Relativity, Thermodynamics, and Cosmology

November 7, 2016 @ 4:23 am

Relativity, Thermodynamics, and Cosmology

Language: English

Pages: 502

ISBN: 0404202624

Format: PDF / Kindle (mobi) / ePub


This landmark study by a distinguished physicist develops three important themes: a coherent and inclusive account of Einstein’s theory of relativity; the extension of thermodynamics to special and general relativity; and the applications of relativistic mechanics and relativistic thermodynamics in the construction and interpretation of cosmological models.
The first three chapters cover the special theory of relativity, in particular the kinematical, mechanical, and electrodynamic consequences of the two postulates of special relativity. Chapter IV develops the close relationships between special relativity and electromagnetic theory, while Chapter V explores less familiar consequences of the theory, including the effect of relativity in providing a natural starting-point for the energy content of thermodynamic systems.
Chapter VI considers the general theory of relativity together with some of its more elementary applications. Included are the principle of covariance, the principle of equivalence, and the hypothesis of Mach, along with other topics. Chapter VII, on relativistic mechanics, is divided into two parts — general mechanical principles and solutions of the field equations. Chapter VIII discusses relativistic electrodynamics, presenting further extensions to general relativity both for the Lorentz electron theory and for the Minkowski macroscopic theory.
Chapter IX deals with relativistic thermodynamics and considers the extension of thermodynamics from special to general relativity, together with its applications. Finally, in Chapter X, the author takes up the application of relativistic mechanics and relativistic thermodynamics to cosmological models.
Among the important features of this study, which set it apart from older texts on relativity, are the extensions of thermodynamics to general relativity, the material on non-static models of the universe, and the treatment of gravitational interaction of light rays and particles.
Throughout, stress is on the physical nature of assumptions and conclusions and the physical significance of their interconnection, rather than mathematical generality or rigor. Several helpful appendices complete the book, including formulae for vector and tensor analysis, useful constants, and symbols for quantities.

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indicated in the figure, and with a set of clocks distributed at convenient intervals throughout the system and moving with it. The pOBition of any given point in space at which some event occurs can be specified by giving its spatial coordinates x, y, and z with respect to thA axes of system 8, or its coordinates x/, y', and z' with respect to system S'. And the time at which the event occurs can be specified by giving the clock readings tort' in the two systems. For convenience the two systems

c,J(l-u2fc 2) dt' dx' m0 modi = ,J(I-u2fc2)' dx3 mo ds where 2_ (dx)2 (dy)2 (dz)2 dt + dt + dt • u - (28.4) (28.5) Hence we see at once that our fundamental principles of the conservation of the components of momentum m 0 u:r:/~(l-u 2/c 2 ), eto., of mass m0 f.J(l-u 2/c2), and of energy m0 c2/,J(l-u2/c 2) can all of them be obtained for interacting particles by the simple requirement (28.6) where the summation 2 is to be taken over all the particles of the system. This expression is not a

let it be at rest with the same temperature Ta = 1i as the reservoir R1 , and having the energy content and volume Ea and va; and let the first step of the cycle consist in a change to state (b) by the reversible isopiestio absorption of heat from the reservoir R 1 . For the heat Q1 absorbed from the reservoir and the work W1 done by the system we cab. evidently write Ql = Eb-Ea+P(Vb-Va) (70.1) and ~ = p(vb-va)· (70.2) In the second step of the cycle let us change to state (c) by a reversible

energy and momentum has been of great importance in obtaining an insight into mechanics, and we shall not hesitate to employ it in this book. (d) Covariant expression for interval. In the development of the special theory of relativity we have found that the principles of physics can be treated with great effectiveness with the help of a fourdimensional space-time geometry, characterized by the formula for the element of interval (73.1) where x, y, z, and tare our usual spatial and temporal

certain analogy with the appearance of the derivatives of the Newtonian gravitational potential in the older expreBBions for trajectory. This dual character of the fundamental tensor may be recognized by refeiTing to the ten independent quantities g~-'" either as the components of the metrical tensor or as the gravitational potentials in the Einstein theory of gravitation. The dependence of the geometry of space-time and hence also of space itself on gravitation, arising from this dual character

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