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Novel Relativity Theories of Synthetic Aperture Radar
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
The principle of relativity commonly involves dual interrelated theories through Albert Einstein: special relativity and general relativity. Special relativity applies to fundamental particles and their interactions, describing all their physical phenomena barring gravity. General relativity, however, describes the regulation of gravitation and its relation to different forces of nature. It implements to the cosmological and astrophysical realm, which includes astronomy.
Special relativity
Published in Andrew Norton, Dynamic Fields and Waves, 2019
When most people hear the words ‘Einstein’ and ‘special relativity’, if they think of anything it is probably the most famous equation in all of physics: E = mc2, which describes the equivalence between mass and energy. So you may be wondering why this book concludes with a chapter about special relativity, when the rest of it has been about Dynamic fields and waves such as are used to describe electricity and magnetism. The reason is that Einstein’s first scientific paper describing his theory, in 1905, was entitled ‘Zur Electrodynamik bewegter Korper’ (‘On the electrodynamics of moving bodies’, Annalen der Physik, 17, p. 891; Figure 4.3). In it he showed that Maxwell’s equations obeyed the so-called principle of relativity, provided that a new way of transforming between different frames of reference was used and that the concepts and laws of mechanics are suitably altered. Maxwell’s equations of electromagnetism are therefore already in accord with Einstein’s special theory of relativity, and the demonstration of this will form a suitable finale to this book.
Stoichiometry
Published in Franco Battaglia, Thomas F. George, Understanding Molecules, 2018
Franco Battaglia, Thomas F. George
where c is the speed of light in vacuum (whose value, reported in Table B1, is by definition, an exact value, meaning that any updating into the measured speed of light amounts to an updating on the length of the meter, the unit of length). Hence, upon the formation of a nucleus from its nucleons, some of the mass has been transformed into energy and delivered outside the nuclear system. The equivalence between mass and energy is a consequence of the theory of Special Relativity, established by A. Einstein at the beginning of the last century. The mass of a nucleus is smaller than the mass of the separated nucleons, a circumstance which has been experimentally confirmed to be in agreement with Eq. (2.1).
The limits of Riemann solutions to the relativistic van der Waals fluid
Published in Applicable Analysis, 2021
Thus, the first goal of this paper is to solve the Riemann problem for the relativistic van der Waals fluid (1), (2). According to the principle of special relativity, the velocity of relativistic fluid should be less than c, the speed of light. Thus, the physically relevant region of solution to the relativistic van der Waals fluid (1) and (2) in this paper is which is obviously quite different from that of the isothermal and polytropic gas. In the region , we consider the following Riemann initial data for (1) and (2), where and are arbitrary constants. In fact, the study of Riemann problem for relativistic flow plays a vital role in the field of mathematics and physics as well as in engineering. By means of the Lorentz transformation, the specific expression of the shock wave is formulated and the geometric properties of rarefaction wave and shock wave curves are analyzed. Then, by the method of analyzing in the phase plane, we establish the existence and uniqueness of Riemann solutions with five different structures. See Section 3 below.
The Sagnac effect and the role of simultaneity in relativity theory
Published in Journal of Modern Optics, 2021
Gianfranco Spavieri, George T. Gillies, Espen Gaarder Haug
In conclusion, by adopting Einstein synchronization, for the circular Sagnac effect we find the same difficulties and inconsistencies that emerge in the interpretation of the linear Sagnac effect considered in the previous section. Considering that two different synchronization procedures can be deemed to be physically equivalent if both interpret physical reality equally well and coherently, an immediate consequence is that Einstein synchronization is not equivalent to absolute synchronization, as proved independently in [5]. It is not that Einstein synchronization cannot be applied to a rotating platform or to an inertial frame. Einstein synchronization can be formally applied to both the circular and linear Sagnac effects. However, in both cases it fails to provide a coherent physical interpretation because, if the local light speed is c along the length (or ) of the whole contour, the expected result is , in contrast with observation. The theoretical result agrees with observation if the local light speed is c along an open section only of the whole contour, as shown for both the linear and circular effect. Thus, the bottom line is that a coherent interpretation of the Sagnac effect favours the ‘natural’ absolute synchronization and simultaneity, as shown also by Lee [23] for special relativity in cylindrical spacetime.
Inhomogeneous wave equation, Liénard-Wiechert potentials, and Hertzian dipoles in Weber electrodynamics
Published in Electromagnetics, 2022
Notably, not only is this force-carrier model compatible with the two postulates of special relativity, Maxwell’s equations and wave Equation (106), it can also explain the specific elliptic form of the Weber force (62). Furthermore, this model offers new opportunities for interpreting quantum effects due to its field quantization. Unfortunately, little investigation has been conducted on the consequences of the mechanism postulated here for phenomena outside of classical electrodynamics. However, it is known that one can derive from the Weber force not only magnetism, but likely gravitation and inertial effects as well.3 Therefore, further study of these new ideas may be promising.