December 2, 2023 # How many dimensions does the universe have?

At the moment, planar systems are likely to have the greatest impact in physics. Claus von Klitzing gave the go-ahead for the research direction in 1980 when he did Discover the quantum Hall effect: At low temperatures and under the influence of a strong external magnetic field, the conductivity of some materials changes only abruptly. To explain this unexpected phenomenon, one has to describe the behavior of electrons in a plane. This has already shown that 2D and 3D physics are fundamentally different.

All special properties of graphs are related to their two-dimensionality.

In 2004, Andre Geim and Konstantin Novoselov finally succeeded in creating a stable 2D material for the first time, for which they were awarded the 2010 Nobel Prize in Physics. The so-called graph, which was predicted as early as 1947, consists of One atom layer of graphite. The unusual mechanical, thermal, and electronic properties of a material are related to its two dimensions. This discovery caused a real stir in materials science – there are now many monolayer materials that can be used in many ways.

### Why exactly three dimensions?

There have been many attempts to explain the three dimensions of our world. The first discussion goes back to the Pythagoras, whom Aristotle considers in his treatise “Across the sky” spasm. In it he wrote: “All” and “all” are denoted by three numbers: the end, the middle and the beginning constitute the number of the universe, i.e. the number of the Trinity. In his “Dialogue on the Two World Systems” published in 1632, Galileo declared that there could be no more than three Dimensions because at most three vertical lines can pass through a point.

### A world of ten dimensions

One of the biggest challenges in physics is unifying general relativity with quantum mechanics. Albert Einstein’s theory describes how energy and matter distort the four-dimensional structure of spacetime. On the contrary, it shows how the corresponding curvature determines the motion of the material. In other words: gravity arises from the geometry of spacetime. At about the same time, the strange laws that govern the microscopic world were discovered. Quantum physics successfully describes elementary particles and their interactions with each other.

However, some situations, such as the moments after the Big Bang or the interior of a black hole, require a quantum physics formulation of gravity. The first attempts failed: the resulting equations lead to infinite quantities that cannot be eliminated.

In the late 1960s, researchers discovered a promising way to reconcile the two theories. By replacing the point particles with small vibrating strings, the infinities that occurred previously can be avoided. The basic mathematical formalism is very complex. It was soon recognized that string theory only works in 26-dimensional spacetime!

But this first version of the theory had other problems, for example it could not describe particles with half-integer spin, such as electrons or quarks. In 1971, Pierre Raymond, André Neveu, and John Schwartz extended the approach to so-called supersymmetry, which associates particles with integer spins (such as photons) and those with half-integer spins. This superstring theory now requires only ten-dimensional space.

In order to go from this theory to our four-dimensional universe, one would have to compress the extra dimensions: at each point in space, we twist it to be small. Since there is no extension of it, we cannot perceive it directly. These six coiled dimensions form a mathematical object, the Calabi-Yau space. All variants of such a structure lead to a model of a world with its own characteristics. However, it is estimated that there are about 10500 Possible Calabi-Yau rooms – there can be many. How do you know which configuration corresponds to the real universe? At the moment physicists have no answer to that.

Immanuel Kant also dealt with this topic. He tried in vain to prove that the three dimensions of space follow Isaac Newton’s law of gravitation, according to which bodies attract each other inversely with the square of the distance. Rather than looking at the problem metaphysically or geometrically, he was the first to take a physical approach. In fact, Kant’s conjecture can not only be proven, but also generalized: in one nDimensional space takes gravity by 1/sn – 1 with distance s Away. Thus Newton’s law of gravitation is a direct consequence of the three dimensions of space. In a four-dimensional world, gravity would be one s3 is missing.

In 1917, according to the Austrian physicist Paul Ehrenfest The movement of the stars in one nDimensional space. As he explained, there are only stable and finite solutions in two or three dimensions. In addition, if the attraction of two objects approaches zero at a great distance, then only three spatial dimensions remain as a possibility. This is the only way that the planets can have a stable orbit for several hundred million years – a prerequisite for the emergence of life.

Dimensions also affect the microcosm. Since we are surrounded by stable particles, the fundamental energy of the atom must be limited: the electrons do not collide with the nucleus, and they cannot separate. If the Bohr model of the atom is applied to a hydrogen atom located in a space of more than five dimensions, then the radius of the electron’s orbit decreases with increasing energy, and the particle falls into the nucleus. Stable atoms can exist only if space is at most three dimensional.

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