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 decided to change the scale of research, both in one direction and in the other.

Consider two fundamental physical theories. The first of these is the general theory of relativity, well known to all. 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. Combine these two theories and get an almost complete picture of the universe: from internuclear interactions to the behavior of galaxies.
However, there is one catch in obtaining a unified 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 with both the theory of relativity and quantum mechanics, and at the same time combine them. Creating a unified theory of everything is 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 began, as usual, with mathematics. In the 18th century, the famous mathematician Leonard Euler studied the properties of functions, which he himself invented. One of these functions is called the Euler beta function. It looks like this:



It is not so difficult for people familiar with integral calculus. Euler described the properties of the function, and, having not found practical application, for two centuries the beta function was forgotten.
In 1968, a young physicist Gabriel Veneziano, working 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 perfectly to describe particle interactions, but no one understood why. If we take the famous Einstein's formula, then its physical meaning can be expressed by the phrase "energy is proportional to mass." Euler’s formula didn’t have a physical meaning - it’s just variables, when assigned to certain values, a result is obtained that is consistent with the experiment. Two years later, such a meaning was found - physicists have found that if elementary particles are replaced by oscillating one-dimensional strings, then the interaction of such strings is represented in the form of the Euler formula. One-dimensionality means



Since the strings are small enough, they look like elementary particles, therefore, do not contradict the experiments already conducted. String theory has now changed dramatically from its original form, but the basic idea has remained the same.

Strings as a mechanism of the Universe

This picture pretty well depicts the ideas of a typical layman 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 of gravity, which has been sought since Newton's. 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 in the form of musical instruments familiar to us as strings. Take the guitar, for example. The oscillation of each string has two important properties:
1. The amplitude responsible for the sound volume.
2. The frequency that determines the pitch.
Sounds whose frequencies differ by less than 1 Hz are almost indistinguishable to the human ear. The higher the frequency of sound, the less perceptible is the change in this frequency. Therefore, in music, the frequency difference of adjacent notes varies from 1 Hz for low sounds to several hundred hertz for high sounds. In general, for the performance of musical works, we get only a certain limited set of frequencies corresponding to the accepted notes. We can play mi with a frequency of 330 Hz or fa with a frequency of 349 Hz, but the frequencies between them are inaccessible to us in music. This particular type of vibration is called a mode , and the totality of all possible modes is called a vibration spectrum .
The oscillation energy depends on the volume of the sound and the mode of its oscillation. Intuitively, you can understand that a loud and high sound has more energy than a quiet and low one. Now let’s give our guitar to Einstein’s hands, who will notice that energy is generally proportional to mass. In string theory, this relation is used precisely: 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 relationships between the string mode and particle characteristics, such as charge, particle response to gravitational action, etc. Moreover, the same principle holds true not only for the properties of particles, but also for the particles themselves. Photons, gluons, u-mesons, and other exotic particles are just different vibration modes of identical strings.
This leads to the following conclusion: knowing all possible vibration modes of a string, “notes” that can be played on it, we could explain all the properties of all elementary particles. A 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 from bottom to top, or pull the string away from you and let go. If the string were fixed between two points in a free 3-dimensional space, the number of possible directions of vibrations would increase. Having at our disposal a greater number of measurements than three, we would also increase the number of possible directions of oscillations. However, we are severely limited to three dimensions.
But not in string theory. Upon further investigation, a new catch arose: some calculations led to impossible results, for example, negative probability. Physicists struggled for a long time over this problem and found a solution with which all calculations were consistent: the Universe should have ten dimensions - nine spatial and one temporal.
If you can somehow come to terms with the temporal dimension, then where do six more dimensions come from that we cannot even imagine? These six dimensions are convoluted - they are so small that on the usual scale we can not take them into account. The car, having made a circle, will return to the same coordinates in three-dimensional space. Over this circle he crosses six rolled dimensions countless times. However, for very small strings, the coordinates in convoluted measurements begin to take on serious significance.

What's next?

The development of string theory can no longer be stopped. The ten-dimensional theory is called superstring theory. When the measurements again began to disagree with the expected ones, a new, eleventh dimension was introduced. This is how the M-theory appeared: the mention of strings disappeared from the name, since analogues 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 an impasse, and it has every chance of someday becoming a unified theory of everything.

What to read?

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