The Marvelous Theory of Special and General Relativity

On May 29, 1919, the English astronomer Sir Arthur Eddington must have jumped when, while observing a total eclipse of the sun, discovered that the man, who four years earlier had published the controversial theory of General Relativity, had been right. We are talking about one of the most famous physicists of history: Albert Einstein. His career as a great scientist had begun in 1905 when, by a half-known employee of the patent office in Bern as he was, he published his first two articles regarding the Special Relativity. I am going to introduce the reader to the restricted and general Theory, which is the theme of this work, without too many scientific claims. However this topic can not be fully grasped without the mathematical and physical bases gained in high school. I will try to explain the restricted and general Theory with an innovative approach, different from many other educational treatises, which often neglect the mathematical aspects necessary for a correct understanding of this subject. On the contrary I am going to teach this topic through rigorous mathematical demonstrations, graphs and diagrams. I have paid particular attention to the idea of Relativity, already present in Galileo's observations. Furthermore I have exposed the main works of James Clerk Maxwell, Albert Abraham Michelson, Edward Morley, and Hendrik Antoon Lorentz in order to reach the absolutely innovative idea postulated by the Theory of Special Relativity. Once immersed in this new theory, in the second chapter I analyzed the concepts about the times dilation and the distances contraction from an analytical point of view concluding with a solution to this fascinating paradoxes. Subsequently, the present work focuses on the duality between mass-energy (E = mc2) and gravitational mass-inertial mass. In order to a better understanding of the theory effects there are references to "mental experiments" and Minkowsky' s diagram. The themes of the four-dimensional space-time curvature, the exposure of the famous Einstein Field Equations, the Gravitational Redshift, the Deflection of Light, the Precession of Mercury Perihelion and the Gravitational Waves will be addressed in the discussion of General Relativity. In conclusion, we can't forget that Albert Einstein, besides being a famous physicist, was very active in various cultural fields, therefore becoming one of the most important thinkers of the last century. For this reason I chose to quote his most and curious aphorisms interluding them between chapters and paragraphs. I'm thankful to all the people who have supported me while writing of this book; as well as to whoever should like to propose any improvements or suggestions with the hope that my work can be useful to all those who are approaching the study of the fascinating Theory of Relativity.