From Special Relativity to Feynman Diagrams.pdf

Changes in the reference frame of an observer can be

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Changes in the reference frame of an observer can be of different kinds: spatial translations, rotations, or any change in its state of motion. As we shall see in the sequel, the latter transformations are the most relevant as far as the implications on the description of the physical world are concerned. R. D’Auria and M. Trigiante, From Special Relativity to Feynman Diagrams , 1 UNITEXT, DOI: 10.1007/978-88-470-1504-3_1, © Springer-Verlag Italia 2012

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2 1 Special Relativity The simplest relative motion is of course the uniform rectilinear motion or inertial motion , and the requirement that the physical laws be independent of the particular inertial frame means that the theory satisfies the requirements of the principle of relativity only as far as inertial frames are concerned. We recall that inertial frames are those in which the Galilean principle of inertia holds, and that, given any inertial frame such as, for instance, the one attached to the center of mass of the solar system, with axes directed towards fixed stars (the fixed star system ), all other inertial frames are in relative rectilinear uniform motion with respect to it. In the following two chapters we shall refrain from considering accelerated (and thus non-inertial) frames of reference, restricting ourselves to the analysis of the implications of the principle of relativity only as far as inertial frames are concerned, which is the main subject of the special theory of relativity . The extension of the principle of relativity to any kind of relative motion between observers, that is to accelerated reference frames, however, has a very deep impact on our ideas of space, time and matter and leads to a beautiful new interpretation of the gravitational force as a manifestation of the geometry of four-dimensional space–time. This analysis, which is the subject of Einstein’s general theory of rel- ativity , requires, for its understanding, a solid knowledge of differential geometry and goes beyond the scope of this book; in Chap. 3 , however, we shall give a short introduction to general relativity by discussing the principle of equivalence and tidal forces. Furthermore an intuitive picture of the four-dimensional geometry of space– time and its relation to gravitation will be outlined. 1.1.1 Galilean Relativity in Classical Mechanics In order to verify whether a theory satisfies the principle of relativity we need to know the transformation laws relating the measures of physical quantities obtained by different observers. When describing the motion of a system of bodies with respect to a reference frame all the quantities we need can be expressed in terms of length, time and mass. 1 It is therefore sufficient to find the transformation laws for these fundamental quantities.
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