{"id":623,"date":"2018-11-12T05:58:11","date_gmt":"2018-11-12T05:58:11","guid":{"rendered":"http:\/\/phyp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=623"},"modified":"2019-04-29T06:47:18","modified_gmt":"2019-04-29T06:47:18","slug":"special-theory-of-relativity","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp01\/chapter\/special-theory-of-relativity\/","title":{"rendered":"Special Theory of Relativity"},"content":{"raw":"
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  1. Introduction<\/strong><\/li>\r\n<\/ol>\r\n \r\n

    In Newtonian world view space and time are independent absolute entities. The Newton\u2019s Laws of motion are invariant under Galilean transformations when we go from one inertial frame to another which is moving with a uniform velocity with respect to the one another. The Galilean transformations are given by . \u00a0and \u00a0are the position vectors measured in the unprimed and primed initial frames which are moving with a relative velocity \u00a0with respect to each other. In Newtonian frame work time is independent of the reference frame. Maxwell\u2019s equations of electro\u2013magnetism however, do not satisfy the principle of Galilean relativity. Maxwell\u2019s equations predicted that the speed of light in vacuum is a universal constant and is equal to C. If this is true in one coordinate system, it clearly will not be true in another coordinate system moving with a uniform velocity and defined by the Gallilean transformations. The pioneering attempts for the resolution of the problem of relativity in electrodynamics and mechanics were made by Lorentz and Poincare. The problem was finally resolved by Einstein in 1905 in the form of Postulates of Special Theory of Relativity namely,<\/p>\r\n \r\n

    (i) The Laws of physics are invariant in all inertial frames.<\/p>\r\n

    (ii) The velocity of light in free space is a universal constant independent of the frame of reference.<\/span><\/p>\r\n \r\n

    In Einstein\u2019s world view space and time are still absolute entities but they are not independent. They form a four\u2013dimensional Minkowski space.<\/p>\r\n\r\n

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    1. Lorentz Transformations<\/strong><\/li>\r\n<\/ol>\r\n \r\n

      Lorentz transformations have the fundamental property of keeping the velocity of light constant in all inertial frames which means that<\/p>\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n

      The matrix tensor has the following property:<\/p>\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n

      and we see that differentiation w.r.t. contravariant component of the coordinate vector transforms as a component of a covariant vector operator.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\nCentre of Mass (CM) Frame<\/strong>\r\n\r\n \r\n

      It is more convenient to consider a scattering process in the CM frame, in which the CM is at rest and therefore the particles 1 and 2 approach each other with equal and opposite momenta and after scattering travel in opposite directions with equal momenta.<\/p>\r\n \r\n\r\n\"\"\r\n\r\nNow\r\n\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n

      Can also be expressed as<\/p>\r\n\"\"\r\n

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      1. Summary:<\/strong><\/li>\r\n<\/ol>\r\n