# R^{3}=T^{2} -- Space-time Expression of Conservation of Momentum

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–– Space-time Expression of Conservation of Momentum (I)Question What is the mass of matter? What is the coefficient of gravitation in the Universal gravitation? Are there any formulas for them? What kind of relationship is there between Newton’s Law of Universal gravitation and the third Motion Law of Kepler? Why was Einstein able to use the idea of equalization of inertial force and gravitational force in the solar system by making use of the equalization of inertial mass and gravitational mass? Answers to these questions will show there is a basic rule which hides in the third motion law of Kepler on which the classical physics was founded. Thus we come to the overall root-- (The third motion law of Kepler) Now every physicist is trying to find out the formula about the mass of matter. The formula should be some kind of functions between space and time, in which the one nearest to the eased value is a kind of relation of function of a complex variable. However, there are too many defined coefficients in this formula, so it is so complex that it can not let people clearly understand that space and time are real factors that decide the mass of matter. People have doubted the gravitational coefficient much earlier. People of all nations show great interest in the different numerical values tested in different dimensions. Someone in the Australian Queens land University has already tested out a much Larger gravitational coefficient value G=6.73(unit)which is a distinguished one compared with the original value 6.672(unit). Nevertheless, people usually carry out the research work about mass of matter and gravitational coefficient separately. The two jobs are not connected, and even fewer people observe them from the point of the establishment of Newton’s classical physics. Through new investigation on the original data of the third motion law left by Tycho and Sorted out by Kepler, after reanalysis on the data, I find out these data coincide with today’s theory and also find out the origin of these questions. (II)Data of Kepler and their resolutions Kepler takes the distance between the sun and the Earth as one astronomical unit and the period (year) needed when the Earth finishes revolving round the Sun for one cycle as the time unit. The third notion Law was produced after comparison among different Stars. His data are in chart 1. Chart 1 Number Name of Star Period(T) Distance(R) R 1 Mercury 0.241 0.387 0.058 0.058 2 Mars 0.615 0.723 0.378 0.378 3 The Earth 1.000 1.000 1.000 1.000 4 Mars 1.881 1.524 3.54 3.54 5 Jupiter 11.862 5.203 140.7 140.85 6 Saturn 29.457 9.539 867.7 867.98 and ––Periodic Law 1 now we resolve it into two parts or Here –– angular velocity It is just the Second motion Law of Kepler. Within the Same period of time, the area Swept by the radius vector of each planet on its orbit plane is the same. In order to find out and prove the meaning of this resolution further, we Separate chart 1 into two parts, too. One part is R2/T(chart 2)the other part is T/R(chart 3) Chart 2 Chart 3 Number Number 1 0.6214 1 0.6227 2 0.8605 2 0.8506 3 1.0000 3 1.0000 4 1.2347 4 1.2342 5 2.2822 5 2.2798 6 3.0889 6 3.0880 Then Let (III)Illustrate G= According to Newton’s Law of universal gravitation And according to the equivalence principle in the General Relativity, we can always find a reference frame when the gravitational force is made equal to the inertial force, so there will be At this time we may take as the Centripetal acceleration Since gravitational force mass equals inertial mass, we delete and rewrite the left as M, then Or –– is right the result of multiplication between the gravitational coefficient and the mass of sun, which is the appearance of Kepler’s third motion Law in the gravitational force and which is equal to the result of multiplication of two “Kepler factors”. Then charge the form of So when This is just the rotating velocity of a particle in the General Relativity when it rotates in the gravitational field, as its center. So is proved to be in existence. Actually, this kind of illustration is taking the branch for the root. This is because there exists a kind of “regression”phenomenon in the development of science. So far, Newton’s Theory and Relativity are well accepted by People of the world. To “regress”here requires you to use the old theory to prove the “new one”. This is a kind of circling method worthy of people’s thought. However, can we go directly without circling? Because in the field of Astronomy, data in (Chart 2)and (Chart 3)Can be deemed as equal, we can reach a very important conclusion by proving the multiplication of two factors on the left side of is 1. -- and also ; and thus comes the equations set. There are two groups of roots for it Since M is not the velocity in I, and is a function of practically detected dimension, so root of group two exists. General Relativity proves that can be understood as velocity, and another “Kepler factor”R2/T is right M. Because in Newton’s Law of Universal Gravitation, there is already a relation about the mass and the square of Linear Special distance, we may call as “area mass” --(M) So Simultaneously --(G) (IV)The appearance of equation (M) and (G) in Law of Universal Gravitation, General Relativity and the third motion Law of Kepler is not incidental. 1. If we understand the gravitational coefficient G=R/T as today’s “velocity”we can find out the right hand of the following equation --(M) is right the expression for the Law of conservation of momentum. That is to say, the expression of the third Law of Kepler R3=T3 is also the space – time expression for the theory of Conservation of momentum, which could therefore explain the moving rule of the six planets found at that time is the action of the principle of conservation. Now this can be seen as Up till now another three planets have been found. There are nine planets in total. They are still within this rule. Since the above Laws coincide with relativity theory, so they still “control”rotating motion of all planets in the Solar system around the sun. Certainly, both Kepler Law and Relativity theory have drawn their conclusions on the basis that all planets were taken as “particles”in the solar system Errors could be caused by this if there is any. 2. Now Let’s take a look at the”Phenomenon of Laws” If expression(M)exists there can always be force F is the force in Newton’s Second Law Then This is the formula for gravitation. This result completely accords with Kepler Law, Newton’s Law and Relativity theory. What dose this “phenomenon of laws” imply? a. the necessity and meaning of resolving Kepler’s third motion Law into two individual “Kepler factors” b. This”phenomenon of Laws”Shows expression has theoretical root nature about gravitation, thus we name equation “primitive equation” c. From “phenomenon of Laws expression could be proved to be in accordance with Relativity theory, but Relativity theory did not conclude that gravitational coefficient is .”Space –– time time” is not velocity any more. d. Either Newton’s theories or Relativity theory, they all originated from the same origin –– Kepler’s theories. e. Although there exists difference between Newton and Einstein as to their views and explanations about natural phenomenon, “Simple mathematical deduction”can prove there is something in common between them except their individuality. f. it can prove with strength that Newton’s inertial theory is included in Einstein’s acceleration theory. g. “phenomenon of laws”has a strict sense of direction. it can only multiply R/T with F and then divide it with F, then gravitational equation could be obtained by transposition toward the M/R direction. The result of an opposite moving is If seeing this with the method of “dimensional analysis”, the above expression might be when When doing dimensional analysis, the unit of m and M could be deleted from this expression. Then Since finally we get --F The Law of conservation of impulse can be obtained from the opposite direction. That is 1=F*T, which can right prove Law of conservation of momentum exists simultaneously with Law of conservation of impulse. In fact, when we carry out this to, strictly speaking, date back to the expression of Kepler’s motion Laws, there might not exist abstract coefficients in the equations about inertial force, gravitational force, mass, gravitational coefficient, Relativity etc. when the exact coefficient could be shown, we would have arrived at relational expressions of absolute dimension way of expression 1 .Therefore, all relations given above totally belong to dimensional relation, such as gravitational force. No longer will exist a G=6.672(unit)I. force F is not an indispensable element in the”primitive equation”. For example, we simplify gravitational force from the already existing gravitational world, and let it have This illustrates: (1) we have escaped from the old stage and arrived at a new stage with no mass (m and M are eliminated by each other) (2) the elimination of Shows that a stage with no Linearity and complete space(R3)has been achieved. (3) the arrival at a rotation ,which is the only one of its kind, is the stage of force. The knowledge about (1);(2) and (3) shows only black hole is similar to this stage It is the origin of the solar system, or perhaps just the opposite, the final settling or disappearing place of the solar system. 1. Since the black hole (white hole) stage reached by (h) right provides us with an excellent way to know various stages of the world as well as the nature of those notion bodies in these stages. For example, this question to us––when the black body particle radiates, its energy has both corpuscular property and adulatory property,. Or in other words, what is radiated are particles or waves? This method equips us with an ability to identify this. We are sure that Planck is right in (Formula for black body radiation) In which, E is the”unit”energy radiated by the black body. h is Planck constant and is frequency. The basic idea of this method can be understood as dating all the motion things back to their original (or dead) state, that means condition there will be. (include M) Condition on the earth will be Because the Earth originates from it, So its ( Call it as original point of the space) State is “Primitive State”, but all the motion things on Earth do not have “Primitive state”. Now Let us analyze Planck formula by using this method. In fact, that is trying to know what is Planck Constant. If h is known, all can be understood either. The key process of this problem is the following. Questions brought forward out of physics are with physical concept, but the solution of these questions almost all depend on mathematical methods. Maths is a kind of pure logical deduction. Under the Condition of Conservation, no physical explanations will be given. So there exists a transition from physics to mathematics, and also a transition from maths back to physics after solutions are reached. At the first Stage, Let Planck formula back to”Primitive State”. Since frequency v equals reciprocal of period In the”primitive state” So This is the nature of Planck constant. it is only a limited part of linear space R, How to understand this Sudden result? We can use another kind of existence to prove the existence in doubt: Since and So and because so This is the well-known”de Broglie wave formula”. So it is obvious that the relation between the black body energon and the. de Broglie wave is”there are particles in waves and there are wares in Particles”. The existence of ware-Particle dualism proves with strength that they are two sides of the same question. Here is wave length. and because Finally from de Broglie wave formula this can be also proved The Second stage is to explain h=R. That is back to the physics Period. From the Simultaneous existence of both Particles and waves, we can see h only represents R a( Limited distance), then Planck constant is the Length of one”wave cell”,but it is a changeable Length, not a fixed Constant (Length), because the other nature of it is adulatory property, till this Length. Because of radiation and material contact, this Length becomes”infinity”,Then the wave cell disappears and Oscillation is gone, too. The above example is used only to explain”method” by identifying energon, but this is not only a method but also it defines a Set of new concepts clearly. (1) force (2) energy We can See that in the Primitive state energy is velocity and this velocity is not Shown in any motion forms of Substance. Actually, our original concept names as Velocity. Now this stage has been Leaped over. This matter is no Longer on the Earth, even no longer in the Solar System. If it is also called as velocity, it can not give explanations we want. We give the mathematical relation–– a name”time-space conversion”and when “Space-time conversion”, all referring to conversions from the denominator state to the numerator State, when moving in the”Positive direction”. In the solar System, if planets are seen as particles, or compared with Son, they can all be seen as particles, then the time-space conversion in the solar system is the time-space conversion of the whole space and the acceleration System t2. That is This kind of time-space conversion is already a”stereoscopic spiral motion”if shown on the moving orbits of particles. When we understand as Kepler second motion Law––the area Swept by the radius vector of stars and Particles Per unit of time. In that case, no doubt this can be understood as the multiplication of these two is”the plane deflection swept by the radius vector”. This can right prove the Planets of the sun do not revolve in the Same orbit plane. The revolution orbits are not in the same Plane, not an enclosed oval plane, but they are moving in the stereoscopic space of spiral shape. Since their moving activity is too slow in the eyes of human beings on Earth, this moving in the spiral space can be approximately seen as a gradual, deflection in an enclosed oval plane. When the deflection completes a cycle, the surface formed by the orbits is an apple-like sphere, the upper and the Lower part of which both dent towards the Center. Since this conversion can also be shown as law of conservation of momentum, we can further know conservation of momentum contains the spiral motion in the stereoscopic space. This is also the root of the saying “geometry and physics are from the same family”. (3) momentum and impulse In the physical textbook of middle school, there is a formula about the equable nature of momentum and impulse which is reasoned out from Newton’s Second Law and kinematics. Why? If we explain this by using general physics, the result can only be achieved by conceptual reasoning. Now, we can achieve this result immediately from the relations in “primitive state” Because So the relation of conservation of momentum Can be Certainly, we have already done experiment to test it on earth. To obtain the result here is meant to point out the universal function and general suitability of the “Primitive state” method. This result is not Limited to the earth, so it is not necessary to define various concepts on earth before achieving this result. Here the result is directly deduced to the state of earth from the “primitive state” after obtaining all relations of concepts on the earth. In is just because we have already known the function of , then we try to prove momentum equals impulse with a specific purpose. It came into being after being known by people on the earth. Once obtaining it with purpose, this can be said to have been deduced to the State of earth. From this we can draw a conclusion, more remote or tiny state can be reached by deduction from this “primitive state”. We do not do this just because we have not known or can not know the relations of things and being there. For instance, because , we can also express gravitational coefficient in various states, but only we can not tell its real content and meaning and also where, on which stage it exists. People on earth call it as “gravitational coefficient. However, in the being of another stage, it has Lost its original content. It will be renamed according to the relations of specific moving objects at different stages.” When we express this as Then show in it, the above formula can be turned into Then we come back to the relation between the earth and the sun again. This is a big event worthy of thinking really! J, the dividing relation is the conversion from the state of denominator to the state of numerator when finishing the conversion of definition at the same time. It is a rotating motion. If we say is the area swept by radius vector it is also the area formed by the rotation of radius vector, because this is the product of multiplication of . Here there exists a rotating angular velocity 1/t, but it is also force in the “black hole”(or white hole). If we say is the volume produced by the deflection of the plane swept by radius vector, then it is also the volume formed by rotation of this plane, because this is the product of multiplication of these two items and in which are two directionally vertical forces. not only has rotating nature in the celestial body motion rules, but also has this nature in the atomic system. Now, we can draw a preliminary conclusion that similar various forces exist in the nucleon motion. k. In order not to disturb the development of physics today definitions which are not necessary to be changed remain the same as before. Name as “Kepler gravitational coefficient factor”, shortened as “gravitational coefficient”. Name as “Kepler area mass factor”, shortened as “mass”. Name as “conservation law of momentum in solar system”. Corresponding to the existence of this “conservation law of momentum in solar system”, there should also exist a “conservation law of impulse in solar system”, and it should be expressed as Supposedly, it should be a rule that describes the overall motion of the solar system in the milky way system. At this time, compared with the milky way system, the solar system can be taken as a particle too. we can not eliminate the possibility that this law also exists in the atomic system. (Five) extension From the very beginning, there is the simultaneous existent problem of gravitational coefficient and mass. They are connected. New we can sec clearly when Kepler discovered “1”, The fates of mass and gravitational coefficient G were decided. This is certainly established only when Limited in the solar system and taking the revolving period of the earth around the sun and the revolving semi diameter as “1”. How to understand the new definition––mass of matter? The motion of an object or particle in the real objective world is always a relative rotation no matter how human beings recognize and explain it. This is the result of human beings long-time experience and observation. It includes the motion of celestial body and nucleon, and is based on “matter”. Matter no matter on which stage is not stationary. Since there is motion, there is velocity. The existence of velocity requires a reference frame be chosen first before the velocity is decided. When adjusted to an immediate reference frame, all moving objects are doing a kind of round or oval-like rotating motion. There is no ideal inertial motion in the world, but accelerating motion. People have believed that the path of light is absolutely straight since long time ago. However, proved by relativity, path of photon in the gravitational field is not straight, too. Since we know from the former chapter, it is necessary to change time into “angular velocity” of the angle of rotation, that is , t is time, but its nature is a kind of force . From this we can see, the reference frame acts all the rotations conducted by the moving objects around the reference frame on! A car is always rotating under the earth gravitation with the center of the earth as reference; the rocket having escaped from the earth is always rotating under the solar gravitation with the sun as reference..., Likewise, a microscopic particle rotates under the gravitational force of nuclear at its various stages. Supposing we took a car as a particle of the earth, when its speed reaches “velocity of light”, Like the moving speed of electron when it centers around the atomic nucleus, then we can believe that all space is occupied by itself within the limit of its moving space. Because at present stage we can only know that velocity of light is absolute velocity and it is not known yet if there exists a larger speed than that. So we say the moving scope of the car is already a “substance”, the space of which can not be occupied by other particles with lower speed than velocity of light. If the moving speed of electron is really the maximum speed in the atom, we can certainly view the atom as materially absolute substance particle. However, actually atoms can be seeped through and their structures can be rearranged. Furthermore, the velocity of electron is not the maximum speed, and when atoms are broken apart, new particles will come out. Their speed might be much higher. There is no substance in nature which is composed of particles which are absolute stationary and closely lined around the nuclear one by one with no motion at all. All we have are substances with particles (planets) at various Layers which keep rotating with the nuclear (stars) as their center. The different basic natures of these substances are caused by or decided by the speed of their planet particles (or the ability to occupy the space). All substances in the world are composed of such microscopic structures. Therefore, the mass of matter is distinguished and decided by the following three factors––the size of space occupied by the particles of the substance; the space-occupying ability of the particles; the number of particles. we call this kind of substance as “relative substance”, and “absolute substance” which is absolutely stationary with inner particles arranged motionless does not exist. Do you want to use scientific method instead of political or military way to occupy a much bigger space than you have now in a real sense? I can tell you this cannot be achieved unless you improve your moving speed in this space and this is the only way out. As far as the present stage is concerned, if you possess the velocity of speed, then yon owns the whole space. Therefore, you are justified in saying: “My substance has extended to the whole space”, or when others point at you, you can say “this is me” if only they point at any part of the space. If you could really do this, you would have a new image and being in this objectives world. When you slow clown your speed out of a certain reason, such as tiredness or preference of the old image instead of the new one, you will return to your original state after your speed has been back to the stage of relatively motionless with the earth or there is only a minor difference between your speed and the limiting velocity. This is the so called “relative substance”. Through the above accounts about the concept of “relative substance”, we know “the innate nature of substance” (Newton’s words) is determined by two elements-one is the space it occupies; the other is its space-occupying ability which is also the moving speed of its satellites. These two elements are right the two factors in the expression about the new concept of mass of matter. -- the Particle moving Linear Space (distance) -- the velocity of the Particle(ability) Because , , So velocity is energy in the “primitive state”. The following way of writing is also ok, by using the “dimensional motion method” found before to restore and because So It can be seen here that the velocity produced is a kind of ability. While the mathematical relation which can express the concept of “relative substance” can decide the product of multiplication of its two elements (two factors also) equals the mass of the “relative substance”. The relation of multiplication between the space occupied by the particle and its moving speed is in accordance with the concept of “relative substance”. The Formula of mass can also be established by begriming from the concept. Then, How to understand the new concept of gravitational coefficient? After we have had the “dimensional motion method”, we can investigate gravitational coefficient by dating back to the primitive state. On the earth, we call it “gravitational coefficient”. Since in the primitive state it is expressed as which is right the expression for energy If taking the gravitational force in solar sys tem as an example, this G is no longer a concept about coefficient, and it is the energy determined by the distance from the center of the sun. So F can be expressed as( ) This gravitational Force F is Part of the whole force , and is the number of percentage that force F takes up in , when this is changed into a rotational motion of a particle with M as its center. This kind of understanding comes from the solar gravitation. If we understand this from the aspect of kinematics, G is the deflecting notation of plane in a stereoscopic helical motion in conservation of momentum. This kind of motion is a sort of geometrical motion in nature. The root of the statement “geometry and physics are of one family” lies in the finding. Before these are found, things are not clear and rather vague. When they are made clear, the indistinct and vague thing will be upgraded and enter the hard-understanding stage “primitive state”. The question will be turned into another stage which is not necessarily a sad thing. As to the question of mass of matter, the former conclusions are drawn on the basis that everything is deemed as a particle. If it is not a particle, then mass of matter should be considered by having the whole space in mind. Here is the complete space, is the linear space. Calling mass of matter in the complete space as “complete mass of matter” which is “the innate nature of matter” in a true sense. We say the division right means “...if you could travel at the speed of light, then the space can be said to be occupied by you, so... you have a new image and a new you in the objective world.” Only when new Larger or smaller space v is occupied can you achieve the necessary conditions to bring new substances into being. New substances come into being after petrol is burned and the mass of petrol is also the mass of new substances. Petrol is transformed into. New substances (Carbon dioxide) Sulphur dioxide hydrogen sulphide and water, etc.) The burning Process is the heated transformation process. Obviously, relation of division is rotational motion from mathematical Point of view. Thus it is also a kind of oscillation with its special “wave length”, “frequency”. Therefore, It is the “density” not “specific gravity” that is important when discovering a very important character of an element in the periodic a Law of Mendeleev. The mathematical expression for the density of an element is Since we have had a new understanding to the concept of mass of matter and the concept of mass is extended. So we know the elements listed in the periodic table of elements are only elements of “one Channel in the composition of the nature, not elements” of “all Channels”. To human bergs, it likes a Channel with visible Light and there are still channels with invisible light which cannot be Seen or felt before or behind it. Therefore periodic table of elements about these channels should also be worked out to make up the all-channel elements together with the periodic table of. This prediction has already been testified to be true by the discovery of the existence of Long-lived substance composed of celestial bodies and the existence of Short-Lived Substance existing among various layers of the inner parts of atoms! The new concept of mass of matter can also explain the existence of “all-channel” elements, which is consistent with the facts. Because the establishment of new concept of mass of matter, now we can correct the “error” which occurs in the former concept of mass of matter. The new concept of mass of matter lays much emphasis on the internal physical characters of particles and the product of multiplication of the space occupied in the internal composition of the substance and the capacity to occupy space. Mass of matter has nothing to do with the external things. The former concepts of mass of matter, either inertial mass or gravitational mass, all measure the mass of matter by considering either its inertial relation with the earth (a fixed v), or its gravitational relation with the sun (a fixed G), which is a data –correcting Support Completely based on experiments. Supposing mass is “the inertia measurement of matter” , we should also correct and supplement this “inertia measurement of matter”. Because this statement includes a very deep understanding about mass of matter with the concept of internal motion things of matter in it. Thus mass of matter is not and cannot be measured by a steelyard. Once there occurs a new Substance Coming into being by combination of two kinds of substances and there also occurs a new mass of matter, (this exists in atoms, molecules, ac well as among atoms, among molecules) the new concept does not disturb this kind of participation and combination. If only the new member achieved “equal status” with the old one, occupied Space and possessed the capacity to occupy space, then either the new member or the old member can all be included in the new definition of mass of matter. The so called new mass of matter concept takes the variation of the occupied space and the change of capacity to occupy space into consideration. So if all of this is considered, there will be no problem. We have pointed out the other development of theory of the all-channel elements was the meaning of the universal existence of law of Conservation of momentum. The motion of celestial bodies;Newton’s mechanics and microscopic particles all obey Low of conservation of momentum. This Law has the property of both waves and particles which is determined by how we embody the law of motions. For instance, the nature of Planck constant h we have mentioned before is the wave length of de Broglie wave. Because ,so This is the formula for de Broglie wave, but it can also be understood as the value of energon (the level of quantity size) (erg second) the two equations are in fact just the same one. The reason is if multiplying , it can be seen as a motion of particles, but if h is divided by , it can be seen as a motion of waves. No matter what, kind of physical meaning has been given to Symbol h and by Planck and de Broglie, logical especially mathematical logical forms once take h and into a new relation, the physical content and meaning defined by Planck and de Broglie must obey the arrangement of logic and accept new content. We should not hold prejudice against h and .We Should treat them like we do towards At the same time, we should also See one fact, the quantity of after it multiplies does not change since defined in the “Standard quantity level”, So the result is the Same whether multiplying or not, but its physical meaning has been changed by this multiplication. Its wave motion is turned into motion of particles. Similarly, the quantity is not changed if h is divided by , but physically, the motion has been changed from particles to waves. So we can see the relevance and uniformity of mathematics and physics in “relative particles”. The excellent use of multiplication and division of Shows again the universal feasibility of law of conservation of momentum, and also shows that a moron is of wave or particles which is determined by how it is shown in front of people. Only by “one multiplication and one division” can we describe two motion laws in nature. It can be predicted that this method can also be used to find some other rules in the nature. But this needs the cooperation of Scientific experiments for certification. This “1” is worthy of profound thinking. It can appear in the solar system. Newton’s mechanics and motions of microscopic particles are identically to the idea of “holographic principle with single value”. When the limit of the three concepts, Infinity, infinitesimal and number “1” is broken, we recognize that they exist relatively. Then mathematics and physics can be joined here and a brand-new subject “physical maths” can be established. This is only the beginning. Of it.