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- W2613587978 abstract "Chapter 6 starts the more advanced part of the book. The concept of 4-vectors and their dot product are introduced and used to define the general Lorentz transformation using matrices. With the help of Appendix B , the chapter extends the two-dimensional Lorentz transformations to the full four-dimensional Lorentz boosts. The general transformation of the coordinates of a four-dimensional event (its time and the three coordinates of its location) is derived as the building block of other 4-vectors. The general relativistic law of addition of velocities is an immediate consequence of this transformation. Aberration of light is introduced in a new light by deriving the formulas from the general relativistic law of addition of velocities. General Doppler formula and global positioning systems are discussed. The notions of 4-velocity and 4-momentum are introduced next and the general Lorentz transformation of energy and momentum 3-vector is derived. The invariant length of the 4-momentum is identified as (mc 2 ) 2 ( m c 2 ) 2 and the idea of independence of mass from velocity is reiterated. Four-acceleration is defined as the derivative of 4-velocity with respect to proper time and used to introduce 4-force and the second law of motion." @default.
- W2613587978 created "2017-05-19" @default.
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- W2613587978 date "2017-01-01" @default.
- W2613587978 modified "2023-09-28" @default.
- W2613587978 title "Relativity in Four Dimensions" @default.
- W2613587978 doi "https://doi.org/10.1016/b978-0-12-810411-8.00006-7" @default.
- W2613587978 hasPublicationYear "2017" @default.
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