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Special relativity
Published in Andrew Norton, Dynamic Fields and Waves, 2019
Einstein’s special theory of relativity is one of the greatest achievements of physics. The theory holds enormous appeal for a wide audience, and many people who have never studied physics at least know of its existence. To physicists, the appeal of special relativity comes largely from its logic, internal consistency and agreement with experiment. The theory demands that we throw away our prejudices, and put our trust in a few simple experiments and our own powers of reasoning. Once we have accepted Einstein’s postulates, all else follows inevitably; we are carried along on an irresistible tidal wave of logic. If we sometimes feel uncomfortable with the results, that’s just too bad; they are unavoidable once the postulates have been accepted, and they are supported by a wealth of experimental evidence.
Miscellaneous Algorithms
Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017
Einstein's general theory of relativity is the geometrical theory published between 1915 and 1916 (Einstein, 1915, 1916), which also explains the distortion of space-time by mass, energy, and momentum. According to the general theory of relativity (also called Einstein's equivalence principle), the curved geometry of space-time can be interpreted as the geometrical distribution of gravity. That is, the gravitational force observed locally by two reference frames, one in a space free from gravitational fields and one with uniform acceleration, are physically equivalent. According to Einstein's equivalence principle, the result of a local nongravitational experiment in an inertial frame of reference is independent of its own velocity or location. This means, in other words, the effects of gravity are exactly equivalent to the effects of acceleration.
Spherical metrics in general relativity
Published in Maricel Agop, Ioan Merches, Operational Procedures Describing Physical Systems, 2018
This property allows one to establish a local equivalence between the inertial frames situated in gravitational field and those noninertial. In other words, an inertial reference system is equivalent to a certain kind of gravitational field. For example, a uniformly accelerated frame is equivalent to a constant and homogeneous gravitational field [13]. On the contrary, a non-uniformly accelerated frame moving in a straight line is equivalent to a homogeneous, but variable gravitational field. All these facts lead to a postulate which in general theory of relativity is known as the equivalence principle.
Estimation and interpretation of equilibrium scour depth around circular bridge piers by using optimized XGBoost and SHAP
Published in Engineering Applications of Computational Fluid Mechanics, 2023
Nasrin Eini, Sayed M. Bateni, Changhyun Jun, Essam Heggy, Shahab S. Band
RPSO is a variant of the PSO, which was introduced by Roder et al. (2020). We introduce the theory of relativity to illustrate the RPSO. The theory of relativity is one of the most significant theories in physics, proposed by Albert Einstein in 1916. Conventional mechanics’ theories were implemented to numerically model the phenomena detected by Einstein. One of the most famous theories pertains to momentum, which can be calculated in three-dimensional coordinates as: where M is the momentum, v = (vx, vy, vz) and m are the velocity and mass of a body, respectively. is the Lorentz factor, which is defined as follows: where |v| denotes the size of vector v, and c is the speed of light.