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Einstein's greatest dream in his life was to build a universe made entirely of marble. However, with the development of quantum mechanics, his dream was shattered. But the standard model theory based on quantum mechanics is not only mathematically ugly, but also cannot include gravity. Therefore, the pursuit of the unity of quantum theory and gravity is called "the biggest scientific problem in human history". The mass media calls it the "holy grail" of physics, and the resulting theory is called "everything is rational".

All the physics giants tried to solve the problem, but they all failed. Einstein devoted the last 30 years of his life to the unified field theory. Even Heisenberg, one of the founders of quantum theory, spent the last years of his life on unified field theory. In 1958, Heisenberg even said on the radio that he and Pauli finally succeeded in finding a unified field theory, but lacked some technical details.

Later that year, Pauli finally gave a lecture on the Heisenberg-Pauli unified field theory, and physicists were eager to know the missing details. Bohr finally stepped forward and said ∶, "We all agree that your theory is crazy."

By the 1980s, however, the "quantum theory of wood (matter)" began to fail. It is the world of marble that attracts the next generation of physicists.

Of course, several esoteric problems stand in the way of the theory of quantum gravity. One of the difficulties in constructing some kind of gravity theory is that gravity is so weak that people don't know what to do. From the point of view of classical mechanics, gravity is negligible compared with electromagnetic force, so it is extremely difficult to measure. But if we try to build a theory of quantum gravity, the situation will be reversed. The quantum correction caused by gravity is of the order of magnitude of Planck energy, that is, about 10 ^ 28 electron volts, which far exceeds the maximum energy available on Earth.

This puzzling situation deepens when we try to establish some complete theory of quantum gravity. Recall that when quantum physicists tried to neutralize the force, they broke it down into tiny packets of energy called quantum. If you try to quantize the theory of gravity, you would speculate that it works by exchanging tiny packets of gravity called graviton ∶, which quickly exchanges gravity between matter, causing matter to be attracted by gravity. But whenever physicists try to do simple calculations to deduce quantum corrections to Newton and Einstein's laws of gravity, they find that the results are always infinite.

For example, let's examine what happens when two charged neutral particles collide with each other. In order to calculate the Feynman diagram of this theory, we must adopt an approximate method, so we assume that the curvature of space-time is small, so the Riemannian metric tensor is close to 1. As the first step of guessing, we assume that space-time is nearly flat and uncurved, so we decompose the components of the metric tensor into

Where 1 is flat, and HQ 11 is the graviton field. In this way, we come up with a seemingly canonical quantum theory.

(a) in quantum theory, the quantum of gravity is called the graviton and is represented by h. Gravity is formed by decomposing the Riemann metric tensor. In this theory, matter interacts with each other by exchanging this gravitational packet. In this way, we completely lost Einstein's beautiful geometric picture. (B) Unfortunately, all circles are infinite, which has hindered the unity of gravity and quantum theory over the past half century.

In the figure, we see that two neutral particles exchange a force, which is marked by the field h. When we sum all the cycles, the problem arises. We find that they are divergent, as shown in (b). For the Yang-Mills field, we can use some techniques to make these infinitely large quantities either gradually eliminate or be absorbed into some immeasurable quantity. However, it can be proved that when we apply them to the theory of quantum gravity, we find that the usual renormalization steps are completely ineffective.

In the early 1980s, a wonderful phenomenon appeared. Physicists began to overcome their prejudice against invisibility and hyperspace and prepared to adopt some alternative, which is the Kalucha-Klein theory.

Although the Karucha-Klein theory is still irreducible, it offers the hope of constructing a theory out of marble. But in the 1930s and 1940s, little was known about the nature of matter (what Einstein called "ugly wood" in his field equation). In the 1970s, however, the standard model finally solved the mystery of wood. ∶ matter consists of quarks and leptons that follow the Yang-Mills field of SU (3) × SU (2) xU (1) symmetry. The question is how to derive these particles and mysterious symmetries from geometry (what Einstein called beautiful marble).

This seems impossible. After all, these symmetries are the result of the exchange of point particles. If N quarks in a multiplet disturb each other and recombine, then the symmetry is SU (N). These symmetries seem to be unique to wood rather than marble. What does SU (N) have to do with children's learning?

Turn wood into marble

The first small clue emerged in the 1960s. Physicists have found another way to introduce symmetry into physics. When physicists extended the old (five-dimensional) Kalucha-Klein theory to N-dimension, they realized that there was freedom to impose some kind of symmetry on hyperspace. When the fifth dimension was curled up, they saw Maxwell field jump out of the Riemann metric. But when the N-dimension was curled up, physicists found that the famous Young-Mills field (the key to the standard model) jumped out of their equations.

To understand how symmetry emerges from space, consider an ordinary floating balloon. It has a symmetry ∶ that we can rotate around its own center, and the floating balloon still retains its original shape. The symmetry of a floating balloon, or the symmetry of a sphere, is called O (3) symmetry. Similarly, in a higher dimension, you can make a hypersphere rotate around its center and keep its shape unchanged. The symmetry of this hypersphere is called O (N).

If we vibrate the floating balloon in a certain way, then we can induce a regular vibration on the sphere, which is called resonance. These resonances can only vibrate at certain frequencies. If the floating balloon vibrates fast enough, it can produce a tone of a certain frequency. These vibrations can be classified by O (3) symmetry.

Like floating balloons, membranes can induce resonance frequencies. For example, the vocal cords of our throat are stretched membranes that vibrate, or resonate, at a certain frequency, thus producing tones. For the super ball, the effect is the same. Like a membrane, it can resonate at various frequencies, and these vibrations can be determined by its O (N) symmetry. On the other hand, mathematicians have long envisioned the use of complex numbers to describe more subtle and complex surfaces in high dimensions, corresponding to the symmetry of the complex "hyperspheres" is SU (N).

The key now is ∶. If the wave function of a particle vibrates along this surface, it will inherit this SU (N) symmetry. In this way, this mysterious symmetry SU (N) in subatomic physics can now be regarded as a by-product of hyperspace vibration. In other words, there is an explanation for the origin of the symmetry of matter ∶ they do come from geometric symmetry.

Now, if we take a Karucha-Klein theory defined in 4 N dimensions, and then curl up N dimensions, we find that the equation is divided into two pieces. The first piece is the usual Einstein equation, which is what we hope to find. But the second piece is not Maxwell theory. We find that the rest happens to be the Young-Mills field, which is the basis of all subatomic physics. This is the key to transforming wood symmetry into marble symmetry.

At first, it seemed inconceivable that the symmetry of matter automatically emerged from the higher dimensions. The symmetry of matter is discovered by examining the waste generated from the Atomic Collider. It is hard to imagine that the symmetry discovered by disrupting quarks and leptons should originate in hyperspace. There is an analogy that may help us understand this. Matter may be compared to shapeless and rugged clay, which lacks the beautiful symmetry inherent in geometric patterns. However, clay can be pressed into a mold, and the mold can be symmetrical. In this way, the clay inherits the symmetry of the mold. Clay (like matter) inherits its symmetry because molds (such as space-time) are symmetrical.

If this is correct, it means that the strange symmetry we see between quarks and leptons can now be seen as a by-product of vibration in hyperspace. For example, if those invisible dimensions have SU (5) symmetry, then we can write the SU (5) grand unified theory as some kind of Kalucha-Klein theory.

This can also be seen in the Riemannian metric tensor. We recall that the Riemannian metric tensor is very similar to the Faraday field except that it has more components. By separating the fifth column and the fifth row of the checkered chessboard, we can separate the Maxwell field from the Einstein field. Now, the same practice as the Kalucha-Klein theory is implemented in the (44th N) dimensional space. If these N rows and N columns are separated from the previous four rows and columns, a metric tensor describing both Einstein's theory and Young-Mills theory will be obtained.

As shown in the figure, we have depicted a metric tensor of the (4N) Vicarucha-Klein theory, in which the Einstein field is separated from the Young-Mills field.

DeWitt, a physicist who studies quantum gravity, was one of the first physicists to do so. Once the knack of decomposing the metric tensor is found, the calculation of the Yang-Mills field is very simple. DeWitt found it so mathematically easy to separate the Young-Mills field from the N-dimensional theory of gravity that he assigned it as a homework at a summer physics seminar in France in 1963.

Figure 6.2 if we come to the Nth dimension, then the metric tensor will be a series of N numbers that can be arranged into a Nx N square. By cutting off the fifth and fifth rows and the subsequent columns, we can remove the Maxwell electromagnetic field and the Young-Mills field. In this way, hyperspace theory allows us to unify Einstein field (describing gravity), Maxwell field (describing electromagnetic force) and Young Mills field (describing weak force and strong force). These basic forces are put together like a jigsaw puzzle.

The extraction of Young-Mills field from Kalucha-Klein theory is only the first step. Although the symmetry of matter can now be seen as derived from hidden symmetry in the invisible dimension, the next step is to create matter itself entirely by geometry (made up of quarks and leptons).

Supergravity still faces some thorny problems in converting matter into geometry. Because, according to the standard model, all particles are spinning. For example, we now know that matter is made up of quarks and leptons. Both quarks and light ones have two quantum spin units (measured in the Planck constant h). Particles with semi-integer spins (1pm, 2m, 3pm, 2m, 5p, etc.) are called fermions. However, the force is described by a quantum with integer spin. The example photon has 1 spin unit. The same is true of Yang-Mills Field. The hypothetical graviton has two spin units. They are called bosons.

Traditionally, quantum theory keeps fermions and bosons strictly separated. Any effort to transform matter into geometry will inevitably face the fact that ∶ bosons and fermions are two worlds of different nature. For example, SU (N) can disrupt quarks and reorganize them, but fermions and bosons must not be allowed to mix with each other. So when a new symmetry called supersymmetry is discovered, it is shocking that it does mix bosons with fermions. The supersymmetric equation allows a boson to exchange with a fermion while still maintaining the original appearance of the equation. In other words, a supersymmetric multiplet contains an equal number of bosons and fermions. When bosons and fermions are disrupted and recombined in the same multiplet, the supersymmetric equation remains the same.

This gives us the possibility of putting all the particles in the universe into a multiplet. As Nobel laureate Sallam emphasized

Supersymmetry is the final solution in which all particles are completely unified.

Supersymmetry is based on a new type of digital system, and it is obvious that most of the correct multiplication and division operations are invalid for supersymmetry. For example, if an and b are two "supernumbers", then a × baked house b × a.

Of course, this is absolutely impossible for ordinary numbers. Because, if a × aximura × a, then a × axi0. If these numbers were ordinary numbers, then this would mean that the system of numbers crashed.

However, because it is supernumeric, the system of numbers will not crash. It is quite surprising to say that even a ≠ 0 can have axa=0. Although these supernumbers run counter to almost everything we have learned about numbers, it can be proved that they produce some kind of self-consistent and very extraordinary system. Obviously, we can build a new super algorithm system based on them.

Three physicists, Friedman, Ferrara and Fannie Uvenhey, established the theory of supergravity in 1976. The theory of supergravity is the first practical attempt to construct a world made up entirely of marble. In supersymmetry theory, all particles have supercouples, which are called superparticles. Friedman's theory of supergravity consists of only two kinds of graviton fields with ∶ spin 2 (it is a boson) and their gametes with spin 3go 2, which is called gravitational neutrinos. Because these particles are not enough to include the standard model, people are trying to match this theory with more complex particles.

The easiest way to include matter is to establish the theory of supergravity in 11-dimensional space. In order to establish the super-Karucha-Klein theory in 11 dimensions, one must greatly increase the weight in the Riemann tensor, which now becomes the super-Riemann tensor. To understand how supergravity turns wood into marble, let's write out the metric tensor and show how supergravity manages to fit the Einstein field, the Young-Mills field and the matter field into a hypergravitational field. The basic feature of this diagram is that matter, as well as Young-Mills equation and Einstein equation, are now contained in the same 11-dimensional supergravitational field.

Supergravity almost fulfilled Einstein's dream of using pure geometry to derive all the forces and particles in the universe. To understand this, note that if we add supersymmetry to the Riemannian metric tensor, then the size of the metric doubles, thus giving the super-Riemannian metric. The new components of the super-Riemann tensor correspond to quarks and leptons. By decomposing the hyper-Riemannian tensor into its components, we find that it contains almost all the elementary particles and forces in nature, ∶ Einstein's gravitational theory, Yang-Mills field and Maxwell field, as well as quarks and leptons. But the fact that some particles are still missing in this picture forces us to move towards a more powerful expression of ∶ superstring theory.

Supersymmetry is the symmetry that transforms matter into geometry in a supergravitational field and vice versa. Therefore, they are various manifestations of the same force, which is called super force. Matter no longer exists as a single isolated entity. It is now merged with geometry to form hypergeometry.

In supergravity, we have achieved some unity of almost all known forces (marble) and matter (wood). Like jigsaw puzzles, they are pieced together within the Riemannian gauge tensor. This almost fulfilled Einstein's dream.

On April 29, 1980, cosmologist Stephen Hawking accepted the position of Professor Lucason (also held by Newton and Dirac) and gave a lecture with the questionable title ∶ "is the end of theoretical Physics not far from us?"

We have made a lot of progress in recent years, and as I will describe, there are some reasons for cautious optimism that some of us here now, it is possible to see some kind of complete theory in their lifetime.

The simple metric tensor introduced by Riemann in the 19th century has only 10 components. The Riemannian metric tensor has now been replaced by the supergravitational transmetric tensor, which has hundreds of components, which greatly increases the mathematical complexity of the equation. With the emergence of supergravity and hyperscale tensor, the mathematical threshold of physics has been greatly increased.

The decline of supergravity however, after trying to search, no superparticles were seen in any experiments. For example, an electron with a spin of 1 stroke 2 does not have any gametes with a spin of 0. However, physicists firmly believe that in the great energy created by the universe, all particles are accompanied by their supercouples. Only in this incredible energy can we see a completely supersymmetric world.

However, after dozens of international seminars, the situation became clear. This theory cannot be quantized correctly, thus temporarily putting an end to the dream of a theory made up of pure marble. Like every attempt to construct a theory of matter entirely out of marble, supergravity fails for a very simple reason ∶ whenever we try to calculate some numbers from these theories, we always get some meaningless infinity.

However, just as people's interest in supergravity began to decline, another new theory emerged, which may be the strangest and most powerful physics theory ever proposed, the ∶ ten-dimensional superstring theory.

This article comes from the official account of Wechat: Lao Hu Shuo Science (ID:LaohuSci). Author: I am Lao Hu.

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