Tao level 0: relativity of Tao and Tao relative

In 1905, in what can be described with the same words Einstein himself used for the Newton's Principia as the "largest single contribution produced by a single individual in all the history of physics", Einstein introduced a revolutionary new paradigm, laying the foundations of Special Relativity.

ON THE ELECTRODYNAMICS OF MOVING BODIES

By A. EINSTEIN

June 30, 1905

It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the reciprocal
electrodynamic action of a magnet and a conductor. The observable phenomenon
here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. For if the
magnet is in motion and the conductor at rest, there arises in the neighbourhood
of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the
magnet is stationary and the conductor in motion, no electric field arises in the
neighbourhood of the magnet. In the conductor, however, we find an electromotive
force, to which in itself there is no corresponding energy, but which gives
rise—assuming equality of relative motion in the two cases discussed—to electric
currents of the same path and intensity as those produced by the electric
forces in the former case.

Einstein started from the consideration that the classical Newtonian mechanics transformations that bind space and time between inertial reference frames, who have between them a relatively constant speed, without acceleration, were the Galilean transformation, where time and space are absolute. In other words, the laws of Newtonian mechanics are invariant under Galilean transformations, that is co-variate with them, while this is not the case with the laws of classical electromagnetism.
Einstein showed that the correct transformations for electromagnetism that make invariant the Maxwell's field equations, are the Lorentz transformation where, unlike those of Galileo, time and space are no absolute but relative: both depend on the relationship between the relative velocity in relation to that of light between the two systems of reference .
When the Lorentz transformations are applied to the Newtonian mechanics to create relativistic mechanics, a new series of phenomena occurs against the common sense, which is based on the experience of objects which are large (compared to the atomic nucleus) and slow (compared to the speed of light), typical of classical physics, such as length contraction and time dilation measured between two reference systems that travel together to relative velocities close to that of light.
A typical apparent paradox due to the relativity of time is the twin paradox, a typical thought experiment (Gedankenexperiment), an experiment that is considered impossible to perform experimentally, or for its intrinsic structure or due to inadequate technologies, but the result, even conceptually, is significant: of two twins on earth one starts with a spaceship and reach speeds close to that of light. When he returns to earth he finds the other twin has aged, or he is younger. This is a direct consequence of special relativity largely confirmed experimentally. The paradox is that the twin on the ship could be argued that the other twin has left with the earth at the speed of light, so both should be rejuvenated to return. The paradox is only apparent and assumes that the situation of the twins is symmetrical why it is not: only the twin on earth has remained in an inertial frame, while the one on the ship in at least two times, acceleration and deceleration, is was in a non-inertial reference frame.

The extension of relativity to non-inertial systems and the integration of the last part of classical physics, the theory of gravity, was made by Einstein in 1916 as a theory of General_relativity, central to any cosmological model of the Universe.

As speed becomes smaller than the light, Lorentz transformations are reduced to those of Galileo, and Relativistic mechanics reduces to the Newtonian, in which case the Theory of Relativity is considered as an extension of classical physics.