Special Theory Of Relativity | V. A. Ugarov

This book is a very comprehensive treatment of the Special Theory of Relativity with all advanced topics treated well.

It is in this book that I first read about the superluminal speeds which are possible and are indeed result of STR. Section 8.1 deals with these phenomena and there are 5 of them discussed here. These are for real and are indeed observed in nature. For example the hot-spot in case of radio jets appeared to move at faster-than-speed-of-light. The easiest one which you can indeed do is to take a torch and make a spot on the wall, there is no limit on how fast the spot can travel. Let us see what Ugarov has to say on this topic:

Let us place a searchlight at the origin of coordinates and start rotating it at the angular velocity $latex \Omega$. Let us circumscribe a stationary sphere of radius $latex c$ around the origin. Then the light spot will run along the surface of this sphere at the linear velocity $latex v = \Omega c$. This velocity can exceed the velocity of light. The example of such a beam is provided by a rotating pulsar. The light spot of the Crab Nebula pulsar runs along the Earth surface at the velocity equal approximately to $latex 10^{22} m/s$. But as in the previous cases no signal is transmitted at such a velocity. As a matter of fact, every point of a screen (the Earth) receives a new portion of light energy from a searchlight (pulsar), but not from a neighbouring point of the screen. Therefore, it is impossible to transmit information from one point of the screen to another.

The 4-forms, electrodynamics, transformations are discussed with substantial emphasis on the physical meaning. These kind of discussions make this book a wonderful resource to learn.

The book was translated from the Russian by Yuri Atanov and was first published by Mir in 1979.