By R. Katz
ISBN-10: 0442387083
ISBN-13: 9780442387082
Read Online or Download Introduction to the Special Theory of Relativity PDF
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Extra info for Introduction to the Special Theory of Relativity
Sample text
Mv2• As demanded by the correspondence principle, our two expressions for kinetic energy agree in the limit of low velocities. 5) + me2 In Eq. 5, E and are often expressed in MeV, so that a convenient unit of momentum is MeV Ie. Incidentally, Eq. 5 is often remembered through the analogue of a right triangle, in which E is the hypotenuse. It is remarkable that the relativistic relationship between energy and momentum is valid for all particles-even those of zero mass, like neutrinos or photons.
First we must station a set of observers everywhere in the laboratory frame. Of course, if the motion is along the x axis, we only need observers along the " axis. Then we instruct these observers to note their coordinates and synchronize their clocks. If we wish to measure the length of a moving rod, we instruct the observers to note whether or not an end of the rod was at their coordinate position at a predetermined time. The difference in the coordinates of the two observers who are coincident with an end of the rod is defined as the length of the moving rod.
9c (a) b' ,~I~ -~ Q- ~~ c' (') Proper ( ) Loboratory frome from. (b) FIG. 2 Headlight efled [After V. F. Weisskopf, Physics Today 13, 24 (1960)]. the laboratory frame (the unprimed frame) with speed V. Radiation emitted at an angle 8' with respect to the x' axis will be observed to make an angle 8 with respect to the x axis. We find this angle by noting that V'z = c cos 8' and V", = c cos 8, and substituting these values into Eq. 3) On Fig. 9, using Eq. 3. 9 and 8 ± 25°, and so on. The rays are strongly concentrated in the forward direction with very little radiation coming off in the backward direction, as seen in the laboratory.