String theory for guitarists

The goal of physics as a classical science is to study the laws of our world. Most of these patterns have already been studied enough to apply them in everyday life. And modern physicists have decided to change the scale of research, both in one and in the other direction.

Consider two fundamental physical theories. The first one is the well-known general theory of relativity. The theory of relativity answers the questions of the origin and development of the Universe and well explains the large-scale behavior of the cosmos. The second - quantum mechanics - on the contrary, has achieved great success in explaining the physics of the microworld. Let us combine these two theories and obtain an almost complete picture of the Universe: from inter-core interactions to the behavior of galaxies.
However, there is one catch in obtaining a single picture of the world: these large-scale theories, confirmed by many calculations and experiments, are completely incompatible with each other. Each theory has its own foundations, its own mathematical and physical principles. The application of quantum mechanics to galactic interactions, as well as the use of the theory of relativity to study nuclear interactions, leads to absurd results. There is only one way out: to come up with a new theory that would be consistent both with the theory of relativity and with quantum mechanics, and at the same time united them. Creating a unified theory of everything - the main task of physicists since the time of Einstein. One of the candidates for the title of a unified theory is string theory.

A bit of history

It all started, as usual, with mathematics. In the 18th century, the famous mathematician Leonhard Euler studied the properties of functions that he himself invented. One of these functions is called the Euler beta function. It looks like this:
')


Not so difficult for people familiar with integral calculus. Euler described the properties of the function, and, having not found practical application, the beta function was forgotten for two centuries.
In 1968, the young physicist Gabriel Veneziano, who works at the Swiss CERN, accidentally discovered that all the properties of particles involved in nuclear interaction can be described using the Euler beta function. The formula worked fine for describing particle interactions, but no one understood why. If we take Einstein's famous formula, then its physical meaning can be expressed by the phrase “energy is proportional to mass”. Euler's formula did not have a physical meaning - just variables, by assigning certain values ​​to which a result was obtained that was consistent with the experiment. Two years later, such a meaning was found - physicists discovered that if we replace elementary particles with oscillating one-dimensional strings, the interaction of such strings is just represented in the form of the Euler formula. One-dimensionality means that the thickness of such a string is infinitely small compared to the length.



Since the strings are rather small, they look like elementary particles, therefore, they do not contradict the experiments already performed. Now string theory has changed a lot compared to the original look, but the basic idea remains the same.

Strings as a mechanism of the Universe

This picture quite well depicts the typical man in the street about string theory. In reality, everything is exactly the opposite: everything follows from string theory, it is in excellent agreement with both quantum mechanics and the theory of relativity. In addition to this, the theory also finds an explanation for gravity, which has been sought since the times of Newton. Such versatility outweighs some absurdity of the idea that all matter consists of the smallest strings.
To explain the basic idea of ​​string theory, one-dimensional strings can be represented as strings of musical instruments that are familiar to us. Take, for example, a guitar. The oscillation of each string has two important properties:
1. The amplitude responsible for the volume of the sound.
2. The frequency that determines the pitch.
Sounds whose frequencies differ by less than 1 Hz are practically indistinguishable to the human ear. The greater the frequency of the sound, the less perceptible changes in this frequency. Therefore, in music, the frequency difference of neighboring notes varies from 1 Hz for low sounds to several hundred hertz for high sounds. In general, for the performance of musical works, we receive only a certain limited set of frequencies corresponding to the adopted notes. We can play with a frequency of 330 Hz or a fa with a frequency of 349 Hz, but the frequencies between them in the music are not available to us. Such a specific type of oscillation is called a mode , and the totality of all possible modes is called a spectrum of oscillations.
The oscillation energy depends on the volume of the sound and its oscillation mode. Intuitively, one can understand that loud and high sound has more energy than low and low. And now let's put our guitar in the hands of Einstein, who will notice that, generally speaking, energy is proportional to mass. In string theory, this ratio is used: the mass of an elementary particle is determined by the vibrational energy of its string.
Using more abstract reasoning, physicists have established that there are other connections between the mode of the string and the characteristics of the particle, such as the charge, the response of the particle to the gravitational effect, etc. Moreover, the same principle is valid not only for the properties of particles, but also for the particles themselves. Photons, gluons, u-mesons and other exotic particles are just different modes of vibration of the same strings.
This leads to the following conclusion: knowing all the possible modes of string vibration, the “notes” that can be played on it, we could explain all the properties of all elementary particles. Serious application for a unified field theory, is not it?

Nine-dimensional guitar

Consider our guitar from the guitarist. The design of the guitar allows the strings to oscillate only in certain specific directions. You can hit the strings from top to bottom or bottom to top, or pull the string away from you and release. If the string were fixed between two points in a free 3-dimensional space, the number of possible directions of vibrations would increase. If we have more measurements at our disposal than three, we would also increase the number of possible directions of oscillations. However, we are strictly limited to three dimensions.
But not in string theory. Upon further investigation, a new snag emerged: some calculations led to impossible results, for example, negative probability. Physicists have long struggled with this problem and found a solution with which all calculations were consistent: the Universe must have ten dimensions — nine spatial and one temporal.
If one can somehow reconcile with the time dimension, then where do six more dimensions come from, which we cannot even imagine? These six dimensions are collapsed - they are so small that at the usual scale we can not take them into account. The car, making a circle, will return to the same coordinates in three-dimensional space. Over this circle, he will cross six rolled measurements countless times. However, for very small strings, the coordinates in the convoluted dimensions begin to take on a serious meaning.

What's next?

The development of string theory is unstoppable. The ten-dimensional theory is called superstring theory. When the measurements again began to disagree with the expected, a new, eleventh dimension was introduced. So M-theory appeared: the mention of strings disappeared from the name, since analogs of two-dimensional strings appeared - membranes, three-dimensional, four-dimensional strings. The complexity of the theory increases every year, but so far its development has not reached a dead end, and it has every chance of ever becoming the unified theory of everything.

What to read?

1. Stephen Hawking, “A Brief History of Time”, “The World in a Nutshell”, “The Theory of Everything” - tells about the modern picture of the world in a popular language.
2. Brian Green, “The Elegant Universe. Superstrings, hidden dimensions and the search for the ultimate theory ” is an excellent book on string theory without too much physics.
3. Michio Kaku, “Introduction to the theory of superstrings” is a serious textbook for those who know physics and want to know even more.