A short journey from quarks to the universe. Selected solutions (Q535928)

This book is the first volume of a newly inaugurated collection (Springer Briefs in Physics) and is the outcome of several lectures delivered over the years by the author to a broad audience. It aims to cover some of the main chapters of modern physics by combining short expositions of the basic ideas and worked examples that obviously require a minimum background knowledge. In order to cope with such an ambitious task on less than 150 pages the author adopts as a main tool the dimensional analysis which allows a short-cut derivation of several quantitative results appearing at the classical or quantum level. The method of dimensional analysis is outlined in Chapter 5 and consists in selecting ``relevant'' independent variables and parameters of a certain physical object or system and then finds the most general combination of these quantities having the same dimensions (i.e., same powers of length, time and mass) as the physical quantity under analysis (emitted energy per unit time, photon scattering cross-section, ionization potential, Hubble constant, average kinetic energy of a planet atmosphere, etc.). For example, in section 12.4, the Schwarzschild radius \(R_S\) of a black hole of mass \(M\) is derived by the following dimensional argumentation: It is expected that this function contains the gravitational constant \(G\), since black holes are entirely controlled by gravitation, the velocity of light \(c\), since these exotic objects are governed by extreme relativistic laws, and Planck's constant \(\hbar\), since in black holes quantum mechanical effects play a non-negligible role. Consequently \(R_S=\eta G M/c^2\), and the numerical factor \(\eta\) is simply popped out as from a magician's hat, the reader being therefore stimulated to find in other textbooks the justification of \(\eta\)'s value. This typology is similar for other discussed cases.