47392.
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The critical thickness of high temperature barrier coating is derived to avoid cycling of temperature from the finite speed heat conduction equations. When a cylinder is subject to a step change in temperature at the surface of the cylinder the transient temperature profile is obtained by the method of separation of variables. The finite speed of heat propagation is accounted for by using the modified Fourier’s law of conduction with a heat velocity of √α/τr. In order to avoid pulsations of temperature with respect to time the cylinder has to be maintained at a radius no less than 4.8096√ατr. In the asymptotic limit of infinite heat velocity the governing equation becomes parabolic diffusion equation. In the limit of zero velocity of heat and infinite relaxation time the wave equation result and solution can be obtained by a relativistic coordinate transformation. In the asymptote of zero velocity of heat and zero thermal diffusivity the solution for the dimensionless temperature is a decaying exponential in time. The average temperature of the naval warhead as indicated by UL 1709 test was estimated by using a idealized finite slab, and Leibnitz rule and an analytical expression for the average temperature was obtained using convective boundary condition. The solution is: For1/2>=Bi,<u>=exp(−τ(1/2+sqrt(1/4−Bi*)))ForBi>1/2,<u>=exp(−τ/2)Cos(τsqrt(−1/4+Bi*))) The average temperature is damped oscillatory in time domain. Further the transient temperature profile is represented by an infinite series of decaying exponential in time and Bessel function of the first kind and 0th order. The constant can be obtained from the principle of orthogonality. The bifurcated nature of the exact solution gives rise to the lower limit on the radius to avoid cycling of temperature with respect to time. The exact solution is thus, u=Σ0∝cnJ0(λnX)exp(−τ(1/2−sqrt(1/4−λn2))) and when λn > 1/2 u=Σ0∝cnJ0(λnX)exp(−τ/2Cos(τsqrt(−1/4+λn2)) where, λn=(2.4048+(n−1)π)(√α/τr/R) cn is given by equation (53). The term in the infinite series onward where the contribution is oscillatory is identified.