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- W4386234461 abstract "The principle of relativity requires that the laws of physics have the same mathematical expression in all inertial coordinate systems. When applied to special relativity, this “law of laws” requires that the mathematical expressions for the laws of physics be Lorentz covariant. Therefore, when formulating physics in the framework of special relativity, all the known laws of physics should be inspected; those that satisfy this requirement remain laws, while those that do not must be reformed until they meet this criterion. First, we inspect Maxwell’s theory of electromagnetism. Maxwell’s equations are endowed with Lorentz covarianceLorentz covariance (which can be seen more explicitly in its 4-dimensional formulation, see Sect. 6.6 ), and thus can be integrated into the framework of special relativity without being reformed. This is in fact not strange at all, since one of the important reasons special relativity came about is that Maxwell’s theory contradicts the notion of pre-relativity spacetime. Next, we will inspect Newton’s laws of motion. As an example, consider the law of conservation of momentum. As we pointed out at the beginning of Sect. 6.3 , if the definition of momentum $$vec {p}=mvec {u}$$ is still used, then conservation of momentum violates Lorentz covariance and must be modified. By redefining momentum as $$vec {p}=mvec {u}(1-u^2)^{-1/2}$$ , the law of conservation of momentum is now Lorentz covariant, making it a valid law in the framework of special relativity. Thirdly, let us inspect Newton’s theory of universal gravity. The basic equation in Newton’s theory of gravity is Poisson’s equation $$nabla ^2phi =4pi rho $$ , which indicates the relation between the gravitational potentialGravitational potential $$phi $$ and the mass density $$rho $$ ." @default.
- W4386234461 created "2023-08-29" @default.
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- W4386234461 date "2023-01-01" @default.
- W4386234461 modified "2023-09-30" @default.
- W4386234461 title "Foundations of General Relativity" @default.
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- W4386234461 doi "https://doi.org/10.1007/978-981-99-0022-0_7" @default.
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