Understanding Special and General Relativity (PDF)

The English astronomer Sir Arthur Eddington must have jumped when, on May 29, 1919, intent on observing a total eclipse of the sun, he discovered that the man, who four years earlier had published the controversial theory of General Relativity, he was right. Albert Einstein, one of the most famous physicists in history, whose career as a great scientist began in 1905 when, by a half-known employee of the patent office in Bern, he published his first two articles on Restricted Relativity. It is without too many scientific claims that I am going to introduce the reader to the Theory of Relativity Restricted and General which is the theme of this work which however can not be fully grasped without the fundamental mathematical and physical skills that are learned in a high school. With an innovative approach compared to many other educational treatises on the subject, which often neglect the mathematical aspects necessary for a correct understanding of the phenomenon, I will try to deal with the issues, so as to understand mainly the concepts, through rigorous mathematical demonstrations or 'aid of graphs and diagrams. After a brief but indispensable historical and biographical introduction on Albert Einstein I paid particular attention to the thought of Relativity already present in Galileo's observations and I exposed the fundamental works of James Clerk Maxwell, Albert Abraham Michelson, Edward Morley, and Hendrik Antoon Lorentz to reach to the absolutely innovative idea postulated by the Theory of Special Relativity. Once immersed in the new theory, in the second chapter, I analyzed analytically the concepts on the dilation of the times and the contraction of the distances until the solution of the always fascinating paradoxes. Subsequently, the present work focuses on the mass-energy duality (E = mc2) and gravitational mass-inertial mass. There is no lack of "mental experiments" and the use of the Minkowsky diagram in order to better understand the effects of the theory. In the discussion on General Relativity, the themes of the four-dimensional space-time curvature will be addressed, the exposure of the famous Einstein Field Equations, the Gravitational Redshift, the Deflection of Light, the Precession of the Perielion of Mercury and the Gravitational Waves. In conclusion, we can not forget that Albert Einstein, besides being a famous physicist, is very active in various fields of culture becoming one of the most important thinkers of the last century for whom the most cited and curious aphorisms of the illustrious interlude between chapters and paragraphs. I thank all those who have been close to me during the writing of this paper and with the hope of having set up the work so that it can be useful to all those who approach the study of the fascinating Theory of Relativity I am grateful to now who will want to propose improvements or any suggestions.