The provisions of this principle apply to the study of gravitational and inertial forces. The equivalence principle that we are considering is a heuristic principle that was applied by the great Albert Einstein when he was developing his greatest scientific discovery - the general theory of relativity.
In its most general form, Einstein’s equivalence principle states that the forces of gravitational interaction between objects are directly proportional to the gravitational mass of the body, and the inertia forces of the same body, in this case, are proportional to the inert mass of the body. And in the case when both body masses are equal, then it is not possible to determine which of the forces acts on this body.
To prove these conclusions, Einstein used such an experiment. It is necessary to mentally imagine that two bodies are in the elevator. This elevator is infinitely far from the gravitating bodies acting on it and moves with acceleration. In this case, inertia will act on all the bodies that are in the elevator , and they will have a certain weight.
If the elevator is stationary, then the bodies inside it will also have weight, and this means that all mechanical transformations in both elevators will occur equally. Einstein extended this effect to all phenomena of mechanics, and even to all physics, then the scientist's conclusions supplemented the fundamental principles of equivalence.
Today, some researchers believe that the principle of equivalence can be considered as fundamental in the whole theory of relativity, and therefore, the gravitational field is a non-inertial reference system. However, such a statement can be considered reliable only partially. The fact is that each non-inertial system in A. Einstein's special theory of relativity is based on the usual linear space-time. In the general theory, which includes the metric concept of gravity, space-time is curved. This discrepancy is explained by the fact that metric concepts do not contain global inertial systems at all. Here the principle of equivalence can manifest itself only if we neglect the curvature itself.
It is also advisable to differentiate between the weak and strong versions of the manifestation of the equivalence principle, the difference of which is that at small distances between objects there will not be any special differences in the actions of the laws of nature, regardless of which reference frame these objects are in.
A. Einstein formulated the fundamental foundations of this theory in 1907. When considering the significance of this principle on the scale of physics as a whole, it should be said that Einstein’s discovery continues and develops Galileo’s statement that all bodies, regardless of their mass, acquire accelerations in the gravitational field. This position allowed us to conclude that the inert mass is equivalent. Later this equivalence was measured metrically, with accuracy up to the 12th digit.
It is important to note that the use of Einstein's discovery is effective only for small spatial volumes, because only under such conditions can gravity be considered a constant value.
Einstein extended his principle of equivalence to all reference frames in a state of free fall, and also developed the concept of a local system in more detail. This was necessary because the Universe has a gravitational field everywhere, and gravity is variable - it differs from point to point, because each point has its own parametric characteristics. Therefore, these systems, according to Einstein, should not be identified with inertial ones, which violates Newton’s first law.