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The evolution of string theory to M-theory

Good day, dear habrasociety. After my long absence, I decided to once again take up the pen keyboard. Today we will try to trace the evolution of string theory to the M-theory, and find answers to the questions: what prompted scientists to develop this theory, what problems they had to face, and what the best minds of mankind are breaking their heads now.

String theory


On Habré there was already an article on string theory. If in brief in 1968, scientists noticed that a mathematical function called the Euler beta function ideally describes the properties of particles that participate in the so-called strong interaction - one of the four fundamental interactions in the Universe.

During further checks, this fact was confirmed, it was interesting that earlier this function was mainly used in the description of vibrations of tensioned strings.

At the sight of all this, the researchers asked a reasonable question: “But what if elementary particles are not particles at all, but microscopic finest strings, and what we observe in practice is not the trajectory of the particle’s motion, but the trajectory of the vibration passing along this string? ". Moreover, the nature of the vibration also indicates which particle is in front of us: one type of vibration ( vibrational mode ) is one particle, another type is another.

The first studies showed that string theory has achieved significant success in describing the phenomena observed. One of the modes of string vibrations can be identified as a graviton. Other vibrational modes exhibit the properties of photons and gluons.

With good reason, it seemed that string theory was able to reduce all four fundamental interactions of the Universe to one - the vibration of a one-dimensional string with the corresponding energy transfer. Moreover, string theory also allows us to explain the basic constants of the microworld from a mathematical point of view. It became clear why, for example, the masses of elementary particles are exactly what they are.

In addition, string theory gave hope for the combination of general relativity (general theory of relativity) and quantum mechanics within the framework of one theory. In the calculations, it turned out that the natural vibrations of the strings are able to damp and balance quantum fluctuations and thereby eliminate perturbations at the microscopic level, due to which GR and quantum mechanics could not be made friends.

However, in deeper research and verification of the theory, serious contradictions of the consequences with experimental data were revealed. For example, in string theory, a particle was necessarily present - a tachyon (whose square of mass is less than zero, and moving at a speed greater than the speed of light) - as one of the vibrational modes of the string, which implied an unstable state of the string and clearly showed that string theory requires modification.

Superstring Theory


In 1971, a modified string theory was created called the “ Super String Theory ”.

To understand the modifications, let's try to deal with such a characteristic as spin. There is a common version of explaining the essence of the spin “on the fingers”: a spin is the number of revolutions around its axis that a particle needs to make in order to look the same as at the beginning. For spins within a unit, everything seems to be clear (any object of irregular shape can be assigned a “spin” equal to one), and to try to imagine the shape of an object that needs to be scrolled around the axis twice so that it looks the same as at the beginning, you can look at illustration to the right. It depicts a four-stroke engine, which returns to its original state when the crankshaft is rotated 720 °, which is a kind of analogue of a half-integer spin.

At the moment, it is believed that elementary particles can have only half-integer or integer spins. Bosons are those particles that have an integer spin. Fermions are particles in which the spin is half-integral. Based on this, the first version of string theory described only bosons, which is why it was also called the " bosonic string theory ". The theory of superstrings included fermions - with this approach, the problem of the presence of tachyons, as well as many other contradictions in the theory, were resolved!

But there were some new problems. In superstring theory, it turned out that for each boson there must be a corresponding fermion, that is, a certain symmetry must exist between bosons and fermions. This kind of symmetry was predicted before - under the name " supersymmetry". But experimentally, the existence of supersymmetric fermions has not been confirmed. This was explained by the fact that, according to calculations, supersymmetric fermions must have a huge mass for the microworld, and therefore, under ordinary conditions, they cannot be obtained. In order to register them, huge energies are needed, which are achieved when light particles collide at almost light speeds.

Even now they are trying to register supersymmetric fermions in experiments at the Large Hadron Collider, but so far without success.

Multidimensional Universe


At the same time, the equations of the theory of superstrings did not want to be consistent with quantum theory, giving as a result negative or greater units of probability.

In order to understand the prerequisites for the further development of the theory, we make a short excursion into history. Back in 1919, the German mathematician Kaluza sent Einstein a letter stating his theory in which he made the assumption that in reality the Universe can be four-dimensional in space, and in evidence of his words he cited his calculations, from which it turned out that under such a condition GTR is wonderful consistent with Maxwell's electromagnetic field theory, which is impossible to achieve in the ordinary three-dimensional Universe. Contemporaries ridiculed the theory, and soon Einstein, initially interested in the theory, became disillusioned with it.

In 1926, physicist Oscar Klein was also interested in the work of Kaluza and improved his model. According to Klein, it turned out that an additional dimension may indeed exist, but it is in a “curtailed” and fixated on itself form. Moreover, the fourth dimension is collapsed very tightly - to the size of elementary particles, so we don’t notice it. The theory was called the five-dimensional world of Kaluza - Klein (four dimensions in space + time), but it also remained in oblivion until the 80s of the 20th century.

Scientists in an attempt to explain the inconsistencies of string theory with quantum mechanics have suggested that the problems in the calculations were due to the fact that the strings in our theory can fluctuate in only three directions that our universe has. Now, if the strings could oscillate in four dimensions ...

Calculations have shown that in this case the problems remain, but the number of contradictions in the equations decreases. Researchers continued to increase the number of measurements until they introduced as many as 9 measurements in space, at which, finally, the theory of superstrings converged with quantum mechanics and GR. This moment went down in history as “the first revolution in string theory". Exactly from this moment, exclamations began to sound that we actually live in a ten-dimensional Universe - one dimension in time, three dimensions familiar to us are deployed to cosmic dimensions, and the remaining six are minimized on a microscopic scale and therefore invisible.

From a practical point of view, it is neither currently possible to confirm nor to refute experimentally, since we are talking about such small scales of strings and folded measurements that are not available for fixing with modern equipment.

With further development, scientists were able in theory to establish a general view of six collapsed dimensions, in which our world remained as it is. This view corresponds to mathematical objects from a group called " Calabi-Yau manifolds"(On the right.). But this did not bring any promising consequences, although the general form of these objects was calculated, but the exact form, as it turned out, cannot be established without experiment. And without finding the exact form of the Calabi-Yau space of our Universe, the whole theory of superstrings was essentially reduced to fortune-telling on coffee grounds.

However, the work continued, and gradually the scientists managed to isolate five more or less plausible theories from the total mass of hypotheses that could describe our Universe. These are 5 well-known superstring theories, and all of them equally claimed the title of the only true one and at the same time looked incompatible with each other, which caused great concern among scientists.

M theory


Only in the mid-nineties of the last century did the so-called “ second revolution in string theory ” take place. Edward Witten hypothesized that various superstring theories are different limiting cases of the yet undeveloped 11-dimensional M-theory.

The introduction of another dimension as a whole does not violate the connection between quantum theory and general relativity, and moreover, it removes very many accumulated problems in superstring theory. Including successfully crosses all five superstring theories into one single M-theory, which today is, without exaggeration, the highest achievement of physicists in the knowledge of the Universe.

According to M-theory, it turns out that the basis of the Universe is not only one-dimensional strings. There may exist two-dimensional analogs of strings - membranes, and three-dimensional, and four-dimensional ... These constructions were called branes (a string - 1-brane, a membrane - 2-brane, and so on). M-theory operates on two-dimensional and five-dimensional branes, but even the basic theory of branes is still under development. The existence of branes is not experimentally confirmed - at this stage in the development of the theory it is believed that branes are fundamentally unobservable.

For all this, the M-theory at low energies is approximated by supergravity in eleven dimensions. The connection with gravity makes the M-theory a contender for becoming a connecting theory between all the fundamental interactions in the Universe, or in other words - “The Unified Theory of Everything”.

However, the problem with the final form of the Calabi-Yau space in M-theory is still unresolved - on a macroscopic scale, the theory should be reduced to the well-known and very well-tested elementary particle physics. But, as it turns out, there are at least 10,100 , or even 10,500 , or even infinity methods of such reduction . Moreover, each of the resulting four-dimensional theories describes its own world, which may be similar to reality, or may fundamentally differ from it.

All this is due to the fact that the properties of particles are considered as a method of vibrating strings, and the possible methods of vibrating strings depend on the exact geometry of additional measurements. The existing approximate equations satisfy a huge number of different geometries. That is, these equations would be valid not only in our world, but also in a huge number of other worlds, and possibly in any world. If these approximate equations were final, the theory could be considered non-falsifiable according to Popper, that is, an unscientific theory. And so - finding the exact equations may still put it in its place.

At the moment, the development of M-theory is complicated by the fact that the equations describing it are so complex that scientists mostly operate only on their approximate forms, which does not lead to an increase in the accuracy of the results. Moreover, such a situation often arises that even the corresponding mathematical methods have not been created to solve these equations, which also creates significant problems. Recently, where physics comes to a standstill, in fact, it is often mathematics that come to a standstill. Some scientists say that M-theory will receive a noticeable development only if a “mathematical breakthrough” occurs.

String theory and, in particular, M-theory, today is one of the most dynamically developing areas of modern physics. And although some scientists, due to fundamental problems, are rather skeptical that this theory will ultimately lead to a physical theory that describes our real world. A significant part of the researchers does not give up their hopes and believes that one day the M-theory will take shape in an elegant and mathematically elegant Unified theory of everything.

I hope that this article did not leave you indifferent, and I will be very glad if you decide that you did not waste time reading.

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