The dawn of a new era in physics was prepared by J. Thomson’s discovery of the electron in 1897. It turned out that atoms are not elementary, but are complex systems composed of electrons. An important role in this discovery was played by the study of electric discharges in gases.

In the late 19th and early 20th centuries. H. Lorentz laid the foundations of the electron theory.

At the beginning of the 20th century, it became clear that electrodynamics requires a radical revision of the concepts of space and time, which were the basis of Newton’s classical mechanics. In 1905 Einstein created the private (special) theory of relativity – a new doctrine of space and time. This theory was historically prepared by the works of Lorentz and A. Poincaré.

Experience has shown that the principle of relativity formulated by Galileo, according to which mechanical phenomena proceed equally in all inertial reference systems, is also true for electromagnetic phenomena. Therefore, Maxwell’s equations must not change their form (must be invariant) when passing from one inertial reference frame to another. However, it turned out that this is true only if the transformations of coordinates and time in such a transition are different from the Galilean transformations that are valid in Newtonian mechanics. Lorentz found these transformations (Lorentz transformations), but could not give them a correct interpretation. This was done by Einstein in his private theory of relativity.

The discovery of the private theory of relativity showed the limitations of the mechanical picture of the world. Attempts to reduce electromagnetic processes to mechanical processes in a hypothetical medium-the ether-failed. It became clear that the electromagnetic field is a special form of matter whose behavior does not obey the laws of mechanics.

In 1916 Einstein built the general theory of relativity – the physical theory of space, time and gravitation. This theory marked a new stage in the development of the theory of gravitation.

At the turn of the 19th-20th centuries, before the special theory of relativity had been created, the greatest revolution in the field of physics connected with the appearance and development of the quantum theory had begun.

At the end of the 19th century it became clear that the energy distribution of thermal radiation over the spectrum, derived from the law of classical statistical physics on the uniform distribution of energy in the degrees of freedom, was contrary to experience. It followed from the theory that matter must emit electromagnetic waves at any temperature, lose energy, and cool down to absolute zero, i.e. that thermal equilibrium between matter and radiation was impossible. However, everyday experience contradicted this conclusion. The way out was found in 1900 by M. Planck, who showed that the results of the theory agree with experience, if we assume, in contradiction with classical electrodynamics, that atoms emit electromagnetic energy not continuously, but in separate portions – quanta. The energy of each such quantum is directly proportional to the frequency, and the coefficient of proportionality is the action quantum h = 6.6×10-27 erg×sec, later called Planck’s constant.

In 1905, Einstein extended Planck’s hypothesis, suggesting that the emitted portion of electromagnetic energy also spreads and is absorbed only as a whole, i.e. behaves like a particle (it was later called a photon). On the basis of this hypothesis, Einstein explained the laws of the photoelectric effect, which do not fit into the framework of classical electrodynamics.

By this time E. Rutherford (1911) on the basis of experiments on the scattering of alpha particles by matter discovered the atomic nucleus and built a planetary model of the atom. In the Rutherford atom, the electrons move around the nucleus, just as the planets move around the sun. However, according to Maxwell’s electrodynamics, such an atom is unstable: electrons moving in circular (or elliptical) orbits, experience acceleration and, consequently, must constantly emit electromagnetic waves, lose energy and, gradually approaching the nucleus, in the end (as shown by calculations, in a time of about 10-8 seconds) fall on it. Thus, the stability of atoms and their linear spectra turned out to be inexplicable within the laws of classical F. Bohr found a way out of this difficulty. He postulated that atoms have special stationary states, in which electrons do not emit radiation. Radiation occurs during the transition from one stationary state to another. The discreteness of the energy of the atom was confirmed by the experiments of J. Frank and H. Hertz (1913-14) on the study of collisions of electrons accelerated by an electric field with atoms. For the simplest atom, the hydrogen atom, Bohr constructed a quantitative theory of the radiation spectrum consistent with experience.

At the same period (the end of the 19th-beginning of the 20th centuries) the F. of solids in its modern understanding as the F. of condensed systems with a huge number of particles (~1022-cm-3) began to take shape: F. of the crystal lattice and F. of electrons in crystals, first of all in metals. Later these directions closed on the basis of the quantum theory.