Waves in Special Relativity
The electromagnetic waves, which are inevitably studied in Special Relativity, do not exhaust all types of waves. Indeed, as it has been remarked already in many cases, Special Relativity is a theory of all physical phenomena including electromagnetism. Therefore within Special Relativity one must be able to deal with e.g. thermal waves, acoustic waves etc. In this section we discuss the generic concept of a wave in Special Relativity. Waves are rather difficult to understand properly, even in Newtonian Physics where one has a direct sensory observation of space, time and motion. Moreover even there when the subject is approached at a slightly higher level demands rather heavy mathematical formalism and one gradually creates the opinion that somewhere Physics is lost and mathematics prevail. The situation is even worse in Special Relativity where one is obliged to work with a geometric concept of motion right from the beginning. Therefore in order to study the waves in Special Relativity it is best to reformulate the Newtonian wave theory in a geometric rather than in the standard formalism. The subject of relativistic waves is vast and in this book we aim to deal only with the basic elements of it, in fact we shall take the subject up to the point that one can apply properly optics and understand the deBroglie waves, which are required for a proper understanding of Schröndinger equation and consequently of Quantum Mechanics.