In the general theory of relativity the four-dimensional space-time described the accelerated motion or moves in a gravitational field of a mass body, from the perspective of integral geometry, although it is a curved Riemannian geometric space, but for any instantaneous position of the moving mass body, there is a local Flat Space of Riemannian geometric space. The local Flat Space is a Mincowski space in which the inertial coordinate system can be used in the local small area. Between the proper coordinate systems of two interacting moving masses, or between a series of follow-up proper coordinate systems experienced by a mass body moving in any way, there must be a coordinate transformation relationship similar to the traditional special theory of relativity. However, they have an important difference: In these instantaneous local inertial systems, the speed of light is no longer the constant c of vacuum, the effect of gravitational field or acceleration on the speed of light is the same as that of a medium with a dielectric constant of ε and a permeability of μ. Using the special theory of relativity with variable speed of light that the author has established can discuss relevant relativity physics issues in these instantaneous local inertial systems. This article uses the special theory of relativity with variable speed of light to infer the functional relationship between a moving mass and the change of speed. In addition to obtaining the traditional continuous increasing function relationship, a step function relationship with stepped discontinuous changes is also obtained. At the same speed, the mass can have two values, such as a ladder upgrade one level; the same mass can be matched with two different speeds, such as one step extension forward on the same step stair. From the perspective of the increase in speed, the mass is stagnant on the step platform (the speed increases, the mass does not change), and it jumps in the step up ladder (the speed does not change, the mass has a jump change). This obviously incorporates the main image of quantum theory into the theory of relativity, which is the result that all physics researchers care about and expect.

Figure 1

This preprint is available for download as a PDF.

There is **NO** Competing Interest.

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Posted 07 May, 2021

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Posted 07 May, 2021

###### No community comments so far

In the general theory of relativity the four-dimensional space-time described the accelerated motion or moves in a gravitational field of a mass body, from the perspective of integral geometry, although it is a curved Riemannian geometric space, but for any instantaneous position of the moving mass body, there is a local Flat Space of Riemannian geometric space. The local Flat Space is a Mincowski space in which the inertial coordinate system can be used in the local small area. Between the proper coordinate systems of two interacting moving masses, or between a series of follow-up proper coordinate systems experienced by a mass body moving in any way, there must be a coordinate transformation relationship similar to the traditional special theory of relativity. However, they have an important difference: In these instantaneous local inertial systems, the speed of light is no longer the constant c of vacuum, the effect of gravitational field or acceleration on the speed of light is the same as that of a medium with a dielectric constant of ε and a permeability of μ. Using the special theory of relativity with variable speed of light that the author has established can discuss relevant relativity physics issues in these instantaneous local inertial systems. This article uses the special theory of relativity with variable speed of light to infer the functional relationship between a moving mass and the change of speed. In addition to obtaining the traditional continuous increasing function relationship, a step function relationship with stepped discontinuous changes is also obtained. At the same speed, the mass can have two values, such as a ladder upgrade one level; the same mass can be matched with two different speeds, such as one step extension forward on the same step stair. From the perspective of the increase in speed, the mass is stagnant on the step platform (the speed increases, the mass does not change), and it jumps in the step up ladder (the speed does not change, the mass has a jump change). This obviously incorporates the main image of quantum theory into the theory of relativity, which is the result that all physics researchers care about and expect.

Figure 1

This preprint is available for download as a PDF.

There is **NO** Competing Interest.

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