Part 1
The only problem is to accept this theory as physical, it is too mathematical. Why?
Because it owes its appearance to one simple function - Euler's beta function is actually not as complex as it seems at first glance. This function is studied in the course of mathematical analysis.
So why exactly this function was the beginning of such a large and confusing theory?
Euler's beta function (Graph of the beta function with real arguments).
In 1968, a young Italian theoretical physicist Gabriele Veneziano tried to describe how particles of an atomic nucleus interact: protons and neutrons. The scientist had a brilliant guess. He realized that all the numerous properties of particles in an atom can be described by one mathematical formula (Euler's beta function). It was invented two hundred years ago by the Swiss mathematician Leonard Euler and described integrals in mathematical analysis.
Veneziano used it in his calculations, but did not understand why she was working in this area of physics. The physical meaning of the formula was discovered in 1970 by American scientists Yoichiro Nambu, Leonard Susskind, as well as their Danish colleague Holger Nielsen. They suggested that elementary particles are small vibrating one-dimensional strings, microscopic strands of energy. If these strings are so tiny, the researchers reasoned, they will still look like point particles and, therefore, will not affect the results of the experiments. This is how string theory came about.
For a long time, philosophers have argued about whether the universe has a certain origin or whether it has always existed. General relativity implies the finiteness of the "life" of the Universe - the expanding Universe should have arisen as a result of the Big Bang.
Promotional video:
However, at the very beginning of the Big Bang, the theory of relativity did not work, since all processes taking place at that moment were of a quantum nature. In string theory, which claims to be the quantum theory of gravity, a new fundamental physical constant is introduced - the minimum quantum of length (i.e., the shortest length in essence). As a result, the old scenario of the Universe born in the Big Bang becomes untenable.
Space at the quantum level.
Strings are the smallest objects in the universe. The size of the strings is comparable to the Planck length (10 ^ –33 cm). According to string theory, this is the minimum length that an object in the universe can have.
The Big Bang still took place, but the density of matter at that moment was not infinite, and the universe may have existed before it. The symmetry of string theory suggests that time has no beginning or end. The universe could have arisen almost empty and formed by the time of the Big Bang, or go through several cycles of death and rebirth. In any case, the era before the Big Bang had a huge impact on modern space.
In our expanding universe, galaxies scatter like a scattering crowd. They move away from each other at a speed proportional to the distance between them: galaxies separated by 500 million light years, scatter twice as fast as galaxies, separated by 250 million light years. Thus, all the galaxies we observe should have started simultaneously from the same place at the time of the Big Bang. This is true even if the cosmic expansion goes through periods of acceleration and deceleration. In space and time diagrams, galaxies travel along winding paths to and from the observable portion of space (yellow wedge). However, it is not yet known exactly what happened at the moment when galaxies (or their predecessors) began to fly apart.
History of the Universe.
In the standard Big Bang model (pictured left), based on general relativity, the distance between any two galaxies at some point in our past was zero. Until then, time is meaningless.
And in models that take into account quantum effects (in the figure on the right), at the moment of launch, any two galaxies were separated by a certain minimum distance. Such scenarios do not exclude the possibility of the existence of the Universe before the Big Bang.
Part 2
And now I'll try to tell you why there are so many of these theories: string theory, superstrings, M-theory.
More details about each of the theories:
String theory:
As you and I already know, string theory is a purely mathematical theory, which says that everything in our world (and not in ours either) is a consequence of the "vibrations" of microscopic objects of the order of the Planck length.
Perhaps all matter is made of strings.
The properties of the string resemble a violin string. Each string can make a huge (actually infinite) number of different vibrations, known as resonant vibrations. These are vibrations in which the distance between the maxima and minima is the same, and exactly an integer number of maxima and minima fit between the fixed ends of the string. For example, the human ear perceives resonant vibrations as different musical notes. Strings have similar properties in string theory. They can carry out resonant oscillations, in which exactly an integer number of uniformly distributed maxima and minima fit along the length of the strings. In the same way that different modes (a set of types of harmonic vibrations typical for an oscillatory system) of resonant vibrations of violin strings give rise to different musical notes,different vibration modes of the fundamental strings give rise to different masses and coupling constants.
According to the special theory of relativity, energy and mass (E is equal to em tse square:) are two sides of the same coin: the more energy, the more mass and vice versa. And according to string theory, the mass of an elementary particle is determined by the vibration energy of the inner string of this particle. The inner strings of heavier particles vibrate more intensely, while the strings of light particles vibrate less intensely.
Most importantly, the characteristics of one of the string modes are exactly the same as those of the graviton, ensuring that gravity is an integral part of string theory.
I do not want to go into details about the "geometry" of strings for now, I will just say that massless particles, which can be photons, come from vibrations or open or closed strings. Gravitons come only from the vibrations of closed strings, or loops. The strings interact with each other to form loops. Larger particles (quarks, electrons) arise from these loops. The mass of these particles depends on the energy released by the loop when it vibrates.
In string theory, there can be only two fundamental constants (in other theories there are many more constants, even the most fundamental ones. For example, the Standard Model requires 26 constants). One, called string tension, describes how much energy is contained per unit length of the string. The other, called the string coupling constant, is a number indicating the probability of a string breaking into two strings, respectively causing forces; since it is a probability, it is just a number, no dimensional units.
Superstring theory:
All there is to know and understand from this phrase is that this theory is a generalized string theory. In this theory, everything is considered from the point of view of supersymmetry - … BUT!
Before moving on to discussing supersymmetry, let's remember the concept of spin. Spin is the intrinsic angular momentum inherent in each particle. It is measured in units of Planck's constant and can be whole or half-whole. Spin is an exclusively quantum mechanical property, it cannot be represented from the classical point of view. A naive attempt to interpret elementary particles as small "balls", and spin - as their rotation, contradicts the special theory of relativity, since points on the surface of the balls must then move faster than light. Electrons have spin 1/2, photons have spin 1.
Supersymmetry is the symmetry between particles with integer and half-integer spin.
In short, it consists in constructing theories whose equations would not change when fields with integer spin are transformed into fields with half-integer spin and vice versa. Since then, thousands of articles have been written, all models of quantum field theory have been subjected to supersymmetrization, and a new mathematical apparatus has been developed that allows building supersymmetric theories.
Particles known in nature, according to their spin, are subdivided into bosons (whole spin) and fermions (half-integer spin). The first particles are carriers of interactions, for example, a photon, which carries electromagnetic interactions, a gluon, which carries strong nuclear forces, and a graviton, which carries gravitational forces. The second is made up of the matter of which we are made, such as an electron or a quark.
Fermions (particles that obey Fermi-Dirac statistics) and bosons (particles that obey Bose-Einstein statistics) can coexist in the same physical system. Such a system will have a special kind of symmetry - the so-called supersymmetry, which maps bosons to fermions and vice versa. This, of course, requires an equal number of bosons and fermions, but the conditions for the existence of supersymmetry are not limited to this. Supersymmetric systems live in superspace. Superspace is obtained from ordinary spacetime when fermionic coordinates are added to it. In a superspace formulation, supersymmetry transformations look like rotations and translations in ordinary space. And the particles and fields living in it are represented by a set of particles or fields in ordinary space, and such a set,in which the quantitative ratio of bosons and fermions is strictly fixed, as well as some of their characteristics (primarily spins). Particles-fields included in such a set are called superpartners.
So conventional string theory only described particles that were bosons, so it was called bosonic string theory. But she didn't describe fermions. Therefore, quarks and electrons, for example, were not included in bosonic string theory.
But by adding supersymmetry to bosonic string theory, we got a new theory that describes both the forces and the matter that makes up the universe. It is called superstring theory.
There are three different superstring theories that make sense, i.e. without mathematical inconsistencies. In two of these, the fundamental object is the closed string, while in the third, the open string is the building block. Moreover, by mixing the best aspects of bosonic string theory and superstring theory, we have got consistent string theories - heterotic string theories.
Thus, a superstring is a supersymmetric string, that is, it is still a string, but it does not live in our usual space, but in superspace.
M-THEORY:
In the mid-1980s, theorists came to the conclusion that supersymmetry, which is the centerpiece of string theory, could be incorporated into it in not one but five different ways, leading to five different theories: type I, types IIA and IIB, and two heterotic string theories. For reasons of common sense (two versions of the same physical law cannot operate simultaneously), it was believed that only one of them could claim the role of a "theory of everything", moreover, the one that at low energies and compactified (i.e. sizes of Planck lengths.
It turns out that we just observe our 4-dimensional Universe without these 6 dimensions, which we simply do not see) six additional dimensions would be consistent with real observations. Questions remained about which theory was more adequate and what to do with the other four theories.
The essence:
If, in this case, the size of the compact dimension turns out to be of the order of the size of strings (10 to -33 degrees of a centimeter), then due to the smallness of this dimension we simply cannot see it directly. Ultimately, we will get our (3 + 1) -dimensional space, in which a tiny 6-dimensional space corresponds to each point of our 4-dimensional Universe.
Research has shown that this naive view is wrong. In the mid-1990s, Edward Witten and other theoretical physicists found strong evidence that all five superstring theories are closely related to each other, being different limiting cases of a single 11-dimensional fundamental theory. This theory is called M-Theory.
When Witten gave the name M-theory, he did not specify what M stood for, presumably because he did not feel the right to name a theory that he could not fully describe. Assumptions about what M might stand for has become a game among theoretical physicists. Some say that M means "Mystical", "Magical" or "Mother". More serious assumptions are "Matrix" and "Membrane". Someone noticed that M can be an inverted W - the first letter of the name Witten (Witten). Others suggest that M in M-theory should mean Missing or even Murky.
The development of 11-dimensional M-theory allowed physicists to look beyond the time before which the Big Bang occurred.
Branes in 10-11 dimensional space collide and create a Big Bang on the * surface * of the branes …
A theory was created according to which our universe is a consequence of the collision of objects in another universe, which, in turn, can be countless. Thus, the disclosure of one question led to the emergence of even more questions.
M-Theory was taken by scientists as the theory of everything. That is, this theory is suitable for explaining everything: how the Universe was born, what was before the birth of our Universe, answers the question of the existence of time before the birth of the Universe (time existed even before the birth of the Universe), reveals the future of the Universe.
Part 3
String holes:
The now generally accepted theory of black holes, put forward forty years ago by physicist John Wheeler, says that after a star "burns out", its remains are compressed with such force that the force of gravity exceeds the force of repulsion, and as a result, a singularity remains: a point in space where matter is in a state of "infinite density". The singularity is surrounded by the so-called "event horizon", a hypothetical border that is not able to overcome the matter and energy inside it. They are "drawn" into the black hole and remain inside forever.
Representation of a black hole.
It is this "forever" that raises questions.
In 1975, the largest black hole theorist Stephen Hawking of the University of Cambridge established (albeit only theoretically) that black holes slowly but inevitably evaporate. In accordance with the laws of quantum mechanics, pairs of "virtual" particles and antiparticles are constantly boiling in empty space. Hawking showed that the gravitational energy of black holes can be transferred to "virtual" particles at the very event horizon. In this case, the "virtual" particles become real and go beyond the horizon along with positive energy in the form of Hawking radiation. Thus, over time, the black hole evaporates.
Hawking radiation temperature (radiation near the black hole event horizon with a thermal spectrum):
Black hole radiation temperature
where is Planck's constant, c is the speed of light in vacuum, k is Boltzmann's constant, G is the gravitational constant, and, finally, M is the mass of the black hole. For example, it is easy to calculate that a black hole with a mass of 2 * 10 ^ 30 kg (the mass of the Sun) will have a radiation temperature equal to 6.135 * 10 ^ (- 8) Kelvin. This is a very low temperature, even when compared to the background radiation of the Universe with a temperature of 2.7 Kelvin.
But the temperatures of the black holes known to astronomers are too low to detect radiation from them - the masses of the holes are too large. Therefore, the effect has not yet been confirmed by observations.
However, this view leads to an "information paradox". It turns out that according to the theory of relativity, information about matter falling into a black hole is lost, while quantum mechanics claims that information can eventually escape outward.
Hawking noted that the chaotic nature of Hawking's radiation means that energy is bursting out, but information is not. However, in 2004, he changed his mind - and this is just one of the points of modern science revising all of its views on black holes.
The fact is that now theorists are trying to "try" on black holes (and all theoretical discrepancies associated with them) string theory. String theory is now the best attempt to combine general relativity and quantum mechanics, since the strings themselves carry a gravitational force, and their vibration is random, as predicted by quantum mechanics.
In 1996, Andrew Strominger and Kamran Wafa of Harvard University decided to approach the information paradox problem by defining how a black hole might be built from the inside.
It turned out that string theory allows the construction of extremely dense and small-scale structures from the strings themselves and other objects described by the theory, some of which have more than three dimensions. And these structures behaved just like black holes: their gravitational pull does not release light out.
The number of ways to organize strings inside black holes is overwhelming. And, what is especially interesting, this value completely coincides with the value of the black hole entropy, which Hawking and his colleague Bekenstein calculated back in the seventies.
However, determining the number of possible string combinations is not all. In 2004, Ohio State University's team Samir Matura set out to clarify the possible arrangement of strings inside a black hole. It turned out that almost always the strings are connected so that they form a single - large and very flexible - string, but much larger than the point singularity.
The Matura group has calculated the physical dimensions of several "string" black holes (which the group members prefer to call fuzzballs - "fluff balls", or stringy stars - "string stars"). They were surprised to find that the size of these string formations coincided with the size of the "event horizon" in the traditional theory.
In this regard, Mathur suggested that the so-called. The “event horizon” is actually a “foaming mass of strings,” not a rigidly delineated boundary.
And that a black hole does not actually destroy information for the reason, for example, that there is simply no singularity in black holes. The mass of the strings is distributed over the entire volume up to the event horizon, and information can be stored in strings and imprinted on the outgoing Hawking radiation (and therefore go beyond the threshold of events).
However, both Wafa and Mathur admit that this picture is very preliminary. Matura has yet to test how his model fits into large black holes, or understand how black holes evolve.
Another option was suggested by Gary Horowitz of the University of California at Santa Barbara and Juan Maldasena of the Princeton Institute for Advanced Study. According to these researchers, the singularity in the center of the black hole still exists, but information simply does not get into it: matter goes into the singularity, and information - through quantum teleportation - is imprinted on Hawking radiation. Many physicists dispute this point of view, rejecting the possibility of an instantaneous transfer of information.
Extreme black holes:
Diversity (Euclidean space is the simplest example of diversity. A more complex example is the surface of the Earth. It is possible to make a map of any area of the earth's surface, for example, a map of the hemisphere, but it is impossible to draw a single (without breaks) map of its entire surface) along which a string can move is called a D-brane or Dp-brane (when using the second notation, 'p' is an integer characterizing the number of spatial dimensions of the manifold). An example is two strings that have one or both ends attached to a 2-dimensional D-brane or D2-brane:
D-branes can have a number of spatial dimensions from -1 to the number of spatial dimensions of our spacetime. The word 'brane' itself comes from the word 'membrane', which is a two-dimensional surface.
Why I wrote about it here, but here:
Branes have made it possible to describe some special black holes in string theory. (This discovery was made by Andrew Strominger and Kumrun Wafa in 1996, above.)
The relationship between branes and black holes is indirect but compelling. Here's how it works: You start by turning off the gravitational force (you do this by setting the string coupling constant (the number that represents the probability of a string breaking into two strings is one of the two fundamental constants in string theory. The first is the "tension" of the string) at zero). It may seem strange to describe black holes, which are nothing more than gravity, however, let's see what happens next. With gravity turned off, we can look at geometries in which many branes are wrapped around extra dimensions. We now use the fact that branes carry electrical and magnetic charges. It turns out that there is a limit to how much charge a brane can have, this limit is related to the mass of the brane. Maximum charge configurations are very specific and are called extreme. They include one of the situations where there are additional symmetries that allow more accurate calculations. In particular, such situations are characterized by the presence of several different supersymmetries that link fermions and bosons.
There is also the maximum amount of electrical or magnetic charge a black hole can have and still be stable. They are called extreme black holes and have been studied by specialists in general relativity for many years.
Despite the fact that gravitational force has been turned off, the extreme brane system shares some properties with extreme black holes. In particular, the thermodynamic properties of the two systems are identical. Thus, through studying the thermodynamics of extreme branes wrapped around extra dimensions, one can reproduce the thermodynamic properties of extreme black holes.
One of the problems in the physics of black holes was the explanation of the discovery by Jacob Bekenstein and Stephen Hawking that black holes have entropy and temperature. The new idea from string theory is (in the case of extreme black holes) that you can make headway in exploring similar systems of extreme branes wrapped around extra dimensions. In fact, many of the properties of the two systems are exactly the same. This almost supernatural coincidence arises because in both cases there are several different supersymmetric transformations linking fermions and bosons. It turns out that they allow us to construct a compelling mathematical analogy that makes the thermodynamics * of two systems to be identical.
***
* Thermodynamics of a black hole (properties):
- The force of gravity is the same over the entire surface of the event horizon
- The area of the event horizon of a black hole cannot decrease with time in any classical process.
- In any non-equilibrium processes involving black holes (for example, when they collide), the surface area increases.