singularity

Concepts in physics and cosmology

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Odd (q í) point yes Big Bang Cosmology Traced Cosmic evolution Start of^[3] Or the point at the center of a black hole. The density of the singularity is infinite Spatiotemporal curvature infinity.^[4]

Chinese name: Odd (q í) point
Foreign name: singularity^[2]
singular point
Alias: Space time singularity (q í) 、 Gravitational singularity (q í)

Presenter: Hawking
Proposed time: 1970
Applicable fields: Astronomy, physics
Applied discipline: Theoretical physics

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This is the black hole simulation diagram

Singularity is Big Bang A former form of the universe. It has a series of strange properties, including infinite density of matter, infinite curved space-time and infinite approaching zero Entropy Etc. Scientists proved that General relativity Of cosmology In, "singularity" is inevitable, even Isotropy Our universe is expanding from the "singularity". 1970, UK Theoretical physicist Hawking and others proposed“ singularity theorem ”It is proved that when general relativity is applied to cosmology, "singularity" will inevitably occur, not only large scale The universe will have a "singularity", and the final result of gravitational collapse of a supermassive star when it is dying is also a "singularity" (this "singularity" refers to a black hole, which has similar characteristics to the singularity). Other scholars believe that the inevitability of "singularity" in general relativity may be a manifestation of the limitations of general relativity. Einstein said: "One cannot assume that these equations are still valid for high field density and material density, nor can one conclude that 'the beginning of expansion' must mean a mathematical singularity." One speculate that the beginning of the evolution of the universe may not have a "singularity". For example, Steven Weinberg (1933 -) said, "The universe has never really reached the state of infinite density. The expansion of the universe may begin at the end of a previous contraction, when the density of the universe reached a very high, but still limited density."

Singularity is the point where space and time are infinitely curved^[1] 。 Scientists believe that the singularity exists in the center of the black hole. According to the nature of the singularity, it can be the form of the universe before the Big Bang, or the "singularity" of the black hole formed by the collapse of a super star. For example, in a black hole, the mass of all stars is compressed in a narrow space, and may even become a single point^[1] 。 Contemporary physical theory believes that this point is infinitely dense, although scientists believe that it is due to general relativity and quantum mechanics The product of the collapse of physics caused by the inconsistency of. In fact, scientists suspect that singularity is very dense, but not infinite^[1] 。

Space and time -- the infinity of time curvature A little bit. Space - time, which starts and ends here. Einstein said that time and space are illusions of people's understanding. Time is because of the change of everything in the universe, which makes people have the concept of time. At the singularity, with the birth of the universe, there began to be changes, which is the beginning of the universe. classic General relativity There is a singularity in prediction, but because the existing theory fails there, that is to say, quantitative analysis cannot be used to describe what is at the singularity.

If there is one or more Class time Or light like incompleteness Geodesic line Then the space-time is called Singularity In space-time, the point that incomplete geodesic lines tend to is spacetime singularity 。

As the "singularity of cosmology", most scientists believe that it is the point where the universe was formed by explosion at the beginning of the universe. It has the potential energy of all substances, and this potential energy is transformed into cosmic substances from the Big Bang Mass and energy We can imagine that a singularity is an inconceivable existence without fixed shape and volume. At the beginning of a world, it should have all the potential energy that forms all the matter in the universe, and this potential energy is what we call energy. We can imagine that energy is an invisible thing, so the singularity is invisible. At the same time, we can also imagine that at some point Cosmic singularity This potential energy balance of is broken, so accidentally, energy is constantly transformed into matter, and after several years, our universe - matter and energy Symbiont 。 It existed before the formation of the universe“ First push ”(Although there was no concept of "time" before the formation of the universe) - What we can't imagine is what triggered the destruction of the potential energy balance of this singularity. Mathematically, a singularity is a "geometric point" without size, that is, it does not actually exist. It is also difficult to understand that a matter with no size singularity is actually a matter with infinite energy levels. These are incompatible with our existing theories and concepts.

Grand View of Singularity (14 sheets)

singularity

In general relativity, the study of singularities is an important topic Energy conditions One of the earliest applications is also an example of the global approach in general relativity. It was mentioned in the introduction to the energy condition that Classical solution , such as Schwarzschild solution - existence Singularity 。 Some of the singularity - for example, r=2m in Schwarzschild's solution - can be obtained by coordinate transformation It is eliminated, so it does not represent a physical singularity; Some singularities - such as r=0 in Schwarzschild's solution - are real physical singularities. Obviously, the real physical singularity is the object of interest in singularity research. Singularities are obviously those spatiotemporal structures with some pathological behavior Space-time point 。 However, after a little deliberation, we will find that there are many problems with this statement. First of all, "pathological nature" is a very vague concept. What kind of nature is pathological? Obviously, it needs to be refined. Secondly, there is a big difference between general relativity and other physical theories, that is, other physical theories presuppose the existence of a background space-time, so if there is a singularity in those theories - such as Electromagnetic theory Where the midpoint charge is located field strength Singularities can clearly identify the position of the singularity in the background space-time. But general relativity describes the nature of space-time itself. Therefore, the singularity in general relativity often means that the nature of space-time itself cannot be defined. on the other hand, Physical space-time Is defined as four dimensions with Lorentz metric manifold It has good properties at every point. Therefore, physical space-time is by definition free of singularities, in other words, singularities do not exist in physical space-time.

Since the singularity does not exist in physical space-time, it is impossible to say which space-time point is a singularity, and thus it is impossible to define the singularity as a space-time point with ill conditioned space-time structure. Even so, the obvious fact that Schwarzschild solution has singularity is still undeniable, so the key is to find a reasonable definition.

singularity

Physicists have done a lot of research on the nature of singularity. Through these examples, they have a preliminary understanding of the complexity contained in the definition of singularity. Although its expression is simple, it ingeniously contains various complex space-time types that are difficult to list completely. On the other hand, although this definition has a great coverage, it is still not enough to cover all types of singular points. This point was also pointed out by Geroch, who singularity theorem In the research of, he is a very important person who can be as famous as Hawking and Penrose. In 1968, after proposing the above Counterexample In the same paper of, Geroch gave another kind of spacetime, but detailed research shows that this description is also not enough to cover all singularities. In 1968, R. P. Geroch gave a spacetime (R4, Ω 2 η ab) conformal to Minkowski spacetime, where the conformal factor Ω 2 has a sphere Symmetry In the region r>1, it is always 1, and t2 Ω→ 0 (t →∞) is satisfied on r=0. Obviously (please prove by yourself), for such space-time Geodesic line R=0 has no along t → ∞ Completeness , so this Space-time manifold It has time like and geodesic incompleteness. On the other hand, all optical geodesics will cross the area r ≤ 1 and enter Flat spacetime Therefore, they are geodesic complete. It can be seen that this space-time has the time like geodesic incompleteness, but not the light like geodesic incompleteness. This counterexample shows that not all singularities can be understood as points (or point sets) dug out from space-time.

Definition method

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According to the black hole theory, there is a singularity with infinite density and mass at the center of the black hole, so the singularity must be defined before the black hole is defined. Using the analogy of Einstein's general relativity rubber membrane model, if an object's energy or mass is large enough, it will puncture the "rubber membrane" into a hole, and this hole is likely to be a singularity. Since the existence of a black hole has been proved, the center of the black hole is determined to be a singularity. Here we start with the black hole. Obviously, light cannot escape from the black hole, which means that the black hole Gravitational acceleration And surface Escape speed Both Superluminal speed Of. The existing theorem regards the matter hitting the singularity as "vanishing". In fact, when the object approaches the singularity, it will be accelerated to the speed of light faster than the speed of light. According to the previous proof, if it exceeds the speed of light, it will jump to another space-time, so we don't need to care about this pitiable object at all. It has nothing to do with the current space-time. According to the above reasoning, we can make a new definition of singularity, which is a broken point in the existing space-time. In other words, the singularity is the entrance to the space-time tunnel acceleration Resulting Tidal force You can go out from here. (If there is any doubt about this, another way of understanding can also be used, that is, matter has been transformed into energy, and whether the energy "exceeds the speed of light" is meaningless.)

Discuss the life of a singular point Naked singularity , then the energy required to maintain it is basically 0. Since the singularity is a hole, its mass is basically 0, using Einstein's equation E=mc^2 (E is the energy, m is the mass, and c is the speed of light). That is to say, a singularity is similar to a blackbody, which has many of the same properties as a blackbody. First, because Absolute blackbody It does not exist, so suppose that a small hole on a closed box is a black body. Similarly, the previous assumption is similar to this. Considering the quantum benefits, the blackbody has radiation. Here must be considered Quantum effect , because in most cases the singularity is a quantum level point, according to Uncertainty principle It is easy to conclude that the singularity has tiny energy, which makes the singularity have temperature (like a black hole), which is similar to Blackbody radiation It is temporarily called singularity energy radiation here.

Because of the great attraction of the singularity, it will not have a naked singularity, because it will soon be wrapped by matter and energy, forming a black hole. Then a new problem arises. It is assumed that this definition can best describe the reality theoretical model One (can not be said to be "correct"), then for a Observer For example, the singularities energy radiation from the bare singularities that he can observe may have a certain amount of discrepancy with the theoretical value. Because based on the assumption that the singularity may connect to another space-time, the energy or radiation of another space-time can enter space-time through this point. If this effect is observed, it can be obtained Nobel Prize 。 Unfortunately, in most cases, these radiation will be extremely weak (because the assumed Black hole radiation It cannot be observed. Black hole radiation is stronger than this Background radiation Is almost impossible to measure. However, this phenomenon may be roughly measured in the following special cases.

The above discussions actually assume that the energy level of another space-time connected by the singularity is lower than that of space-time, and discuss other situations. Because here Quantum effect It is obvious, so it is easy to prove that it is impossible to show the same energy level of two spacetimes in the observation. When the energy level of another spacetime is higher than spacetime, the energy of that spacetime will enter spacetime, which can be understood as white hole 。 It can be inferred that most white holes will not radiate material. It can be easily found that under this theoretical framework, many anomalies in actual observation can be easily explained, such as dark substance 。 To "prove" or falsify this hypothesis, we need to make actual observations to determine whether it can best describe the current situation theoretical model 。

mathematical analysis

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Put“ geometry Singularities "and" physical singularities "shall be applied to Big Bang Theory That is, the "point from scratch" of the universe, which exists and cannot be described, namely“ Big Bang Singularity before ".

because boundary condition It can only be given by the creator outside the universe, so the fate of the universe is in the hands of the creator. This is from Newton It has been puzzling human intelligence since the times First driving force Problems.

See some descriptions of singularity theory in geometry. Example: Equation

In real numbers, when a point seems to "approach" to ± ∞ and undefined, it is a singular point x=0. Equation g (x)=| x | (see absolute value ）It also includes the singular point x=0 (because it is not differentiable at this point). Similarly, there is a singular point (0,0) at y=x, because this point contains a vertical tangent 。 An algebraic set in the (x, y) dimension System definition There is a singular point (0,0) for y=1/x because it does not allow tangents here.

Theoretical basis

According to Hawking's“ Singularity theory ”The "black hole" is located at the "singularity" (i.e Square nanometer After the pressure reached several hundred million to ten billion tons. Singularity is just a point on a supermassive black hole. According to the inference provided by the NRAO Observation Organization of the U.S. VLBA astronomical website in January 2007, the mass of the so-called supermassive black hole is Solar mass From millions to tens of millions of times, and according to the calculation of the mass of the sun itself for the mass of the black hole Supermassive black hole Its mass density reaches tens to tens of billions of tons per cubic centimeter. front Soviet Union In the 1980s, scientists calculated that the material density at the "singularity" was up to 10.45 tons, while the area at the singularity was 10-33 tons square centimetre 。 The material at the "singularity" has only 10-5g mass, and Stellar fetus The temperature reached 1016 degrees (equivalent to 1 trillion billion degrees) in just 10-35 seconds, and at this time, there were only various rays in the universe in this space, such as β and Gamma ray Various "radiation", x-rays and the so-called "antimatter fountain" have been unable to release the "excess energy", and the temperature after the explosion may be as high as 10 trillion times per second today computer It is very difficult to make statistics. Today's 10 trillion times/second electronic computers and 58 million tons are used 10 ^ - 43 seconds after the outbreak TNT · equivalent Of Hydrogen bomb The particles with "very high density and extremely high temperature" are produced in the high temperature which is difficult to describe and count experimentally. One second after the explosion Particle production The "temperature" and "density" of the hour can already be counted with the 10 trillion times/second computer on the earth, or 58 million tons TNT equivalent Hydrogen bomb experiment, and High-energy physics Neutron+neutron Collider Simulation, description and inference are carried out.

Whether it's 10 ^ - 43 seconds of the big bang, 10 ^ - 35 seconds of the big bang, or 1 second of the big bang, it's entirely reasonable to think that Cosmic expansion The speed is the square of the speed of light. Since then, the universe has been Superluminal speed When the neutron and proton appear, and then, from Neutrons and protons The universe has been expanding at the speed of light and continuously producing matter for 1 billion years from the appearance of the atom to 13.7 billion years later. according to Stephen Hawking /Xu Mingxian, Wu Zhongchao Translated Brief History of Time >>>, the temperature of the universe one second after the Big Bang is 10 billion degrees, which is probably the sun Center temperature 1000 times, which is equivalent to the hydrogen bomb explosion experiment conducted by human beings. The particles continue to collide and collide at the speed of light under the original first power of the original "Big Bang" and generate (in the cosmic vacuum nuclear fusion The power generated can easily make particles and substances Movement speed Or the speed of impact reaches the speed of light. High energy on earth Particle accelerator In addition to the gas composed of special elements and connected to the magnet and power supply with very high voltage, the pipeline is generally vacuum, so that various particles and substances can be accelerated to the speed close to light) "neutron cloud" and "proton cloud" Cosmic temperature It may still be quite high, and the generation of neutrons and protons may have taken tens of millions to hundreds of millions of years; At this time, the expansion speed of the universe may still be equivalent to 300000 km/s. Otherwise, according to Einstein's formula E=MC ^ 2, atoms cannot be generated by the collision of neutrons and protons in the expanding universe. Perhaps these neutron clouds and proton clouds, which still have extremely high temperature and energy, continue to "explode and contract as well as release a large amount of energy" in the "collision" and "friction", which is very similar to the "hydrogen bomb experiment" conducted by humans. Hawking, a British astrophysical scientist, believes that: 1 billion years after the "singularity" eruption Atomic formation Has. The temperature of the universe after the generation of atoms may have dropped to about - 270 degrees. According to the report of "The Voice of Germany - Science and Technology Program" (Russian), the British astronomer Mary has been working on Galaxy According to the observation of the center, the center of the galaxy is generally empty, and the temperature is lower than the average temperature of the universe. (The reason why scientists think that the vacuum is filled with neutrons+protons after a lot of time after the big explosion of the universe is that nuclear tests and nuclear fusion Experiments and for stars and cosmic rays The conclusion drawn from long-term observation. Scientists found that sunlight Not only does it emit a lot of ultraviolet rays and neutrino It also emits a large number of high-energy protons and electromagnetic particles. As early as the early last century, British scientist Rutherford and his assistant used a Particle bombardment Nucleus In the 1930s, German physical scientist Heisenberg believed that the neutrons and protons in atomic nuclei can exchange electrons and combine together. Protons become neutrons after they get an electron, while neutrons become protons after they lose an electron. In 1932, Rutherford's student Charley Wei found a neutral particle when he used a particle to bombard the nucleus of beryllium, which is called neutron. Chinese scientists pointed out after experiments in the 1970s that the so-called a particle is a small group of nucleons, which consists of two neutrons and two protons. In January 2007, Academician of CAS Ge Changchun Controllable nuclear fusion It is pointed out that deuterium and Tritium nucleus Fusion produces a large number of neutrons and a particles, as well as electromagnetic radiation. Because the experimental results in the laboratory are similar to those of astrophysical scientists solar radiation The observation of properties is completely consistent with the experimental results, so it can be very sure that the source of solar energy is nuclear fusion).

Cosmic evolution

From Singularity to Singularity

The vastness of the universe cannot be described in words, and《 Brief History of Time From the Big Bang to the Black Hole adds another layer of mystery to it, and of course it is also Hawking's pursuit Ultimate truth Our indomitable soul was deeply impressed. His personality charm is just like that in the black universe Blue giant It also radiates vitality and wisdom.

As early as ancestors Fuxi He began to study the universe until 1905, when Einstein in the West published General relativity 。 The temptation of the universe to scientists has never stopped.

Looking back in the past, it is estimated that in about 14.1 billion years, "everything is empty" was "nothing", and a groundbreaking event occurred. A very small, extremely high temperature, extremely dense singularity exploded, and this small singularity gave birth to the universe.

In the framework of classical general relativity, it is proved that under very general conditions, there must be singular points in space time, and singular points can be seen as the edge or boundary of space time. Only when the boundary conditions at the singular point are given can Einstein equation The evolution of the universe is obtained, but the boundary of the universe is only known by the creator. Many scientists have neglected to eat and sleep for it.

Hawking explained this problem, and he believed that quantum state Is in a ground state Space time can be regarded as a finite and unbounded four-dimensional surface, just like the surface of the earth, only two more dimension nothing more. All structures in the universe can be attributed to quantum mechanics Of Uncertainty principle The minimum allowable fluctuation. From some simple model calculations, it can be concluded that Astronomical observation Consistent inference, such as the clustering structure of galaxies, stars, etc, large scale Of Isotropy And uniformity, the flatness of space and time, that is, space and time are basically flat, which makes the development of galaxies and even life possible, as well as time Direction arrow wait. Hawking's Quantum cosmology So that we can have a systematic study of the universe.

Before that, scientists all agreed that Gravitational attraction The universe must be expanding or shrinking. According to general relativity, the universe must have an infinite density state at a certain time in the past, that is, the Big Bang, which is the effective start of time. Similarly, if the entire Cosmic collapse In the future, there will be another state of infinite density, namely Large extrusion This is the end of time. Even if the whole universe doesn't Collapse Singularities exist in any local region that collapses to form a black hole. These singularities are the end of time for anyone who falls into a black hole. At the Big Bang or other singular points, all laws fail, and the problem remains unsolved.

Hawking believes that his contribution to life is Classical physics In the framework of Big Bang Singularity The black hole becomes bigger and bigger; But in Quantum physics He pointed out that the black hole became smaller and smaller due to radiation, and the singularity of the Big Bang was not only Quantum effect And the whole universe started here.

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