This is a bilingual snapshot page saved by the user at 2024-7-8 11:16 for https://app.immersivetranslate.com/word/, provided with bilingual support by Immersive Translate. Learn how to save?


"Unified Field Theory"

2024.7.1


7th edition


Author: Zhang Xiangqian


Chapter 1, Unified Field Theory


Chapter 2: Revealing the mystery of the nature of gravity


Chapter 3: Revealing the mystery of the nature of electric charge and electromagnetic field


Chapter 4, Zhang Xiangqian’s mathematical theory


Chapter 5, a concise version of Zhang Xiangqian’s unified field theory


Chapter 6: Revealing the Essence of Light


Chapter 7: Successful test of changing electromagnetic field to generate gravitational field (with theoretical derivation)


Chapter 8: Application report for research and development of artificial field scanning technology


Chapter 1, Unified Field Theory


About the Author:


Zhang Xiangqian is from Lujiang County, Anhui Province, China, male, farmer, junior high school level, born in 1967.


In the summer of 1985, I contacted extraterrestrial civilizations and learned from them the essential mysteries of the universe, time, space, mass, charge, field, light speed, momentum, energy, force, motion...


Obtained the grand unified equation of the universe, wrote the four forces of the universe in one equation, and obtained the core secrets of the universe, the unified field theory, the universe space information field theory, the secrets of light-speed flying saucers, artificial field scanning technology, etc.


For the first time in the world, it was discovered experimentally that changing electromagnetic fields produce gravitational fields.


Now living in Erlongxin Street, Tongda Town, Lujiang County, he makes a living by welding and repairing bicycles. He studies and promotes unified field theory theory and artificial field scanning technology in his spare time.


I welcome collaboration between polytechnics and research institutions.


The author’s phone number and WeChat address are 18714815159


Email zzqq2100@163.com


Table of contents:


Foreword.


1. The composition of the universe and the basic principles of unified field theory


2. Definition of matter


3. The falsity of the physical world


4. How do physical concepts arise?


5. Basic physical concepts and derived physical concepts


6. Classification of basic physical concepts


7. How to describe the movement of space itself


8. Why do objects and space in the universe move?


9. The law of spiral motion


10. Parallel principle


11. Geometric symmetry is equivalent to physical conservation


12. Continuity and discontinuity of space


Thirteen, the description of motion cannot be separated from the observer


14. Why is space three-dimensional?


Fifteen, space can store unlimited information


16. Basic assumptions of unified field theory


17. The physical definition of time


18. Space-time identity equation


19. Spiral space-time wave equation


Twenty, understand the nature of the speed of light


21. Explain the constant speed of light in Lorenz transformation


Twenty-two, the general definition of the four major fields in the universe


Twenty-three, the defining equations of gravitational field and mass


Twenty-four, unified field theory momentum formula


25. Unified field theory dynamic equations


Twenty-six, explain Newton’s three major theorems


Twenty-seven, prove that inertial mass is equivalent to gravitational mass


Twenty-eight, explain the nature of gravity


Twenty-nine, gravitational field and space-time wave equation


30. Definition equations of charge and electric field


Thirty-one, velocity multiplied by the rate of change of mass with time is the electromagnetic field force


Thirty-two, the defining equation of nuclear force field


Thirty-three, the definition equation of magnetic field


Thirty-four, derivation of Maxwell’s equations


Thirty-five, the gravitational field that changes with time produces an electric field


36. Changes in the gravitational field of an object moving in a straight line at a uniform speed produce an electric field


Thirty-seven, the magnetic field of moving charges produces a gravitational field


38. Experimental conditions of gravitational field generated by changing electromagnetic field


Thirty-nine, unified field theory energy equation


Forty, photon model


Appendix: Main Applications of Unified Field Theory


Preface


The unified field theory was first proposed by Einstein. He spent more than 40 years hoping to unify the electromagnetic field and the gravitational field, but failed.


Human beings have discovered that there are four different forms of forces in nature: weak force, electromagnetic field force, universal gravitation, and nuclear force. Among them, electric field force and magnetic field force have been unified by human beings. Nuclear force is currently very imperfectly understood by human beings. In the eyes of mainstream scientists, the weak force is It is also unified in the electromagnetic field force.


This article believes that electric field force and magnetic field force are not the same force. The weak force is the resultant force of electromagnetic field force and nuclear force, not a fundamental force.


The unification of electric field force, magnetic field force, universal gravitation and nuclear force discussed in this article is simply to write the electric field force, magnetic field force, universal gravitation and nuclear force in one mathematical formula, and to use mathematical formulas to write out the electric field, magnetic field and universal gravitation field. The relationship between [gravitational field] and nuclear force field.


Since the unified field theory involves time, space, motion, force, light speed, speed, mass, charge, energy, momentum...these are the essential issues of physics, the completion of the unified field theory is of great significance to mankind, but it is also extremely important. Great difficulty.


Notice:


In this article, unless otherwise noted, capital letters are vectors.


This article only describes the simplest and most basic movement of particles in a vacuum, and does not describe the movement of shaped objects in media.


The concept of mass point that appears in this article is that in order to conveniently describe the movement of object particles, we idealize the object and regard it as a point, regardless of the shape and line length of the object particles. It is meaningless to discuss the volume and geometric length of the particle in this article because it violates our convention.


The unified field theory attributes all the properties of the particle to the movement of the particle in space or the movement of the space itself around the particle. It is meaningless to discuss the internal conditions of the particle.


The unified field theory mainly describes the movement of the space itself around the object [or particle], so the unified field theory can also be called spatial kinematics.


The basic assumption of the unified field theory is that the speed of light moves divergently in the space around an object. Based on this assumption, the explanation, modification, expansion, and in-depth understanding of Newtonian mechanics, relativity, and Maxwell's equations are launched.


The core idea of ​​the unified field theory is that the existence of the physical world is false, and all physical phenomena are just human descriptions!


This idea must be carefully understood, otherwise the unified field theory cannot be understood.


The "vertical principle" of the article is difficult to understand, so you should pay attention to this when reading.


The composition of the universe and the basic principles of unified field theory


The universe is composed of objects and the space around them, and there is no third thing that coexists with them.


All physical phenomena and physical concepts are descriptions of the movement of objects in space and the movement of space around the objects by our observers.


Without the description of our observers, only the objects and space that really exist in the universe, and the rest would not exist. The rest are the results of our observers’ description of the objects and space.


The universe we see and feel before our eyes is false, and the real universe that exists behind it is composed of objects and space.


Space and objects do not exist and are composed of a more basic thing. Space and objects cannot be transformed into each other. The universe is dualistic, not unidimensional.


The human brain describes objects and spaces in the universe in different ways, giving birth to the geometric world and the physical world.


When we describe the movement of objects and space, the physical world is born; when we describe the size, quantity, direction, and structure of objects and space, the geometric world is born.


The physical world is mainly processed by people based on their own feelings, while the geometric world is mainly processed by people based on their own rationality.


The physical world is described by our observers, and the geometric world is also described by our observers. Without our observers, there is neither a physical world nor a geometric world. The only things that exist are objects and space.


The main differences between the physical world and the geometric world are:


Physics mainly describes motion, or the phenomena that occur due to motion.


The geometric world is the primary and simple processing of objects and spaces in the universe by the human brain; physics is the deep and complex processing of objects and spaces in the universe by the human brain, especially when it comes to the description and processing of motion.


Compared with physics, the scope of geometric description is wider, and the geometric world is closer to the origin of the universe.


We know that mathematics includes geometry. In fact, mathematics also includes physics. We can also think that physics is just the part of mathematics that describes motion.


As for why the universe is composed of objects and space, why can't objects and space transform into each other?


Unified field theory cannot answer these questions. Unified field theory only identifies this fact and uses this fact as the theoretical basis to carry out reasoning.


The main task of the unified field theory is to explain time, displacement, mass, charge, gravitational field, electric field, magnetic field, nuclear force field, energy, speed of light, speed, momentum, gravity, electromagnetic force, nuclear force, motion...


The nature of these basic physical concepts, and the relationships between them.


2. Definition of matter


Things that exist objectively independent of our observers are matter.


In the universe, only objects and spaces exist truly and independently without relying on observers. Therefore, matter is composed of objects and spaces. Except for objects and spaces, everything else is just human description and does not exist apart from our observers.


For example, a tree or a river in front of us are "things", and the growth of the tree and the flow of the river are "things".


In the universe, objects and space are "things", and the rest, such as time, displacement, mass, charge, field, energy, speed of light, speed, momentum, force, temperature, sound... are all "things" and are relative to "things" A property described by our observers when they move.


This basic principle denies that energy and time are part of matter, and denies that field is a special kind of matter.


Fields are either effects caused by the motion of matter particles or effects caused by motion in space.


The unified field theory determines that the essence of the field is the effect caused by the changing space.


Starting from the basic principles of unified field theory, we can also infer that dark matter, dark energy, God particles, gravitons, ether, strings and membranes in string theory... all do not exist and are all fabricated by people.


The space of the universe is infinite, and the objects in the universe are also infinite. Time is just a description of how people feel about space movement. Time is a physical quantity described by the observer.


As long as there are observers, the time of the universe exists.


The universe has neither beginning nor end. The space and age of the universe are infinite. The Big Bang theory can only adapt to local areas of the universe. It is wrong to say that the entire universe was created by the Big Bang.


3. The falsity of the physical world


Physics is born from the perception of objects and spatial movement by our observers, and then the description of it by the brain.


The existence of the physical world we see and feel before our eyes is false and does not exist apart from our observers. What really exists is the geometric world behind it composed of objects and space.


The geometric world is closer to the origin of the universe, and the physical world is mainly the description and processing of the geometric world by the brains of our observers.


4. How do physical concepts arise?


It is meaningless to discuss how objects and space are created and how they originate, because objects and space are the most basic things that make up the universe, and objects and space cannot be made of more basic things.


Objects can be transformed from one form to another, but they will not appear or disappear without reason.


Objects and space have always existed, just like the universe has always existed. It is meaningless to discuss how the universe came into being and the origin of the universe.


We cannot use a more basic thing to define objects and space, because there is nothing more basic than objects and space. However, we can use objects and spaces to define other physical concepts.


All phenomena and physical concepts in physics essentially come from the sensations of objects and spatial movement. Physical concepts are the result of the human brain processing these sensations.


Except for objects and space, all other physical concepts, such as time, field, mass, charge, speed of light, force, momentum, energy... are the movement of objects in space, or the movement of the space itself around the object, relative to our observers The properties displayed are all formed by motion and are therefore related to displacement.


It can be considered that time, field, mass, charge, speed of light, force, momentum, energy... are all functions of spatial displacement, and we can all express them in terms of spatial displacement.


Among physical concepts, physical concepts such as sound, color, force, and temperature are formed when the movement of objects in space touches our observers and causes our observers to feel, and we observers analyze and summarize these feelings.


However, field and time are a bit special. Field is the effect of spatial motion around an object, and time is the sensation caused by our observation of spatial motion around the body.


5. Basic physical concepts and derived physical concepts


Some physical concepts are basic, and some physical concepts are derived from these basic concepts. For example, time and displacement are basic, and velocity is derived from time and displacement.


Is there any more fundamental physical concept than displacement and time?


Since the universe is composed of two things, object and space, object and space are the most basic physical concepts and the basic bricks that constitute the universe building. They cannot be defined, while other physical concepts can be defined by objects and space. .


Below is a schematic diagram representing these physics concepts from advanced to basic to low level.


Object [or particle], space → time, displacement, field → speed, speed of light → mass, charge → momentum → force → energy, work → temperature, light, sound, color, etc.


6. Classification of basic physical concepts


Basic physical quantities are divided into two categories, one is scalar, and the other is vector. Scalar quantities can be represented by numbers, while vectors can be represented by numbers plus direction.


Scalars can be divided into positive and negative scalars and purely positive scalars without distinction between positive and negative. For example, a positive charge is a positive scalar, and a negative charge is a negative scalar.


7. How to describe the movement of space itself


Unified field theory believes that space itself is moving all the time. Modern physics describes the movement of objects in space. So how do we describe the movement of space itself qualitatively and quantitatively?


We divide space into many small pieces, and each small piece is called a spatial geometric point, referred to as a geometric point, or a space point. The route along which a space point moves is called a space line. By describing the movement of these space points, the movement of space itself can be described.


The mathematical methods of fluid mechanics and wave equations are also suitable for describing the movement of space itself. In fact, we regard space as a special medium similar to fluid.


The unified field theory also confirms that space exists objectively. The existence of space does not depend on the feelings of our observers. If there are no people, space will still exist. However, if there are no people, time will not exist.


8. Why do objects and space in the universe move?


Physics is our description of the geometric world [composed of objects and space]. Therefore, for any physical phenomenon, we can always find a corresponding geometric state.


The state of motion we describe in physics is equivalent to the vertical state in geometry. If we don't describe it, the state of motion is actually the vertical state in geometry.


Note that part of this is reasoning, because the state of motion always has a corresponding geometric state. As for what geometric state corresponds to the state of motion, this requires assumptions.


In unified field theory, the vertical principle is used to explain why objects and space move. The vertical principle is expressed as follows:


Relative to our observers, any object in the universe can draw up to three mutually perpendicular straight lines at any point in the surrounding space. This is called the three-dimensional vertical state of space.


Any spatial point in this vertical state must move relative to our observer, and the changing direction of movement and trajectory can reconstitute a vertical state.


The above can be called a qualitative description of the vertical principle. In the future, we will also need to prove the quantitative description of the vertical principle.


Movement with constantly changing directions must be curved motion, and circular motion can have up to two mutually perpendicular tangents.


Since space is three-dimensional, at any point along its motion trajectory, three mutually perpendicular tangent lines must be drawn, so linear motion must be superimposed in the vertical direction of the circular motion plane.


A reasonable view is that points in space move in a cylindrical spiral [which is the combination of rotational motion and linear motion perpendicular to the plane of rotation].


Objects exist in space, and the location of the object will move due to the influence of the movement of space itself.


This is the explanation for why all objects in the universe move.


We think that the reason why objects move is due to force, which is only a superficial understanding. The reason behind the movement of all objects in the universe is caused by the movement of space itself. In turn, we can use spatial motion to explain the nature of force.


Objects can affect the surrounding space, and then affect the objects existing in the space, so that objects can interact through space without any special medium to transmit the interaction force.


We must realize that the movement of the space around an object is caused by the object. The object exists in the space and can have an impact on the surrounding space. The degree of this impact can be measured by the degree of movement of the surrounding space.


An object exists in space, affects the surrounding space, and causes movement in the surrounding space. The movement of the space will inevitably affect the position of other objects existing in the space, causing the position of this object to change, or have a tendency to change.


All interactions between objects, including gravitation, electric field force, magnetic field force, and nuclear force, are essentially carried out through the movement of space itself. Objects transmit forces to each other through the changing space of motion.


Space exists objectively and does not depend on our observers. We can also think of space as a special medium.


Does the object cause the movement in space, or does the movement in space cause the movement of the object? This can only be said to be cause and effect, regardless of priority. Objects and space are closely connected.


We should note that the description of motion in space has the same points as our description of the motion of ordinary objects, but also has differences.


The spatial motion described by the unified field theory refers to the space around the object. If there are no objects, it is meaningless to simply describe the motion of the space.


Because describing motion requires determining the starting moment of time and the spatial position of the initial state, pure space cannot determine the starting moment and the spatial position of the initial state.


Determining the starting moment of time and the spatial position of the initial state requires joint determination by the object and our observers.


The movement of space itself originates from objects and ends with objects. Without objects or observers, it is meaningless to describe the movement of pure space.


The vertical principle is one of the core secrets of the universe and is closely related to spiral motion. Faraday's electromagnetic induction principle in physics is also related to the vertical principle.


Vector cross products and curls in mathematics are also related to the vertical principle. However, the argument is too complicated and is omitted here.


9. The law of spiral motion


Everything in the universe, as small as electrons, photons, and protons, as large as the earth, the moon, the sun, the Milky Way... all the particles that exist freely in space, without exception, move in a spiral, including the space itself, which also moves in a cylinder. Moving in a spiral shape.


The law of spiral motion is one of the core laws of the universe. Everything in the universe seems to be moving over and over again, but it is not closed.


The vector cross product in mathematics is related to the spiral law. However, the argument is too complicated and is omitted here.


10. Parallel principle


The parallel state described in physics corresponds to the proportional property in mathematics.


If two physical quantities can be represented by line segments and are parallel to each other, they must be directly proportional.


The vector dot product in mathematics is closely related to this.


11. Geometric symmetry is equivalent to physical conservation


Conservation properties described in physics are equivalent to symmetries in geometry.


A conserved physical quantity, if it can be represented by a line segment, is line symmetric in geometric coordinates; if it can be represented by area, it is plane symmetric in geometric coordinates; if it can be represented by volume, it is stereosymmetric in geometric coordinates. of.


12. Continuity and discontinuity of space


When we humans come into contact with space and understand space, we all think that space is continuous. Many of our mathematical systems for humans dealing with space assume that space is continuous.


However, in some cases, space can appear to be discontinuous. For example, if an object moves relative to our observer at the speed of light, the length of space along the direction of motion shortens to zero, and the space in which the object is located can appear discontinuous relative to our observer. This is the fundamental reason for quantum entanglement in quantum mechanics.


This is related to the theory of relativity and quantum mechanics, but this is another vast research field that will take many years and many people to figure it out, so it will not be discussed in detail here.


Thirteen, the description of motion cannot be separated from the observer


The theory of relativity holds that many physical concepts such as time, displacement, electric field, magnetic field, force, and mass are relative. For different observers measuring relative motion, there may be different values. The word "relative" is extended to mean that it is relative to the observer.


Because time, displacement, speed, force, mass, energy...these physical concepts come from the movement of an object [relative to our observer] or the movement of the space itself around the object.


Therefore, it is meaningless to describe motion without our observer, or without specifying the observer. Time, displacement, speed, force, mass, energy... many physical concepts lose their meaning.


At first glance, the above view seems to be a kind of idealism. However, idealism believes that once there are no observers and no one, everything is gone. This is also wrong.


The correct view should be this:


All movements in the universe are relative to our observers. Once there is no observer, the scene of the universe is like a freeze-frame shot of a camera, rather than non-existence.


The state of motion in physics is a vertical state from a geometric point of view. Behind the two phenomena, they are the same phenomenon. It is because we observers look at them from different angles [that is, from a physical point of view and a geometric point of view] that different phenomena appear. the result of.


The state of motion is the result of us constantly affirming, denying, affirming, denying, affirming, denying... the position of an object in space.


Some people believe that everything in the universe was still moving before humans existed, so the existence of motion has nothing to do with humans.


In fact, the phrase "before human beings" is a wrong sentence. Without human beings, there is no such thing as before human beings.


The three words "no one" means that people have been excluded. Since you have excluded people, you can no longer use people to define before or after.


Before or after are all defined by people. Without us people, where would the front and back, up and down, left and right, east, west, north and south come from?


Note that the motion described in physics must have three things: space, object [or particle], and observer. Otherwise, the motion will lose its meaning.


Describing changes in time is a bit special. The observer and the object are actually the same thing - our human body.


Human beings' understanding of motion has a developmental process. Newtonian mechanics believes that to describe the motion of an object, one must find a reference object that is considered stationary. As a reference object, the description of motion emphasizes the object's movement in space during a certain period of time. The distance traveled.


Newtonian mechanics holds that the measurement of time and space length has nothing to do with the movement of the observer.


The theory of relativity inherits the basic views of Newtonian mechanics, but the theory of relativity emphasizes that different observers may measure different values ​​of space, time and other physical quantities.


The theory of relativity holds that the measurement of time and space length is related to the speed of movement of the observer. At low speeds, the relationship is not obvious, but when it is close to the speed of light, it is particularly obvious.


Unified field theory believes that describing motion must be relative to a certain observer. Without an observer, or without specifying that observer, it is meaningless to describe motion.


The physical state of motion is described by us, and the state of rest is also described by us. Without us as observers, there would be no state of motion and no state of rest. The universe would only be left with objects and space.


Without an observer, or without specifying which observer, it is impossible to determine whether objects and space are in a state of motion or rest. It is meaningless to discuss motion or rest.


Choosing a reference to describe movement is sometimes unreliable.


The unified field theory believes that time is formed by the movement of the observer in space, and it must be related to the movement of the observer. That is to say, the measurement of time is related to the observer. The time experienced by the same thing will be different for observers moving with each other. There may be different results.


Since space itself is moving all the time, spatial displacement is also related to the movement of the observer, and different observers may have different results.


The unified field theory, like the theory of relativity, emphasizes that your time and space, and my time and space, are different and cannot be confused when you and I are moving with each other.


14. Why is space three-dimensional?


We know that up to three mutually perpendicular directed straight lines can be drawn along any point in space, which is called a three-dimensional space. Why does it happen to be three, not two, or four?


This reason is caused by the movement of space. If the space moves in a straight line, it produces a one-dimensional space. If the space moves in a curve, it produces a two-dimensional space. The real situation is that the space moves in a cylindrical spiral, so what is produced is a three-dimensional space. .


The reason why space is three-dimensional is that space moves in a cylindrical spiral at all times.


Since the three directions of space are equal, no direction is special. When space moves, it must move in all three directions. Coupled with the continuity of movement, space can only move in a cylindrical spiral. .


In other words, space moves in a cylindrical spiral to form a three-dimensional space. These two statements are causal to each other.


The space we live in is a right-handed spiral space, that is, the thumb of the right hand points in the direction of linear movement in space, and the direction in which the four fingers of the right hand circle is the direction of circular movement in space.


As for whether there is a left-handed spiral space in the universe, the logical analysis is: assuming that a left-handed spiral space exists, it will be repelled by the universal right-handed spiral space. After hundreds of millions of years, it will be repelled to the infinity of the universe. That means there is, We can't find it either.


Two right-handed spiral spaces [facing us as observers, both rotating counterclockwise] collide with each other. The spaces where the rotations touch each other will decrease, showing mutual attraction. When the left-handed spiral space and the right-handed spiral space meet, they will repel each other.


Later, we also pointed out that the space around positive and negative charges is a right-handed helix.


However, this issue still needs to be explored in theory and practice. It is not ruled out that humans can artificially create a left-handed spiral space in the future.


Fifteen, space can store unlimited information


Definition of information: Information is the form of movement of matter [composed of objects and space].


The amount of information can be expressed in terms of possibilities. The more possibilities, the greater the amount of information.


The objects we know are divided into "things" and "things", and information belongs to things.


The amount of information stored or carried by any object particle in the universe is always limited.


Any space in the universe can store all the past, present, and future information of the entire universe. In other words, any piece of space can store unlimited information.


In other words: infinite amounts of information can be stored in any limited space area of ​​the universe.


The reason behind this is: space can be infinitely continuous and infinitely divisible.


It can also be proven logically:


The space around an object radiates in all directions at the speed of light, bringing all the information about the object to the surrounding space.


Due to the three-dimensional space moving at the speed of light, the length of the space along the direction of motion shortens to zero due to the speed of light and becomes a two-dimensional space.


Therefore, the speed of light movement in space can bring all the information of an object to any space in the universe in an instant, rather than spreading step by step at the speed of light as everyone thinks.


The universe has only two-dimensional space and three-dimensional space. There is no one-dimensional space and four-dimensional and above-four-dimensional space.


Since the two-dimensional space has zero volume and can maintain zero distance from any three-dimensional space in the universe, the information stored in the two-dimensional space can permeate any three-dimensional space in the universe.


Conversely, we can also say that any three-dimensional space in the universe contains all the past, present, and future information of the entire universe.


Why is future information also included?


Because time is the feeling of our observers. Without us observers, time does not exist. All the information in the universe hundreds of millions of years ago and billions of years later can be overlapped at a point in space.


In addition to the infinity of time and space, the universe also contains the infinity of information.


The infinite nature of the information contained in the universe can be described in another sentence:


The universe contains infinite possibilities, and the repeated evolution of the universe must express all possibilities, and it must be expressed repeatedly and infinitely.


Information that occurs in a three-dimensional space can be stored in a two-dimensional surface space. For strict proof, Gauss' theorem in field theory can be used.


The information generated in the two-dimensional curved space can be stored in the one-dimensional linear space. For strict proof, Stokes' theorem in field theory can be used.


We need to pay attention to:


The generation of information requires the participation of object particles, which must be completely excluded. Pure space cannot produce information, but it can spread, store and believe it. Information requires description by an observer; without an observer, information does not exist.


16. Basic assumptions of unified field theory


When any object in the universe [including the body of our observer] is at rest relative to our observer, the surrounding space is centered on the object and spirals in a cylindrical shape [a combination of uniform rotational motion and uniform linear motion in the vertical direction of the rotation plane] , with the vector speed of light C [Unified field theory believes that the speed of light can be a vector, represented by the capital letter C (quantity or module, or scalar is c, c remains unchanged), the direction of the vector speed of light C can change] divergent movement in all directions.


The motion in the space around the object in the picture above spreads out in a cylindrical spiral.


The above said that the Big Bang theory of the universe is wrong. The universe has no beginning and no end. The universe has always existed.


The strong evidence for the modern Big Bang theory of the universe is - how is space expanding relative to any observer?


The real reason for the expansion of space is that any object in the universe, including any observer, the surrounding space moves divergently in a cylindrical spiral with the object as the center, at the speed of light, and the stars in the space also move away from our observer.


Then why don't the moon and the sun move away from us observers at the speed of light?


There is another constraint here, which is related to the initial state of motion of objects and planets.


For example, the earth remains stationary with us observers from the beginning, and the moon remains close to stationary with us [compared to the speed of light]. Only very distant planets, which have little relevance to us observers, are moving away from us very quickly.


17. The physical definition of time


The basic principle of unified field theory points out that all physical concepts come from the description of motion by our observers.


There are two most basic forms of motion in the universe, one is the motion of objects in space, and the other is the motion of the space itself around the object.


The most basic physical concept comes from the movement of an object in space or the movement of the space around an object, giving us a feeling as an observer. We observers analyze, describe, and summarize these feelings to form physical concepts.


We feel that time is passing all the time in our lives, and time can also be thought of as something


The movement of the body in space or the movement of the surrounding space gives us a feeling.


So what is it about movement that gives us the sense of time?


We send a person in a spaceship to an area of ​​space tens of billions of light years away. After dropping the person off, the spacecraft immediately flies back.


Other planets in this space area are very, very far away. It can be imagined that this person still has a sense of time.


What is it that is moving that gives this person a sense of time? In this case, there is only the person's body and the surrounding space. Moreover, a person sees his or her body as still, and the only thing that moves is the space around the person.


The correct and reasonable view is:


Time is how we observers feel about the movement of space around our bodies.


Combining the above basic assumptions of unified field theory - all objects in the universe and the surrounding space move divergently in a cylindrical spiral at the speed of light, we can give a physical definition of time:


The space around any object in the universe (including the body of our observer) moves radially around the object in a cylindrical spiral with the object as the center and at the vector light speed C. This movement in space gives us the observer the feeling of time.


Some people believe that there was still time in the universe before humans existed. Therefore, it is wrong to think that time is a human feeling.


In fact, the sentence "before there were humans" is a wrong sentence. Without humans, how could there be a time before humans?


This logical error is: in the first step, you have excluded people from the four words "without people", and in the second step, you use people to define "before". Since you have excluded people, you can no longer use people to define it. .


Without us, where would the front and back, sequence, up and down, left and right, east, west, north and south come from?


"Time" is a physical concept born from a person's description of how the movement of the space around his body feels.


18. Space-time identity equation


The above physical definition of time also defines the speed of light. In the unified field theory, time, space, and the speed of light are bundled together. The speed of light reflects the identity of space and time, that is, the essence of time is how we describe the speed of light movement in space.


We extend the speed of light to a vector. The direction of the vector light speed C [modulo c] can change with time t, the speed of the light source, and the movement speed of the observer.


C = scalar speed of light c times unit vector N.


The scalar light speed c does not change with time t, the movement speed of the observer, or the movement speed of the light source.


From the above physical definition of time, it can be considered that:


Time is proportional to the distance traveled by space around the observer at the speed of light.


With the help of the concept of space point, it can be considered that:


Time is the feeling given to us by the many space points around our observer moving in a cylindrical spiral with the observer as the center and diverging in all directions at the vector speed of light C.


The time t experienced by a space point p at zero time from where our observer is at the vector light speed C is proportional to the distance traveled R.


This leads to the space-time identity equation:

R(t) = Ct = xi+ yj + zk


i, j, k are unit vectors along the x-axis, y-axis, and z-axis respectively. The scalar form is:

r² = c²t²= x² + y² + z²


These two equations can be considered as space-time identity equations, corresponding to the relativistic space-time relativity equation, reflecting that space and time have the same origin. It can also be said that time can be represented by spatial displacement at the speed of light.


What we need to pay attention to is that not only time, but also basic physical concepts such as mass, charge, field, momentum, force, energy... these basic physical concepts, as well as all physical concepts, are caused by and composed of spatial displacement. Trace back We will find that the essence of these physical concepts can ultimately be reduced and decomposed into spatial displacement.


This is also the essence of physics - physics is just a subject that describes motion, and all motion is composed of spatial displacement.


19. Three-dimensional cylindrical spiral space-time equation


As mentioned above: All objects [or particles] in the universe, including space itself, move in a cylindrical spiral. The law of spiral motion is one of the most basic laws of the universe.


The unified field theory believes that the space around the object itself also moves in a cylindrical spiral.


Next, we will establish the three-dimensional cylindrical spiral space-time equation in the unified field theory to replace the four-dimensional space-time equation in the theory of relativity.


Imagine that there is a particle point o in a certain space area, which is stationary relative to our observer. We use point o as the origin to establish a three-dimensional Cartesian rectangular coordinate system x, y, z.


At time t'= 0, we examine any space point p in the space around object point o, and we use x for its position. ,y. ,z. To express, we use R as the spatial displacement loss from point o to point p [abbreviated as position vector]. To represent.


After the movement of point p for a period of time t, it reaches the subsequent positions x, y, z of point p at time t". That is, the spatial position coordinates of point p at time t" are x, y, z,


The spatial displacement from point o to point p [abbreviated as position vector] is represented by R.


In cylindrical spiral motion, it can be decomposed into rotational motion vector and linear motion vector. Note that displacement cannot be confused with linear motion. Displacement can be regarded as the synthesis of rotational motion vector and linear motion vector.


According to the above vertical principle, R changes with the change of spatial position x, y, z and time t, so there is:

R(t) =(x,y,z)


The specific relationship between R(t) and (x, y, z) is given, which is the above space-time identification equation:


R(t) = R. + Ct = (x.+x) i+ (y.+y) j + (z.+z) k


This equation can sometimes be abbreviated as:

R(t) = Ct = x i+ y j + z k


Scalar form: r² = c²t² = x²+ y²+ z²


r is the number of vectors R.


The above equation also appears in the theory of relativity, which is considered to be a four-dimensional space-time distance. The real situation is that the essence of time is our description of space moving at the speed of light. If any one dimension in a three-dimensional space moves at the speed of light, we can think of it as time.


The existence of space is basic, but time is not. Without human observer, time does not exist, but space still exists.


Since time is our observer's description of space moving at the speed of light, the amount of time is equivalent to the spatial displacement of the speed of light.


The theory of relativity obviously does not realize this. The theory of relativity does not know the nature of time. It regards time as another dimension equal to space and ranks it as a four-dimensional space-time alongside the three-dimensional space.


The theory of relativity does not realize that space is basic and real, and it still exists apart from our observers. Time is described by humans. The existence of time is false, and it does not exist apart from our observers.


The understanding in this regard is obviously that the theory of relativity is flawed.


If point p rotates at an angular velocity ω on the x and y planes and moves linearly at a uniform speed h on the z axis, and the projection length of R on the x and y planes is r, then there is:


x = x. + r cosωt


y = y. + r sinωt


z = z. + h t


The above can also be expressed by the following vector equation,


R=R. +Ct


= (x。+ r cosωt)i+ (y。+ r sinωt ) j +(z。+ h t ) k


The above can be called a three-dimensional spiral space-time equation.


Sometimes this equation can be simplified to:


R = r cosωt i+ r sinωt j + h t k


The unified field theory believes that all mysteries of the universe are determined by the above equations, ranging from the Milky Way and planets to the movement of electrons, protons and neutrons, as well as why objects have mass and charge, all the way to human thinking, etc. ..., are all related to this equation.


In the three-dimensional spiral space-time equation, what is the relationship between rotational motion and linear motion?


The spatial rotational displacement vectors X, Y along the coordinates x and y axes and the spatial linear displacement vector Z along the coordinates z-axis should satisfy the following cross-product relationship:


X×Y=Z


Y×X=-Z


The above formulas X and Y are rotation amounts. If X×Y = Z represents a right-handed spiral relationship, then Y×X = - Z represents a left-handed spiral relationship.


The formulas X×Y = Z and Y×X= - Z reflect the connection between rotational motion and linear motion in space.


These two formulas are derived from the previous "parallel principle" and "perpendicular principle".


The "parallel principle" points out that if two physical quantities can be represented by line segments and are parallel to each other, they must be directly proportional.


The "vertical principle" states that the direction of a plane or curved surface is in its vertical direction.


The direction of circular motion is in the vertical direction of the circumferential plane, and the reason behind it is also the "vertical principle".


In the formula X×Y = Z, X×Y can be regarded as a vector area. The size of the area is equal to the number of


According to the parallel principle, the vector area X×Y is proportional to Z. Of course, under certain circumstances, the proportionality constant can also be set to 1, written as X×Y = Z.


For the above three-dimensional spiral space-time equation, we need to pay attention to the following points:


1. There are many space points around point o, and point p is just one of them. Mode:


R=R. +Ct


= (x。+ r cosωt)i+ (y。+ r sinωt ) j +(z。+ h t ) k


, does not mean that there is only one vector like R around point o, but that there are many vectors like this radially and evenly distributed around point o [when point o is stationary relative to us].


However, because the movements are synchronized with each other, no movement direction is opposite. Therefore, in the space around a single particle point, there are no two spirals intersecting in space.


2. Spirals originate from and end at mass points. They will not appear for no reason in a space without mass points.


When the object point o is stationary relative to our observer, the movement in the surrounding space is uniform, and the spiral the space point follows is continuous and will not be interrupted for no reason.


We also need to realize that the establishment and selection of coordinate axes are arbitrary. The coordinate axes are just a mathematical tool for us to describe space and will not affect the distribution of spirals and motion spaces.


3. The cylindrical spiral motion in space is the superposition of linear motion and rotational motion. It can also be considered that linear motion is a special case of r = 0 in the cylindrical spiral motion mentioned above.


The essence of the field is the effect of the cylindrical spiral motion of space. In field theory, divergence describes the linear motion part of the cylindrical spiral motion of space, and curl describes the rotational motion part.


4. What is described in the cylindrical spiral equation is: one endpoint of the space vector R does not move at point o of the object, and the other endpoint p draws a circle and moves in a straight line along the vertical direction of the circle plane. It cannot be understood as just point p. The point is drawing a spiral, but the space vector R is drawing a spiral.


5. The space point p at zero time may start from a plane passing through point o, not exactly from point o.


6. Spiral equation R =R. +Ct


= (x. + r cosωt) i + (y. + r sinωt ) j + (z. + h t ) k, if x and y are equal to zero, the space point moves in a straight line along the z axis, and the spiral equation cannot be considered in this case It is not suitable, but should be changed to the equation of linear motion.


The correct understanding should be that x and y approach zero, and the radius of rotation of the cylindrical spiral motion of point p approaches zero. And the spiral equation still applies.


Of course, there are also situations where x or y approaches infinity and z approaches zero.


These situations can be included in the spiral equation, which simplifies our understanding of the problem.


7. The vector speed of light is obtained by deriving the derivative of the spiral motion equation with respect to time. This cannot be understood as being obtained by simply deriving the derivative of the straight line part of the cylindrical spiral motion with respect to time, because this will result in super-light speed. It is obtained by taking the derivative of the position vector R [linear displacement plus rotational displacement] with respect to time t.


8. A space point corresponds to a spiral, and the spiral radius is between 0 and infinity. It is meaningless to ask how many meters the specific value is, just like it is meaningless to ask how many electric field lines there are around a charge.


9. When the particle o is stationary relative to our observer, the motion in the surrounding space is uniform, and the distribution of the spiral is uniform and continuous.


When point o moves relative to our observer, the uniformity of motion in the surrounding space is expected to be broken. When point o reaches the speed of light, the spiral is expected to be interrupted.


Twenty, understand the nature of the speed of light


1. The nature of the speed of light


With the in-depth development of physics, the importance of the concept of light speed has attracted more and more attention. The speed of light has become equally important as time, space, field, mass, charge, momentum, force, energy...these basic physical concepts.


When people mention the speed of light, they involuntarily think of luminescence. In fact, the speed of light can better reflect the essential laws of nature than the phenomenon of luminescence.


In the unified field theory, extending the speed of light into a vector is equivalent to broadening people's understanding of the speed of light. Unified field theory also has a deep understanding of the speed of light.


In the unified field theory, it is determined that the speed of light reflects the identity of space and time, that is, space is fundamental, and the movement of space forms time. Time is our observer's description of space moving at the speed of light.


The physical definition of time bundles space, time, and the speed of light. It uses motion space to define time and at the same time, it also defines the speed of light.


Time and space have the same origin, and it is the speed of light that connects them.


It is determined that the speed of light is a constant, and space and time are originally the same thing, which means that space is extended, time is extended accordingly, and space is shortened and time is shortened accordingly. This is the identity of space and time.


The above equation R(t) = Ct = x i+ y j + z k is the space-time identity equation.


Electrons in atoms live in a small space, move extremely fast, and have an extremely short period of movement. In the solar system, planets move in a large range of space with small speeds and long periods. Behind all this is the identity of space and time.


The space-time identity of the unified field theory and the space-time relativity of the relativity theory are contradictory on the surface, but they are essentially the same. The space-time identity equation is basic. From the space-time identity, the space-time relativity equation of the relativity theory can be derived. Later we will The derivation process will be given.


2. Explain the relativistic effects related to the speed of light


Let’s first talk about why the speed of light is the highest speed in the universe.


According to the theory of relativity, the speed of light is the highest speed in the universe. The theory of relativity is mainly based on mathematical formulas, because if the moving speed of an object exceeds the speed of light, some physical quantities will appear as imaginary numbers and lose their meaning.


In fact, it is very simple to logically deduce that the speed of light is the highest speed in the universe.


Imagine an alien spacecraft. Its length is 10 meters when it is stationary relative to us. When it moves relative to us at a certain speed, we find that the length of the spacecraft is shortened and becomes 5 meters. When the speed reaches the speed of light, when , shortened to zero.


If the spacecraft moves relative to us at super-light speed, and analyzed according to the changing trend, will it happen that the spacecraft is shorter than the length of zero? ——Apparently not.


The theory of relativity holds that if a clock is placed inside the spacecraft and we hold another clock in our hands, the two clocks will keep the same time when they are stationary.


As the spacecraft moves relative to us, the clock inside the spacecraft slows down relative to the clock in our hands.


An observer inside the spacecraft measures the time interval between two events that occur at the same location inside the spacecraft. From the outside of the spacecraft, we observers see that the time interval between these two events has lengthened.


When the spacecraft reaches the speed of light, from the perspective of our observers outside the spacecraft, the length of the spacecraft shortens to zero, and the clock inside the spacecraft runs very slowly, so slow that it freezes and stops moving.


There is an alien planet 50 light years away from us. The aliens drive a light-speed spacecraft to our earth. We think it will take 50 years for the spacecraft to reach our earth.


However, the aliens in the spacecraft believed that they had traveled an infinite distance in their zero seconds, so they reached our earth in an instant.


If there is super-light speed, according to the trend of motion, is there any faster motion than traveling an infinite distance without taking time? ——Apparently not.


The above involves the famous shrinkage and species slowness of the theory of relativity.


An object has zero length and zero volume. Logically, it does not exist if its volume is zero. Many people cannot accept this conclusion of the theory of relativity.


Some people think that this is an observer effect, caused by the observation of the observer.


Is the clock shrinkage really happening, or is it just an observer effect? In comparison, most people think it is the observer effect.


Many people think:


The slow effect of shrinkage is relative to an observer outside the spacecraft, and the actual size of the spacecraft does not change. When an object moves at close to the speed of light, it does not deform, but the light and electromagnetic waves it reflects change. To our observers, it appears that the object has deformed.


To put it simply, the clock does not slow down and the ruler does not shrink. Everything is just due to your observation and measurement.


However, some people think that shrinkage and slowness do not occur only when you observe it. If you do not observe it, you will not shrink or slow down. As long as there is relative motion speed, the clock slowdown has already happened.


Some people adopt a compromise solution and say that the "shrinking effect" is an observational effect and the "clock slowing effect" is an actual effect.


The unified field theory believes that ruler contraction and clock slowness are tied together, and there is no one that is an observer effect and the other is a real effect.


The unified field theory believes that the shrinkage of rulers and the slowness of clocks are both real effects and observer effects.


In the unified field theory, there is no absolute difference between the real effect and the observer effect, they are unified.


First of all, you cannot completely oppose the observer effect to the real effect. There is no essential difference between the two.


Why does the universe you see happen to look like that - because this is what your brain describes. The real universe only contains objects and spaces, and everything else is just the description and calculation processing of your brain.


In the unified field theory, space is formed by motion. Space is born from positive charges in space, diverging towards the surrounding space at the speed of light, and converging towards negative charges at the speed of light.


Spatial movement requires human description. The space you see is not static, but moving at the speed of light. This movement has definite meaning relative to our observers.


It is meaningless to talk about the movement of space without relating the movement of space to the observer.


The existence state of space is also the state of motion. The three-dimensional vertical state of space is caused by the cylindrical spiral movement of space at all times.


The geometric three-dimensional vertical state of space is equivalent to the physical motion state.


The motion state of space is the result of our description of the three-dimensional vertical state of space. Why does the space you see look like that? Exactly what you described.


The red you see, why is it red, because that's your description. Without our human description, there would be no red color in the universe.


Everything you see, the blue of the sky, the beauty of flowers and plants, are the result of processing and analysis of the electromagnetic wave signals obtained by the brain.


The reason why it is like that is exactly what your brain tells you after calculation.


What is the heat you feel? Heat is described by your brain. Without your brain's description, heat does not exist. The essence of heat is people's description of the degree of irregular movement of molecules.


The sound you feel also comes from your description. The difference between having sound and not having sound is that the positions of molecules in the air are different.


Sound is not actually a real thing. Without human description, sound does not exist.


Many people view the real effect and the observer effect as opposites - this is the thinking of ordinary people.


However, the core idea of ​​the unified field theory is that the existence of the physical world is false. Except for the existence of objects and spaces in the universe, we cannot describe it. All other physical phenomena are just descriptions of us.


In the unified field theory, there is no absolute difference between the observer effect and the real effect.


We say that colors, sounds, and heat are all descriptions of people’s feelings. They are all observer effects. They are not real things. Some people can understand them carelessly now.


However, once it is said that the state of motion is also described by people [we need to note that the state of rest is also described by us, without us observers, there is no state of motion or rest in the universe], many people's thinking You can't adapt anymore.


Except for one situation where it is not the observer effect [that is, there are objects and spaces in the universe], everything else in the universe is the observer effect, which is described by our observers, including the state of motion and the state of rest.


Why is the existence of objects and space not an observer effect?


Because what really exists in the universe are objects and space, and the rest is our description of the movement of objects and space, and the rest is the observer effect.


The existence of objects and space is the basis for the birth of all phenomena in the universe. Everything else is human description, including motion, stillness, time, mass, charge, energy, force...


Someone will ask:


Some observer effects are consistent with what actually happened, and some observer effects are inconsistent with what really happened. How to distinguish between these two situations?


——There are no inconsistencies.


What you see is what really happened, and what really happened must be described by an observer. Without an observer to describe the so-called real situation, it is meaningless to talk about it.


A lot of things are happening in the universe every moment. When we discuss these things, we always have to relate them to a certain observer. To put it simply, it means how it is relative to someone.


You don't say it is relative to someone, you ignore which observer it is relative to, and you often get specious and ambiguous results.


This is where the theory of relativity is often questioned and criticized. It can only be said that the theory of relativity is an incomplete theory, and a thorough theory should be a unified field theory.


According to the unified field theory, the existence of objects and spaces in the universe has nothing to do with our observers. This is an objective fact, and the rest are human descriptions. The rest are subjective and belong to the observer effect.


In the unified field theory, the slow clock effect can be concretely applied.


The unified field theory believes that when an object moves at the speed of light, its length along the direction of motion shortens to zero, and it does not occupy our space. It is possible for an object with zero volume to pass through a wall, and both the wall and the object are intact.


The unified field theory can also use the vertical principle to explain the shortening of space caused by motion. Since the physical state of motion and the geometric vertical state are equivalent, when the object moves in a straight line at a uniform speed along the x-axis at every speed, the x-axis is tilted. When the movement speed reaches the speed of light, it rotates 90 degrees - resulting in The projected length of space along the direction of motion on the x-axis is zero.


In specific applications, the unified field theory believes that objects have mass and charge because the space around the object moves divergently at the speed of light, and the number of divergences is proportional to the mass of the object.


When a changing electromagnetic field is used to generate an anti-gravitational field and illuminate an object, it can reduce the number of light-speed motions in the space around the object. When the number of light-speed motions in the space around the object is reduced to zero, the mass becomes zero, and the object suddenly The speed of light moves relative to us [this is the principle of alien flying saucers flying at the speed of light].


When the mass is close to zero, although it will not move at the speed of light, it is in a quasi-excited state and can pass through walls without causing any damage to walls or objects.


If the clock slowdown is purely an observer effect, it is obviously impossible for the rigid body predicted by the unified field theory above to pass through the wall and both remain intact.


Some people think that the mass of an object is zero, and the molecules inside the object have no force on each other and disperse like dust.


In this case, one observer thinks that the mass of the object is zero, and the other observer thinks that the mass is the same as usual.


This sum has zero mass relative to any observer, and there is a difference.


The theory of relativity holds that a spacecraft moves relative to us at the speed of light. We find that the length of the spacecraft along the direction of motion is zero, resulting in a volume of zero;


Observers inside the spacecraft believe that there is no process from the beginning to the end of the movement of the spacecraft. This trip, no matter how far it is, arrives in an instant.


This is hard for us to accept.


The unified field theory believes that time is formed by the divergent movement of light speed in the space around the observer. When you move at the speed of light, you have caught up with space. If you have caught up with the light speed movement of space, you have caught up with time.


Therefore, from our point of view, you have no space, and your time has stopped moving and has frozen.


This makes it easier for us to understand.


The theory of relativity holds that when an object moves at the speed of light, its moving mass becomes infinite, and it is difficult for us to accept infinite mass.


The unified field theory believes that the mass of an object reflects the number of spatial displacements around the object at the speed of light within a certain three-dimensional angle.


When this object moves close to the speed of light, the solid angle will become close to zero due to the relativistic space contraction, and the number of objects will not change with the speed, so the mass will tend to be infinite.


Since mass is a physical quantity observed by our observers, mass reflects the degree of motion in the space around an object, and the essence of mass is the effect of spatial motion. Therefore, it is easy for us to understand that the mass of an object is infinite or zero.


In the unified field theory, all physical concepts and physical quantities are described by our observers.


Speed ​​is no exception. Only the speed of my movement relative to the observer is the truly meaningful speed. Only the speed of light relative to our observer is the constant speed of light and the maximum speed of light in the universe.


For the speed of movement and the events formed by movement, the beginning and end of the event are related to the observer me, so that there will be a clear result. There is no point in talking about results for speeds and events that have no relevance to me as an observer.


For example, if we rotate our bodies on the earth, one revolution per second, compared to an alien planet that is tens of billions of years old, and relative to our observers, the linear speed of the planet's rotation must be faster than the speed of light.


However, this super-light speed has no causal relationship with us observers, so this super-light speed is meaningless.


For example, we observers stand on the earth and see two spacecraft moving at 0.9 times the speed of light, one moving eastward and the other moving westward relative to each other.


We observers believe that whatever speed that ship is moving relative to our observers is not faster than the speed of light. However, in my opinion, the relative motion speed of the two spacecraft is 1.8 times the speed of light. However, this superluminal speed is not superluminal relative to us observers.


There is no super-light speed relative to us observers.


In the unified field theory, there is a case where the speed of light can be less than 300,000 kilometers per second.


When the light source moves in a straight line with a uniform speed V relative to our observer, the speed of light along the vertical direction of V is indeed less than 300,000 kilometers per second.


3. Use the physical definition of time to explain the constant speed of light in the theory of relativity.


The theory of relativity is based on the constant speed of light. However, the theory of relativity does not explain and has no ability to explain why the speed of light does not change. The theory of relativity only takes the constant speed of light as a factual basis and expands and modifies Newtonian mechanics.


In the theory of relativity, the constant speed of light means:


When the light source is stationary or moving at speed v, the speed c of the light emitted by the light source remains unchanged relative to our observer.


If you know the physical definition of time, you will immediately know why the speed of light does not change.


The above physical definition of time is:


The space around any object in the universe [including the body of our observer] is centered on the object and moves divergently in all directions at the speed of light c, while light is stationary in space and is carried outward by the movement of space. This movement of space The feeling given to us as observers is time.


In this way, the amount of time t is proportional to the displacement r of the moving space with the speed of light c, that is:

r = c t


The speed of light c = r/t is a fraction. From primary school mathematics, we know that a fraction is the numerator divided by the denominator.


The numerator in the speed of light, the spatial displacement r, and the denominator in the speed of light, time t, are actually the same thing. We artificially call one thing two names.


For example, Zhang Fei, also known as Zhang Yide, although they have two names, they refer to the same person.


Therefore, if there is any change in the numerator of the speed of light - the spatial displacement r, the denominator of the speed of light - time t will definitely change synchronously, because r and t are originally the same thing, and they are called two names by us observers.


In this way, the value of the speed of light c = r / t always remains unchanged. This is the reason why the speed of light does not change.


For example, if we see that Zhang Fei has gained weight and gained 5 pounds, we can immediately conclude that Zhang Yide must have gained 5 pounds because the two names refer to the same person.


The weights of Zhang Fei and Zhang Yide are increasing, but the ratio of Zhang Fei's weight to Zhang Yide's weight remains unchanged.


When the light source moves relative to us at a speed v, the change in the spatial displacement r, the numerator of the speed of light, will definitely cause a synchronous change in the denominator of the speed of light, time t.


When the light source moves relative to us in any way, the spatial displacement r, the numerator of the speed of light, changes in a certain way, which will definitely cause the denominator of the speed of light, time t, to change synchronously in that way.


From the above, it can be deduced that the speed of light always remains unchanged whether the light source is moving at a constant speed or accelerating relative to our observer.


This shows that general relativity is basically correct, because the basic principle of general relativity is that observers who accelerate each other observe the same beam of light at the same speed.


21. Explain the constant speed of light in Lorenz transformation


1. Explanation of the constant speed of light in Lorenz transformation


There are two rectangular inertial coordinate systems s and s'. The location and time of any event occurring in the s and s' systems are represented by (x, y, z, t), (x', y', z', t').


This article focuses on the simplest case of Lorenz transformation, which is to examine the point p stationary in the s’ system.


In the picture below,


The x-axis and x' coincide with each other. At the moment t' = t = 0, the origin o of the s system [the observer in the s system stands on point o] and the origin o' of s' [observation in the s' system The person is standing at point o'] and the points overlap each other.


Subsequently, point o' moves linearly along the positive direction of the x-axis at a uniform speed v relative to point o.


Suppose that an explosion occurs at a certain moment. Measured in the s' system, the space and time coordinates of the explosion that occurred at point p are x', y, z' and t' respectively.


That is to say, the explosion occurred at time t', and the coordinate of the location p on the x' axis is at a distance x' from the origin o'. Moreover, point p is stationary relative to the s’ system.


Measured in the s system, the space and time coordinates of the explosion event occurring at point p are x, y, z and t respectively.


That is to say, the explosion occurs at time t, and its coordinates are at a distance x from the origin o on the x-axis. Moreover, point p is moving at a speed v relative to the s system.


Let's find the relationship between the time and space coordinates of an explosion event that occurred at point p, and the coordinate values ​​in the two inertial reference systems.


In the picture above, you can intuitively see:

x'= xvt 

x = x'+ vt'


According to the idea of ​​Galileo’s principle of relativity, the measurement of time and space length has nothing to do with the observer’s movement speed v, so the above formula can be established, and t = t’.


However, the theory of relativity holds that the measurement of time and space length is related to the observer's mutual motion speed v, and the space length shrinks and becomes smaller as the speed v increases.


From the perspective of an observer in the s system, x' in the formula x' = x–vt needs to be shortened and multiplied by a relativistic factor 1/k before the equation can be established. Therefore, there is the formula:


(1/k)x' = x - vt


F:


x'= k(x - vt) (1)


From the perspective of an observer in the s' system, x in the formula x = x'+ vt' must be multiplied by a relativistic factor 1/k to be true, so there is the formula:


(1/k)x = x'+vt'


F:


x = k(x'+ vt') (2)


Since the s system is moving in a straight line at a uniform speed relative to the s' system, we should reasonably think that the relationship between x' and (x–vt), x and (x'+ vt') should be linear, and we are satisfied with the simple direct ratio.


The principle of relativity of the theory of relativity holds that physical laws are the same or equal in all inertial reference systems, and the forms of physical equations in different inertial reference systems should be the same.


Therefore, the same constant k can be used in equations (1) and (2).


For the value of k, the Lorenz transformation is calculated using the constant speed of light.


Imagine that a beam of light traveling in the positive direction of the x-axis is emitted from the origin o and o' at the coincident zero time, and the speed of light is c.


Assume that the space-time coordinates of the wavefront [or photon, space point] point p of the beam are (x, y, z, t) in the s system, and (x', y', z' in the s' system ,t').


The event that the wavefront [or photon, space point] p of the light beam reaches its subsequent location is the object of our investigation.


If the speed of light c is the same in the s system and the s' system, we have


x = ct         (3)


x’= ct’ (4)


Combining equations (1), (2), (3) and (4), we can derive:

ct'= k(x - vt)


ct = k(x'+vt')


Multiplying the above two equations can be derived:

c²t t'= k² (x vt) (x'+ vt') 


= k² (xx’+ xvt’ - vtx’- v²tt’)


= k² (xx’+ ctvt’ – vtct’- v²tt')


= k² (c²tt’ - v²tt’)


Export again:


c²= k² (c² - v²)


k = 1/√(1- v²/c²)


Putting the above formula into formula (1) and formula (2), we can get:


x'= (x–vt) /√(1- v²/c²) (5)


x =(x'+ vt') /√(1- v²/c²) (6)


From equations (5) and (6), eliminating x’, we get:

t'=(tv x/c²)/√(1- v²/c²)     (7)


From equations (5) and (6), eliminating x, we get:


t=(t'+ vx'/c²)/√(1- v²/c²) (8)


Mode:

x'= (xvt) /√(1- v²/c²) 9


y'= y (10)


z' = z (11)


t'=(t–vx/c²)/√(1- v²/c²) (12)


This is the Lorenz positive transformation.


Mode:


x = (x'+ vt') /√(1- v²/c²)

y = y

z = z 


t=(t'+ vx'/c²)1/√(1- v²/c²)


It is the inverse Lorenz transformation.


Note that y and z are unchanged in the Lorenz transformation.


Below we use the physical definition of time to explain the constant speed of light in equations (3) and (4).


According to the previous physical definition of time.


Observers in the s' system believe that there will be a space point p [or wavefront, photon] leaving point o' [or point o, because point o and point o' coincide with each other at zero time], so that The speed of light c moves in a straight line at a uniform speed in the positive direction along the x' axis [or Location. So x’/t’= c.


Observers in the s system believe that there will be a space point p leaving point o at time zero [or point o', because point o and point o' coincide with each other at zero time], along the x-axis [or x'-axis, Because the x-axis and the x'-axis coincide with each other] it moves in a straight line at a uniform speed in the positive direction. After a period of time t, it has traveled a distance of x and reached the position where point p later was.


The above physical definition of time tells us that time is proportional to the distance traveled by a space point p in the space around the observer.


Therefore, the time t in the s system is greater than the time t’ in the s’ system, which is equal to the distance x traveled by the space point in the s system than the distance x’ traveled by the space point in the s’ system, that is:

t/t’ = x/ x’


Make a transformation to the above equation,


x/t = x'/t'


Since x/t and x'/t' are both displacement ratios and time, the dimension is velocity, and x'/t'= c, so


x/t = x'/t' = velocity = c


Therefore, the above shows that there must be a special rate that is closely related to time [we use c to represent it]. From the perspective of two observers moving with each other, the value of c is equal.


As long as the above physical definition of time is correct, it must be able to prove that the speed of light c in equations (3) and (4) is equal.


Next, we use the idea of ​​unified field theory to interpret the above Lorenz transformation.


(1). The Lorenz transformation inherits the Galilean transformation. The s system sees the s’ system moving at speed v, and the s’ system sees the s system moving at speed - v.


The time and space position of the same thing happening in two inertial systems are considered to be invariant in the Galilean transformation. This is negated by the Lorenz transformation.


Lorenz transformation inherits part of the idea of ​​Galileo's transformation and denies part of it, but it is not a complete negation.


(2) Unified field theory believes that all forms of motion and physical phenomena are described by our observers. It is meaningless to talk about physical phenomena and motion states without our observers.


We always default to the s’ system and the s system. There must be an inertial reference system that is the reference system where the observer is located.


(3), s’ series and s series only I think you are a sports person, you think I am a sports person, it is equal rights, not absolutely equal rights.


We always default that only one of the s' system and the s system can be the reference system I am in. The reference system I am in is superior. All physical quantities and physical concepts are described by me, and they can only be determined relative to me. physical meaning, and I only have one.


(4) Unified field theory believes that four basic conditions need to exist to describe motion, one is space and the other is time, including the starting moment, process, and ending moment of time.


One is the observer, and the other is the object being described, that is, the object or the event caused by the movement and change of the object.


4 conditions, without one, it is meaningless to describe motion.


In special cases, the described object and the observer can be the same thing, which is to describe the movement of our observers themselves. However, this description is meaningful only in special cases and is meaningless in general cases.


In the unified field theory, space is in motion. To describe the motion of space, it must be the space around an object. Without an object, or without specifying which object, it is meaningless to describe simple spatial motion.


So, in the Lorenz transformation, we must:


It is necessary to identify the observer, determine the object being described [composed of an object or an event formed by the movement of an object], determine the start and end moments of the event and the elapsed time, and determine the spatial location where the event occurred, otherwise confusion may occur.


(5) Although it cannot be said which one of the s’ series and the s series is moving absolutely, absolute motion is meaningless. However, relative motion [that is, moving relative to a certain observer] is meaningful.


We are accustomed to call the system where the described object point p (an object or an event caused by the movement and change of an object) is stationary called the s’ system, also called the dynamic system, and the s system is called the static system.


Some people think that it is necessary to introduce a third system [the commonly used reference system where the earth's surface is located] to compare the s system and s' before we can determine who is the static system and who is the dynamic system.


If you introduce me [I am the only one] into the reference system, there is no need for a third system for comparison, and you can also distinguish between the static system and the dynamic system.


(6), when I, the observer, am standing in the s system by default [that is, I am moving relative to the point p of the object being observed], Lorenz positive transformation will be used;


When I am standing in the s’ system by default [that is, I am stationary relative to the observed object point p], the Lorenz inverse transformation will be used.


2. Explain why the speed of light does not change in a reference frame


We still have a question: As far as a reference system is concerned, why is the speed of light also constant?


This can be understood in this way, time is completely equivalent to the movement of space around the observer, that is:


Space of motion = time.


In order to prevent dimensional confusion when "moving space = time" holds in physics, we need to multiply time in front of time by a constant that does not change with time or moving space - the speed of light.


Space of motion = speed of light times time.


From a mathematical point of view, when a variable takes its derivative with respect to itself, the result is 1 or a constant.


3. Explanation that the speed of light remains unchanged when the motion direction of a space point is perpendicular to the speed v


Some people may think that light can run in any direction, so doesn’t space also run in any direction? To describe any movement, a reference object is needed. Who does the movement in space refer to?


In the unified field theory, the space around an object is indeed centered on the object and moves divergently around it.


The movement of space refers to objects. When we describe the movement of space, we refer to how the space around an object moves.


In the special case, there are no objects, and the movement we describe in space is relative to our human body.


Without any objects, it is meaningless to simply describe the movement of space.


Next, let us consider the explanation of the constant speed of light when the direction of movement of the space point is perpendicular to the movement speed v of the observation object.


In the figure below, the x-axis and x' coincide with each other. At the moment t' = t = 0, the origin of the two-dimensional rectangular coordinate system s is point o [the observer in the s system is standing at point o] and the two-dimensional rectangular coordinate system The origin o' of the coordinate system s' [the observer in the s' system is standing at point o'] coincides with each other.


Subsequently, point o’ moves linearly along the positive direction of the x-axis with uniform speed V [scalar is v] relative to point o.


Imagine that there is a particle o’ that is always stationary at the origin o’ of the two-dimensional rectangular coordinate system s’.


At zero time, s' is the observer's physical definition of time. He finds that a space point p starts from point o' and travels a distance of o'p in the y' direction at the speed of light c in time t'. [So With o'p / t' = c], when we reach the point p, it is the point p marked in the picture.


The fact that space point p starts to move to point p at zero time, from the perspective of an observer in the s system, point p has traveled a distance of op in time t.


Although op’s distance is farther than o’p, all time t should be longer than time t’.


Because, according to the physical definition of time, time is proportional to the distance traveled by the space point p relative to the observer. Therefore, there is the formula:

op /o’p = t / t’


Transform the above equation to get:


op/t = o’p/t’


Obtained from o’p / t’ = c:

op /t = o’p / t’ = c


The above formula explains why the speed of light remains unchanged relative to the values ​​of two observers moving toward each other.


Let’s find out the relationship between t and t’ to see whether it is consistent with the theory of relativity. Depend on


op /t = o’p / t’ = c,


op = √(o’p²+v²t²), you can get:


t’ = t√(1-v²/c²)


The differential form can be obtained:

d t /dt’ =1/(1v²/c²)


The theory of relativity holds that when something happens, the observer is stationary relative to the location where the event occurred, that is, the start and end moments of the event are both at the same location. The time taken to measure this event is the inherent time, which is the above t'.


The inherent time in the theory of relativity is the shortest, and this result is the same as the result of the theory of relativity.


We take the derivatives of both sides of the Lorenz inverse transformation t=(t'+ vx'/c²)/√(1- v²/c²) with respect to time t', and get:

dt/dt' =1/√(1- v²/c²)


Note that x’ in the formula does not change with time t’, because the quantities of x’ and t’ are both observed in the s’ system, and in s’, the position x’ of point p is stationary.


We take the Lorenz positive transformation t’=(t - vx/c²)1/√ (1- v²/c²) and take the derivatives of both sides with respect to time t, and we get:


dt’/dt =1/√(1- v²/c²)-(v²/c²)/√(1- v²/c²)

= (1- v²/c²)/√(1- v²/c²) =√(1- v²/c²)


F:

d t /dt’ =1/(1v²/c²)


Note that x in the formula is the position of the point p in the s system, which changes with time t, so there are dx/dt = v and d(vx/c²)/dt = v²/c², because the quantities of x and t They are all observed in the s system, and in s, the position x of the point p is moving at a speed v.


This result is the same as above.


We have one more question:


Are the distance traveled by the space point p on the y-axis in the s system and the s’ system equal?


All this special theory of relativity is proved by the imaginary experiment of a train drilling through a cave:


Imagine there is a cave with a train parked outside. The height of the carriage is equal to the height of the cave roof. Now let the train drive into the cave at a constant speed. Will the height of the moving train change?


Assume that the height of the train becomes smaller due to movement. In this way, an observer standing on the ground thinks that the height of the train becomes smaller due to movement, and the height of the cave remains unchanged due to no movement. The train must enter the cave smoothly.


However, the observer inside the train believes that the train is stationary, so the height of the train remains unchanged, but the cave is moving, the height of the cave will decrease, and the train cannot pass through the cave. This creates a contradiction.


However, whether the train can drive into the cave is a certain physical fact and should not be related to the observer's choice. The only reasonable point of view is:


Uniform linear motion cannot shorten the length of space in the vertical direction of motion. For the same reason, it cannot extend, and the result remains unchanged.


Maybe people still have a question? There are many space points in the space around the observer. Why can the movement of one space point represent time?


This should be understood in this way. Time reflects a property of space motion. By describing one of many spatial points in space, we observers can express the changing nature of space with time. This also shows that time It cannot exist independently from the observer.


4. The relationship between the light source movement speed V and the vector light speed C


We introduced the concept of vector speed of light earlier, but did not discuss it in depth.


Whether the speed of light can be regarded as a vector is not discussed in depth in the theory of relativity. According to the theory of relativity, the speed of light has nothing to do with the speed of the light source, the choice of the observer, time, or spatial position. It is purely a constant.


Therefore, the theory of relativity tends to believe that the speed of light cannot be regarded as a vector. In other words, it is meaningless to discuss the vectoriality of the speed of light in the theory of relativity.


The speed of light is a constant first came from Maxwell's electromagnetic wave equation, and the speed of light in the wave equation appears as a constant.


The unified field theory puts forward a different view, believing that the speed of light can be expressed as a vector in some cases, and its direction has a functional relationship with the speed of the light source.


In order to distinguish, the unified field theory calls the vector speed of light the speed of light, represented by a capital C. The size of C [that is, modulus c] does not change, but the direction can change.


The speed of light is called the speed of light, also called the scalar speed of light, represented by the lowercase letter c, which remains unchanged.


The components Cx, Cy, and Cz of the vector speed of light C in the rectangular coordinates x, y, and z axes can change in size. Since the scalar speed of light remains unchanged, the sum of the squares of the three components is always the square of the speed of light.


In the unified field theory, the relationship between the movement speed V of the light source and the vector light speed C is very important. Let's explore this relationship below.


Let's consider a special situation first.


We let the angle between the vector light speed C and the light source movement speed V be θ = (π/2)-β.


Let’s first roughly judge the value range of the scalars v and β of V.


From the theory of relativity, we know that from the constant speed of light, it can be deduced that V can cause changes in the speed of light in the direction perpendicular to V, but it cannot cause changes in the speed of light in the direction parallel to V.


In the unified field theory, the change of C only changes the direction and the quantity remains unchanged.


As V increases, the direction of C gradually deviates from its original position. When the deviation angle β is slightly greater than 0, it corresponds to v being slightly greater than 0. The angle of deviation β = 90 degrees, the corresponding number v is equal to the speed of light c.


Therefore, the β value should be between 90 degrees and 0 degrees, and the value of the number v should be between 0 and the speed of light c [including the speed of light].


In the picture below:


The origin o of the two-dimensional rectangular coordinate system s system and the origin o of the s’ system coincide with each other at time 0, and the x-axis and x’-axis also coincide with each other.


Later, they move in a straight line at a uniform speed V [scalar is v] along the positive direction of the x-axis.


A particle o has been stationary at the origin o of the s’ system. Now, observers of the s system and s’ system jointly inspect a space point p.


At zero time, point p starts from point o and moves along the y’ axis at the speed of light.


If we think of light as a photon, the point o here is the light source, and the point p is a photon. If we think of light as a wave, the point p here is the wave front.


In the unified field theory, light is regarded as excited electrons moving with space. Even if there are no excited electrons or photons, the particle o does not emit light and is not a light source. It is just an ordinary object, but the surrounding space still moves at the vector light speed C Movement outward.


In the latter case, point p can be regarded as a space point, that is, point p is represented as a small space around point o.


An observer in the s' system thinks that point p starts from the particle o at zero time, and after time t', it reaches the position where point p later is, and has traveled so far op = C't' at the vector speed of light C' distance.


An observer in the s system thinks that point p starts at zero time and travels a distance of op = ct at the vector speed of light C [the quantity is c] in time t.


As can be seen in the picture above:

| Vt| /| C t| = sinβ = v/c


Eliminating t, we can get:

| V| /| C | = sinβ = v/c


Since the angle between C and V is θ=(π/2)-β, there is:

cosθ=| V| /| C | = v/c


From the above formula, we can derive sinθ =√(1- v²/c²), which is actually the reason for the relativistic factor.


From the above analysis, the following opinions can be drawn:


When the number v of V approaches zero, V and the vector light speed C are perpendicular to each other in the initial state. In the future, when the number v of V gradually increases, it will cause C to gradually deviate from the original position. When v approaches When the speed of light C is an amount c, C deviates by 90 degrees.


The movement speed V of the light source can cause the direction of the vertical vector light speed C of V to deflect, which can also be explained by the inverse theorem of the previous vertical principle.


The principle of verticality tells us that the vertical state of space at a 90-degree angle can cause movement.


The converse theorem is: Movement can cause the vertical state of space to tilt. When the movement speed reaches the speed of light, the vertical state disappears completely [lying flat].


The above formula sinβ = v/c or cosθ= v/c can be regarded as a quantitative analysis of the vertical principle.


The essence of the vertical principle is that the angle of space and the speed of movement are equivalent and complementary.


The above only analyzes the relationship between the vector light speed C and the light source movement speed V [scalar is v] under special circumstances.


To reveal the universal relationship between them, the vector light speed C needs to be transformed between the inertial frame s’ and the s frame.


In s’, the three components of the vector light speed C’ are: Cx’, Cy’, Cz’,


In s, the three components of the vector light speed C are: Cx, Cy, Cz,


Using the positive velocity transformation of relativity theory [we have proven above that the Lorenz transformation is correct, and the relativistic velocity transformation is obtained by taking the time derivative of the Lorenz transformation, so the relativistic velocity transformation can be used] we can derive the three The relationship between the components and the three components of C is:

Cx’ = (Cx – v)/[1- (Cx v/c²)]


Cy’ = [Cy√(1-v²/c²)]/ [1- (Cx v/c²)]


Cz’ = [Cz√(1-v²/c²)]/ [1- (Cx v/c²)]


From the above it can be derived:


(Cx’)²+(Cy’)²+(Cz’)²


= [(Cx – v)²+ Cy² (1-v²/c²) + Cz² (1-v²/c²) ]/[1- (Cx v/c²)]²


= c²c²[Cx²+ Cy²+ Cz²-2 Cx v+ v²-(c²-Cx²)v²/c²]/(c²-Cx v)²


= c²c²[c²-2 Cx v+ v²-(c²-Cx²)v²/c²]/(c²-Cx v)²

= c²[c²c²-2 c²Cx v+ Cx²v²]/(c²-Cx v)²


=c²


It is derived from this that the vector light speeds C and C’ satisfy the following relationship:

C’·C’ = C·C = c²


The directions of C and C’ are different, but the quantities are the same.


The above does not fully explain the relationship between C and V. This issue still needs to be explored.


5. Derivation of the invariance of time and space intervals in the theory of relativity


Now imagine that there are two observers in the s system [the space-time coordinates are (x, y, z, t)] and the s' system [the space-time coordinates are (x, y, z, t')]. The s system is relative to s' moves along the positive direction of the x-axis at a speed V.


Imagine that at time t = t’= 0, the origins o and o’ of the s system and s’ system coincide with each other. A space point p starts at time 0, starting from points o and o’, and after a period of time reaches the current position of point p.


Dot multiply the formula R(t) = Ct = x i+ y j + z k by itself, the result is:


r²= c²t² = x²+ y²+ z²


r is the number of vectors R. r reflects the movement distance of the space point p relative to the origin measured by the observer in the s system.


The above equation also appears in the theory of relativity, which is considered to be a four-dimensional space-time distance.


By the same token, it can be derived that in the s’ system, the observer measures the movement distance of point p relative to point o’:


r’² = c²t’²= x’²+ y’² + z’²


From r² = c²t²= x²+ y²+ z² it can be derived:


c²t² - (x² + y² + z²) = 0


From r’² = c²t’² = x’²+ y’² + z’² it can be derived:

c²t’²-x’²+ y’² + z’²) = 0


From the above equation, it can be concluded that the space-time interval is constant in two inertial systems moving in a relatively uniform straight line.


The unified field theory believes that the invariance of the space-time interval is essentially the unification of space-time, and time is formed by the movement of space at the speed of light.


6. Correct interpretation of twin Yang Miao


According to special relativity, a moving clock runs slowly.


So some people imagine that as soon as twins A and B are born, A takes a high-speed spaceship to travel to distant space, while twin B stays on the earth and returns to the earth after a few years.


According to B on the earth, A is in motion and A's life process proceeds slowly, so A is younger than B;


From the perspective of person A on the spacecraft, person B is moving, so person B is younger.


Returning to the comparison of encounters, the result should be unique. It seems that the special theory of relativity has encountered insurmountable difficulties.


The explanation of the twin paradox is quite confusing for both those who support the theory of relativity and those who oppose the theory of relativity.


According to the unified field theory, describing and calculating a motion process requires determining the observer, the starting moment and place, and the ending moment and place.


There is no point in discussing the results of a movement without being sure of the observer, the moment and place of its beginning and end.


In the twin problem, A and B break up, and the final place where A and B meet is on the earth, so the earth can be used as a reference point.


Since A is moving relative to the earth, A is younger than B. B is stationary relative to the earth, and B's time is proper time.


What if Person A and Person B were born in space, embraced each other, and later broke up, without the Earth as a reference point? How do we judge?


At this time, it is necessary to determine which of the two people started to accelerate and move away from the other.


This actually involves a fundamental issue about motion - there is a reason for the change of the object's motion state [that is, acceleration], and the object will not change its motion speed for no reason [including accelerating from a static state of zero speed to a certain speed】. That is to say, A and B, who were originally hugging each other, will not separate for no reason.


Suppose that at a certain moment, A starts to accelerate and leaves B, A turns around and comes back, and the two meet, then A is young.


If two people A and B hug each other in space, and then kick each other, they both leave each other with the same force and the same kicking method, and then meet each other after turning around in the universe, who is younger?


In this case, A and B should be equally young.


Twenty-two, the general definition of the four major fields in the universe


In mathematics a field is defined as:


If each point in the space (or a certain part of the space) corresponds to a certain quantity, then such a space is called a field.


When the quantity corresponding to each point in the space is a quantity, the space is called a quantity field. When the quantity corresponding to each point in the space is a vector, the space is called a vector field.


It can be seen from the definition of mathematical field that a field is represented by a point function in space. On the contrary, if a function of a certain point in space is given, a field is given.


We have done a lot of analysis before, connecting the gravitational field (referred to as the gravitational field), electric field, magnetic field, and nuclear force field with the movement of space itself, and identified the four major fields in physics [gravitational field, electric field, magnetic field, and nuclear force]. The fields together form a space that moves in a cylindrical spiral.


In the unified field theory, it is believed that the weak force field is not a basic field, but a combination of electric field, magnetic field and nuclear force field. The electric field and the magnetic field are not the same field, because the electric field and the magnetic field sometimes have different directions, cannot superimpose each other, and cannot directly exert force.


Fields of the same kind can superimpose or subtract from each other, and can also produce interactive forces.


Therefore, we give a unified definition of the four major fields of physics here. Later, we will give precise definitions of the gravitational field, the nuclear force field, the electric field, and the magnetic field respectively.


The unified definitions of the four major fields of physics are:


Relative to our observer, at any space point p in the space Ψ around the particle o, the displacement vector [referred to as the position vector] R from point o to point p changes with the spatial position (x, y, z) or changes with time t , such a space Ψ is called a physical field, or it can also be called a physical force field.


Mathematically speaking, the field is the derivative of the spatial position around the object or the derivative of time. In fact, it is the degree of movement of space relative to our observer.


In actual operation, we use the degree of motion in the movement space around the object particles to define the four major physical fields.


This is also in line with our previous basic principle of unified field theory - all physical phenomena are caused by the movement of a particle in space (or the space itself around the particle) relative to our observer.


To put it simply, a field is a moving space. It is the space itself that is moving. All the effects of the field are the movement effects of the space.


The influence of the field on the object, the application of force on the object, and the movement of the object are all achieved by changing [or will change, or have a tendency to change] the spatial position of the object.


From the above definitions, we can know that the four major fields of physics are all vector fields. Different fields have different degrees and forms of motion because our observers observe the cylindrical spiral motion space from different angles and different ways.


Note that the field is a property shown by the movement of the space around the particle relative to our observer. None of the four basic conditions of space, particle, observer, and motion are indispensable [In special cases, the particle and the observer can be the same things], otherwise, the field loses its meaning.


We also need to realize that fields come in three forms.


We describe the movement of an object in space relative to our observer, measure the displacement of the object in space, and then take the derivative of time, that is, compare it with time, to get the speed. Speed ​​represents the degree of movement of the object in space, and Acceleration represents the degree of change in the speed of motion.


Because the essence of the field is the derivative of the displacement of the moving space around the object with respect to the spatial position or time [relative to our observer].


To describe a field, our first step is to indicate the amount of displacement in the space around the object. In the second step, we look for a motion quantity like time that can be used as a reference to compare with the spatial displacement.


Of course, we can say that the field is:


In a certain time interval, what is the spatial displacement of a certain place in the space around the object?


However, in many cases we can say that the field is:


What is the amount of spatial displacement within a certain static three-dimensional range?


What is the amount of spatial displacement within a certain three-dimensional range of motion?


What is the displacement in space on a stationary surface?


What is the displacement in space on a certain moving surface?


What is the displacement of space on a stationary curve.


What is the amount of spatial displacement on a certain motion curve.


In a certain time interval, what is the spatial displacement in a certain spatial range.


Thus, fields come in three forms:


The distribution of fields in three dimensions.


Distribution of fields on a two-dimensional surface.


The distribution of a field on a one-dimensional curve.


With the help of Gauss's theorem of field theory, we can use divergence to describe the relationship between the distribution of the field on the solid surface and the distribution on the curved surface.


With the help of Stokes' theorem of field theory, curl can be used to describe the relationship between the distribution of the field on the surface and the distribution of the field on the curve.


With the help of the gradient theorem of field theory, the distribution of physical quantities on a certain curve in the scalar field [or quantity field] can be described.


The essence of the field is a space that moves in a cylindrical spiral. The cylindrical spiral motion is the synthesis of rotational motion and linear motion in the vertical direction of the rotation plane. The divergence describes the linear motion part of the space, and the curl describes the rotational motion of the space. part.


Twenty-three, the defining equations of gravitational field and mass


In the unified field theory, the mass m of object point o represents the number of spatial displacements R of divergent movement in a cylindrical spiral at the speed of light within a 4π solid angle around point o.


The gravitational field A generated around point o represents the number of spatial displacements that move divergently at the speed of light through the Gaussian sphere s surrounding point o.


1. The definition equation of gravitational field:


Imagine that there is a particle point o that is stationary relative to our observer, and any space point p in the surrounding space starts from point o at the vector light speed C at time zero, and moves in a cylindrical spiral in a certain direction, after time t, At time t' it reaches the position where p will be later.


We let point o be at the origin of the rectangular coordinate system xyz, and the vector radius R from point o to point p is given by the previous space-time identity equation R = C t = x i+ y j + zk:


R is a function of spatial position x, y, z and time t, which changes with the change of x, y, z, t, and is recorded as:


R = R(x,y,z,t)


Note that the trajectory of point p in space is a cylindrical spiral. We can also think that one endpoint o of the vector diameter R does not move, and the other endpoint p moves and changes, causing R to draw a cylindrical spiral in space. type trajectory.


We take the scalar length r of R in R = Ct as the radius and construct a Gaussian sphere s = 4πr² [In general, the Gaussian sphere may not be a regular sphere, but the sphere is continuous and cannot have holes] surrounding the particle o.


We divide the Gaussian sphere s = 4πr² evenly into many small pieces. We select a small vector surface element ΔS where the p point is located [We use N to represent the ΔS direction, and its number is the surface Δs]. We inspect and find that there are Δn displacement vectors R of space points similar to p pass through vertically.


Note: The radius of the Gaussian sphere s may not be equal to the scalar length of R. We set it to be equal. The advantage is that the inspection point p happens to fall on the Gaussian sphere s.


In this way, the gravitational field A generated by point o at point p in space [the quantity is a]:


a = constant times Δn/Δs


The definition of the gravitational field given by the above formula is simple and clear, but it is too rough and cannot express the vector properties of the gravitational field, nor does it bring the spatial displacement R moving at the vector speed of light into the formula.


In order to achieve the above purpose, we mainly examine the situation around point p.


The vector displacement R = C t of point p passes perpendicularly through ΔS. In general, the vector displacement R = C t may not be perpendicular through ΔS, and may have an angle θ with the normal direction N of the vector surface element ΔS.


At point o, it is stationary relative to our observer. The motion of the space around point o is uniform, and no direction is special. Moreover, the Gaussian sphere we use is a perfect round sphere. Under these conditions, the vector R = C t is the vertical passage through the vector surface element ΔS.


In this way, the gravitational field A [vector form] generated by point o at point p in the surrounding space can be written as:


A = - g kΔn (R/r)/Δs


In the formula, g is the gravitational constant and k is the proportionality constant. Note that the gravitational field A is in the opposite direction to the position vector R pointing from point o to point p in space.


Imagine that there are n space displacement vectors similar to R around point o, with point o as the center, distributed in a radial shape, but the directions of any two are different.


The physical meaning of n times R = nR means that the directions of n spatial displacements are all the same and are superimposed together.


Therefore, when the above R is a vector, it has physical meaning only when Δn=1. However, we should note that n multiplied by r [r is the quantity of R], when n is an integer greater than 1, it still has physical meaning.


So there is the formula:


A = - g kΔn (R/r)/Δs = - g k (R/r)/Δs


Why is the unit vector R/r of R used in the above formula instead of using the vector R directly?


This is because we can only examine the direction and number of vector R on the Gaussian sphere s, but not the length of vector R, so the formula Δn R/Δs actually has no physical meaning.


If R is not completely vertical through the vector surface element ΔS [the number is Δs], and has an angle θ with the normal direction N of the vector surface element, when the number n of the spatial point displacement R is set to 1, the above equation It can also be expressed using the vector dot product formula.

A·ΔS = - a Δs cosθ = - g kΔn


In the above formula, a is the quantity of gravitational field A.


The gravitational field A is determined by two quantities: magnitude and direction cosine.


The size refers to the density (1/Δs) of the distribution of the spatial displacement R of the speed of light on the Gaussian sphere s.


1/Δs or Δn/Δs represents a function with two independent variables, which changes as Δn and Δs change.


The direction cosine is the cosine of the angle θ between the normal directions N and R of ΔS, which is cosθ.


The direction cosine cosθ is a function containing only one independent variable, and this function changes as θ changes.


The physical meaning of the formulas a = constant times Δn/s and A = - g kΔn(R/r)/Δs tells us:


On a small vector surface element ΔS of the Gaussian sphere s=4πr², the density of the vector displacement R [R = C t] vertically passing through the space reflects the gravitational field strength there.


We express Δs in the formula A = - g k Δn (R/r)/Δs by the solid angle Ω and the radius r of the Gaussian sphere, that is, Δs = Ωr².


A = - g k Δn(R/r)/ Ωr² = - g k ΔnR/Ω r³


In the figure above, we represent a small vector surface element Δs in the Gaussian sphere as ds. but:

ds = r dθ r sinθ dφ = r² dθ sinθ dφ = r²dΩ


2. The definition equation of mass


What is the essence of quality? What is the relationship between mass and gravitational field?


Since the concept of mass originated from Newtonian mechanics, we compare the above definition equation of the unified field theory gravitational field geometric form A = - g k ΔnR/Ω r³ with the Newtonian mechanics gravitational field equation A = - g m R/r³, and we can get The mass definition equation of object point o should be:

m = kΔn/Ω


The differential is:

m = k dn /dΩ


The above formula k is a constant. Since space can be divided infinitely, the above differential of n, that is, dn, is meaningful.


Integrate around the right side of the above equation, and the integration area is between 0 and 4π, then:

m = k∮dn / ∮dΩ =k n /4π


The physical meaning of the above formula is:


The mass m of point o represents that there are n spatial displacement vectors R = C t distributed within the surrounding solid angle 4π.


The above m = k dn /dΩ is the differential defining equation of the geometric form of mass.


In many cases, we set n to 1 and get a simplified definition of mass:

m = k /Ω


Once we know the nature of mass, we can explain the gravitational field equation A = - g m R/r³ in Newtonian mechanics.


According to Newtonian mechanics, we take the earth [represented by point o, our observer is standing on the earth] as an example. There is a satellite [represented by point p] above the earth, and the position vector from point o to point p [indirect position vector] Expressed by R [the quantity is r].


Then the gravitational field A = - g m R/r³ generated by point o at point p is expressed on the Gaussian sphere s = 4πr² with radius r, divided into a small vector surface element ΔS, and ΔS passes through 1 Vector R , and R and A are in opposite directions.


The number of ΔS The reciprocal of Δs reflects the size of the gravitational field, and the opposite direction of ΔS is the direction of the gravitational field.


What we need to pay attention to is that the gravitational field equation of the unified field theory reflects the situation at a certain moment, or at a certain moment.


Calculate the curl of the stationary gravitational field A = - g k Δn R/Ω r³ of the unified field theory. When Δn and Ω are constants [that is, the mass is a constant], only R/ r³ is a variable, and the result is zero:

▽×A = 0


Find the divergence of the stationary gravitational field A = - g k Δn R/Ω r³. When (m = kΔn/Ω) is a constant, only R/ r³ is a variable, and the result is also zero:

▽·A = 0


But when r approaches zero [it can also be said that the space point p approaches point o infinitely], and point o can be regarded as an infinitesimal sphere, the formula appears 0/0. Using Dirac δ function, we can get:

▽·A = g u


g is the gravitational constant, u = m/ΔxΔyΔz is the density of object point o.


The curl and divergence of the gravitational field definition equation given by the unified field theory are consistent with the divergence and curl of the gravitational field given by Newtonian mechanics.


4. Derive the relativistic mass-speed relationship from the mass definition equation


The theory of relativity uses momentum conservation and the relativistic speed transformation formula to derive the relativistic mass-speed relationship - the mass increases as the object's speed increases.


The theory of relativity also uses the mass-velocity relationship to derive the relativistic mass-energy equation, so the mass-velocity relationship is very important.


Below we use the definition equation of mass to directly derive the mass-velocity relationship.


Imagine a particle o with mass m’, always resting on the coordinate origin o of the s’ system.


The s system moves in the positive direction of the x-axis at a uniform speed V [scalar is v] relative to the s’ system, and the x-axis of the s system and the x’-axis of the s’ system coincide with each other.


From the perspective of an observer in the s system, the mass of point o is m. We use the above mass geometric definition equation m∮dΩ =k ∮dn to find the mathematical relationship between V, m, and m’.


When point o moves, we should reasonably believe that it will not cause a change in the number n of the spatial point vector displacement R, but may only cause a change in the solid angle Ω. Therefore, we only need to find the relationship between the motion speed V and Ω, which is the relativistic transformation of Ω, and then we can find the relationship between m’ and m.


The solid angle Ω is defined as:


On the spherical surface s with point o as the center and radius r = 1, divide a small piece Δs, with Δs as the base and point o as the vertex, to form a cone h, then Δs is equal to the solid angle of the cone h.


The solid angle Ω of the cone h is the ratio of the base area Δs of the cone to the square of the radius r of the sphere. When Δs becomes infinitely small, it becomes ds, which is:

dΩ = ds/r²


When r = 1, the above equation becomes dΩ = ds.


The above is to use the base area of ​​the vertebral body to define the solid angle. Now we generalize the above definition of the solid angle and use the volume of the vertebral body to define the solid angle.


On the spherical surface s with point o as the center and radius r = 1, divide a small piece Δs, with Δs as the base and point o as the vertex, to form a cone h, then the volume of the cone h


Δv is equal to the solid angle of the cone h.


The solid angle Ω of the cone h is the ratio of the volume Δv of the cone to the radius r cube of the sphere. When Δv becomes infinitely small, it becomes dv, which is:

dΩ = dv/r³


When r = 1, the above equation becomes dΩ = dv.


With the above preparatory knowledge, let us consider that the above point o is in the s’ system, and the mass at rest is

m = k∮dn/∮dΩ


We use a unit sphere with a radius of 1 and divide it into a cone with a vertex at the center point o and a volume of dv’, replacing dΩ’ in the above formula, then:

m = k∮dn/∮dv


Correspondingly, in the s system, when point o moves in a straight line at a uniform speed V [scalar is v], the mass

m = k∮dn/∮dv


Note that n is the same in the s’ system and the s system, that is, the movement speed V of point o cannot change the number n of geometric point displacement.


We only need to find the relationship between dv’ = dxdydz’ and dv = dx dy dz, and then we can find the relationship between m and m’.


According to the simplest version of the Lorenz positive transformation in the theory of relativity [because we default to the observer I in the s system, the particle o is moving relative to me]:


x’ = (x - vt )/√ (1- v²/c²)

y = y

z = z


In the simplest version of the Lorenz transformation, since the position x’ of the point o in the s’ system is stationary, it moves at a speed V in the s system.


Only when we take the time t in the s system to be a fixed moment can it make sense to compare x and x’ with each other. Therefore, dt/dx=0, and we get the differential formula:

dx = dx/√(1- v²/c²)

dy = dy

dz = dz


from that we get:

m = k∮dn/∮dv = k ∮dn/∮dxdydz

m = k ∮dn/∮dv = k∮dn/∮dx dy dz

由∮dxdydz = ∮dy dz dx/√(1- v²/c²)


Can export:


m’= m√(1- v²/c²)


When point o moves at speed V, the mass increases by a relativistic factor √ (1- v²/c²). This result is consistent with the theory of relativity.


5. Lorenz transformation of gravitational field


With the definition equations of the gravitational field and mass, the mass velocity relationship equation, and the Lorenz transformation of the theory of relativity, we can derive the transformation of the gravitational field between the two reference systems s’ system and s system that move in a straight line with each other at a uniform speed.


Assume that the inertial reference frame s moves in a straight line at a uniform speed along the x-axis with a speed V [scalar is v] relative to the s’ frame. In the s’ system, a stationary thin rectangular panel with mass generates a gravitational field A on the thin panel.


We make the sheet perpendicular to the x-axis,


Then from the perspective of an observer in the s system, the component Ax of the gravitational field A along the x-axis does not seem to change.


Because the previous definition equation of the gravitational field tells us that the strength of the gravitational field is proportional to the number of spatial displacements passing through the surface, that is, proportional to the density. The area of ​​the thin plates here does not change, the number of strips does not change, and the density does not change.


However, the mass of the sheet increases by a relativistic factor √(1- v²/c²).


The increase in mass, from a geometric point of view, should be the corresponding change between the direction of the spatial displacement vector and the examined solid angle, so:


Ax = Ax’/√(1- v²/c²)


Ax’ is the component of the gravitational field A in the s’ system along the x’ axis.


When we place the thin plate parallel to the x-axis,


The thin plate shrinks by a relativistic factor, plus increases in mass by a relativistic factor. Note that the positive and negative components of the projection of the tilted gravitational field line on the x-axis cancel each other to zero. So, we get:


Ay = Ay’/(1- v²/c²)


Az = Az’/(1- v²/c²)


Ay’ and Az’ are the two components of the gravitational field A in the s’ system on the y’ axis and z’ axis.


From the previous definition equation of gravitational field, we get:

Ax = -g mx’/r³

Ay = -g my’/r³

Az = -g mz’/r³


Derived from this:


Ax = -(g m’x’/r’³)/√(1- v²/c²)

Ay = -(g my/r³)/(1- v²/c²)


Az = -(g m’z’/r’³)/(1- v²/c²)


From this we get:

Ax = - g mγ( x- vt)/{√[γ²(x-vt²+y²+z²]}³

Ay = - g mγy /{√[γ²(x-vt²+y²+z²]}³

Az = - g mγz /{√[γ²(x-vt²+y²+z²]}³


From this we get:

A= - g mγ[( x- vt)i+ yj+zk]/{√[γ²(x-vt²+y²+z²]}³


Let θ be the angle between the vector radius R [the scalar is r =√[γ²(x-vt)²+y²+z²] and the speed V [the scalar is v], A can be expressed in polar coordinate form:

A = - g m /γ²r² [√(1- β ²sin²θ)] ³【r】


In the formula, g is the universal gravitational constant, γ = 1/√ (1- v²/c²), β = v/c, [r] is the unit vector of the vector diameter R (scalar is r).


This result is the same as the relativistic transformation form of the electric field. This shows that Gauss's theorem is applicable to the stationary gravitational field and to the gravitational field of uniform linear motion.


In the s’ department, there are,


▽·A=∂Ax'/∂x' +∂Ay' ∂y'+∂Az' /∂z' = g m'/dv'


In the S series there are:

▽·A=Ax/x +Ay /y+Az /z = g m/dv


Where g is the universal gravitational constant, dv’=dxdydz’ in the s’ system, the mass is m’, dv=dxdydz in the s system, the mass is m.


From the above gravitational field transformation, it can be proved that both Gaussian formulas can be established. Gaussian theorem is not only applicable to the stationary gravitational field of stationary objects, but also to the gravitational field of moving objects.


Note that γdx = dx’ in the formula is obtained by differentiating the Lorenz forward transformation x’ =γ(x-vt).


Twenty-four, unified field theory momentum formula


1. Rest momentum formula of unified field theory


The basic assumptions of unified field theory are:


When any object o in the universe is stationary relative to our observer, the surrounding space always moves outward in a cylindrical spiral with the object as the center and at the vector speed of light.


Suppose there is a particle point o that is stationary relative to our observer. Any space point p in the surrounding space starts from point o at zero time and moves in a certain direction at the vector light speed C', after time t', at t" Time reaches the position where point p is later.


Assume that there are a total of n vector displacements of space points in the space around the particle o. We use R’ = C’t’ to represent the displacement of one of them.


We take an appropriate solid angle Ω around point o, which happens to contain a space vector displacement R = C’t’


L = k R’/Ω


It can reflect the amount of space movement in the local area around point o. k in the formula is the constant of proportionality, and Ω is a solid angle of any size.


Calculating the partial derivative of R' in L = k R'/Ω with respect to time t' can reflect the degree of motion of the local area of ​​point o with time t'.


∂L /∂t' = k (∂R'/∂t')/Ω = kC'/Ω


Note that R’ = C’t’. Using the previous definition equation of mass m = k / Ω,


The above equation can be rewritten as the rest momentum formula of the unified field theory:


Pstatic = m’C’


In the momentum definition equation here, the mass is represented by m' in order to distinguish the motion mass m that will appear, and C' is in order to distinguish the motion vector light speed C that will appear.


The rest momentum of point o reflects the degree of motion of the surrounding space when point o is stationary.


We must realize that the rest momentum of point o is the degree of change of the motion displacement R’ of the surrounding space point p with the change of the solid angle Ω and time t’, and does not change with the change of the distance between point o and point p.


Therefore, when we measure the static momentum of point o of an object, we do not need to consider the distance between point o and an inspection point p in the surrounding space. This is different from the gravitational field. When point o moves, the situation of motion momentum is similar.


2. Motion momentum formula


Assume that the s’ system moves linearly along the positive direction of the x-axis at a uniform speed V [scalar is v] relative to the s system.


The above point o is stationary relative to the observer in the s’ system and has rest momentum m’C’.


We analyzed earlier that when point o moves at speed V relative to the observer in the s system, the two parts of the rest momentum - mass and vector light speed - will change.


In the s’ system, the rest mass at point o is m’, which becomes a moving mass m in the s system.


In the s' system, the vector light speed of the space point p around point o relative to the observer in the s' system is C'; in the s system, the vector light speed of the space point p around the o point relative to the observer in the s system is C .


The directions of C and C’ are different, but the modules are the same, both are c, that is:

C·C’= C·C = c²


The detailed proof is in Section 22, "Explanation of the Invariance of the Speed ​​of Light in the Lorenz Transformation", Section 4, "The Relationship between the Movement Speed ​​of the Light Source V and the Vector Light Speed ​​C."


In the s system, can the momentum of motion be written as m C?


Obviously not, because C is the speed of the space point p around the particle point o relative to the observer in the s system, not the movement speed relative to the particle point o.


Momentum reflects the movement of the space around the particle o, rather than the movement of the space around the observer.


In the s’ system, the observer and the particle point o are relatively stationary, and there is no difference between the speed of point p relative to the particle point o and the speed relative to the observer.


However, there is a difference in the s system, because in the s system the particle point o moves in a straight line along the x-axis with a speed V relative to the observer.


In the s system, C is the speed of point p relative to the observer in the s system, and C is also the superposition of the movement speed of point p relative to particle point o [we use U to represent it] and V, that is, C = U+V.


Therefore, in the s system, the movement speed of point p relative to point o should be:


U=C-V


Therefore, the momentum of motion can be written as:


P = mU = m(C-V)


Relativistic mechanics and Newtonian mechanics believe that the speed of light motion in the space around an object does not exist, that is, C = 0. Therefore, the momentum equation of Newtonian mechanics and relativity is


P = m V


It can also be said that the momentum mV of the theory of relativity and Newtonian mechanics is just a change when m C changes in the momentum formula P of the unified field theory = m (C-V).


The unified field theory momentum formula only expands the Newtonian and relativistic momentum formulas to include the vector light speed motion in the surrounding space when the object is stationary. It does not completely negate the relativity theory and Newtonian mechanical momentum formulas.


3. The momentum of an object when it is moving is equal to the amount when it is at rest.


Multiply both sides of the motion momentum formula P motion = m (C–V) by themselves, and the result is:


p² = m² (c²– 2C·V + v²)


p = m√(c²– 2C·V + v²)


We should reasonably think that the quantity m'c of the stationary momentum m'C' of the object when it is at rest, and the quantity m√(c ² – 2C·V + v²) of the motion momentum m (C–V) when it is moving should be Equal, the only difference is the direction. So, there should be:


m’c = m√(c²– 2C·V + v²)


Due to the constant speed of light and the limitation of the maximum speed of light, when the moving speed V of an object is very large, it is close to the speed of light C, and the angle θ between V and C will also tend to zero. If it does not tend to zero, there will be super-light speed. Appear. The strict proof is as follows:


The s’ system moves in a straight line relative to the s system at a uniform speed V along the x-axis [or the x’-axis, the x’-axis and the x-axis coincide with each other].


In the s' system, let the vector light speed of the space point p around the object point o be C', Cx' be the component of C' on the x' axis, θ' be the C' and x' axes [or Cx', because Cx 'parallel to the x' axis]. F:

cosθ= cx/c


cx’ is the scalar of Cx’, and c is the scalar of C’.


In the S series, there are:

cosθ= cx/c


θ is the angle between C and Cx in the s system. cx is the scalar component of C on the x-axis.


According to the inverse transformation formula of Lorenz velocity transformation:

cx=(cx+v)/(1+ cx v/c²)


Adding the above cosθ= cx/c, cosθ’= cx’/c, it can be derived:

cosθ= (cosθ+v/c) / [1+(v/c)cosθ]


It can be seen from the above formula that when the quantity v of the speed V is close to the speed of light c, cosθ is close to 1, that is, θ is close to zero.


When the motion speed V and the speed of light C are very close, we ignore the difference between the number v of V and the number c of C, and the angle θ between V and C also tends to zero. The results are:


When v≈c, C·V≈v² [If we choose C·V≈c², the result will be an imaginary number and meaningless], the results are:


m’c = m√(c²–v²)


Note that although we ignore the difference between c and v in the above formula, we retain the difference between c² and v².


For example, the difference between 9 and 8 is 1, and the difference between 9² and 8² is 17. We can only ignore the small values ​​and retain the large values, which is reasonable.


Dividing both sides of the above equation by the scalar speed of light c, we get:


m’= m√(1–v²/c²)


Does this style look familiar to everyone? Yes, it is the famous relativistic mass velocity formula.


It turns out that when an object moves at speed V, the increase in mass m is at the expense of reducing the original speed of light C in the surrounding moving space, and the total amount of momentum is still conserved.


This is to expand the scope of momentum conservation to different reference systems, that is, when observers moving with each other measure the momentum of the same object, the total quantity remains unchanged.


The philosophical idea is that the observer can only observe the state of motion, but cannot change the state of motion.


We then use the component form of (C–V) to analyze the formula m’c = m√ (c²– 2C·V + v²).


The three components of (C–V) are (Cx–Vx), (Cy–Vy), (Cz–Vz). Let the number of (C–V) be u, then:


u = √[(Cx–Vx)²+(Cy–Vy)²+(Cz–Vz)²]

=√(Cx²+Cy²+Cz²+Vx²+Vy²+Vz²- 2C·V)


=√(c²+ v²- 2C·V)


The situation is the same.


Multiplying both sides of m’ = m√ (1 - v²/c²) at the same time by the square of the scalar light speed can get the energy equation of relativity:


Energy = m’c² = mc²√(1 - v²/c²)


There are detailed arguments later.


25. Unified field theory dynamic equations


1. General definition of force


Force is the degree of change in the motion state of an object [or particle] in space relative to the motion of our observer [or the motion of the space around the object itself] in a certain space range [or a certain period of time].


Mathematically speaking, force is the derivative of an object's motion with respect to its position in space and time.


Forces are divided into inertia forces and interaction forces.


The inertial force is the derivative of the motion of an object with respect to its spatial position, which is the solid angle. Therefore, the force-receiving object has nothing to do with the distance between the force-exerting object and the observer. Inertial forces are relatively simple.


The interaction force is the derivative of the motion of the object with respect to the spatial position. This spatial position can be a volume, a curved surface, or a position vector.


Therefore, the force-receiving object is related to the force-exerting object and the distance from the observer.


There are inertial force and universal gravitation in Newtonian mechanics.


The inertial force of an object has nothing to do with the distance between the object receiving the force and the object exerting the force. The gravitational force is an interaction force and is related to distance.


In electromagnetism, the Lorenz force is an inertial force and the Ampere force is an interaction force.


In this section we will also extend the inertial force of Newtonian mechanics to electromagnetic force and nuclear force.


2. Write the four inertial forces of the universe in an equation


We use the degree of motion of a certain space point p in the space around particle o to describe the momentum P of point o = m (C–V). The momentum of point o has nothing to do with the distance between point o and point p, and has similar properties to the inertial force.


We follow the idea of ​​Newtonian mechanics - inertial force is the derivative of momentum with respect to time. We can think that the degree of change of universal momentum P = m (C-V) with time t is the four inertial forces of the universe.

F = dP/dt = Cdm/dt - Vdm/dt + mdC/dt - mdV/dt


(C-V)dm/dt is the added mass force, and m(dC–dV)/dt is the acceleration force.


In the unified field theory, Cdm/dt is considered to be the electric field force, Vdm/dt is considered to be the magnetic field force, mdV/dt is the inertial force in Newton's second theorem, which is also equivalent to universal gravitation, and mdC/dt is the nuclear force.


mdC/dt This force is considered a nuclear force in the unified field theory for the following reasons:


The energy of an atomic bomb explosion can be calculated using the mass-energy equation e = m c² [E is not used here but e is used because this article stipulates that capital letters are vectors]. Therefore, the integral of the product of displacement and nuclear force along the direction of the nuclear force should be the same as mc². and similar forms, and mdC/dt meets this condition.


The dynamic equations of the unified field theory should include nuclear forces, because the unified field theory believes that all interaction forces come from the change of the motion state of the particle in space, or the change of the motion state of the space around the particle.


If we consider the mass-energy equation e = mc² in the theory of relativity, it can be reflected that the nuclear force [F = m(d/dt)C] is the work done by the object particles moving a distance R along the direction of the nuclear force. From the definition equation of work and energy, Then there are:

e=∫0,r F·dR = F·R


r in the above formula is the number of displacement vector R, and the integration range is between 0 and r.

e = F·R = mC·R(d/dt)


From the previous space-time identity equation R=Ct [differential formula dR/dt=C] we get:

e = F·R = mC·R(d/dt)= mC·C = mc²


The motion caused by the added mass force (C-V) dm/dt can also be called the added mass motion. The motion of adding mass is a discontinuous motion. The change in the speed of light when it is reflected back from the glass does not take time and is discontinuous. Light is a motion of adding mass.


Mass-added motion means that it takes time for the mass of an object to change with time. When the mass changes to zero, it can suddenly reach the speed of light from a certain speed. Observers who move with the object find that this motion process does not take time, and they start from Suddenly disappear in one place and suddenly appear in another place.


There is a discontinuous quality to changes in mass. The reason why the energy of electromagnetic wave radiation is discontinuous in quantum mechanics is:


A photon requires a fixed amount of energy that causes its mass to become zero before it can be excited into a photon. If the energy is less than this, the photon cannot be excited to move at the speed of light. When the energy of the photon reaches the excitation condition, it will move away at the speed of light. If more energy is added, it cannot be added.


If it is assumed that space is stationary, that is, C = 0, then the formula

F = dP/dt = Cdm/dt - Vdm/dt + mdC/dt - mdV/dt


C = 0, which returns to the dynamic formulas of relativity and classical mechanics:

F = dP/dt = - Vdm/dt - mdV/dt


Inertial force and interaction force are related, and they have both similarities and differences. For both forces, we can use the motion of a space point p in the space around the force-bearing particle o to examine the force on the particle o.


However, the inertial force has nothing to do with the distance r from point o to point p, while the interaction force is related to r.


We use solid angle to examine inertial force, and solid angle has nothing to do with distance. As for the interaction force, we use a three-dimensional cone or Gaussian surface to examine it. The three-dimensional cone or Gaussian surface is related to distance.


Twenty-six, explain Newton’s three major theorems


Newtonian mechanics includes three major theorems and the universal gravitation theorem.


The three major theorems of Newtonian mechanics are expressed as:


1. Any object [or particle] attempts to maintain a state of uniform linear motion or a state of rest until an external force changes.


2. When the force exerted on an object causes the object to accelerate, the resulting acceleration is directly proportional to the force received and inversely proportional to the mass of the object, and the direction of acceleration is consistent with the direction of the force.


3. An object exerting a force on another object always experiences an equal and opposite reaction force from the other object.


According to modern views, Newtonian mechanics should only be established relative to a certain observer.


Newton defined the mass m and velocity V of an object as momentum P = mV,


A careful analysis shows that the core of Newtonian mechanics is the concept of momentum. The concept of momentum originally came from Newtonian mechanics. Now we use the concept of momentum to restate Newton's three major theorems.


1. Relative to an observer, any particle point with mass m in space tries to maintain a certain momentum mV. V is the speed of the particle moving in a straight line in a certain direction, including when the speed is zero [the momentum must also be zero] static state.


2. When the particle is acted upon by an external force, the momentum will change. The rate of change of momentum P with time t is the external force F= dP/t = d(mV)/dt = m A


3. The momentum of a particle is conserved. In an isolated system, when the particles interact, the momentum gained by one particle is always lost by the other particle, and the total momentum remains unchanged.


In Newtonian mechanics, the mass m is considered to be an invariant, while the theory of relativity believes that the mass can change. However, the theory of relativity inherits some other views of Newtonian mechanics.


The momentum formula of the theory of relativity is the same as the form of Newtonian mechanics, except that in the theory of relativity the mass m can be a variable.


Unified field theory reveals the nature of mass and thus can completely explain Newtonian mechanics.


According to the view of unified field theory, Newton's three major theorems can be further understood as:


1. Compared to our observer, the space around any object moves outward at the vector speed of light C. Within the solid angle range of 4π, the number n of space displacements at the speed of light is the mass of the object m = k n/4π .


Therefore, when the object is at rest, it has a rest momentum mC. When we try to make the object move, we must apply a momentum [mass m times speed V,] to make mC change.


2. Force is the cause of changing the state of motion of the space around an object that diverges at the vector light speed C and moves at the speed V. It is also the cause of the change in momentum. Therefore, we use the derivative of momentum with respect to time to express force.


Force is defined as: Force is the amount of change in the motion state of an object moving in space [or the movement of the space around the object itself] in a certain space range [or a certain time].


3. Momentum is the composite m(C-V) of the motion of an object in space (mV) and the motion of the space around the object (mC), and is a conserved quantity. The forms of momentum measured by observers who move with each other are different. , and the total amount of momentum remains unchanged, regardless of the observation of the observer.


Twenty-seven, prove that inertial mass is equivalent to gravitational mass


Newtonian mechanics believes that inertial mass reflects the degree to which an object is not easily accelerated, while gravitational mass reflects the ability to accelerate other objects.


In the above point o with mass m, when it is stationary relative to our observer, if there is a point p with mass m' far away from r, it will be affected by the gravitational force F of point o, which will make point p have a points to point o with acceleration - A, and

F= - (g m m’/r²)


F=-mA


Without giving any explanation, Newton equated the inertial mass m' in the formula F= - mA with the gravitational mass m' in the formula F= - (g m m'/r²) [R], and we got the following Mode:


A= -(g m /r²)【R】


r is the quantity of R, and [R] is the unit vector of R. This is what people often say that inertial mass is equivalent to gravitational mass.


If we prove that the acceleration A from point p to point o is equal to the gravitational field generated by point o at point p, we can prove that inertial mass is equivalent to gravitational mass.


Below we give the proof.


In the gravitational field equation A = - g k n R/Ω r³ given earlier, in order to facilitate the analysis of the problem, we set the number n of the light speed motion space displacement vector R = C t to 1, and the position vector from point o to point p, Let us use R to represent it, then the gravitational field equation is:

A= - g k R/Ωr³


In the above equation, we keep the quantity r of R constant, but the direction changes. In this way, the gravitational field A becomes the corresponding change between the direction of the spatial displacement R of the speed of light and the solid angle Ω.


Ω is a solid angle on the Gaussian sphere s = 4πr² surrounding point o. When r takes a fixed value, the size of Ω is proportional to R·R = c²t².


Because although the quantity r of R remains unchanged, R is a vector, and an area can be drawn on the Gaussian sphere s through changes in two directions perpendicular to the radial direction of R, and this area is proportional to Ω. Because the size of Ω is equal to an area on the Gaussian sphere s = 4πr² (r is set to 1 or a constant).


F:

A= - g k R/ c²t²r³


Since g, k, c, and r are all constants, combining the constants, we get:


A = - constant times R/t²


Taking the derivatives of R and t² with respect to t twice we get:


A= - constant times d²R/ dt²


Since Newtonian mechanics is the earliest mechanical system in human history, the above constants can be set to 1, just like the proportionality constant of Newton's second theorem can be set to 1. F:

A= - d²R/ dt²


Proof completed.


Twenty-eight, explain the nature of gravity


The most puzzling question about universal gravity for mankind is how the gravitational force between any two objects in the universe is generated, and how the gravitational force is transmitted to each other.


In fact, the nature of gravity is very simple.


For example, if a car is coming toward you, and the driver feels that he is stationary, he must think that you are moving towards the car. If a car is accelerating towards you and the driver feels that he is stationary, he must think that you are accelerating towards the car.


It doesn’t matter whether you are moving or the car is moving. The key and meaningful thing is that the space between the car and the person is changing.


The essence of universal gravitation is the change in spatial motion between particle points, a property displayed relative to our observers.


The motion change of the space between two mass points and the relative motion between the two mass points should essentially be the same thing.


Human beings are blinded by the word "force" called gravitation. They always think about what force is. What is force? The more I think about it, the more confused I become!


A girl walked by me. I said the girl was very beautiful. I had a knife. I said it was very sharp. Beauty is a quality we describe to a girl, and sharpness is a quality we describe to a knife.


Force is a property that we describe relative motion between objects. Force is not a specific thing.


When two objects move at a relative acceleration or have a tendency to move at a relative acceleration, we can say that there is a force acting between them.


Imagine that in China, a person holds a small ball in his hand. At a certain moment, the person puts down the small ball, and the small ball accelerates from a static state and hits the earth. According to the previous view, it can also be said that the ball is always stationary, and it is the earth that hits the ball.


Some people may object that if we put a small ball in Brazil, our symmetrical country, at the same time, wouldn't it mean that the small ball will fly into the air at an accelerated speed?


This rebuttal actually requires a premise: space is static and motionless, and all objects move in the static ocean of space like fish. The existence of space has nothing to do with the movement of particles.


The key point is: space itself is moving and changing all the time, and the movement of space and particles are closely linked. As for why space moves, please refer to the previous "Vertical Principle".


We observers stand on the earth and drop a stone casually. The stone does not receive any other force but is affected by the earth's gravitational force. It starts a free fall from a stationary state and falls toward the center of the earth. .


Without this stone, the space where the stone is still falls toward the center of the earth in the same way as the stone. If you could dye space with color, you would see that space is constantly falling toward the center of the earth. This is the essence of the gravitational field.


Compared to our observers, the movement of space around a single particle on the earth is uniform, the distribution of the gravitational field is also uniform, and there is no universal gravity.


When a stone with mass exists in the space around the earth, the uniform motion state of the earth and the space around the stone will be changed. The amount of change within a unit solid angle is the universal gravitation.


We set the stone as point p, use m to represent the mass of the stone, set the earth to point o, and use m’ to represent the mass of the earth.


According to our previous explanation of Newton’s three theorems, the gravitational force F on point p by point o can be expressed as:


F=mA


In the previous proof that inertial mass is equivalent to gravitational mass, we know that the gravitational field A generated by the earth at point p (essentially the acceleration of space itself) and the acceleration of point p (the acceleration of an object in space) are equivalent. so:

A = - g mR/r³


In the above formula, g is the universal gravitational constant, R is the position vector from point o to point p, and r is the distance between point o and point p.


The formula of universal gravitation is derived from the formulas F = - m A and A = g m’R/r³:

F = - g m mR/r³


The above tells us that the essence of gravity comes from relative motion, and the essence of interaction force is also an inertial force. This is in line with the basic principle of the unified field theory mentioned above - all physical phenomena are formed by motion.


We regard the gravitational field A = - g m'R/r³ around the earth as the degree of motion in the space around the earth. If another particle p suddenly appears around the earth, the space around the particle p will also have the same motion as the space around the earth. In this way, the gravitational field A = - g m'R/r³ around the earth will change.


We understand the gravitational force F on the earth at point p as the degree of change in the gravitational field around the earth caused by the mass m at point p [m is proportional to n/4π].


The degree of change can certainly be expressed as n changes within the angle range of 4π


A = g m’R/r³, so,


F = - constant times n/4πg (m’R/r³) = - g m m’R/r³


An object with mass m’ generates a gravitational field A around it, and another object with mass m is in the gravitational field A, causing a change in A. The degree of change is the universal gravitation.


What we need to note is that the change in the gravitational field A here is not the degree of change of A with time and spatial position changes, but the change in A caused by A multiplied by the mass m of the object point p.


This is like a line segment multiplied by another line segment in the vertical direction, causing the original line segment to change and become a rectangle.


According to Newtonian mechanics, a satellite [represented by point p] above our earth [represented by point o] rotates in a perfect circle around the earth. At a certain moment, the acceleration A from point p to point o is the acceleration A produced by the earth at point p. gravitational field.


We can imagine that this satellite is very small, and its acceleration A toward the earth can still represent the size and direction of the gravitational field where point p is located.


According to the idea of ​​unified field theory - the field is the movement of space itself. When we take away the satellite, only the space point where the satellite is located [we still use point p] rotates around the earth, and its acceleration towards the earth can still represent space. The magnitude and direction of the gravitational field where point p is located.


We use R to represent the position vector diameter from point o to point p. Then R and A are proportional to each other, but in opposite directions, satisfying the following relationship:

A = - k R


k is a constant. The above equation indicates that the gravitational field generated by a stationary object around it is a gradient field.


Since the gravitational field is equivalent to acceleration, we know that acceleration and displacement are proportional and opposite in direction, which is a wave process.


This shows that the gravitational field is volatile. This kind of fluctuation is the fluctuation of space itself, a spiral wave, and the speed of fluctuation is the speed of light.


If the size of the vector radius R remains unchanged and only changes in direction, one end is fixed and the other end circles around, and the above static gravitational field curl is zero, then:

∮A·dR = 0


The above indicates that the gravitational field generated by a stationary object in the surrounding space is a conservative field.


From the perspective of cylindrical spiral motion in space, the gravitational field is the acceleration part of the first circle of cylindrical spiral rotation in space that points toward the center.


The space around the earth and the sun [facing us as observers] both rotate counterclockwise. Where the rotations contact each other, the motion of space is in opposite directions, which offsets a part of the space, causing the space between the sun and the earth to decrease and approach each other, which is shown as mutual attraction.


Twenty-nine, space-time wave equation and gravitational field


As pointed out earlier, the space around the object moves divergently in a cylindrical spiral manner, and the vector displacement of the space point outside the particle changes with the position in space and with time.


The physical quantity [here is the displacement of the spatial point outside the particle point, referred to as the position vector] changes with the position in space and with time, and can be considered to have a wave process.


We know that there is a big difference between waves and cylindrical spiral motion. Waves are the propagation of vibration in the medium, unlike spiral motion, which is the movement of the position of the particle in space. But for this special thing called space, the two movements are compatible.


The movement of one space point will not have a fluctuation effect, but the situation is different for a group of space points.


You may remember a famous saying: There are no two identical leaves on a tree, but this is not true for points in space.


There is absolutely no difference between one space point and another space point. It can be concluded that the cylindrical spiral motion of space contains wave forms.


Next, we derive the wave equation of space-time from the previous space-time identification equation R(t) = Ct = x i+ y j +z k, and point out the relationship with the gravitational field.


Suppose there is a particle point o somewhere in the universe, which is stationary relative to our observer. According to the previous physical definition of time and the space-time identity equation, the time t between point o and the observer can be determined by the displacement R of a space point p around point o. (t) = Ct = x i+ y j +z k to represent.


We take the derivative of R with respect to time t, and the result is:

dR/dt = C


Square both sides of the above equation and the result is:


(dR/ dt)·(dR/dt )= c²= dr dr/dt dt


c is the scalar of the vector light speed C, and r is the scalar of R.


Let us now consider another space point p'. Point p' moves around point o. We use L to represent its displacement. L changes with time t and is a function of time t. From the relationship between R and t, we can conclude that L is R function.


We take the derivative of the displacement L of the space point p' with respect to the quantity r of the space displacement R twice, and the result is:

²L/ r² = ²L/ c ²

²L/x² + ²L/y² +²L/z² = ²L/c²


r is the number of vectors R. The above differential sign d has been changed to the partial differential sign ∂.


Solving the partial differential equation ∂²L/∂t²=c²∂²L/∂r², the general solution is:

L(r, t) = f(t r /c)+g(t + r /c)


f and g represent two independent functions. The equation L(r,t) = f(t - r/c) can be considered as a wave of space points traveling outward from the particle point o.


The equation L(r,t) = f(t + r/c) is traditionally believed to not exist in physics, and is considered to be a wave that converges to point o from infinite distance.


For ordinary media, it seems that there is no such physical meaning, but for a special medium like space, it does have physical meaning. This can actually explain the source of negative charges, which will be discussed in detail later.


The above equation also includes the form of straight-line motion in all directions with point o as the center, and the movement of straight lines from all directions converging to point o. This motion can be viewed as a limiting case where the amplitude of the spiral wave approaches zero.


The equation ∂²L/∂t²=c²∂²L/∂r² has two special solutions L = Acosω (t–r/c) and L = Asinω (t–r/c) that satisfy this equation.


The fluctuation speed c above is the speed of light, and the fluctuations in space-time are transverse waves.


If the continuity of motion is considered, the components Lx and Ly of the displacement L on the x-axis and y-axis are combined, and the motion form on the vertical plane of the z-axis should be a circle.


Therefore, in some cases, one of Lx and Ly takes a cosine wave, and the other takes a sine wave. Therefore, there is the following cylindrical spiral space-time wave equation:


Lx = Acosω(t–z/c)


Ly = Asinω(t–z/c)


In the unified field theory, the gravitational field is the source of fluctuations caused by space vibrations, while the electromagnetic field is the propagation of space vibrations, and the propagation speed is the speed of light.


Thirty, the defining equations of charge and electric field


1. The definition equation of charge


In the unified field theory, charge and mass are the motion effects of the space around the particle moving divergently in a cylindrical spiral at the speed of light. They have a common origin - the speed of light and spiral divergent motion of space.


Assume that the particle point o is stationary relative to our observer, and the position vector from point o to a surrounding space point p is R. We use the number r of R to build a Gaussian sphere s=4πr² to surround point o.


One endpoint of R is at point o, and the other endpoint p is moving in a cylindrical spiral, and the rotational motion will draw a solid angle Ω on the Gaussian surface s.


As pointed out earlier, point o with mass m can be expressed as:

m = k(1/Ω)


Mass m represents the solid angle 4π surrounding point o, passing through n light speed motion space displacement vectors R.


The formula m = k(1/Ω) is a simplification of the mass definition equation, which means that there happens to be an R on the unit solid angle Ω.


In the unified field theory, if the particle o carries a charge q, q represents the number of R that passes through the unit solid angle in unit time. That is to say, the degree of change of mass m with time t is the charge. Therefore, there is the definition equation of charge:

q = k’dm/dt = - k’k (dΩ/dt)/ Ω²


In the formula, k’ is a constant.


The above is the differential definition equation of charge, which can also be considered as the geometric form definition equation of charge.


This charge definition equation reflects that the size of the charge is related to the angular velocity of the solid angle of the rotational movement in space around the particle.


Since Ω is a solid angle, 4π is one of the most important values. This is the fundamental reason for charge quantization.


The change in (dΩ/dt) is a change in angle, and the change is reciprocating, so the change in time t is periodic.


It can be seen from this definition that the nature of charge is closely related to the rotation frequency of space.


The definition of charge here is partly an assumption and partly a reasoning. That is to say, the electric charge is the degree of motion of the space around the object particles diverging in a cylindrical spiral at the speed of light.


We get this charge-defining equation and see if it matches the knowledge we have. If it all agrees, it means that the charge-defining equation is correct and reliable.


This charge definition equation can only be applied to a single charged particle. For macroscopic objects, which contain many positively and negatively charged particles, it cannot be directly applied, because most of the positive and negative charges of macroscopic objects cancel each other out.


2. Prove the relativistic invariance of charge


In the theory of relativity, charge does not change with the speed of motion, but the theory of relativity does not prove it. Below we give the proof using the charge definition equation.


When the object particle point o is stationary relative to our observer, it carries a charge q. According to the above relationship equation between charge and mass:

q = k’dm/dt


We can easily see that when point o moves at speed v relative to our observer, mass m and time t [compared to the proper time] simultaneously increase by a relativistic factor √ (1- v²/c²), so, q Still unchanged.


3. Some issues we need to pay attention to regarding the definition of charge


The dm/dt in the definition of charge q indicates that the charge amount of the particle is proportional to the mass change rate of the particle. This does not seem to be consistent with the facts. In practice, we have not found that the mass of charged particles changes drastically, nor have we found any The continuous increase or decrease in quality over time.


The reason may be that the mass change of charged particles changes periodically, rather than changing to infinity with time.


Moreover, the frequency of this change may be extremely fast, just like alternating current. Because the frequency of change is so fast, we cannot feel and detect the change.


In the above mass definition equation m = k n/Ω, k is a constant. For a single object particle, when no other particles are close around it, the number n of spatial motion displacements will not change. The change is the change of the solid angle Ω. And we know that the change of solid angle is periodic.


If this situation is confirmed, then in quantum mechanics matter waves, particles have wavelengths and frequencies, which are likely to be related to this.


4. Geometric definition equation of electric field


Point o, which is stationary relative to our observer, carries charge q, and generates an electric field E at point p in the surrounding space. We surround point o with a Gaussian sphere s = 4πr². p is an inspection point on s, and points from o to p. The position vector is R, so the number of R is r.


The electric field definition equation given by Coulomb's theorem is E = q R/4πε. r³, 4π ε. is a constant, we don’t need to consider it, R is the spatial displacement vector, r is the radius of the Gaussian sphere, the only thing we don’t know is what the charge q means.


Once we understand the geometric meaning of charge q, we also completely understand the geometric meaning of electric field E. Therefore, we define the equation of charge q

q = k’dm/dt = - k’k (dΩ/dt)/ Ω²


Bring in E = q R/4πε. r³, the geometric definition equation of the electrostatic field E is given:


E = - k’k (dΩ/dt) R/Ω²4πε. r³


The electric field is expressed as the spatial displacement R passing through the Gaussian sphere s per unit time, and the density distributed on s has more time factors than mass.


When the direction of the electric field of a charged particle is consistent with the surrounding space displacement, it is a positive electric field, and on the contrary, it is a negative electric field.


5. Explain Coulomb’s law


Coulomb's law is expressed as follows:


Relative to our observer, the force F between two stationary point charges q (electricity is q) and q' (electricity is q') in vacuum is proportional to the product of their electric charges, and is proportional to the distance r between them. are inversely proportional to the square of , and the direction of the force is on the line connecting them.


Charges can be either positive or negative. Charges with the same sign repel each other and charges with different signs attract each other. The mathematical formula is:


F = (k q q’/r²)【R】= q q’R/4πε. r³


where k is the proportionality constant, ε. is the dielectric constant in vacuum, R is the position vector pointing from q to q’, its quantity is r, [R] is the unit vector along R.


From the above definition equations of charge and electric field, it can be seen that the electric field generated by charge q at q’ should be


E = - k’k (dΩ/dt)R/Ω²4πε. r³


Since the charge q’ = k’k ​​(dΩ’/dt’)/Ω’² appears at point p near q, the electric field E of the charge q at point p changes.


We understand this kind of field change [because the nature of the field is to move space in a cylindrical spiral shape, in fact, the space is changing] as the force of q on q', and use the product of E and q' to express this change. The effect is the above Coulomb's theorem.


6. Positive and negative charge model


In the unified field theory, it is determined that particles are charged because the space itself around the particles moves in a cylindrical spiral at all times.


We know that cylindrical spiral motion can be decomposed into rotational motion and linear motion perpendicular to the rotation plane.


The particle carries a positive charge and generates a positive electric field around it. This is caused by the linear motion part of the space around the particle diverging in all directions relative to our observer with the particle as the center, and the rotating part rotating counterclockwise, and it satisfies the right-handed spiral.


The radial speed [note that it is different from the speed of motion in a straight line, but the rotational speed superimposed on the speed of motion in a straight line] is the vector speed of light, pointing from the positive charge to space at infinity.


Particles are negatively charged and generate a negative electric field around them. This is caused by the fact that the linear motion part of the space around the particle converges towards the particle from infinite distance relative to our observer, and the rotating part is also counterclockwise. The same applies to right-hand spirals.


Radial velocity is the vector speed of light, directed from infinity to negative charge in space.


The cylindrical spiral shape of the space around charged particles is the reason why the particles are charged. We know that cylindrical spiral motion is the superposition of rotational motion and linear motion in the vertical direction of the rotation plane. We can use the right-hand rule to explain.


We draw many rays from the positive charge to the surrounding space around the positive point charge. If we hold any one of the rays with our right hand, and the thumb is in the same direction as the ray, then the direction of rotation of the four fingers is the rotation direction of the space around the positive point charge.


We draw many rays around the negative point charge that point to the negative charge from any space. We hold any one of the rays with our right hand, and the thumb is in the same direction as the ray. Then the direction of rotation of the four fingers is the rotation direction of the space around the negative point charge. .


The space around positive and negative charges is a right-handed spiral space.


Space around a positive charge rotates counterclockwise toward us as an observer.


The space surrounding a negative charge rotates clockwise toward us as an observer.


The definition equations of electric field and charge given above are partly our assumptions and partly our logical reasoning.


If this equation is consistent with all the knowledge we already have, then these defining equations are reliable.


One thing we should also note is that the above definition equations of electric field and charge are not absolute and unique. We can give other forms of definition equations based on the nature of charge and electric field.


7. Geometric figures explain the repulsion of similar charges and the attraction of different charges


Since electric charge is formed by the cylindrical spiral divergent motion in the space around the object particles, can we use a cylindrical spiral motion model to explain all the laws of electric charge?


Also, when equal amounts of positive and negative charges come together, why do the charges cancel each other out to zero? Can this be rigorously proven mathematically?


The answer is yes, and the proof is similar to Gauss's theorem for magnetic fields. It is to use a tiny curved surface dS to intercept the vector displacement line of cylindrical spiral motion in space.


On a finite surface with a certain size, as many spatial displacement lines enter, there will definitely be as many spatial displacement lines coming out, and the two cancel each other out to zero. Integrate dS all over the Gaussian sphere surrounding the object particles, and the total result is zero.


Why do positive and negative charges attract each other?


In the figure above, red represents positive electric field lines and blue represents negative electric field lines.


When positive charges and negative charges of equal amounts are brought close to each other, the space around the charges moves in a cylindrical spiral. The radial part starts from the positive charges at the speed of light and ends with the negative charges.


Where rotating parts of space touch each other, they cancel each other out because they are in opposite directions.


Note that every electric field line has rotation. The electric field lines are actually cylindrical and spiral. For the sake of simplicity, not all the rotation lines are drawn in the above picture.


In this way, the amount of space between positive charges and negative charges is decreasing, and there is a tendency to contact each other, which is manifested as mutual attraction.


Whether the two charges move away from each other or approach each other depends on the cylindrical spiral rotating part of the space, because the speed of movement in the radial direction is the speed of light. According to the theory of relativity, the space moving at the speed of light shortens to zero, or it no longer belongs to where we are. space.


Once the positive and negative charges are very close to each other and are equivalent to a point, the surrounding linear motions cancel each other out due to their opposite directions, and the rotational motions also cancel out each other due to their opposite directions.


This is the reason why when equal amounts of positive and negative charges come together, the motion effect in the surrounding space [including stationary mass] disappears, and the charges can cancel each other out.


The picture above shows two equal positive charges approaching each other. Since the rotating parts of space are close together, the direction of movement is the same, which increases the amount of space.


Note that each electric field line has a rotation. The electric field lines are actually cylindrical and spiral. For the sake of simplicity, not all of them are drawn in the above picture.


In this way, the amount of space between the two positive charges is increasing, and they tend to move away from each other, showing mutual repulsion.


The picture above shows two equal negative charges approaching each other. Since the rotating parts of the space are close to each other, the direction of movement is the same, which increases the amount of space. In this way, the amount of space between the two negative charges is increasing, and they tend to move away from each other, showing mutual repulsion.


Thirty-one, velocity multiplied by the rate of change of mass with time is the electromagnetic field force


The momentum formula P = mV given by the theory of relativity and Newtonian mechanics is different from the momentum formula P = m (C-V) given by the unified field theory.


Dynamic equations of unified field theory:

F = dP/dt = (d/dt)m(C-V


= Cdm/dt-Vdm/dt+mdC/dt- mdV/dt


where, m is the mass of the particle, C is the vector speed of light, V is the velocity of the particle, and t is time.


In the above formula, (C-V)dm/dt= Cdm/dt -Vdm/dt is the velocity multiplied by the force that the mass changes with time, which is referred to as the added mass force.


The unified field theory believes that its essence is the electromagnetic field force, where Cdm/dt is the electric field force and Vdm/dt is the magnetic field force.


According to the unified field theory, when the above point o is stationary in s', it has a rest mass m', and the surrounding space moves away from the point o at the vector light speed C', carrying a charge dm'/dt' [Why is this possible? Expression, refer to the previous charge definition equation], if it is affected by the electric field force of other charges, the electrostatic field force F static can be expressed as:


F static = C’dm’/dt’,


In the s system, when point o [moving mass is m] moves along the x-axis at speed V, the surrounding space leaves point o at the vector light speed C [the directions of C and C' are different, but exactly the same] and moves along V The motion in the parallel direction (that is, along the x-axis direction) subjected to the electric field force Fx can be expressed as:


Fx dynamic = Cx dm/dt,


The quantitative formula is:


fx motion = c dm/dt,


corresponding,


Fxstatic = Cx’dm’/dt’


The quantitative formula is:


fx static = c dm’/dt’


Since neither the speed of light c nor the charge changes with the speed V, that is, dm’/dt ’= dm/dt, so,


Fx static = Fx moving


c is a scalar for C, v is a scalar for V, and f is a scalar for force F. C’x represents the vector light speed C’ on the x-axis in the s’ system, and Cx represents the vector light speed C on the x-axis in the s system.


Note that t and t’ are different. The directions of C’ and C are different, but the modules are both scalar light speed c, and c is constant.


If the vector light speed C’ and C are in the vertical direction along V, they are subjected to electric field force:


In the s’ department,


Fyjing = Cy’dm’/dt’


The quantitative formula is:


fystatic = c dm’/dt’


In the S series,


Fy action = Cy dm/dt,


According to the relativistic velocity transformation, its quantitative formula is:


fy = [c√(1-v²/c²)]dm/dt


F:


√ (1-v²/c²) Fy static = Fy moving


The same reason can be derived:


√ (1-v²/c²) Fz static = Fz moving


The above conclusion is consistent with the transformation of relativistic electromagnetic force. Let the charge at point o be q, if the electrostatic field is expressed as:


E’=Fjing/q = (C’dm’/dt’)/q


The dynamic electric field is expressed as:


E =F moving/q = (Cdm/dt)/q


When point o moves in a straight line along the positive direction of the x-axis at a uniform speed V, the quantities of C and C' on the x-axis are the same, both are c. Since dm'/dt' and q are unchanged, so ,

Ex = Ex’


On the y-axis and z-axis, the quantity of C is c√(1-v²/c²), the quantity of C’ is c,


so,


Fy = (dm/dt) c√ (1-v²/ c²)


= (dm/dt )c[√(1-v²/ c²)] [√(1-v²/ c²)]/[√(1-v²/ c²)]


=(dm/dt)c(1-v²/c²)/√(1-v²/c²)


If we think Ey’=Fystatic/q = (Cy’dm’/dt’)/q


is the component of the electrostatic field E’ on the y-axis,


If Ey=(dm/dt)c/q√(1-v²/c²) is the component of the moving electric field E on the y-axis, then:


Ey’= Ey√(1-v²/c²)


Note, (dm'/dt') c/q = (dm/dt) c/q


The analysis of Ez will get the same result, which is the same as the electric field transformation of relativity theory.


We can also see that the moving electric field force in the vertical direction of the speed V can be written as;

F垂=(dm/dt c(1-v²/ c²/√(1-v²/ c²


It becomes two parts, one part has nothing to do with the speed V [the quantity is v], and the other part is related to the speed V.


If we think that (dm/dt) c/√ (1-v²/ c²)


is the electric field force, the part of the force related to the speed V [amount is v]


(dm/dt )c (v²/ c²)/√ (1-v²/ c²)


is the magnetic field [expressed by B] force, then E and B satisfy [expressed by vector] the following vector cross product relationship:

B= V×E/c²


This result is the same as the theory of relativity.


Thirty-two, the defining equation of nuclear force field


All fields can be obtained by changes in the gravitational field. The nuclear force field, like the electromagnetic field, can also be represented by changes in the gravitational field.


The electric field is generated when the mass in the gravitational field changes with time. The difference in the nuclear force field is that the position vector R [modulo r] of the space point in the gravitational field changes with time.


Gravitational field A= - g m R/r³= - g (k/Ω) R/ r³ R/r³ changes with time t, resulting in a nuclear force field:

D = - g m [d(R/r³)dt]

= - g m[(dR/ dt)- 3 (R/r)(dr/dt)]/ r³


= - g m[(C- 3 (R/r) (dr/dt) ]/ r³


C above is the vector speed of light.


The above formulas are just guesses. The nuclear force field is different from electric fields and magnetic fields. Human beings already have formulas to describe electric fields and magnetic fields. It’s just that humans don’t know what the charge is in the electric field and magnetic field formulas. Once we know the geometric form of the charge, we only need to put the charge By bringing the geometric form definition equations into the electric field and magnetic field formulas, the unified field theory can completely express the electric field and magnetic field in geometric form.


However, nuclear force fields are different. Human beings do not have any formulas about nuclear forces and nuclear force fields.


In addition, nuclear force comes from protons and neutrons in the nucleus, and protons and neutrons are always in motion. Therefore, even if the above nuclear force field formula is correct and reliable, it cannot be used directly and needs to be extended to moving particles. use.


Whether the above nuclear force field formula is reliable, as well as the precise formula of nuclear interaction force, requires humans to continue to explore theoretically and experimentally.


Regarding the nuclear interaction force, here is a guess: the nuclear force exerted by a particle (mass m) on a nearby particle p (mass m') is equal to the nuclear force field D generated by point o at point p (from the above The definition equation of the nuclear force field is given) times the mass m' of point p or cross times the momentum m'V of point p or the angular momentum R×m'V.


Thirty-three, the definition equation of magnetic field


In the unified field theory, the magnetic field and the electric field are not the same field, and they cannot directly interact or superpose.


Human beings have discovered that when charged particles move in a straight line at a uniform speed relative to our observer, they can cause changes in the electric field. We can think of the changing part of the electric field as a magnetic field, that is, the electric field that changes with the speed produces a magnetic field. The unified field theory inherits this. kind of view.


Imagine that in the inertial reference system s', a point o is stationary relative to our observer, has mass m' [m when moving at speed V], has a positive charge q, and is in the surrounding space p [point p can be seen It is a space point, which can also be regarded as a field point or an inspection point. An electrostatic field E' is generated at [if it is a negative charge, add a negative sign, and it is E when moving at a speed V], pointing from point o to point p. The vector diameter of is R' [R when moving at speed V].


We use the length r’ of R’ [r when moving at speed V] as the radius to make a Gaussian surface s’ = 4πr’² to surround point o.


In the inertial reference frame s, when point o moves in a straight line relative to us at a uniform speed V along the x-axis, it can cause changes in the electric field in the vertical direction of V. We can think of the changed part as the magnetic field B.


A very simple idea is that the moving electric field E multiplied by the speed V is the magnetic field B. Since the magnetic field generated when the speed V and the electric field E are perpendicular to each other, the magnetic field generated is the largest, so they should be a vector cross product, so there is the following relationship,


B = constant times (V×E)


In order to obtain the geometric form equation of the moving electric field E, we define the electrostatic field obtained from Coulomb’s theorem as the equation E’= q R’/4πε. r’³, corrected using the Lorenz positive transformation [because the charge o point is moving relative to our observer], we can get:

E =γq [( x-vt)i+ yj+zk]}/ 4πε。{√[γ²(x-vt²+y²+z²]}³


so,


V×E =γq V×[( x- vt)i+ yj+zk]/4πε. {√[γ²(x-vt)²+y²+z²]}³


Let the vacuum permeability be μ. , because what we are discussing here is in a vacuum situation, then:


B=μ. {γq V×[( x- vt)i+ yj+zk]}/4π{√[γ²(x-vt)²+y²+z²]}³


=μ. ε. {γq V×[( x- vt)i+ yj+zk]}/ 4πε. {√[γ²(x-vt)²+y²+z²]}³


=μ. ε. V×E


Because μ. ε. = 1/c²


Therefore, the above formula can also be written as B = V×E/c²


Therefore, the definition equation of magnetic field is:


B=μ. {γq V×[( x- vt)i+ yj+zk]}/4π{√[γ²(x-vt)²+y²+z²]}³


In the above equation, humans have never been clear about the charge q before. Now once we understand the geometric form of the charge q, we can use the above charge definition equation q = kk' (1/Ω²)dΩ/dt to get the geometric form of the magnetic field. Define the equation:


B =μ。{γ[-kk' (1/Ω²)dΩ/dt] V×[( x- vt)i+ yj+zk]}/4π{√[γ²(x-vt)²+y²+z²] }³


Let θ be the angle between the vector diameter R [the scalar is r=√[γ²(x-vt)²+y²+z²]] and the speed v, B can be expressed in polar coordinate form:

B=μ。{[-kk’ (1/Ω²)dΩ/dt]v sinθ/4πγ²r² [√(1- β ²sin²θ)] ³}【r】


β=v/c in the formula, c is the speed of light, v is the scalar form of V, [r] is the unit vector of the vector R (the scalar is r).


Using the relationship between mass and charge q =k’dm/dt, the definition equation of the magnetic field containing mass can be obtained:

B =μ。{γ(kdm/dt,)V×[( x- vt)i+ yj+zk]}/4π{√[γ²(x-vt²+y²+z²]}³


In the figure below, a positively charged particle o point that is stationary relative to us generates an electrostatic field E' at the surrounding space point p. When point o moves in a straight line with a uniform speed along the x-axis at a speed V relative to our observer, an electrostatic field E' can be generated. Magnetic field B, the essence of this magnetic field is that space rotates with the vector velocity V as the central axis. The rotation of B and V satisfy the right-handed spiral relationship.


The magnetic field B, the moving electric field E and the charge velocity V satisfy the following relationships:

B = V×E/c²


According to the custom of ordering the vector cross product and Stokes' theorem, the y cross multiplied by z forms a vector surface element in the x direction, the z cross multiplied by x forms a vector surface element along the y direction, and the x cross multiplied by y A vector surface element along the z direction is formed, and the three components satisfy the following right-handed spiral relationship:

Bx = 0

By = -V×Ez/c²

Bz = V×Ey/c²


where V is the velocity of the charged particle o along the x-axis.


According to the unified field theory, when the object particle is stationary, the moving speed of the surrounding space points is the vector speed of light C’. When the object particle moves at the speed V, the moving speed of the surrounding space points is C-V.


When point o is stationary, the surrounding space point p is moving at the vector speed of light C'. When point o moves in a straight line along the x-axis at speed V, the vector light speed of point p is consistent with E, and a movement speed -V is also superimposed. It is exactly opposite to the movement speed V of point o.


When we place the inspection point at point p, we should replace the movement speed of point o with the movement speed of space point p. The above component relationship becomes the following left-handed spiral:

Bx = 0

By = V×Ez/c²


Bz = -V×Ey/c²


When we examine the situation of point p in space, it is more direct and convenient to use this component formula.


In the figure below, when the charge point o starts from point a and moves in a circular motion at a uniform speed to point b, the rotational motion of space enters and exits on the positive and negative sides of the circle. The side that enters is the S pole, and the side that comes out is the S pole. The side is called the N pole.


Judging from the geometric form of the magnetic field, there are no magnetic monopoles in nature.


Thirty-four, derivation of Maxwell’s equations


The four equations of Maxwell's equations can describe all the laws of electromagnetic phenomena, but they are not the most basic.


Maxwell's four equations can be derived using the defining equations of electric and magnetic fields, Gauss's theorem and Stokes' theorem in field theory, and the Lorenz transformation in relativity theory.


1. Curl of electrostatic field E’


For a stationary charge point o, with a charge q, the electrostatic field E’ is generated around it, and the electric field is used to define the equation

E’ = f (dΩ/dt) R/Ω²r³


Directly finding the curl, we get:

×E’ = 0


Note that only R/r³ is a variable on the right side of the formula.


The above equation can be decomposed into the following three equations:


∂Ez’/∂y’ – ∂Ey’/∂z’= 0


∂Ex'/∂ z' - ∂Ez'/∂x'= 0


∂Ey'/∂ x' - ∂Ex'/∂y'= 0


2. Divergence of electrostatic field E’


Define the equation for the electric field

E= f (dΩ/dt) R/Ω²r³


Find the divergence directly. Note that only R/r³ is a variable on the right side of the formula, we get:

▽·E’ = 0


r in the above formula is the radius of the Gaussian sphere s surrounding point o. When r approaches zero [it can also be said that the inspection point on the Gaussian sphere - the space point p is infinitely close to the charge point o], and point o can When viewed as an infinitesimal charged sphere, the equation appears to be 0/0. Using the Dirac delta function, we can get:

▽·E’ = ∂Ex/∂ x+ ∂Ey/∂y+ ∂Ez/∂z= ρ’/ε


ρ’ is the density of charges, ε, in the Gaussian sphere s surrounding charge point o [the volume of s is very small and infinitely close to point o]. is the vacuum dielectric constant.


What we need to note is that if point o is outside the Gaussian sphere s, s does not surround point o, and its divergence is always zero.


3. Derive Gauss’ theorem of the moving electric field E


Assume that the charge point o is stationary in the s' system. Although the charge q is an invariant, the charge q moves in a straight line along the positive direction of the x-axis at a uniform speed V in the s system. According to the theory of relativity, the movement causes space to shrink. Its volume will shrink to 1/γ [γ = 1/√ (1 - v²/c²) is the relativistic factor] times, and the corresponding charge density of q will increase to γ ​​times.


Therefore, the density ρ of q in the s system is greater than the density ρ in the s’ system by a relativistic factor γ.

ρ = γρ’


The charge q moves in a straight line along the positive direction of the x-axis at a uniform speed V [scalar is v] in the s system, so there is a current density:

J = i ρv = i γv ρ’


i is the unit vector along the x-axis.


From the Lorenz positive transformation of x'=γ(x-vt) we get ∂x'/∂x =γ, and then from the relativistic transformation of the electric field Ex = Ex', Ey = γ Ey', Ez = γ Ez', and Divergence of electrostatic field E':

▽•E’ = ∂Ex’/∂ x’ + ∂Ey’/∂y’ + ∂Ez’/∂z’ = ρ’/ε。


Gauss's theorem for the moving electric field E can be derived:

▽•E = ∂Ex/∂ x + ∂Ey/∂y + ∂Ez/∂z


= γ(∂Ex’/∂ x’ + ∂Ey’/∂y’ + ∂Ez’/∂z’)


= γρ’/ε. =ρ/ε.


4. Derive Gauss’ theorem of magnetic field


Using the above differential operators ∂/ ∂y = ∂/ ∂y’, ∂/ ∂z = ∂/ ∂z’,


The relationship satisfied by the magnetic field B and the electric field E at the previous space point p:


Bx = 0,


By = v Ez /c²,


Bz = -v Ey’/c²,


The first formula of curl when electrostatic field E’ is applied


∂Ez’/∂y - ∂Ey ’/∂z’= 0


Relativistic transformation formula plus electric field


γEz’=Ez, γEy’=Ey,


Gauss's theorem for magnetic fields can be derived:

▽•B = ∂Bx/∂ x + ∂By/∂y + ∂Bz/∂z


= 0 + (v Ez /c²)∂/∂y - (v Ey /c²)∂/∂z


= 0 +(γv Ez’/c²)∂/∂y’- (γv Ey’/c²)∂/∂z’


= γ(v/c²)(∂Ez’/∂y’- ∂Ey ’/∂z’)= 0


5. Derive Faraday’s electromagnetic induction theorem


From the first formula of the curl of the electrostatic field E’

∂Ez’/∂y’)-(∂Ey’ /∂z’)= 0


From the relativistic transformation of the electric field Ez’= Ez/γ, Ey’= Ey/γ, ∂y = ∂y’, ∂z= ∂z’, it is derived:


(Ez/γ)(∂/∂y)-(Ey/γ)(∂/∂z)

= (1/γ)(∂Ez/∂y)-(Ey/∂z=0


so,


∂Ez/∂ y - ∂Ey/∂z = 0


The second formula for the curl of the electrostatic field E’

∂Ex/∂ z’)-(∂Ez/∂x’)= 0


From the relativistic transformation of the electric field Ex'= Ex, Ez'= Ez/γ, ∂z = ∂z', and from the partial differential of the Lorenz positive transformation x'=γ(x-vt), we get γ/∂x'= 1/∂x, derived:


∂Ex/∂z - (1/γ²) (∂Ez/∂x)=0


∂Ex/∂z - (1-v²/c²) (∂Ez/∂x)=0


∂Ex/∂z -(∂Ez/∂x)= -(v²/c²)(∂Ez/∂x)


Derive v/∂x= 1/∂t from v=dx/dt


so:

∂Ex/∂z∂Ez/∂x = -(v/c²)∂Ez/∂t


From the relationship By = v Ez /c² satisfied by the magnetic field B and electric field E at the space point p, we get:


∂Ex/∂z-∂Ez/∂x = −By /∂t


The third formula of the curl of the electrostatic field E’


∂Ey’/∂ x’- ∂Ex’/∂y’= 0,


From the relativistic transformation of the electric field Ex’= Ex, Ey’= Ey/γ, and then from the above differential operator of the Lorenz positive transformation γ/∂x’=1/∂x, ∂y=∂y’,


get:


(1/γ²)∂Ey/∂ x-∂Ex/∂y=0


(1 - v²/c²)∂Ey/∂ x-∂Ex/∂y=0

∂Ey/∂ x∂Ex/∂y =v²/c²)∂Ey/∂ x


From v/∂x = 1/∂t


get:


∂Ey/∂ x-∂Ex/∂y =(v/c²)∂Ey/∂ p


From the relationship Bz = -v Ey/c² satisfied by the electric field E and magnetic field B at the space point p, we get:


∂Ey/∂ x-∂Ex/∂y =-Bz/∂ t


From Tokes’ theorem:


▽×E = (∂Ez/∂y−∂Ey/∂z) i+ (∂Ex/∂z−∂Ez/∂x) j + z (∂Ey/∂x−∂Ex/∂y) k

= 0 i ∂By/∂tj -(∂Bz/∂tk

=-(∂Bx/∂ti-(∂By/∂tj-(∂Bz/∂tk


= -∂B/∂t


6. Derive current and change electric field to generate magnetic field


The relationship satisfied by the electric field E and magnetic field B at the space point p


Bz = -v Ey/c², By = v Ez/c², we can get:


∂Bz/∂y -∂By/∂z = -(∂/∂y)(v/c²)Ey -(∂/∂z)(v/c²)Ez

= -v/c²(∂Ey/∂y ∂Ez/∂z


= -μ. ε. v(ρ/ε.-∂Ex/∂x)


Note that μ. ε. =1/c², ρ is the charge body density of point o in the s system. Gauss’ theorem of the moving electric field E is used here.

▽•E = ∂Ex/∂ x + ∂Ey/∂y + ∂Ez/∂z =ρ/ε。


so,


-μ. ε. v(ρ/ε.-∂Ex/∂x)


= -μ. vρ+μ. ε. v ∂Ex/∂x


The above is obtained from the investigation at the space point p, because the movement speed v of the charge point o is exactly opposite to the movement speed -v of the point p.


μ. v ρ is the current. If the above formula represents the magnetic field generated by the current and the changing magnetic field, the negative sign must be removed. Then v/∂x = 1/∂t, so the vector expression of the above formula can be written as:


μ. J + μ. ε. (∂Ex/∂t)i


i is the unit vector of the electric field E along the x-axis, and J is the current.


由Bx=0,Bz = - v Ey/c²,v/∂x=1/∂t,so:

∂Bx/∂z∂Bz/∂x = - ∂Bz/∂x


= (v/c²)∂Ey/∂x


=(1/c²)∂Ey/∂t


=μ. ε. ∂Ey/∂t


From Bx=0, By = v Ez/c², v/∂x=1/∂t, so:

∂By/∂x∂Bx/∂y = ∂By/∂x


= (v/c²)∂Ez/∂x


= (1/c²)∂Ez/∂t


=μ. ε. ∂Ez/∂t


According to Stokes' theorem,


▽×B = (∂Bz/∂y−∂By/∂z) i+ (∂Bx/∂z−∂Bz/∂x) j + z (∂By/∂x−∂Bx/∂y) k


= (μ.J +μ.ε·∂Ex /∂t) i+(μ·ε·∂Ey /∂t )j+ (μ·ε·∂Ez/∂t ) k


=μ. J+μ. ε. (∂E /∂t)


Thirty-five, the gravitational field that changes with time produces an electric field


In the unified field theory, the gravitational field is the parent field, the electric field, magnetic field, and nuclear force field are all formed by changes in the gravitational field, and charges are formed by changes in mass.


In turn, changes in the electric field, magnetic field, and nuclear force field can also form a gravitational field, but the form of this change is more complicated, while the change of the gravitational field to form other fields is simpler.


We first find out how the changing gravitational field produces an electric field when point o of the object particle is stationary relative to our observer. Next, we find out the electric field generated by changes in the gravitational field when the object particles move relative to us.


convert the gravitational field equation


A = - g m R/r³ = - g k (1/Ω)R/r³


Taking the partial derivative of (1/Ω) with respect to time t, we get:

A/t = g k (1/Ω²)(dΩ/dt)R/r³


From the above electrostatic field geometry definition equation


E = - k’k (dΩ/dt)R/Ω²4πε. r³


You can get:


E = -(k’/g 4πε.)dA/dt


Since g, k’ ,4π,ε. are all constants, and the combined constant is f, then:

E = - f dA/dt


From this we get the relationship between the three components:

Ex = - f Ax /t

Ey = - f Ay /t

Ez = - f Az /t


When the charged object particle o point moves with uniform velocity V [scalar is v] along the positive direction of the x-axis relative to us in a straight line, the electric field of the moving object can be calculated by using the relativistic transformation of the electric field and the relativistic transformation of the gravitational field. and the gravitational field satisfy the relationship.


In order to distinguish, we use primed letters to represent the electric field and gravitational field generated when point o is stationary, and unprimed letters represent the electric field and gravitational field generated when point o is moving.


The relationship between the electric field and the gravitational field when point o is stationary:

Ex = - f Ax /t

Ey = - f Ay /t

Ez = - f Az /t


From the Lorenz transformation of the electric field in the theory of relativity, we know: Ex = E’x, Ey =γE’y, Ez =γE’z, where γ=1/√ (1- v²/c²).


From the previous relativistic transformation of the gravitational field, it can be seen that: Ax =γAx, Ay=γ²Ay, Az =γ²Az.


For the Lorenz time positive transformation t’ =γ(t-vx/c²) in the theory of relativity, partial differentiation of time is obtained, and the time of motion is extended:


∂ t’/∂t=γ (∂ t/∂t - v²/c²)


∂ t’/∂t =γ(1 - v²/c²)=γ/γ²=1/γ

/t /t


From the above, we can find the relationship between the moving electric field E and the moving gravitational field A when point o moves:

Ex= - f Ax /t

Ey= - f Ay /t

Ez = - f Az /t


From the calculation results, it can be seen that the relationship between the electric field and the gravitational field is the same when the object particles are stationary and moving in a straight line at a uniform speed.


36. Changes in the gravitational field of an object moving in a straight line at a uniform speed produce an electric field


It is pointed out above that when the object particle point o is stationary relative to our observer, the divergence of the surrounding gravitational field A is:


∇·A= ∂Ax/∂x' + ∂Ay/∂y + ∂Az/∂z'


Ax, Ay, and Az are the components of A on the three coordinate axes respectively.


When point o moves in a straight line with a uniform speed in the positive direction of the x-axis at a speed V [scalar is v] relative to us, the divergence of the gravitational field A is:

·A = Ax/ x + Ay/y + Az/z


Calculate the partial differential of the Lorenz positive transformation x'=γ(x-vt), and get ∂/γ∂x=∂/∂x', plus ∂y=∂y', ∂z= ∂z', and then The above relativistic transformation of the gravitational field yields:

·A =(Ax/γ)/γx + Ay/γ²y + Az/γ²z


=(1/γ²)∇·A


From the above we can get:

·A=(1- v²/c²)·A


= ∂Ax/∂x + ∂Ay/∂y + ∂Az/∂z - (v²/c²)∂Ax/∂x - (v²/c²)∂Ay/∂y - (v²/c²)∂Az/∂ z


= ∂Ax/∂x + ∂Ay/∂y + ∂Az/∂z - (v/c²)v ∂Ax/∂x - (v/c²)v ∂Ay/∂y - (v/c²)v ∂ Az/∂z


Change the above formula into vector form. Since this is divergence, not curl, we use the point product of the three components of the velocity V [along the x direction, the scalar is v] and the gravitational field A.

·A=(1- v²/c²)·A


= ∂Ax/∂x + ∂Ay/∂y + ∂Az/∂z - (v/c²)V·∂Ax i /∂x - (v/c²)V·∂Ay j /∂y -(v/ c²)V·∂Az k /∂z


In the above formula, i, j, and k are the unit vectors of the three components Ax, Ay, and Az of the gravitational field A on the x, y, and z axes respectively. According to the vector dot product theorem in mathematics, we can get:

·A=(1- v²/c²)·A

= Ax/x + Ay/y + Az/z - (v/c²)v Ax /x

= Ax/x + Ay/y + Az/z -(v/c²)Ax /t

=Ax/x + Ay/y + Az/z +(v/c²)Ex /f


Note that the above formula uses the relationship between the component Ex of the electric field E on the x-axis and the component Ax of the gravitational field A on the x-axis Ex= - f ∂Ax /∂t, and v ∂/∂x = ∂/∂t.


The above shows that when the object particle o is stationary relative to our observer, it generates a gravitational field A in the surrounding space. When it moves in a straight line with a uniform speed V [scalar is v] along the x-axis, the gravitational field changes [after change]. The gravitational field, represented by A, has become two parts. One part has nothing to do with speed, and the other part has to do with the speed of movement. The part that is related to speed and distributed along the x-axis is actually the electric field.


Using the relationship between the gravitational field and the electric field of moving object particles, the relationship between the curl of the magnetic field and the changing gravitational field can also be derived.


Bring the above relationship E = - f ∂A/∂t between the moving electric field E and the moving gravitational field A into Maxwell's equations:


μ. J + (1/c²)∂E /∂ t = ∇×B


, get:

μ。J -(1/c²)f ²A/ t ²= ×B,


In the formula, J is the density ρ [ρ/ε. = ∇·E】The electric current formed by the electric charge body moving along the x-axis at speed V,


μ. J【μ. J=μ. ε. Vρ/ε. =(1/c²)Vρ/ε. ] In Maxwell's equations it can be written as (V/c²)∇·E【∇·E=ρ/ε. ], so the above formula can be written as:

(V/c²)·E -(1/c²)f ²A/ t ²= ×B


so:

(1/c²)f ²A/ t ²=(V/c²)·E - ×B


∂²A/∂ t²=(V/ f)∇·E - ∇×B(c²/f)


The above formula shows that a changing gravitational field can produce an electric field or a magnetic field.


This situation is similar to Maxwell's equations. The gravitational field can be incorporated into Maxwell's equations as an expanded form of Maxwell's equations.


Thirty-seven, the magnetic field of moving charges produces a gravitational field


1. The magnetic field of charges moving in a straight line at a uniform speed produces a gravitational field


The core of unified field theory is that a changing gravitational field can produce an electric field, and conversely, a changing electromagnetic field can also produce a gravitational field.


Relativity and electromagnetism believe that moving charges not only produce electric fields, but also produce magnetic fields.


The unified field theory further believes that moving charges not only generate a magnetic field, but also a gravitational field. Next, we find the relationship between the electromagnetic field and the gravitational field generated by the moving charges.


Above we pointed out that the direction of the electric field produced by changing the gravitational field does not change. The directions of the gravitational field and the electric field are consistent, and the electric field is generally perpendicular to the direction of the magnetic field. Therefore, the direction of the gravitational field and the direction of the magnetic field are generally in the same direction. Also vertical.


Let's explore the relationship between the curl of the gravitational field and the magnetic field, because curl describes the change of the field along the vertical direction, while divergence describes the change of the field along the parallel direction.


Imagine a point charge o, starting from the origin at time 0, moving in a straight line at a uniform speed in the positive direction of the x-axis at a speed V [scalar is v] relative to our observer. The point charge o generates an electric field E at the surrounding space point p. Magnetic field B and gravitational field A, as shown below.


We take the space point p as the inspection point to carry out the analysis.


The surrounding directions of the gravitational field A and the electric field E are the same, and both are left-handed spirals. However, near a certain point on the surrounding line, A and E are perpendicular to each other.


In order to prove that the electric field E, the magnetic field B, and the gravitational field A satisfy the relationship shown in the figure above, we first find the curl of A:


∇×A = (∂Az/∂y - ∂Ay/∂z)i+(∂Ax/∂z - ∂Az/∂x)j + (∂Ay/∂x-∂Ax/∂y) k


When the previous object is at rest, the curl of the gravitational field is zero, that is: ∇×A=0, and the component form is:

Az/y- Ay/z = 0

Ax/z - Az/x = 0

Ay/x-Ax/y = 0


Then through the relativistic transformation of the gravitational field, we get:


∂Az/∂y' - ∂Ay/∂z' =∂Az/γ²∂y - ∂Ay/γ²∂z

= Az/y - Ay/z =0


γ=1/√(1- v²/c²) is the relativistic factor, ∂y=∂y’, ∂z=∂z’.


Taking the partial differential of the Lorenz positive transformation x’=γ(x-vt) of the theory of relativity, we get ∂/γ∂x=∂/∂x’, and then using the relativistic transformation of the gravitational field, we get:


From ∂Ax/∂z’ - ∂Az/∂x’ = 0, we get:


∂Ax/γ∂z - ∂Az/γ³∂x = 0,so:

Ax/z - Az/γ²x = 0

Ax/z - (1- v²/c²)Az/x = 0

Ax/z - Az/x = -(v²/c²)Az/x

Ax/z - Az/x = -(v/c²)v Az/x


From v ∂/∂x = ∂/ ∂t, so:

Ax/z - Az/x = -(v/c²)Az/t


From ∂Ay/∂x’ - ∂Ax/∂y’ = 0 and the relativistic transformation of the gravitational field, plus the above ∂/γ∂x=∂/∂x’, we get:


∂Ay/γ³∂x - ∂Ax/γ∂y = 0,so:

Ay/γ²x - Ax/y = 0

1- v²/c²)Ay/x - Ax/y = 0

Ay/x - Ax/y =(v/c²)v Ay/x


From v ∂/∂x = ∂/ ∂t, so:

Ay/x - Ax/y = (v/c²)Ay/t


From the previous relationship between the gravitational field and the electric field of the moving object:

Ex= - f Ax /t

Ey= - f Ay /t

Ez = - f Az/t


You can get:

Az/y - Ay/z =0


∂Ax/∂z - ∂Az/∂x = (v/c²)This is /f

Ay/x - Ax/y = -(v/c²)Ey /f


We pointed out earlier that when the charge moves in a straight line with a uniform speed in the positive direction of the x-axis at a speed V [scalar is v], we use a space point p around the charge as an inspection point. The movement speed of point p -V, the electric field E and the magnetic field B are three components satisfy the following relationship:

Bx = 0


By = (v/c²)Ez


Bz = -(v/c²)Ey


From this, we can get:

Az/y - Ay/z = Bx

Ax/z - Az/x = By /f

Ay/x - Ax/y = Bz/f


Combining the above three equations, we can get the relationship satisfied by the curl of the gravitational field A and the magnetic field B:

×A= B /f


This is the basic relationship equation that satisfies the magnetic field and the gravitational field. This equation tells us that when the charge moves in a straight line at a constant speed at a certain speed, the magnetic field generated can be expressed in the form of the curl of the gravitational field.


At a certain moment [due to the unification of space and time, or at a certain point in space], the magnetic field, electric field, and gravitational field are perpendicular to each other.


This equation may be the final explanation of the AB effect in quantum mechanics.


Dot multiply both sides of the equation ∇×A= B /f by the vector surface element dS [which can be regarded as a small area on the Gaussian sphere s = 4πr² surrounding the point o of the charged particle, with its positive direction, that is, the normal direction outward], Using Stokes' theorem in field theory, we can get the integral equation of the relationship between the magnetic field B and the gravitational field A:

 A·dL= (1/f)∮ B·dS


2. Magnetic fields that change over time produce electric fields and gravitational fields


Imagine that a point charge o starts from the origin at time 0 and moves in a straight line at a uniform speed V [scalar is v] in the positive direction of the x-axis relative to our observer. The point charge o is generated at any surrounding space point p. Moving electric field E, uniform magnetic field B:

B= V×E/c²


When point o moves relative to us in the positive direction of the x-axis with acceleration -A, charge o generates a moving electric field E, a magnetic field dB/dt that changes with time t, and a gravitational field A at any surrounding space point p.


We take the space point p as the inspection point, and calculate the derivative of the magnetic field definition equation B= V×E/c² with respect to time t, as follows:

dB/dt=dV/dt×E/c²+(V×dE/dt)/c²


If we can prove that dB/dt= (V×dE/dt)/c² means:


A change in the magnetic field produces a changing electric field, which is the Faraday principle of electromagnetic induction. Correspondingly, dB/dt=dV/dt×E/c² should be a changing magnetic field that produces a gravitational field.


Because dV/dt=A is the acceleration of space point p, according to the unified field theory, the acceleration of space itself is equivalent to the gravitational field.


We first prove that dB/dt= (V×dE/dt)/c² is Faraday’s principle of electromagnetic induction.


Since the inspection point is no longer at point o, but at point p in space, we use the left-handed spiral formula for the relationship between magnetic field B and electric field E:

Bx = 0


By = (v/c²)Ez


Bz = -(v/c²)Ey


The three components of dB/dt= (V×dE/dt)/c² are as follows [the differential sign d is changed to the partial differential sign ∂]:

Bx/t = 0


∂By/∂t = (v ∂Ez/∂t)/c²


∂Bz/∂t = -(v ∂Ey/∂t)/c²


Since the curl of the electrostatic field is zero ∂Ex'/∂z' - ∂Ez'/∂x'=0, and Ex= Ex', ∂z' = ∂z, γEz'= Ez, ∂ in the Lorenz transformation /γ∂x=∂/∂x', γ=1/√(1- v²/c²), we get:


∂Ex/∂z – (1/γ²)∂Ez/∂x = 0


∂Ex/∂z – (1- v²/c²)∂Ez/∂x = 0

Ex/z Ez/x = -(v²/c²)Ez/x


From v ∂/∂x = ∂/ ∂t, we get:

Ex/z Ez/x = -(v/c²)Ez/t


Similar to the above operation, you can get:

Ey/x Ex/y = (v/c²)Ey/t


Combine these two equations with the three components of dB/dt= (V×dE/dt)/c² above as follows:

Bx/t = 0


∂By/∂t = (v ∂Ez/∂t)/c²


∂Bz/∂t = -(v ∂Ey/∂t)/c²


By comparison, we can get:

Ez/y Ey/z = 0

Ex/z Ez/x = - By/t

Ey/x Ex/y = - Bz/t


Combining the above three equations, it is Faraday’s electromagnetic induction equation:

×E= - B/t


Next, we analyze the equation dB/dt=dV/dt×E/c² that produces the gravitational field A due to changes in the magnetic field B.


The three components of this equation are as follows:

Bx/t = 0

By/t = (V/t) ×Ez/c²=A ×Ez/c²

Bz/t = -(V/t) ×Ey/c²= - A×Ey/c²


The above equation can be written as dB/dt=A×E/c², and this equation can be understood as:


When the positively charged point o accelerates in the positive direction of the x-axis, at any point p in the surrounding space, an electric field E and a gravitational field A in the opposite direction of acceleration are generated.


A, E, and dB/dt satisfy the cross product relationship. When the three are perpendicular to each other, the value is the largest.


3. The relationship between the electric field, magnetic field and gravitational field of accelerating moving charges


Since the gravitational field generated by a changing electromagnetic field is the core of the unified field theory and the key to the application of artificial field technology, below, another method is used to deduce the gravitational field generated by accelerating positive charges.


The various relationships between electric fields, magnetic fields, and gravitational fields can be seen as derivatives of the basic relationship B = V×E/c², which defines the magnetic field, and can all be derived from this basic equation.


The formula dB/dt = A×E/c² can only be applied to certain microscopic single elementary particles. The object particles we see macroscopically are composites of many tiny charged particles. Their positive and negative charges cancel each other out, and the magnetic fields also cancel each other out. .


The gravitational field formula derived above from a changing magnetic field, dB/dt = A×E/c², may only apply to positive charges, because the space around positive charges moves divergently at the speed of light, which can distort the space [including accelerating electric fields, accelerating magnetic fields and The gravitational field formed by the changing electric field spreads out at the speed of light.


However, the speed of light in the space around negative charges converges inward, so it is logical that the space distortion effect cannot be diverged. However, according to the Lorenz transformation, the space where the speed of light moves is shortened to zero and is no longer the same space as ours. It is unobservable to us observers and there is uncertainty. Therefore, whether this formula can be applied to negative charges requires further theoretical discussion and practice to judge.


In order to further understand the relationship between the electric field, magnetic field, and gravitational field of accelerating electric charges, we will analyze it with an example.


Imagine a point charge o that is stationary relative to our observer, with a positive charge of charge q, generating an electrostatic field E at the surrounding space point p.


At zero moment, when point o suddenly accelerates in the positive direction of the x-axis with vector acceleration G [amount is g] relative to us.


According to the unified field theory, the accelerated motion of point o will cause the space point p to come out of point o and move outward at the vector light speed C, while superimposing an acceleration -G.


According to the definition of the gravitational field of the unified field theory - the gravitational field is the acceleration motion of the space point itself. The gravitational field A [amount is a] is equivalent to the acceleration -G of the space point p. Therefore, the location of the space point p, A gravitational field will be generated due to the acceleration of point o:


A【Quantity is a】=–G.


Let us find the relationship between the electrostatic field Er, the accelerating twisting electric field Eθ, and the gravitational field A.


Assume that the positive point charge o is always stationary at the origin o of the Cartesian coordinate system relative to our observer, and starts from time t = 0 to move in a straight line with uniform acceleration along the positive direction of the x-axis with an acceleration G [amount of g].


At time t = τ, point o stops accelerating when it reaches point d. At this time, the speed reaches v = gτ. From then on, it continues to move uniformly along the x-axis at speed v until it reaches point q.


As shown below:


For the sake of simplicity, we consider that v is much smaller than the speed of light c, and the od distance is much smaller than oq.


Next we consider the electric field distribution around the charge o at any time t (t is much larger than τ).


During the period from time 0 to time τ, the electric field lines around it are distorted due to the accelerated motion of the positive point charge o, and this distorted state will also extend outward at the speed of light c.


The unified field theory clearly points out that the electric field line of a positive charge is the motion displacement of a point in space moving at the speed of light around the charge.


The above twisted state moves outward at the speed of light, just like a faucet that sprays water all around at a constant speed. Once the faucet shakes, it causes the water flow to twist. This twisted state will definitely extend outward at the speed of the water flow.


The twisted state of the electric field caused by the accelerating charge o extends outward at the speed of light c. In the figure above, you can see that the thickness of the twisted state is cτ, sandwiched between two spherical surfaces.


The latter spherical surface has spread a distance of c (t-τ) to all directions at time t. This spherical surface is centered at point q and has a diameter of c (t-τ).


The previous spherical surface has spread a distance of ct to all sides at time t. This spherical surface is centered at point o and has a diameter of ct.


Since the charge o moves at a uniform speed starting from time t=τ, the electric field distributed in this spherical surface with a diameter of c (t-τ) should be the electric field of the charge moving in a straight line at a uniform speed.


According to our previous setting, the moving speed v of charge o is much smaller than the speed of light c, so the electric field in this spherical surface is approximately an electrostatic field at any time.


The electric field line of this electric field at time t is a straight line along the radius drawn from the position q of point o at this time.


Since t is much larger than τ and c is much larger than v, r=ct is much larger than vτ/2 (that is, the distance from point o to point d). Therefore, the two spherical surfaces at the front and rear edges of the twisted state are almost concentric circles.