Mass energy and momentum in the special relativity with variable speed of light

Article Keywords: mass and energy-momentum vector in space-time four-dimensional space, the ontological collocation of mass, energy, and momentum, the conversion relationship of the three collocation types of mass, energy and momentum between the inertial system S and S’, the upgrade and downgrade of the complete special relativity system Abstract On the basis of establishing the special theory of relativity with variable speed of light and obtaining the step function relationship between mass and speed, this article further seeks the proper collocations of mass, energy and momentum allowed by the "ontology" of moving masses which are in various stages of motion properties or in different physical environments. Three ontology collocation types are obtained. If we consider the basic fact that the lower the energy, the more stable it is, the real physical world ranges from astrophysics issues such as white dwarfs, red giants, and celestial space speeds, to the various light and heavy elementary particles existence, combination and performance ， which qualitative knowledge can all be derived from the "ontology collocation ". Two of these three types of collocations are derived from the mass-velocity step function relationship contented of quantum properties, so all the quantum phenomena of modern physics will not be obliterated. It is hoped that the modern physics knowledge accumulated in the laboratory and the scattered various theories will be explained under the dominance of a classic theory. The article also deduced the conversion relationship between the inertial system S and S’ of the three collocation types of mass, energy and momentum of the moving mass. Derive the upgrade and downgrade law of the complete special relativity system, this also greatly expands the way to understand modern physics from the theory of relativity.


Introduction
The momentum ) , , ( . This is the basic content of relativistic mechanics. [1] The force on a mass body moving at speed u  is equal to the derivative of its momentum with respect to = 2 can be obtained. This is the famous formula of the theory of relativity that introduced mankind into the nuclear energy era. However, in the face of the vast and colorful knowledge market of modern atomic physics and nuclear physics, the current theory of relativity can only take this formula from time to time in and out, and nothing else. In fact, the proper collocation of mass, energy and momentum allowed by the "ontology" of a moving mass in various stages of motion or in different physical environments should not only be the one situation given by the traditional special theory of relativity. This situation has dragged on for more than a century because another jumping step function relationship between the mass of the moving mass and the speed has not been discovered; Moreover, outside the atom in the case of 0   c and c c   , the step function solution is very close to the traditional solution, even if the physical phenomenon of the step function solution exists objectively, it is difficult to be discovered. The author has established the special theory of relativity with variable speed of light [2] 、 [3] , and the step function solution of the mass-velocity relationship has been obtained [4] , that can collude inside and outside the atom , and the theory of relativity is no longer only take the single form of one formula going when enter the inside of the atom.
In the traditional special theory of relativity, there is only one type of fourdimensional vector formed by energy and momentum. Now, because in the special theory of relativity with variable speed of light, there are two independent and noncoexisting function relationships between mass and speed [4] . A moving mass body due to its own acceleration, or enters and exits the medium, or is in the gravitational field, its mass can realistically exist two numerical values of large or small for the same speed； however for the same speed its energy can realistically exist three numerical values of large, medium and small, the small value can even be as small as negative value. Therefore, when energy and momentum are realistically combined into energymomentum four-dimensional vectors suitable for mutual conversion between any twocoordinate systems, there are three different types of collocations. This article gives out in detail three types of reasonable collocations of mass, momentum, and energy in the 'ontology' that conform to the existence of the moving mass, two of them are derived from the mass-velocity step function relationship of the content of quantum properties, so all quantum phenomena in modern physics will not be obliterated. On this basis, the conversion relationship between the three types of collocation types of mass, energy and momentum of the moving mass body in the inertial system and ′ is further derived, and the upgrade and downgrade law of the complete special relativity system is obtained. It has greatly enriched the basic account of how the mass, energy, and momentum of the moving mass body in the real physical world can ontologically be matched existence and transformed.
2 Three sets of collocation types of mass, energy and momentum in the four-dimension space Now starting from the two independent and non-coexisting function relationships between mass and speed, we will discuss three reasonable combinations of mass, energy and momentum in the 'ontology' that conform to the existence of the moving mass. The so-called "ontology" refers to the "ontology" that grasps all physical quantities based on the transformation between any two coordinate systems. Specifically, it means that certain physical quantities are actually matched to form vectors, tensors..., etc., suitable for mutual conversion between any two-coordinate systems. The 'ontology' of vectors, tensors... should not be changed, because of the difference in the observation coordinate system. So that the laws of physics linking these physical quantities do not differ depending on the coordinate system.
In [4], we have obtained two independent and non-coexistent function relations of the mass of the moving body with the speed. One of them is the traditional continuous increasing function relationship: = ( ) = 0 √ 1− 2 2 .Under the assumption that the rest mass is 0 and the known speed , the combination of mass, energy and momentum of a moving mass body can be written as a set of basic formulas in the inertial system : There are also three values for energy: It can be calculated: When < 2 < , then When < 2 < 2 , then 2 E does not exist.
The curve of the energy E versus the square of velocity 2 u in the three sets of collocation types is shown in (Fig. 1), and the changes in the three energy values of can be clearly seen.
( Fig. 1) The three sets of collocation types (1), (2) and (3) can be expressed as: It should be noted that ( Fig. 1) does not indicate that the mass of the three types of 'ontology collocation' also changes in this way. The mass of the two types (1) and (3) is less than the mass of type (2) for any speed-this is a key. Look at the energy comparison in (Fig. 1), it varies with the speed: when the velocity square 2 is less than the Q value, the energy of type (2) 2 is the smallest; 2 is between R and S, (2) type has the largest energy 2 , and it rises more sharply when it is close to S; when the velocity square 2 is greater than the Q value, the energy of type (3) 3 is the smallest; when 2 crosses the Q point and R point, the energy of (2) type increases rapidly and surpasses type (3) and (1) respectively, at this time, type (2) is most likely to change to other types. This is even more an important key. A universal fact in the materialistic world is that the lower the energy, the more stable the state. Therefore, a moving mass body with a moving speed square 2 far below the Q value must generally exist as type (2); the moving mass bodies with the moving speed square 2 far above S must be of type (3); only when 2 is around close to the three values of Q, R, S and between QS, the moving mass bodies can likely change from (2) type to other types, and its masses change from large to small. The mass changes from large to small causes the split of the moving mass. For example, when the velocity square 2 u of type (2) moving mass body increases to a value equivalent to point R, its energy has reached the intersection of the two types of energy curves (1) and (2), and it is easy to automatically "degenerate" into (1) Type. This can explain the natural disintegration of radioactive elements and the emergence of "new stars" that suddenly increase in brightness in the distant horizon. Although the values of a series of physical quantities of "ontological collocation "involved are very different.
There are quite a few definite reasons to explain many real physical phenomena based on the details provided in the three sets of collocation types of mass, energy and momentum. For example: (A) (1) and (2)  transition between L m and S m is completely allowed by the relativity with variable speed of light, and has the characteristics of "ontology", and is neither "split" or "merge", nor "diminish small" or "grow up"; (E) The jump conversion of L P  , M P  and S P  also meets the requirements of the relativity with variable speed of light, and there is no need to pursue the reason of 'force', because in the theory of relativity, "force" is not a real physical quantity that can be included in the "ontological collocation"; (F) Special attention should be paid to (3) the negative energy instinctively equipped by the mass body; etc. These are all the results of the special theory of relativity that allows c c   between S and S. It is hoped that all the modern physics knowledge accumulated in the laboratory and the observation of the universe, and the various theories that have been scattered about this knowledge, will be explained under the dominance of a classic theory of relativity, In the end, it will be able to explain all the physical problems of the interior of the atom, the interior of the nucleus, nucleons, elementary particles and cosmic rays, thermonuclear subgroups, as well as white dwarfs, red giants, variable stars, supernovae, and earth cores. If in understanding and explaining the internal structure of atomic nuclei and the decay and annihilation phenomena of various elementary particles in the laboratory, the "great unification theory" that attempts to unify all the interacting "forces" in nature is still faltering and hopeless, then you might as well throw away Develop hypotheses about various "forces" and explore how the mass, energy, and momentum of the moving mass body in the real physical world can "ontologically" collocation exist and transform. Isn't it possible that a mass body with the same static mass 0 m exhibits several elementary particles with masses between and ? A closer look at the conversion of the four-dimension energy-momentum vector between S and Swill certainly help to understand these problems. Now use the three collocation types of mass, energy and momentum of the moving mass body to find the conversion relationship between them in the inertial system S and S. The relative motion of the inertial system S and Sis as in the previous literature [1], [2], [3] .
For the first type collocation given by (1) and (1'), the transformation of the fourdimension energy-momentum vector composed of it between S and S, even in the case of c c   , is the same as the traditional special theory of relativity. There is no big difference in the calculation process. Using the formula of velocity transformation given in [1], the transformation between can be obtained, , thus the transformation relationship between mass, momentum and energy obtained : The symmetry relationship can also be introduced: Compared with the coordinate transformation relationship between the inertial system S and S given in [1], it can be seen that the transformation between and ( ′ , ′ , ′ , ′ ) . If "  "means equivalent,"  "means transformation, and "1" is added to the lower left corner to indicate the first collocation type given by equation (1), then the above corresponding transformation relationship can be expressed as: Undeniable, this " " represents "equivalent" indeed shows that P  and E in formula (1) coexist with the four-dimensional space and time dominated by Lorentz's transformation formula, and they are true. It is easy to calculate that the square of the absolute value of this energy-momentum vector ) , , ,  [4]. We did not make any other assumptions about m0, such as the issue of whether m0 is divisible or not. "Undividable" is against the correct philosophical point of view. Therefore, m0 can be a combined system of many smaller mass bodies, and the sum of its static mass is not equal to m0; the difference between its positive and negative can be expressed as various kinds of energy in the system. This ' difference ' is always there. Unable to know for sure. The value of m0 can only be determined from the value of the relevant quantity that can be observed on the left side of equation (4b), and it is equal in S and S, and its existence is a universal constant. But at the same time, the analysis combination of m0 does not have the eternal certainty of 'one hoe to the end'.
For the second type collocation given in (2) and (2'), the transformation of the four-dimension energy-momentum vector composed of it between S and S, as long as it is assumed to replace c and c with respectively in the Lorentz transformation formula , all calculations from (4) to (4b) above can be obtained in the same way, and the results are as follows: The symmetric relationship can also be written one by one: can be expressed as: For simplicity, the three components of momentum ( , , )are written as , and ) , , (  z  y  x is written as r .
If in these results, let w c c , that is, the speed is replaced by the same ratio; then: These are just the transformation relations (4) between S and Sof the first collocation of mass, momentum, and energy given by equation (1). This leads to a very important conclusion: if the related speed in S and Sis converted according to the same proportion of the upper limit speed, the second type of collocation of mass, momentum and energy given by equation (2) exists between S and Sin the special relativity of the upper limit respectively, just like the first type of collocation given by equation (1) exists between S and Sin the special relativity of the upper limit speed c and c in the same way. The so-called "same" means that the speed is converted according to the same ratio, so this ratio is also used for the upper limit speed. The above equivalent conversion relationship can be illustrated as: As pointed out when defining the inertial coordinate system in [2], a necessary condition for the existence of an inertial coordinate system is that there is a fixed upper limit in the observed speed group, that is, the upper limit speed; this upper limit speed may not necessarily be c, the speed of light in vacuum, and the application of special relativity is thus broadened. When facing real physical problems, there is no light on the scene, but only, for example, β-rays appearing as the upper limit speed. In this problem, the special theory of relativity conforming to the four-dimension vector formed by the combination of P  2 and E 2 can still be used correctly. It is reasonable that is a negative value, because speed is a vector originally, and it has the meaning of positive and negative; the so-called upper limit speed of course refers to its absolute value. The above results show that the special theory of relativity starts with c and c as the upper limit speed, and exists according to the ratio decreasing (or reducing) orderly. Face ( Figure.1), take the situation of the speed replaced before the schematic diagram (5b) to see, and consider that the smaller the energy of the moving mass is, the more stable it is, then the original special theory of relativity is applied to the right of point R on the E1 curve . The special theory of relativity after the first descending is applied to the left of point R on the E2 curve.
It is easy to prove that the square of the absolute value of the energy-momentum vector in the four-dimension space formed by the collocation of P 