One hundred years

Creativity is the residue of time wasted

This interesting quotation by Albert Einstein linked him with Henri Poincaré not only with the contribution of French math to special relativity, but also for the utility of the creative leisure. Indeed Poincaré told that, after some fruitless attempts to sole a particularly difficult mathematical problem, he decided to go away for a geological excursion, in this way stimulating conditions to resolve the problem!
But the most important reason in order to write something about Einstein is the general relativity birthday, that was presented by Einstein on the 25th november 1915 at the Prussian Accademy of Sciences.

Annus mirabilis

The seeds of the Einstein's success were sown in 1905: at that time Einstein worked at the patent office in Bern and published a series of important results in physics, including doctoral theses and articles.
The first result is the explanation of the photoelectric effect, for which he was awarded by the Nobel Prize in Physics in 1921: when a metal is struck against a given electromagnetic radiation, it emits in response some electrons, also called photoelectrons. Their energies are quantized, so these electrons are emitted at specific energies, linked to those of incident radiation. And the first satisfactory explanation for this phenomenon was dued by Albert Einstein with an article published in Annalen der Physik⁽³⁾, the same journal where they are published, a few years before, two articles by Max Planck^{(9, 10)} that were inspiration for Einstein's paper.
The demonstration of the atomic nature of matter and the existence of the molecules is contained in the doctoral dissertation at the University of Zurich, A new determination of molecular dimensions⁽⁴⁾. In the thesis, his work most mentioned ⁽¹⁵⁾, but also the less well known, Einstein derived the hydrodynamic relationship between the coefficient of viscosity of a liquid with or without particles in suspension. Also he derived a new formula for the diffusion constant, and finally, using experimental data, he obtained a value for the Avogadro constant and the size of the molecules of sugar, made ​​by improving a method proposed in 1865 by Loschmidt⁽¹⁵⁾.

The relativity theory

Special and general relativity are certainly the best known Albert Einstein's theories. The story of these theories started with the special relativity, based on two fundamental ideas: the first⁽⁵⁾ reconciles the laws of electromagnetism with the mechanics. The stimulus for the work comes from an interesting problem associated with the second principle of relativity:

The speed of light is the same in any inertial reference system

The problem is obvious: to determine the contribution of the electromagnetic field to the mass of a moving particle. In practice it is to answer this question that Einstein, starting from the previous work of Lorentz⁽¹³⁾ and Poincaré⁽¹⁴⁾, expressed the famous second principle of relativity⁽⁵⁾.
The second paper⁽⁶⁾ is that of the famous equation \[E = mc^2\] better known as the equivalence of mass and energy.
Also Max Planck contributed to the success of these two works, first with a paper⁽¹¹⁾ which in fact confirmed Einstein's ideas on the mass of the electron, so with a reformulation of the original equation above⁽¹²⁾.

In the trail of Mach

But today I would celebrate the general relativity. In some sense the special relativity is an electromagnetic theory, meaning that arises in response to the questions posed by Maxwell's Theory to the physics, but is primarily a theory about the motion, in particular straight, free from the influence of any external field, in particularly from that of the gravitational field. This, however, is one of the most important fields for the universe: if the electromagnetic force holding together atoms, molecules, and growing the way down to the planets, they are linked to the star around which revolve thanks to the gravitational field generated by star itself (to be picky gravitation is a mutual force), and from there it comes the need to understand how, in point of view introduced by special relativity, it had to deal with this fundamental field.
Einstein begins, then, this new path in 1907 with an article in which he proposed the principle of equivalence of inertial mass and gravitational mass⁽⁷⁾ (inspired by the work of Ernst Mach), where gravitational mass is the quantity that we measure on the scales, while for inertial mass it means the one which opposes the motion. As Einstein himself wrote in The meaning of relativity, the principle of equivalence

(...) is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body.⁽²⁾

A further generalization of the principle of equivalence arrives in 1911 when Einstein observes how, from inside, a box that moves uniformly accelerated motion is indistinguishable from a box stops in a gravitational field⁽⁸⁾.
The last ingredient to complete the picture is the curvature of spacetime generated by the mass of any body immersed in it. In fact it was the latter challenge is resolved in 1915 and celebrated today. In order to solve this last point, Einstein needed the non-euclidean geometry discovered by Bernhard Riemann and the mathematical language to treat these types of idea. An important contribution was dued by Marcel Grossmann, who introduced him Riemann's ideas, and by Tullio Levi-Civita, who suggested him to use his tensor calculus. In this way Einstein's mathematical efforts were crowned on 25th November, 1915, when he presented at the Prussian Academy of Sciences, his conclusive result: \[R _{\ mu \ nu} - \ frac {1}{2 R g}_{\ mu \ nu} = T_{\ mu \ nu}\] These equations imply the existence of a curvature of spacetime, or a deformation induced by the presence of the heavenly bodies.
The existence of this curvature was verified by Arthur Eddington after a few years: on 6th November, 1919, the British astronomer, during a meeting of the Royal Society and the Royal Astronomical Society, showed the results of the observations took place during the total solar eclipse of 29th May of that year: and it was a great success for Albert Einstein and for science.

---

(3) Einstein, A. (1905). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt Annalen der Physik, 322 (6), 132-148 DOI: 10.1002/andp.19053220607 (Wikisource)
(4) Einstein, A. (1905). A new determination of molecular dimensions (pdf)
(5) Einstein, A. (1905). Zur Elektrodynamik bewegter Körper Annalen der Physik, 322 (10), 891-921 DOI: 10.1002/andp.19053221004 (pdf - english translation)
(6) Einstein, A. (1905). Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen der Physik, 323 (13), 639-641 DOI: 10.1002/andp.19053231314 (english translation)
(7) Einstein, A. (1908). Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen, Jahrb. Radioaktiv. Elektron., 1907, vol. 4, p. 411 (pdf)
(8) Einstein, A. (1911). Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes Annalen der Physik, 340 (10), 898-908 DOI: 10.1002/andp.19113401005

---

(9) Planck, M. (1900). Ueber irreversible Strahlungsvorgänge Annalen der Physik, 306 (1), 69-122 DOI: 10.1002/andp.19003060105
(10) Planck, M. (1901). Ueber das Gesetz der Energieverteilung im Normalspectrum Annalen der Physik, 309 (3), 553-563 DOI: 10.1002/andp.19013090310
(11) Planck, Max (1906), "Die Kaufmannschen Messungen der Ablenkbarkeit der β-Strahlen in ihrer Bedeutung für die Dynamik der Elektronen", Physikalische Zeitschrift 7: 753–761 (english translation)
(12) Planck, M. (1908). Zur dynamik bewegter systeme. Annalen der Physik, 331(6), 1-34. (english translation)

---

(13) Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity smaller than that of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences 6: 809–831 (wikisource)
(14) Poincaré M.H. (1906). Sur la dynamique de l’électron, Rendiconti del Circolo matematico di Palermo, 21 (1) 129-175. DOI: http://dx.doi.org/10.1007/bf03013466 (wikisource - english translation)
(15) Straumann, N. (2005). On Einstein's Doctoral Thesis. arXiv:physics/0504201.