2. The speed of light remains constant in any inertial reference system.
3. The uniform gravitational field is equivalent to the reference frame of uniform acceleration.
At present, several postulate explanations of general relativity are studied in different inertial systems, and the mathematical forms of physical laws obtained from mechanical experiments do not change with the change of reference systems; A physical phenomenon is that different mathematical deduction is made in different inertial systems, but the obtained mathematical expressions are all the same results.
Coordinate transformation is satisfied between two inertial systems, which is not a linear description of space-time uniformity in special relativity. According to Lorentz transformation, the concrete transformation of physical laws between different inertial systems can be obtained, but the influence of gravity on inertial systems should be considered. Because gravity bends time and space, a straight line cannot be regarded as a linear transformation. Considering how to choose a suitable reference frame in the simplest local bending space to eliminate the influence of gravity on the results, it is necessary to modify the special theory of relativity.
This needs to describe the equivalence principle. If we don't consider the equivalence principle (which can be regarded as the feasibility of eliminating local gravity), the decisive conditions of the bending space and how the matter is distributed, and then affect the specific situation of the bending space, we can't explain the physical laws in the inertial system in the same form, because the existence of gravity makes the space where the inertial system is located not necessarily evenly distributed. Even if we choose any two different inertial systems to describe the same physical laws, their mathematical forms are not necessarily the same.
Assuming that the elevator moves in a space without any influence of gravity at a speed v, the observer inside the elevator throws a ball with a mass of m in the horizontal direction, ignoring the material of the ball itself, then the trajectory of the ball is parabola, but the observer inside the elevator does not know the situation outside the elevator. The reason why the ball moves along the parabola is not necessarily that the elevator moves at a uniform speed, but that the elevator is still on a celestial body. The trajectory of the ball may also be because the gravitational field of this celestial body bends the surrounding space, so it can be concluded that although the trajectory of the ball is known, the reason for this result is unknown, so this hypothesis can be described in such language: the uniform gravitational field is equivalent to the reference system of uniform motion (the reference system here is the inertial system).
The mathematical language of general relativity is Riemannian geometry, a mathematical subject based on curved space. It calls curved space Riemann space, and holds that gravity is the geometric effect of curved space. This conclusion should actually be the connection between the two when general relativity is concerned.
The curvature of space is described by curvature, which is a curvature tensor in Riemannian geometry.
This is the description of physical terms in the field of mathematics; Why are there two different terms: curvature space and Riemannian space? First of all, Riemannian space is a general term for large-scale curved space, while curvature space can be considered as a small-scale curved space involving a specific research object. Because the curvature of space and the distribution of matter are interrelated, it is impossible to describe a large-scale curved space in the local inertial system.
There are many substances that affect space bending, but we can choose a space-time region, that is, the inertial system can eliminate the influence of gravity on the research results in the local curvature space, so the effect of local elimination of gravity between this inertial system and other different inertial systems is the same; By accumulating different inertial systems, the influence of gravity can be eliminated. Any one of these inertial systems can be used to describe a wide range of curvature space, and the mathematical language involved in such description is connection: the geometric language that connects the local and the whole can be well understood, that is, the situation of local space can be connected with the curvature space containing this local space.
When studying different physical laws, the application of Riemann geometry will be valuable only if the general theory of relativity involves gravity and the gravitational effect is obvious. Usually, the gravitational effect is very weak, which is described by Newton's law of kinematics, that is, the weak field approximation. At this time, Newton's theory and the physical laws predicted by relativity are the same.
The gravity field equation, which is the core of general relativity, is the connection between the tensor of bending space, the tensor of gauge and the tensor of energy and momentum, and the connection between the local and the whole in Riemannian geometry. The coordinate selection of inertial system in curvature space is not necessarily linear, but there are similarities in expression. Due to the symmetry of tensor, the metric tensor describing the spatial range of curvature is related to the large-scale bending space. If a point is selected in a small-scale curvature space, its gravitational effect is related to the gravitational effect of the gravitational source that affects the trajectory of this point in a large-scale curved space. The gravitational effect of particles in curvature space determines its own material distribution, and the gravitational source determines the trajectory of particles.
If the motion of the particle happens to be within the critical range of the gravitational source, the gravitational source is selected as the research object, and the motion of the particle is the curvature space determined by the gravitational source. Contact is the connection between particles in the critical range and the source of gravity, that is, the connection between locality and range.