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Vladimir Karapetoff (1944) "The special theory of relativity in hyperbolic functions", Reviews of Modern Physics 16:33–52, Abstract & link to pdf; Lanczos, Cornelius (1949), The Variational Principles of Mechanics, University of Toronto Press, pp. 304– 312 Also used biquaternions. French, Anthony (1968). Special Relativity. W. W. Norton ...
The concept of a "world line" is distinguished from concepts such as an "orbit" or a "trajectory" (e.g., a planet's orbit in space or the trajectory of a car on a road) by inclusion of the dimension time, and typically encompasses a large area of spacetime wherein paths which are straight perceptually are rendered as curves in spacetime to show ...
Let us assume a static, spherically symmetric perfect fluid. The metric components are similar to those for the Schwarzschild metric: [2] = = By the perfect fluid assumption, the stress-energy tensor is diagonal (in the central spherical coordinate system), with eigenvalues of energy density and pressure:
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The solutions to are multi-component spinor fields, and each component satisfies . A remarkable result of spinor solutions is that half of the components describe a particle while the other half describe an antiparticle; in this case the electron and positron. The Dirac equation is now known to apply for all massive spin- 1 / 2 fermions ...
Ludwik Silberstein (May 17, 1872 – January 17, 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework. His textbook The Theory of Relativity was published by Macmillan in 1914 with a second edition, expanded to include general relativity, in 1924.
The intuitive idea of Birkhoff's theorem is that a spherically symmetric gravitational field should be produced by some massive object at the origin; if there were another concentration of mass–energy somewhere else, this would disturb the spherical symmetry, so we can expect the solution to represent an isolated object.