One of the main tasks of theoretical physics today is to find an answer to the question of whether there are higher dimensions. Does space really only consist of length, width and height, or is it just a limitation of human perception? For millennia, scientists strongly rejected the idea of the existence of a multidimensional space. However, the scientific and technological revolution has changed a lot, and today science is no longer so categorical on the issue of higher dimensions.

## What is the essence of the concept of "multidimensional space"?

Man lives in a world that consists of three dimensions. The coordinates of any object can be expressed in three values. And sometimes two - when it comes to what is on the surface of the Earth.

Length, width and height can be used to describe both terrestrial objects and celestial bodies - planets, stars and galaxies. They are also enough for things inhabiting the microcosm - molecules, atoms and elementaryparticles. The fourth dimension is considered to be time.

There must be at least five dimensions in a multidimensional space. Modern theoretical physics has developed many theories for spaces with different dimensions - up to 26. There is also a theory that describes a space with an infinite number of dimensions.

## From Euclid to Einstein

Physicists and mathematicians of Antiquity, the Middle Ages and Modern times categorically denied the possibility of the existence of higher dimensions. Some mathematicians even deduced justifications for the limitation of space by three parameters. Euclidean geometry assumed only three dimensions.

Before the advent of general relativity, scientists generally considered multidimensional space to be a subject unworthy of study and advancement of theories. When Albert Einstein formulated the concepts of space-time, combining three dimensions with the fourth, time, the certainty in this matter immediately disappeared.

The theory of relativity proves that time and space are not separate and independent things. For example, if astronauts board a ship that moves at high speed for a long time, then upon returning to Earth they will be younger than their peers. The reason is that less time will pass for them than for humans on Earth.

## Kaluza-Klein theory

In 1921, the German mathematician Theodor Kaluza, using the equations of the theory of relativity, created a theory thatwhich for the first time combined gravity and electromagnetism. According to this theory, space has five dimensions (including time).

In 1926, the Swedish physicist Oscar Klein deduced the justification for the invisibility of the fifth dimension, described by Kaluza. It consisted in the fact that the higher dimensions are compressed to an incredibly small value, which is called the Planck value and is 10^{-35. Subsequently, this formed the basis of other theories of multidimensional space.}

## String theory

This area of theoretical physics is by far the most promising. String theory claims to be what physicists have been looking for since the advent of general relativity. This is the so-called theory of everything.

The fact is that two fundamental physical principles - the theory of relativity and quantum mechanics - are in irresolvable contradiction with each other. The theory of everything is a hypothetical concept that could explain this paradox. In turn, string theory is more suited to this role.

The essence of it is that at the subatomic level of the structure of the world, particles vibrate, similar to the vibration of ordinary strings, for example, a violin. This is where the theory got its name from. Moreover, the dimensions of these strings are extremely small and fluctuate around the Planck length - the same one that appears in the Kaluza-Klein theory. If an atom is enlarged to the size of a galaxy, then the string will only reach the size of an adult tree. String theory only works in multidimensional space. And there are severalversions. Some require 10-dimensional space, while others require 26-dimensional space.

At the time of its inception, string theory was perceived by physicists with great skepticism. But today it is the most popular, and many theoretical physicists are engaged in its development. However, it is not yet possible to prove the provisions of the theory experimentally.

## Hilbert space

Another theory describing higher dimensions is the Hilbert space. It was described by the German mathematician David Hilbert while working on the theory of integral equations.

Hilbert space is a mathematical theory that describes the properties of Euclidean space in infinite dimension. That is, it is a multidimensional space with an infinite number of dimensions.

## Hyperspace in science fiction

The idea of multidimensional space has resulted in many science fiction plots - both literary and cinematic.

Thus, in Dan Simmons' "Songs of Hyperion" tetralogy, humanity uses a network of hyperspatial null-portals capable of instantly transferring objects over a long distance. In Robert Heinlein's Starship Troopers, soldiers also use hyperspace to travel.

The idea of hyperspace flight has been used in many space opera films, including the famous Star Wars saga and the TV series Babylon 5.

The plot of the movie "Interstellar" is almost entirely tied to the ideahigher dimensions. In search of a suitable planet for colonization, the heroes travel through space through wormholes - a hyperspace tunnel leading to another system. And towards the end, the main character enters the world of multidimensional space, with the help of which he manages to transfer information to the past. The film also clearly shows the connection between space and time, deduced by Einstein: for astronauts, time passes more slowly than for characters on Earth.

In the movie "Cube 2: Hypercube" the characters find themselves inside a tesseract. So in the theory of higher dimensions is called a multidimensional cube. In search of a way out, they find themselves in parallel universes, where they meet their alternate versions.

The idea of a multidimensional space is still fantastic and unproven. However, today it is much closer and more real than a few decades ago. It is quite possible that in the next century, scientists will discover a way to move in higher dimensions and, therefore, travel in parallel worlds. Until then, people will fantasize a lot about this topic, inventing amazing stories.