The history of physics: the construction of the theory of relativity

In his electronic theory, Lorentz formulated the fundamentals of electrodynamics of moving media and proved that the laws of electromagnetism are the same in all inertial reference frames.

The most general transformations of spatial coordinates and time found by him in 1904 — the so—called Lorentz transformations – played an important role in the preparation of the theory of relativity, which was formulated in 1905 by A. Einstein in the work “On the electrodynamics of moving media”.

This theory replaced the classical views on space and time, which clearly contradicted the facts when it came to movements, where the speed of bodies could no longer be neglected in comparison with the speed of light.

Maxwell’s equations did not change their form during Lorentz transformations, but the formulas of classical mechanics turned out to be non-invariant, so Lorentz’s theory did not solve the differences between classical mechanics and Maxwell’s laws.

Experiments of Fizeau and Michelson

The French physicist Hippolyte Louis Fizeau (1819-1896), who was the first to determine the speed of light in terrestrial conditions, established the influence of the motion

of the medium on the speed of light propagation by measuring in 1851 the speed of light in moving water (Fizeau’s experiment), this experience proved that light is partially captured by a moving medium.
The American experimental physicist Albert Abraham Michelson (1852-1931) in 1881 conducted experiments using a special interferometer made by him, which denied the existence of ether.

In 1887 , Michelson together with Edward William Morley (1838-1923) conducted new experiments, which also gave a negative result about the existence of ether.

Special theory of relativity

The emergence of the special theory of relativity was associated with attempts to overcome the difficulties encountered in constructing the electrodynamics of moving media.

The difficulty was that each of the known phenomena (the phenomenon of stellar aberration, Fizeau’s experience, Michelson’s experience) and the experiments that were used to determine the speed of light in moving bodies could, with some simple assumptions, be easily explained within the framework of existing theories.

For example, to explain the phenomenon of stellar aberration, it was enough to assume that the ether is not captured by moving bodies (Jung), to explain the experience of Physicists — to make an assumption about the partial capture of ether, and to explain the negative result of Michelson’s experience — to use the hypothesis of the English physicist and mathematician George Gabriel Stokes (1819-1903) about the complete capture of ether by the Earth.

Due to the incompatibility of these hypotheses , it became it is obvious that it is necessary to move from classical physics to some new physical theory in which all optical phenomena in moving media could be explained from a single point of view without the use of contradictory hypotheses. There have been other attempts to explain phenomena in moving bodies without changing the basic physical concepts.

Source: Unsplash License, Math equations on a chalk board

The Irish scientist George Fitzgerald and a little later, but independently, Lorenz attempted to explain the negative result of Michelson’s experiment using the hypothesis of Lorentz contraction, according to which moving bodies undergo a contraction in the direction of motion, and it is the greater the higher the speed of the body. However, the Fitzgerald-Lorenz idea seemed too artificial, proposed specifically for one particular phenomenon, it was not supported by any theoretical evidence.

So, the artificiality of all these attempts prompted the idea of the need to abandon Newtonian ideas about space and time and the concept of ether, which were included in the electromagnetic picture of the world. Einstein’s merit lay precisely in the fact that he decisively broke with these ideas and introduced new concepts corresponding to it in electrodynamics.

Unlike all his contemporaries, Einstein saw in the negative result not an accidental difficulty, but a manifestation of a general law of nature, according to which it is impossible to detect a rectilinear uniform and progressive motion of the laboratory relative to the ether. A. Einstein formulated two basic postulates — principles that are the starting points of the theory of relativity. In accordance with the principle of relativity, all physical processes in an inertial system do not depend on the speed of its motion relative to other bodies or systems.

According to the second principle, the speed of light in a vacuum is constant and does not depend on the speed of the light source. A. Einstein formulated new laws of motion that generalized Newton’s laws of motion and reduced to these laws only in the case of very small velocities of bodies.

In the same 1905 supplement “To the electrodynamics of moving bodies”, which was published under the title “Does the inertia of a body depend on the energy content in it?”, Einstein expressed the relationship between mass and energy with his famous equation E = mc2. This formula retains its value at any speeds, if only by m we mean the inert mass of the body, which depends on the speed and rest mass.

The rest mass corresponds to the rest energy.

The presence of this energy made it possible to consider any body as a potential reservoir of energy, and the law of proportionality of mass and energy implied the possibility of the transition of energy associated with matter into energy associated with radiation. This formed the basis of all nuclear physics.
The first physicist who pointed out the significance of the law of mass—energy coupling to explain the deviation of atomic masses from integer values was the French physicist Paul Langevin (1872-1946).

In 1913, he revealed the physical meaning of the mass-energy ratio and for the first time expressed the ideas that make up the essence of modern nuclear power – the ideas about the mass defect in nuclear transformations.

German physicist and mathematician Hermann Minkowski (1864-1909) devoted his scientific activity to the development of the ideas of relativity theory, who formulated the mathematical theory of physical processes in 1907-1908. In a four-dimensional space. In this theory, the Lorentz transformations received a visual geometric interpretation as a rotation transformation of a four-dimensional coordinate system, which played an important role in completing the construction of the special theory of relativity.

A. Einstein also developed the general theory of relativity, which is based on a combination of the principle of equivalence of heavy and inert masses and the principle of relativity. This theory is a relativistic theory of gravity. Einstein proved that in the presence of bodies that they form an attraction, the metric of space and time changes. The Russian mathematician N. I. Lobachevsky (1792-1856) in his memoirs “On the principles of Geometry” (1826-1830) expressed the idea that the metric of real space can have such deviations, and tried to determine them.

In the general theory of relativity, the reason for this deviation is revealed, its mathematical expression is established, and, in particular, it is proved that such deviations in the metric of space cannot be considered separately from the corresponding changes in time. This means that the theory of space, time and gravity shows their inextricable relationship.

Verification and confirmation of the theory

The new laws of attraction lead to consequences that can be tested experimentally. Since energy has mass, it can be concluded from here that attraction must act on energy. As a result, the beam that passes through the gravitational field must be deflected. Experiments carried out during the total eclipses of the Sun in 1919. And 1922 confirmed the general theory of relativity in quantitative terms.

The second proof of the general theory of relativity was obtained by observing the motion of the planets.
One of the consequences of the general theory of relativity is that the trajectory of the planet should slowly rotate around the Sun. Astronomers noticed the displacement of the perihelion of Mercury and finally explained it in 1916. By the German physicist and astronomer Karl Schwarzschild (1873-1916).

The third proof of the general theory of relativity was the confirmation of the shift predicted by the theory. In the direction of the red color of the spectral emission lines of stars in 1925. Now the theory of relativity is generally accepted.

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