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Special relativity
Published in Andrew Norton, Dynamic Fields and Waves, 2019
The correct coordinate transformation was deduced by Einstein in the famous 1905 paper, and is of such importance that it is given a special name — the Lorentz transformation. As noted earlier, the Lorentz transformation was first suggested in 1895 by H. A. Lorentz in connection with his attempt to modify the laws of Maxwell’s electromagnetic theory. It incorporates three basic effects — Lorentz contraction and time dilation, which you have already met, and the relativity of simultaneity, which will be discussed shortly. The Lorentz transformation is the key to a correct understanding of the way length and time measurements transform from one inertial frame to another. It also leads to many other predictions of special relativity, extending beyond our views of space and time to change our views of mass and energy radically, and link electrical and magnetic phenomena.
Transformations
Published in Jamal T. Manassah, Elementary Mathematical and Computational Tools For Electrical and Computer Engineers Using Matlab®, 2017
Einstein’s theory of special relativity studies the relationship of the dynamics of a system, if described in two coordinate systems moving with constant speed from each other. The theory of special relativity does not assume, as classical mechanics does, that there exists an absolute time common to all coordinate systems. It associates with each coordinate system a four-dimensional space (three space coordinates and one time coordinate). The theory of special relativity associates a space–time transformation to go between two coordinate systems moving uniformly with respect to each other. Each real point event (e.g., the arrival of a light flash on a screen) will be measured in both systems. If we distinguish by primes the data of the second observer from those of the first, then the first observer will ascribe to the event the coordinates (x, y, z, t), while the second observer will ascribe to it the coordinates (x′, y′, z′, t′); that is, there is no absolute time. The Lorentz transformation gives the rules for going from one coordinate system to the other.
Review of Effective Medium Theory and Parametric Retrieval Techniques of Metamaterials
Published in Pankaj K. Choudhury, Metamaterials, 2021
On a historical timeline, Hendrik Antoon Lorentz, a Dutch physicist in the late 19th century, derived the electromagnetic Lorentz force and Lorentz transformations. He also described, in classical terms, the interaction between atoms and electric fields by indicating the force between an electron and the nucleus of an atom as the spring-like force that follows Hooke’s law. Therefore, an applied electric field creates an oscillating motion in the electron by stretching or compressing the spring-like force. This is called the Lorentz oscillator model [27].
Inhomogeneous wave equation, Liénard-Wiechert potentials, and Hertzian dipoles in Weber electrodynamics
Published in Electromagnetics, 2022
The first principle of relativity (1) is clearly satisfied in Weber-Maxwell electrodynamics because can be interpreted as the relative velocity between the transmitter and receiver and does not depend on any uninvolved observer. This can also be clearly seen in the wave Equation (106). The second postulate (2) is also satisfied without the Lorentz transformation because an observer can principally measure the wave velocity only in his own rest frame. Thus, an observer is always a receiver, because only receivers can receive and measure an electromagnetic wave. If the observer moves with respect to the transmitter, this motion is explicitly considered in the wave Equation (15), and the calculated force for the receiver propagates at speed . If the receiver does not move with respect to the transmitter, then this lack of motion is taken into account by the wave Equation (15), and the propagation speed of the wave is again exactly . Thus, the speed of the receiver with respect to the transmitter is irrelevant because, after the wave Equation (15) is solved, the force travels for the receiver or observer at speed . This can also be clearly seen in the wave Equation (106), because the d’Alembert operator determines the wave velocity as exactly , independent of the relative velocity between receiver and transmitter.
Matterwave interferometric velocimetry of cold Rb atoms
Published in Journal of Modern Optics, 2018
Max Carey, Mohammad Belal, Matthew Himsworth, James Bateman, Tim Freegarde
so and , from which we determine that the optical phase must at any point track the atomic phase and depend spatially upon . The phase of the optical field must thus have the form characteristic of a travelling plane wave. The rate of variation in optical phase at the position of the atom is again simply the Doppler shift; while we have here considered Galilean transformation between the apparatus and atomic frames, equivalent results may be obtained by relativistic Lorentz transformation [9].
Toward Special-Relativity-on-a-Chip: analogue of Einstein velocity addition using optical add-drop filter (OADF)
Published in Journal of Modern Optics, 2019
Benjamin B. Dingel, Aria Buenaventura, Annelle R. Chua, Nathaniel J. C. Libatique
On the other hand, the expression for two nonparallel velocities given by Equation (2) has a complicated form (26, 27). Consequently, it is hard to understand the inner mechanism of the velocity addition law and cannot provide immediate physical insights. Furthermore, it is obtained only after lengthy derivation from the Lorentz transformation (21, 22) where the terms V1 and v2 are velocity vectors, and the symbols ‘’ and ‘.’ are cross-product and dot-product multiplications, respectively. Later, we will discuss alternative formulation to EVA to simplify the derivation.