In physics, the theory of relativity means a set of theories based on the principle that the form of the laws of physics must be invariant to the change of the reference system.

The first principle of relativity was formulated by Galileo regarding the invariance of the laws of classical mechanics between inertial reference systems in relative motion, a principle extended by Einstein to the laws of electromagnetism with the special theory of relativity. The development of general relativity and the consequent general covariance principle made it possible to extend the principle of relativity also to non-inertial frames of reference.

Restricted relativity

Special relativity, also called special relativity, was presented by Einstein with the article Zur Elektrodynamik bewegter Körper (On the electrodynamics of bodies in motion) of 1905, to reconcile the Galilean principle of relativity, which includes the principle of the composition of velocities, with the equations of electromagnetic waves, in which the speed of light is expressed as a constant, ie independent of the reference system.

Previously, for this purpose, some theories had been proposed that were based on the existence of a means of propagation of electromagnetic waves, the ether, which had to constitute a privileged reference system; however, no experiment had been able to measure the speed of a body with respect to the ether. In particular, thanks to the Michelson-Morley experiment, it was shown that the speed of light is constant in all directions regardless of the motion of the Earth, not affected by the so-called aether wind. Einstein's theory completely discarded the concept of aether, which is no longer part of physics.

The postulates of special relativity can be stated as follows:

first postulate (principle of relativity): all physical laws are the same in all inertial reference systems;
second postulate (invariance of the speed of light): the speed of light in vacuum has the same value in all inertial reference systems, regardless of the speed of the observer or the source.
It is possible to verify that the Lorentz transformations satisfy the second postulate: if for an observer in an inertial frame the speed of light is c, so it will be for any other observer in an inertial frame moving with respect to its own.

The laws of electromagnetism, in the form of classical electrodynamics, do not change under the Lorentz transformations, and therefore satisfy the principle of relativity.

General relativity

The theory of general relativity was presented as a series of lectures at the Prussian Academy of Sciences, starting on November 25, 1915, after a long phase of elaboration. There is a long-standing controversy over the publication of field equations between the German mathematician David Hilbert and Einstein; however, some documents confidently ascribe Einstein to the fore.

The foundation of general relativity is the assumption, known as the equivalence principle, that an acceleration is locally indistinguishable from the effects of a gravitational field, and therefore that the inertial mass is equal to the gravitational mass. The mathematical tools necessary to develop general relativity were previously introduced by Gregorio Ricci Curbastro (1853-1925) who basically introduced what is now known as tensor calculus.

While proving extremely accurate over time, general relativity developed independently of quantum mechanics and never reconciled with it, even though quantum physics could include special relativity. The limits of general relativity are essentially the treatment of states of matter in which gravitational and quantum interactions come to have the same order of magnitude, up to gravitational singularities. Among the theoretical evolutions proposed, the best known and most investigated are string theory and loop quantum gravitation.

[Wikipedia]