Mathematics and human's view of time and space

On Human Understanding of Time and Space

Man's understanding of time and space has gone through a long, complicated and tortuous process. In ancient times, people thought that the universe was round. Later, Newton's absolute view of time and space and Einstein's relativistic view of time and space were established. In recent years, a new concept of time and space has emerged based on the theory of "the change of the speed of light" (VSL), and the multidimensional concept of time and space based on "superstring theory" is even more impressive.

Keywords: absolute space-time relative to space-time chaotic fractal light speed change superstring theory multidimensional space-time

After a hundred years of rapid development of physics and modern high technology, mankind has entered a brand-new era. However, physics still faces many problems to be solved urgently. Einstein's unified theory has not been solved all his life, and it has not been solved so far. In addition, string theory also needs to be improved. BIGBANG's theory is helpless to Planck's time [0. (42 zeros) before the birth of the universe 1 second] and black holes, as well as some important physical experiments and observed phenomena that cannot be explained by existing theories. With the arrival of the new century, physics is faced with the same layers of fog as it was a hundred years ago, and physics theories beyond Einstein's theory may appear. Human's understanding of time and space is a science that constantly discovers, corrects, perfects and challenges the theoretical achievements of predecessors. In the following, the author briefly introduces and discusses the flat view of time and space in Arabia, Einstein's relativistic view of time and space, and the multidimensional view of time and space based on superstring theory.

First, the flat space-time view of ancient "round place"

Since its birth, human beings have been expected to have a certain understanding of their living environment and a preliminary impression of the concept of time and space. In ancient China mythology, Pangu opened heaven and the Qing Dynasty ascended to heaven. Turbidity sinks to the ground, and they think the sky is round. Because * * * the great god pushed down the hill and propped up Tianzhu, the sky tilted to the northwest, the earth tilted to the southeast, and the sun, the moon and the stars rose and set in the west. Human beings have been studying the problems of time and space since they came into being. In order to survive and develop, human beings need to understand the changes of the universe and weather, and want to know how storms, snow and lightning are produced, how they change all the year round, when to sow and when to harvest. Heaven and earth is a huge space, which inspires our infinite imagination and interest. But in feudal society, people always thought that they lived on an absolute plane and the earth was flat. Some people call the laws of the universe in this period Pythagorean Theorem (China people call it Pythagorean Theorem), that is, a2+b2 = c2. "Pythagorean theorem is not only reasonable in mathematical beauty, but also produced the famous Fermat theorem through the study of it in modern times. Fermat's Last Theorem was only proved in 1980s and 1990s. A2+b2 = c2 not only has geometric beauty, but also embodies human understanding of the beauty of time and space. It is the space-time view of plane thinking. It is the first major and perfect theorem for human beings to understand nature. " (Go to Zhu and Zhu's thermal abstraction P7)

In modern times, due to the development of navigation and other factors, people saw that ships appeared in the distance did not simply grow from small to large, but seemed to drill out from below the sea level in the distance, so people began to wonder whether the sea level was really flat and whether the earth was really an infinite plane. Due to various speculations about the shape of the earth, Pythagoras holds that the earth is spherical and the sun, moon and planets move in uniform circles from the viewpoint that the sphere is the most perfect geometric shape. He believes that the earth rotates around a fixed "central fire" along a sphere in space, and there is an "opposite star" on the other side to balance it. This "central fire" will never be seen by human beings. He believes that there must be ten illuminators in the sky, and the distance between these ten celestial bodies and the central fire has the same proportional relationship with syllables, so as to maintain the harmony of the stars and play the music of celestial bodies. This reminds people of the current superstring theory. (Refer to Zhu and Zhu's thermal abstraction P5).

Secondly, the concept of absolute space-time based on "classical mechanics"

The Greeks used geometric methods to explain the motion of planets, and Ptolemaic geocentric theory, which appeared in the 2nd century A.D., was the representative of these theories. This system ruled for fourteen centuries, until Copernicus' Heliocentrism appeared in16th century, and Galileo's theory of relativity based on inertial system appeared in17th century. Thus, classical mechanics based on Newton's three laws of motion and the law of universal gravitation is established, and the concept of absolute time and space based on classical mechanics is also established. Newton believed that absolutely true mathematical time, by its nature, passed away evenly forever, regardless of any external world. Absolute space, by its nature, has nothing to do with any external world. It never moves and will never change. He thinks that space is three-dimensional, OX, OY and OZ constitute three-dimensional space, and he separates space from time. Space has no clear definition of time, but the unified axis of natural flow. Classical space-time thinks the absoluteness of simultaneity, the absoluteness of time interval, the absoluteness of space distance and the invariance of quality. Therefore, the three basic physical quantities of time, length and mass have nothing to do with the motion of the reference system (observer) in classical mechanics.

3. Relativistic view of time and space based on the theory of "constant speed of light"

From 65438 to 0905, Einstein published five articles in succession, among which the special theory of relativity completely changed people's view of time and space. According to this theory, "time or space varies from place to place and will expand or be confiscated". Later, this theory developed into a theory of gravity to explain the phenomena of the universe, that is, general relativity. The two basic assumptions of special relativity are: the first is the principle of relativity. In different inertial reference systems, all physical laws are the same; The second is the principle that the speed of light is constant. No matter what inertial reference system, the speed of light measured in vacuum is the same.

The explanation of the principle of relativity at the same time should start with Einstein's cow dream. Einstein had a very special dream when he was a teenager. The dream is this: in a picturesque pasture, there are many cows lazily grazing near the electrified fence. When the farmer electrified the fence, the farmer saw three cows jumping in turn, while Einstein, who was standing opposite, saw three cows jumping together. (refer to ftl /P 1 1-P8/Joo maguyu (Jo? So who is wrong, the farmer or Einstein? The answer is that no one is wrong. This is the principle of relativity. As shown in figure 1, when the farmer at position A turns on the power switch, the current moves in the direction of the cow at the speed of light, and the total time taken for the scene where the cow jumps by electric shock to return to the farmer's eyes is: where c is the speed of light. Similarly, the time for the farmer to see the jump switch of the cow at position C is: the time for the farmer to see the jump switch of the cow at position D is. Because the three cows are at different distances from the farmer, they will not jump to the farmer at the same time. For the observer E opposite the farmer, because light and electricity travel at the same speed, he saw three cows jumping at the same time. For the same kind of events, the time of occurrence is different because of the different positions of observers. This is the principle of relativity. Einstein thought that there would be no absolute rest in the universe, thus denying Newton's absolute coordinates. He thinks that any inertial system (a system at rest or moving at a constant speed) is no different from a place at rest (coordinates). This is one of the foundations of special relativity, the principle of relativity. Another basis of the special theory of relativity is the principle that the speed of light is constant. Even if the observer or light source is moving, for the observer, light always travels at a speed of 300,000 kilometers per second.

A core problem of the theory of relativity is that time is not absolute. Objects moving at high speed (close to the speed of light) have a slow time flow rate, which is expressed by a formula. Its basic principle is shown in Figure 2. If the spacecraft flies forward at a speed close to the speed of light, there is a beam of light from A to B in the spacecraft. According to the principle of relativity, during the flight, the time for people on the spacecraft to observe the movement of light is: not only does light propagate in a straight line relative to the observers on the spacecraft; For the observer who sees the spacecraft moving outside the spacecraft, the light is emitted from A to D, and the time it takes for the light to move is: obviously because of SAD? SAB=SCD, then there is t2? T 1, that is to say, for observers outside the spacecraft, the time of light movement becomes longer than that inside the spacecraft.

Another core problem of relativity is that when an object moves at high speed (close to the speed of light), space (length) will shrink. Expressed by formula. The basic principle is shown in Figure 3. The observer at A first sees the ship's bow C, while the stern at this time is at E. When the observer looks at the stern, the stern has moved to point D and the bow has moved to point C. Therefore, for the observer, the length of the ship he sees is only the SCD length, not the original SCE length of the ship, and the ship is compressed in the direction of movement.

An amazing prediction of special relativity is that the motion of any object in the universe has an upper speed limit, and this upper limit is the speed of light. In other words, no matter how advanced and advanced technology is used to accelerate an object, the speed of the object cannot exceed the speed of light. When an object accelerates, its mass increases, so the closer it is to the speed of light, the harder it is to accelerate. According to the formula, it is almost impossible for an object to reach the speed of light. We can only understand this by the fact that photons have mass in motion and no mass at rest. Quality and energy are a matter of time. With the formula, not only a small mass can be converted into a very large energy, but also a key point of special relativity.

To sum up, Einstein's four viewpoints on simultaneity and relativity, slow motion clock, shrinking motion space and increasing motion quality have completely subverted Newton's absolute view of time and space. Einstein developed the special theory of relativity and took gravity into account. The four principles put forward by general relativity give us a new understanding of time and space. The principle of general relativity is as follows: first, the principle of equivalence is that there is no difference between inertial force and gravity observed where the motion is accelerated. For example, in a falling box, gravity is completely offset by inertial force, and gravity slips away. This is the equivalence principle. Second, gravity bends light, because light has mass in motion, so it is also affected by gravity, so light bends near the earth or the sun, which can be proved by observing the stars hidden behind the sun during the total solar eclipse. Black holes are also proof that light is bent or attracted by gravity. Third, gravity bends space, massive celestial bodies bend light, and light travels in a straight line in the curved part of space. As a result, space is curved near massive celestial bodies, or the whole universe is a curled space. Fourth, gravity slows down the flow of time. The stronger the gravity, the slower the time flows. The closer to the celestial body near the black hole with particularly strong gravity, the slower the flow of time. If you travel to the black hole horizon, time will even stop. Different from the special theory of relativity, in places with strong gravity, the time flow is not relatively slow, but inevitably slow, which has been proved in the operation of the global positioning system. Unless scientists correct the clock benefits brought by gravity changes, satellite system positioning will not be accurate.

Fourthly, a new concept of time and space based on the theory of chaotic fractal.

Most of nature is not orderly and balanced, but in a state of disorder, imbalance and randomness, and there are countless disordered States. In the nonlinear world, randomness and complexity are its main characteristics. But there are still some natural laws under the performance. Chaotic fractal theory deals with these problems in a new way. By confusing chaotic phenomena and irregular forms, it reveals the laws hidden in complex systems and the relationship between parts and the whole.

The great physicist John? Wheeler (the name of the black hole) said that in the future, if a person can't be familiar with chaos and fractal, he can't be regarded as a scientific and cultural person. Fractal theory is an American scientist Mandelbrot (B? b？ Mandel brot) 1975 first proposed that "fractal" is a set. The establishment and rapid development of fractal theory involves almost the whole natural science and social science. Literally, fractal is extremely fragmented and complex, but it also has self-similarity and self-imitation, which are ubiquitous in nature. Such as unpredictable clouds, magnificent landforms, winding coastlines, biological neural networks, branched tributaries, rivers and tributaries, and so on. Faced with these things and phenomena, traditional science seems helpless, and fractal theory has become a powerful weapon to study these complex things. The simplest example of so-called fractal is a tree, such as folding its trunk, branches and twigs, and you will find that they are strikingly similar. Small branches are like models of big trees, and big trees are like enlargements of small trees; Another example is the similarity of river deltas. From maps, planes and the ground, we can see rivers, streams and streams, and their branching forms are similar to the geometric shapes of triangles. For another example, the human body from arteries, veins to capillaries has the same similarity in its direction and branch morphology. This is the fractal theory that nature shows us. There is a famous saying in our country, "Manage the family, govern the country and level the world", that is, if a person can manage a family well, he can manage the country well and level the world. This is the embodiment of fractal theory in sociology. And "it is quite critical, a bud knows spring" is also the early application of fractal theory. Even the opening of the Romance of the Three Kingdoms, "It is said that the general trend of the world, long is divided, long is combined" is also the application of fractal theory in historical development. To sum up, fractal theory is a new understanding of our view of time and space.

The exploration of chaos was put forward by many scientists who studied three-body as early as the early 20th century. We know that it is easy to calculate the orbit of two bodies by Newton's mechanics, but the motion law between the sun, the earth and the moon has not been well explained so far. This is the so-called three-body and an important beginning of chaos research. Because this problem contains many basic, primitive, intuitive and innovative things about our understanding of nature. This requires new thinking, new ideas, new methods and new theories. Under this historical background, there has been a theoretical confusion about human's new understanding of nature and time and space. As a famous example of studying chaos, "butterfly effect" has become a window for many people to understand chaos. The "butterfly effect" means that the trajectory will change greatly under the slight interference on the established orbit. In order to describe the extreme sensitivity of chaotic complex systems, Lorenz made an analogy. In the southern hemisphere, a small airflow caused by a butterfly's accidental flapping of its wings may turn into a tornado sweeping across the northern hemisphere in a few weeks. "A gunshot of the October Revolution brought Marxism–Leninism to China" is the "butterfly effect" that caused the China Revolution and the world socialist revolution. A horseshoe nail fell on a prince, a prince lost a war, and a war lost a kingdom, but it also changed the whole world. This is the "butterfly effect" in historical development. Chaos studies order in disorder, and many phenomena are unpredictable even if they follow strict deterministic laws. Chaotic events show similar change patterns on different time scales, which is very similar to fractal change patterns on spatial scales. Chaos mainly discusses the instability and divergence process of nonlinear dynamic systems, but the system always converges to an attractor in phase space, which is very similar to the generation process of fractal. Chaos and fractal theory depend on the progress of computer to a great extent, which poses new challenges to traditional mathematics. Because of the uncertainty of chaos theory, the unpredictability of the future and the orderliness in disorder, people will inevitably think of China's Book of Changes, foreign astrology and some religious activities and predictions. Can it be summarized as a chaotic phenomenon that people have solved after thousands of years of exploration? In the confusing cosmology, people only want to use the existing laws of the universe to explain the observed astronomical phenomena, and the latest research has many phenomena in the universe that we don't know and can't explain, such as Mike. ? Whether the new celestial bodies discovered by michael brown and other scientists can be regarded as the tenth largest planet in the solar system, why there are orbital celestial bodies with large inclination outside Neptune, what laws exist in the movements of more than 1000 planets discovered outside Neptune, and how many phenomena in cosmology can only be explored and explained by chaos and fractal theory.

5. The concept of time and space based on the new theory of "the change of the speed of light" (VSL)

With the arrival of the new century, physics is faced with the same layers of fog as it was a hundred years ago, and physics theories beyond Einstein's theory may appear. And Dr. Joao Maguyou (Jo? The VSL theory put forward by o Magueijo is an extraordinary crazy idea to interpret the nature of the universe in recent years, because it challenges the core of Einstein's theory. VSL's theory is that the speed of light in the early universe was faster than it is now. If so, at least some cosmic problems can be explained without inflation theory. In fact, when we use the theory of changing the speed of light to solve the mystery of the universe, the universe almost tells us that light used to travel faster, and the most basic physical theory seems to have to be based on a wider structure than relativity. What is exciting is that Australian National University physicists have recently created a "super optical trap" from the silicic acid crystal of rare earth element Pr. Successfully "frozen" the beam for one second. Since the light beam can be frozen, it is not necessary to deny the theory that the speed of light is constant and prove that the speed of light can be changed. According to VSL theory, the speed of light will not only change with the evolution of the universe, but also change in different spaces. When approaching planets and stars, this effect is almost imperceptible, but when approaching black holes, something more drastic will happen. The research equation shows that the speed of light itself may become zero at the horizon. According to the conservative VSL theory, just like special relativity, the speed of light should be a speed limit, but it may vary from place to place. Your speed must always be lower than the local C, so when the speed limit drops to zero, you will encounter the ultimate red light, and you must stop in front of the horizon of the VSL black hole. On the edge of the cliff, your suicide attempt will be initially stopped. In order to prevent disaster, the VSL black hole will be closed. No matter how we define time, these clocks will make different ticks when they approach a black hole. But the biological process itself has electromagnetic properties, which means that the speed of human aging is actually an excellent electronic clock. We find that when we approach a black hole, we will age faster, not because of Einstein's time lag effect, but because of faster electromagnetic action. Therefore, when we approach the VSL black hole, our heart will accelerate aging, or on the contrary, when we measure it at our own pace of life, we will find that our movement to the horizon will slow down. That is to say, as far as we are concerned, it takes forever to get close to the horizon, but if C remains unchanged, it may only flash for one second. Under the leadership of VSL, the horizon is closer, but it is also more difficult to reach. The horizon of the VSL black hole is like an infinite target, like an untouchable edge of space, and there is a wonderful eternity behind the boundary.

The more amazing theoretical significance of VSL theory is that when C may change in time and space, a "fast orbit" may appear, which is based on the VSL field theory and the form of cosmic strings. The speed of light along these strings may be higher, and the speed of light near the strings will become greater, just like a superluminal cover containing cosmic strings, which will create a corridor with extremely high speed limit extending to the universe, which is exactly the fast orbit sought by space travel. But this is better than the fast lane! Along the VSL cosmic string, time still lags behind, but this effect will become obvious only when the speed of travelers is compared with the speed of light (that is, the local value of C in this theory). Because the value of c along the cosmic string of VSL may be higher, when it is already moving at high speed, it may still be much slower than the local value of c, so the time lag will be negligible. So humans can move along the expressway and explore the farthest corner of the universe, but it is still much slower than the local light speed. He will be able to avoid the influence of the Gemini Paradox, and when he comes back, he will be the same age as his twin brother. He can not only visit distant galaxies in his lifetime, but also return to his hometown in the lifetime of his contemporaries. VSL theory will change our view of ourselves in the universe, and it will also change our expectation of contact with extraterrestrial life.

6. Multidimensional space-time based on superstring theory

At present, there is a new theory that in the subatomic world, that is, in the extremely tiny ultra-microscopic space, elementary particles are no longer the particles I can observe in reality. The existence of so-called elementary particles is only the expression of a tiny vibrating string in the microscopic world, just like an ordinary string in a stringed instrument we see in real life, which can play all kinds of wonderful music. In the ultra-microscopic world, there are many string vibrations that we can't observe with any modern instrument, forming a colorful family of microscopic elementary particles. According to superstring theory, the world is multidimensional, and we now live in a three-dimensional space or a four-dimensional space with a time axis. According to its theory, there should still be six or even ten dimensions of time and space. It is puzzling that Einstein's special and general theories of relativity can be easily deduced mathematically according to this multi-dimensional space-time theory. Relativity is no longer a theory based on Einstein's hypothesis, but a conclusion drawn from rigorous mathematical theory. Under the multidimensional space-time theory, which is the basis of string theory, the four basic forces in the universe (strong interaction, weak interaction, electromagnetic force and gravitation) are unified, and the grand unified theory that has puzzled physics for many years has been perfectly solved on the basis of this multidimensional space-time theory. Although superstring theory and multidimensional spacetime theory are perfect and puzzling, they need huge energy that humans can't get in recent centuries (1028 electron volts, which is 10 15 times the maximum energy that our accelerator can get now). Therefore, this theory belongs to the theory that human beings can never be verified by experiments. Whether this theory can last for a long time, maybe only God knows.

When it comes to multidimensional space-time, we have to start with a one-dimensional world. Here, if there is a "straight country", everyone living there lives in a one-dimensional space-time like a straight line. They can only live in a straight line, and there is no concept of plane in their country. If one day, people in a straight country suddenly leave the straight line, it is difficult to understand why this person suddenly disappears in their country. The two-dimensional world should be just a plane. If there is such a "plane country", people living in this country only have the concept of plane, so we can draw a circle for them. As long as you draw a circle, they will never leave it, because in their world, there is no upward concept. If a ball passes through their world, they can only see a circle from small to large. Finally, the three-dimensional world is the world we live in now. In this world, people think that space is absolute. For them, four dimensions are unimaginable and do not exist. This is like Newton's absolute view of time and space. He separated time from space and thought that space was absolute and time was unified and eternal. Einstein broke Newton's absolute view of time and space and established a four-dimensional space-time composed of space and time. He thinks that time and space are relative. So, is there a five-dimensional time and space? From a mathematical point of view, as early as 1950s, German mathematician Riemann surpassed Euclidean geometry, put forward the concept of four-dimensional space, and creatively put forward a brand-new concept called Riemann geometry, which made theoretical preparations for unifying all physical laws. In the 20th century, multidimensional theory once again became a hot topic in the scientific community. Some scientists put forward the concept of multi-dimensional space-time again and made effective calculations. It is worth mentioning that the wonderful mass-energy equation in Einstein's theory of relativity comes from the early mathematical string theory, which has to make people feel the wonder of nature.

Recently, string theory has become a hot topic in physics, and physicists believe that. There are not only five-dimensional space-time in the universe, but also six-dimensional space-time and even ten-dimensional space-time. In the early universe, it was a singularity in absolute vacuum. There is a ten-dimensional space-time at this time, but it is unstable, which leads to the emergence of our universe. During the creation of the universe, the ten-dimensional space-time was decomposed into four-dimensional space-time and six-dimensional space-time, and the six-dimensional space-time contracted into an infinitesimal singularity, and the four-dimensional space-time was in the BIGBANG stage. So there is our expanding universe now. Scientists who advocate the ten-dimensional space-time theory believe that our universe was created in the explosion, and the future will become a shrinking universe, which will shrink into a singularity again, and then repeat the scene created by the universe. This is the future of the universe. Multidimensional space-time theory can perfectly explain Einstein's grand unification theory, which has not been solved in the end, and unified the four kinds of interaction forces in nature that human beings know at present. Hawking, a physicist and author of A Brief History of Time, believes that the universe will eventually be explained by quantum theory. The universe we live in is one of many parallel universes. For the universe, like many soap bubbles floating in the air, each soap bubble is a universe, and there is no connection between them. This is Hawking's new view of the universe recently. He thinks that we are just a person living in a multidimensional parallel universe. If it is possible to open a hole between two universes,

Seven, three kinds of outer space civilization beyond time and space

Before ending this article, let's first understand that the astronomer Carl Che of the former Soviet Union once classified the future civilization of mankind as follows. He believes that a civilization controls the energy of the whole planet. This civilization can control the climate, prevent earthquakes, mine in the earth's crust and harvest in the ocean. This civilization has completed its exploration in the solar system. The second civilization is a civilization that controls the energy of the sun itself, which does not mean passive access to solar energy. This civilization can make use of solar energy. The energy demand of this civilization is so great that it directly consumes solar energy to drive machines. This civilization will begin to colonize the local galaxies. Three civilizations are civilizations that control the energy of the entire galaxy. In terms of energy, it controls the energy of billions of star systems. It may have mastered Einstein's equations and can manipulate time and space at will. Perhaps this classification of future civilization is wrong, but he did give a reasonable explanation of the laws of physics from the perspective of energy. Our human science and technology has only experienced a short history of several hundred years. At present, we don't have the conditions of the first civilization. There is still a long way to go before mankind enters the first civilization, and there are still many risks. Such as the nuclear crisis, the nuclear weapons stored by human beings are enough to destroy the modern civilization on earth several times. If human lunatics launch a nuclear war, the earth will go to the desert in the nuclear winter. Maybe today's Mars is the fate of the earth tomorrow. Now, with the acceleration of human modernization, the living environment of human beings is becoming more and more fragile. With the explosive growth of population and the increase of modern buildings, the land on which human beings depend will be less and less, and the earth will become a reinforced concrete castle. Environmental pollution, energy crisis, natural disasters and many other factors will make this seemingly powerful human being more fragile than ever. Any unexpected or unexpected natural and man-made emergencies may put this blue planet in an extremely dangerous or even destructive situation. Finally, the author sincerely wishes that human beings can cherish the environment, cherish peace, cherish the harmonious development of nature, and wish human beings a safe, sophisticated civilization and a high degree of modernization.

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2. Hot Abstraction/Zhu Zhu/Guangdong Economic Publishing House/September 2003/Guangzhou

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