Scientists put forward a conjecture about four-dimensional space through the evolution of one-dimensional, two-dimensional and three-dimensional space. A zero dimension is a point that has no length in any direction. One dimension is a line composed of countless points, with only length but no width and height. Two-dimensional is a surface composed of countless lines, which is long and wide, but not high. Three-dimensional is a body composed of countless faces, with length, width and height. What about four dimensions? Four dimensions is a space composed of four mutually perpendicular dimensions of imagination (this is really a headache).
1. What are the characteristics of four-dimensional space?
From the experience of the low-dimensional real world, we can imagine that if a person lives in a two-dimensional world, the world he experiences is only two dimensions. If a three-dimensional sphere passes through this two-dimensional world. A two-dimensional person will see a circle in his world. He can walk around a circle and measure the circumference of the circle, but he can't intuitively perceive the volume of the sphere. In the whole process of the sphere passing through the two-dimensional plane, two-dimensional people will see a circle appear, become bigger, become smaller and finally disappear. By analogy, we can imagine a scene where a four-dimensional sphere passes through a three-dimensional space: we will also see a three-dimensional sphere appear, get bigger, get smaller and disappear.
Obviously, the low-dimensional space is the projection of the high-dimensional space, or the cross section. And we humans are probably the holographic projection of four-dimensional space in three-dimensional space.
When talking about the concept of four-dimensional space, Dr. Li Ran, a researcher at the National Astronomical Observatory of the Chinese Academy of Sciences, thinks that when we say "look", it is actually not rigorous. The nuclear force, weak force and electromagnetic force in our world membrane (theoretical physicists call our three-dimensional space plus one-dimensional time a world membrane, embedded in a higher-dimensional superbody) cannot leave the three-dimensional space and enter a higher dimension. In three-dimensional space, when we irradiate an object with a beam of light (electromagnetic wave), we can see the object through the reflected electromagnetic wave. But an object in four-dimensional space can neither reflect nor emit electromagnetic waves, so we can't see it at all. The only thing that is thought to interact with objects in four-dimensional (or higher-dimensional) space is gravity.
When a four-dimensional object passes through our three-dimensional world, we can only perceive it through its gravitational effect. In the movie Interstellar, NASA team members noticed various gravity anomalies, which are the gravitational effects produced by high-dimensional civilization in the process of helping people on earth.
For example, in our three-dimensional world, gravity is inversely proportional to the square of distance. Planets twice as far away from the sun as the earth feel only 1/4 of the gravity of the earth. However, if there is a fourth straight dimension in our space, the strength of the gravitational field will decrease with the increase of the cubic distance, and neither Jupiter nor Saturn can escape from the solar system with the help of the gravity of the sun. However, scientists still believe that four-dimensional (or higher-dimensional) space does exist, but it can avoid the divergence of gravitational field by curling on the micro scale.
Second, where is the four-dimensional space?
The physicist Stephen W. Hawking once asked when he gave a speech about The Theory of Everything at Cambridge University. If all the extra dimensions outside our three-dimensional world really exist, why don't we realize them? Why do we only see three dimensions?
The explanation for this is that all four dimensions (or higher dimensions) bend in a very small space, and its scale is only about1000 trillion billionth of an inch. This scale is too small for us to detect. What we see is only three-dimensional space. According to the principle of cosmology, the three-dimensional space of the universe is isotropic and almost flat on a large scale. This is like the skin of an orange: if you look closely, the whole skin is bent and wrinkled; However, from a distance, you can't see those raised structures, which are very smooth. The same is true of space, which is four-dimensional (or higher) on a tiny scale and highly curved. But on a larger scale, we can't see bending, or we can't see extra dimensions.
Four-dimensional and higher-dimensional spaces can be constructed by mathematical theory. In quantum mechanics, space is multidimensional, and N-dimension is a space vertically formed by two or more N- 1 dimensional objects. So we can say that four-dimensional space can only exist in the mathematical equation of the most advanced string theory today. String theory predicts the existence of more dimensional patterns, and it is said that there are at least 1 1 dimensions.
Three, four-dimensional hyperbody-Klein bottle
Speaking of four-dimensional space, we have to mention the German mathematician Felix Klein, who once conceived a special four-dimensional object in theory, called Klein bottle. This is one of the typical spaces of topology research, and it is a surface that can be truly expressed in four-dimensional space. This closed space like a sphere has no "edge" but only a "face". Its cross section is a Mobius belt. If two Mobius belts are combined only along their edges in four-dimensional space, a Klein bottle can be obtained.
According to topology theory, Mobius belt can be embedded in our three-dimensional space, while Klein bottle can only be embedded in four-dimensional (or higher) space. According to Wikipedia, mathematicians claim to have solved the mathematical expression on the surface of Klein bottle.
Theoretical physicists believe that Klein bottles cannot be made in our three-dimensional space. It is a continuous surface with no boundary, no interior and no exterior, and only a surface, so it is called a bottle that will never hold water.
Because the four-dimensional space cannot enter our three-dimensional space, any Klein bottle that can be drawn or made is the projection of its four-dimensional space in the three-dimensional space. In other words, a four-dimensional Klein bottle cannot exist in a three-dimensional space.
4. Why is the four-dimensional space small and curly?
The above discussion leads to another problem. Why do four-dimensional (or higher-dimensional) spaces curl into small balls instead of all dimensions? Hawking believed that all dimensions in the very early universe should be highly curved, so why did the three-dimensional space flatten while the other dimensions remained tightly curled?
So far, science has no answer, or a possible answer is the personification principle. In order to develop a complex life like human beings, two-dimensional space is not enough, and space larger than three-dimensional space makes galaxies unstable and face disintegration. Therefore, at least life as we know it can obviously only exist in a stable space-time region, that is, there are three-dimensional space plus one-dimensional time, and they will not become too small because of curling.
String theory can really deduce and allow the existence of our region. There are probably other areas in the universe, and their dimensions are all curled up very small, but such areas will not have intelligent life.
Although it is impossible to prove that the conjecture that there is a four-dimensional (or higher-dimensional) space is accurate, many scientific theories begin with conjecture.
(Thanks for reading)
How to prove the existence of four-dimensional space is a very interesting question, because it is a religious, philosophical and scientific question.
In fact, four-dimensional space is not difficult to prove. Many people always want to use science to prove the existence of four-dimensional space, but it is always difficult to prove it. Why? Because they ignore people's enthusiasm. So far, the clearest explanation of four-dimensional and multi-dimensional space in the world is not science, but Buddhist argument. Many physicists, quantum scientists and other scientists have to admit this and have written some monographs on this issue.
For example, a person has a stomachache, but neither doctors nor medical equipment can find the cause. Is it true or not that this person has a stomachache? No, because the pain has been proved! Therefore, it is not necessary to prove the existence of four-dimensional space with so-called mathematics and physics, but through self-demonstration. Almost everyone has proved the existence of four-dimensional space, but people don't realize it. Let me give you an example.
Almost everyone has seen different people or things and experienced different events in their dreams, but people are asleep and their eyes are closed in their dreams. Why can they still see things in their dreams? In fact, the eyes in the dream are four-dimensional or even multi-dimensional, and they are the reflection of spiritual consciousness.
Many people will say that dreaming is illusory and false. In fact, people and all their activities are the process of life and death of energy, which is changeable and false. If we look at the life and death process of human beings for a century from the perspective of the high-dimensional universe, I am afraid it is not even a moment. In fact, there is no difference between human activities and dreams in essence, and dreams are also a process of energy variation. Therefore, Buddhists say that "everything is like a dream bubble, such as dew and electricity, so we should look at it this way."
The eyes in the dream are the experience that people unconsciously get rid of the shackles of eyes, ears, nose and tongue during sleep, and appear a state similar to meditation, which makes the mind enter different dimensions.
In addition, many people regard time as a dimension, which is incorrect. In high dimensions, there is no past, present and future. The most fundamental dimension is to get rid of all illusions, even the dimension itself does not exist, let alone time.
Give the answer first:
Spatial dimension, which belongs to the category of mathematics, is a measurement and statistical term and has nothing to do with scientific discovery. Four-dimensional space is just a geometric model, which has nothing to do with real existence.
This paper is the author's main viewpoint on space, focusing on strictly distinguishing between "physical space thinking" and "mathematical space thinking"
Multi-context cognition of space since ancient times, human beings have accumulated progressive cognition, which still needs further scientific research.
According to the research results of modern physical science, the author thinks that space is the simplest and most complicated material category that really exists.
Space is a multi-context concept, which is mainly manifested in four types of space: ① the perceptual space of organs, ② the dialectical space of philosophy, ③ the real space of physics and ④ the abstract space of mathematics.
The perceptual space of human organs is named because many people think that the area between entities is absolutely empty without any substance through visual and intuitive reasoning, that is, the perceptual space is empty.
English space: [sp] is the abbreviation of root spect, spic (see/see); [ace] is a variant of the suffix ate. Literally, space is an infinite extension of the outside world.
As far as the simple requirements of survival are concerned, the view that perceptual space is empty has certain merits.
For example, the vacuum quality of hollow iron balls is ≡0, which is beyond reproach, and there is no need to be "bookish" about it.
According to the author's experience, there are three typical philosophical spaces in the dialectical space in the field of philosophy, namely, the Taoist theory of "everything is empty", the Buddhist theory of "color is empty" and Ma Zhe's theory of "spatial matter".
Taoist Space Philosophy of "Four Emptiness"
Generally speaking, the fate of the Millennium comes from the air, and the so-called "gathering into a device"; Returning to the air, the so-called "dispersion is ventilation." This is the space for scientific research.
The author thinks that the space view of "gathering makes a device, dispersing makes a gas" is great wisdom and a very precious world view, which coincides with the scientific explanation of modern physical experiments.
Buddhist Space Philosophy of "Color is Empty"
Empty color is all kinds of tangible substances, tangible things that can be seen and touched.
The color void is a vague intangible substance, something that can't be seen or touched.
Buddhist disciples have the so-called "skeleton skill", which means that when practicing meditation, they can realize that the skeleton is transparent with their minds.
Is the mind really that powerful? According to physics, only UHF electromagnetic waves can pass through the bone at will, as if the space inside the bone is empty.
Ideas can radiate high-frequency waves? Maybe you don't rule out the illusion that Skeleton Gong is possessed? What do readers think?
However, according to the electronic annihilation reaction, the Buddhist disciples' philosophy of emptiness and space is at least "wrong", right?
Ma Zhe's Spatial Philosophy of "Spatial Materialism"
Marxist materialist dialectics holds that the world exists, existence is material, and matter is moving. Since space also exists, space is both material and moving.
Ma Zhe's "Theory of Spatial Matter" can be witnessed by the laws of the immortality of matter and the conservation of energy, and its strict logic is beyond doubt.
Some people may disagree. The author reminds me:
Since space exists, we have to admit that space is not nothingness; Since we admit that space is not nothingness, we have to admit that space is matter; Since we admit that space is material, we have to admit that space is moving. Matter and nothingness must be one of them.
Therefore, Ma Zhe's "theory of spatial matter" is impeccable, at least in formal logic.
The real space of physical science The real space of physical science, referred to as physical space for short, is a vacuum field medium space without subatomic existence, that is, field space.
Remember two words: physical space ≡ rational space ≡ real space. Mathematical space, ideal space and abstract space.
Here are five aspects to explain the expression of real space.
1. On Maxwell's Equation
Vacuum is not empty, and the energy of vacuum field is zero, which has long been a scientific knowledge. Vacuum is a field medium, which is expressed by the dielectric constant (ε? ), magnetic permeability (μ? ), displacement current (j).
According to the definition of the speed of light: c= 1/√(ε? μ? ), the speed of light is an inherent characteristic of vacuum field, and it is a medium that oscillates at the speed of light everywhere, rather than the absolutely static ether before the 20th century.
2. About the Casimore effect.
As early as 1947, the Casimir effect has been confirmed, and the vacuum field can excite electromagnetic waves. The Casimir effect force (F=-Cπ/R? ), prove: real space ≠ geometric space!
The author thinks that the essence of Casimir force is the gravitational wave excited by the electron spin disturbing the field space at the speed of light, and the reaction force opposite to the centripetal force of the electron spin, namely:
F (strong) =-F (kasimo),
m？ c？ /R=-Cπ/R？ ...( 1)
Where r is the thickness of vacuum cavity or vacuum field radius, and c is Casimir effect coefficient, which depends on the field radius of gravitational wave excited by electron spin motion.
Namely: C=(m? c？ /π)R=2.6× 10？ Rare ... (2)
3. About the nature of electron-positron annihilation reaction
According to the annihilation reaction of positive and negative electrons, the electron generator releases photoelectrons (e? Or e↓) is placed in a strong magnetic field opposite to each other, and an electron reverses the north and south poles and becomes a positron (e? Or e), when the positive and negative electrons accelerate to the speed of light, try to collide with them, and the annihilation effect can occur:
e↓+e↑+2×？ m？ c？ ⊙γ↓+γ↑+ 2hc/λ？ ...(3)
The essence of annihilation is that electrons rapidly expand into field quantum (graviton and light quantum), and there is a mutation between real matter and field medium, in which:
Electronic quality? Quantum mass of field, spin potential energy of electron? Gravitator spin potential energy, electron kinetic energy? Photon radiation kinetic energy.
Obviously, the annihilation reaction of electrons confirms the philosophical space of "gathering makes a device, dispersing makes a gas" and "color is empty"
4. Ultrafine structure of atomic spectrum
The experiment of ultra-fine structure distribution of atomic spectrum shows that the outer space of atoms contained in matter is full of electromagnetic waves with different frequencies without gaps.
As far as fullness is concerned, the "container space" for storing electromagnetic waves or field media can be regarded as "field media space".
5. About the internal space and external space of the entity
Generally speaking, we think that macroscopic objects are composed of atoms, atoms are composed of microscopic extranuclear electrons and nuclei, and nuclei are composed of quark rings and muon nuclei.
According to the concept of independent matter, the quark ring of the nucleus can be an electron in the nucleus, and the Muir nucleus can be the highest density field medium. Because quarks, gluons and muons are only theoretical models and cannot exist independently.
Positron is just an electron that reverses the North and South poles. According to this logic, the ultimate components of matter are only electrons and field media.
Previous experiments show that electrons are inseparable, and the internal space of electrons is the only high-density field medium, that is, "color is also empty."
It is not difficult to understand that the space in the nucleus is the highest density field, the space in the electron is the second highest density field, the space in the atom is the high density field, and the space in the molecule is the higher density field.
It is not difficult to understand that the field density (ρ=m/4.2R? ) and the field radius r are inversely proportional to the cube.
Each atom has its own independent internal space and external space. Because of its high-speed electron orbit and anti-degeneracy, atom can be a closed vacuum cavity.
The outer space of atoms is a "photon cloud trusteeship" full of ultra-fine structure of atomic spectrum, and atoms have their own gravitational field space.
Basic properties of physical space From the above basic facts, we can sum up nine basic properties of physical space as the basic principles of space view.
Property 1: field space privacy
Entities have their own internal space and external space. For example, an electron has an inner space rotating at the speed of light and an outer space of a gravitational field.
Similarly, protons have their own internal space and external space; The earth, the moon and the sun all have their own internal space and external space.
Attribute 2: Commonality of field space
An arbitrary spatial region has the private space of each entity, forming an overlapping space in this region.
For example, the internal space of an atom is the superposition space of an electron field and a proton field. The intramolecular space of oxygen is the superposition space of oxygen atoms.
The space of the earth radiation belt is the overlapping space of the lunar stadium, the Mars field, the solar field and the Polaris field.
Attribute 3: Follow-up of site space
The space of the earth's atmosphere rotates with the rotation of the earth, and it is impossible for only air molecules to move with it.
Close the inner space of the carriage, and turn together as the train moves forward. It is impossible for only air molecules to move with it.
It is impossible to close the internal space of atoms, because the atoms roll and oscillate together, and only the electron nucleus follows.
The inner space of a closed nucleus rolls and vibrates with the nucleus, and it is impossible for only the electrons in the nucleus to move with it.
Extranuclear electrons move with bullets, and the frequency of electromagnetic waves excited by bullets interfering with superposition space depends on the following speed of electrons;
? mv？ =(m/m？ )hc/λ...(4)，λ=2hc/m？ v？ ...(5)
Characteristic 4: Energy absorption in field space
According to the principle of gravitational potential energy Ep=GMm/R and entropy increase, the high energy state diverges to the low energy state. The larger the field radius r is, the smaller the field potential energy is and the greater the vacuum degree is, so the more energy is absorbed. For example:
The kinetic energy of electrons moving around the nucleus at high speed is in a high energy state, and it is absorbed into radiation kinetic energy by vacuum field while disturbing the space.
The centrifugal pump rotates at high speed, forming a local vacuum area inside, and the water in high energy state of the conduit is attracted by the vacuum area in low energy state.
The helicopter wing rotates, and the local vacuum area above the wing is in a low-energy state, attracting high-energy aircraft.
Attribute 5: Carrier attribute of field space
Electrons spin at the speed of light, disturb the field space and radiate gravitational waves, which can be understood as the field space carrying gravitational waves.
Electrons move around the nucleus at high speed, disturbing the field space and radiating electromagnetic waves, which can be understood as the field space carrying electromagnetic waves.
The string vibrates at the speed of V. In fact, electrons excite electromagnetic wave phonons following the V disturbance field space, and phonons and excitons excite each other in turn. The field space carries ultra-low frequency electromagnetic waves (optical branches) and mechanical waves (acoustic branches).
Some people say that the jumping movement of electrons outside the nucleus releases photons or electromagnetic waves, but it does not mean that free electrons will also excite electromagnetic waves.
Attribute 6: Force Transfer in Field Space
The space-time equation of light travel: r=ct...(6)
Substitute into the equation of universal gravitation: F=GMm/r? ...(7)
Time-dependent gravity equation: F=GMm/c? t？ ...(8)
Obviously, the propagation of the gravitational field of an object is equal to the square of the field radius (r? ) is inversely proportional to the square of the magnetic field surge time (t? ) is inversely proportional.
Some people say that the law of universal gravitation has a distance effect, which is not very clear. Think about it: What is the inverse square effect of distance?
In fact, any propagation mode of force, energy and wave must be based on field space, otherwise it is distance theory.
Property 7: Entropy of field space increases.
According to the gravitational equation (7), the gravitational force of celestial bodies and gravitational waves radiated by field space are inversely proportional to the square of the radius of field space. If the interference of other celestial bodies is not taken into account, their field density drops sharply, the frequency of gravitational waves drops sharply, and the temperature of field space drops sharply, which is called entropy increase or "down-frequency red shift" of field space.
Attribute 8: Entropy reduction of field space
The inverse analysis of gravity equation (7) shows that the closer to the celestial body, the higher the field density and gravitational wave frequency superimposed on the outside, which is called entropy reduction or "up-frequency blue shift" of field space.
Attribute 9: Validity of field space
Theoretically, the radius of gravitational field of celestial bodies or particles seems to extend infinitely, but it is not. There are two main points:
First, the field space of independent celestial bodies or particles cannot extend to absolute zero, otherwise the field medium will be absolutely static.
Secondly, the field space is always the superposition space of multiple celestial bodies or particles. When the field radius of a celestial body or particle extends far enough, its field strength is not as good as that of other celestial bodies or particles.
There are five lagrange equilibrium points (L 1~L5) and hill sphere regions in the "Earth and Sun" problem. If the radius of the stadium far exceeds the equilibrium point, the gravitational field of the earth can be ignored.
Abstract space in the field of mathematics Mathematical space, also called geometric space, is based on coordinate system space. The origin of coordinates is the zero point of measurement datum, and the number of coordinate axes is the size.
Common low-dimensional space: one-dimensional space ≡ linear coordinate system, two-dimensional space ≡ plane coordinate system, three-dimensional space ≡ solid coordinate system,
Common high-dimensional space: four-dimensional space ≡ rotating three-dimensional coordinate system, five-dimensional space ≡ stretching and twisting three-dimensional coordinate system.
Why "geometric space ≡ abstract space ≠ real space"?
Let's think about it. Does the real world really exist-geometric zero without volume, geometric straight line without thickness, geometric plane without thickness, invisible geometric sphere?
Fermions are small and quasars are far away ... so they can be approximated or abstracted as particles, but they still have volume.
Electromagnetic waves and power lines are very thin ... so they can be approximated or abstracted as straight lines, but they still have cross-sectional areas.
The sun is like a sphere, and electrons are like a sphere ... so it can be approximated or abstracted as a sphere, but there are still apples with north and south poles.