Strange details about building bricks of nature

The strange properties of superconducting cuprates are not described by the known methods of quantum mechanics, but may be related to the properties of black holes from higher dimensions.

In accordance with modern quantum theory, the universe is penetrated by energy fields, and energy waves on these fields, called "particles", if it looks more like a point, or "waves", if it is more blurred, serves as building blocks of matter and acting forces. New discoveries suggest that this view of the waves / particles only superficially describes the components of the universe.

If we represent each energy field filling the space as the surface of a pond, and the waves and particles as disturbances of this surface, then new evidence suggests the existence of a hidden living world under the surface.

For decades, descriptions of subatomic phenomena on the "pond surface" were sufficient for accurate calculations of most physical phenomena. But recently, physicists have drawn into the subatomic depths a new, strange class of matter that resists description with the help of well-known quantum methods.
')
“I grew up in physics living on this flat surface,” says Subir Sachdev , a physics professor at Harvard University who studies these strange forms of matter. And now, according to him, a whole new dimension has appeared, and “you can imagine that particles are only ending on this surface.”

Of all the unusual types of matter, cuprates - metals containing copper, exhibiting high-temperature superconductivity - may be the most unusual. In a new study published in the Journal of High Energy Physics, the University of California at Santa Barbara, physicists studied the phenomena associated with the mysterious "surface" behavior of cuprates. Concentrating in their calculations on the medium lying under the surface, the researchers derived a cuprate conductivity formula, previously known only from experiments.

“It's amazing that you can start with this theory, and suddenly get the conductivity of these strange superconductors,” says Sachev, who is not associated with this work.

The results support the evidence that the new way of describing the building blocks of nature is real, and “surprisingly literal,” says Jan Zaanen, a theoretical physicist at Leiden University in the Netherlands.

Moreover, the results can be interpreted as indirect proof of string theory - a 40-year platform, crosslinking quantum mechanics with gravity, which, on the one hand, is mathematically elegant and has deep explanatory abilities, and on the other, has not yet been proven.

Scientists also claim that these discoveries can have far-reaching consequences in matters related to dark matter - a mysterious substance that makes up 84% of the mass of the Universe - as well as in the search for a "theory of everything" that describes the whole of mathematics.

“There is a real chance that unprecedented progress in fundamental physics will occur in the next few years,” says Zaanen. “Everything is developing very, very quickly.”

Under the surface

If waves and particles are a disturbance on the surface of a pond, then the connection between this disturbance and what is happening in depth was first described by the mathematical principle discovered in 1997. The landmark work of Juan Maldacena, then working at Harvard University, and now at the Institute of Advanced Studies in Princeton, showed that the events occurring in a three-dimensional region of space mathematically correspond to completely different events taking place on the two-dimensional boundary of this region. (Events in 4-dimensional space also correspond to events in three-dimensional, etc.)

Consider our three-dimensional pond and its two-dimensional surface. For the specified correspondence to work, the inside of the pond should be described by string theory, in which electrons, photons, gravitons and all other building blocks of the universe appear as tiny one-dimensional lines, or "strings". Mass and other macroscopic properties correspond to string vibrations, and interactions between different types of matter and forces depend on how the strings split and join. These strings live inside the pond.

Now imagine that the two-dimensional surface of a pond describes quantum mechanics. Particles are bursts on the surface, and waves are ripples from bursts. There is no gravitational force on the surface of an imaginary pond.



Maldacena's discovery, known as holographic duality, showed that events within a region, including gravity and described by string theory, are mathematically transformed into events on the surface that do not experience gravity and are described by quantum particle theories.

“To understand this connection, you need to take into account the main thing - when the theory of gravity is easy to analyze, then particles on the border - or, in our case, on the surface of a pond - interact very strongly with each other,” said Maldacena. The opposite is also true: when particles on the surface are calm, as is the case in most types of matter, the situation in the depths of the pond is extremely complex.

Because of this contrast, dualism is very useful.

The strange class of materials, which includes cuprates, belongs to the first category; experiments show that in these materials the particles interact so strongly with each other that they lose their individuality. Physicists say that particles "strongly correlate." The ripples corresponding to each of the particles overlap so much that a swarm effect occurs. Matter with a strong correlation can behave atypically and unusually, so that in some cases this behavior cannot be described by the well-known methods of quantum mechanics, said Sean Hartnoll, a professor of physics at Stanford University. “You need to describe them in a way that is different from the one that starts with the description of a single particle,” he says. “You cannot describe the ocean through individual water molecules.”

If matter with a strong correlation "lives" on a two-dimensional surface of a pond, then from holographic dualism it follows that extreme turbulence on the surface is equivalent to calmness in depth. Physicists can get a description of the situation on the surface by studying a parallel, but much simpler situation in depth. “In this peaceful world, calculations can be made,” said Zaanen.

In the mathematical expression of holographic dualism, a certain matter with strong correlation in two dimensions corresponds to black holes in three dimensions — infinitely dense objects with gravitational attraction, which cannot be avoided — and they are mathematically quite simple. “These extremely complex collective effects of quantum mechanics miraculously fall into the field of black hole physics,” says Hong Liu, associate professor of physics at the Massachusetts Institute of Technology. "In systems with a strong correlation, when you put an electron there, it immediately" disappears "- it can no longer be traced." This is comparable to how an object falls into a black hole.

Superconductivity model

Over the past ten years, the study of black holes equivalent to forms of matter with a strong correlation, has brought amazing results - for example, the new viscosity equation for liquids with strong correlation and a better understanding of the interaction between quarks and gluons, particles that live inside atomic nuclei.


Jorge Santos and Gary Horowitz

Gary Horowitz , a string theory specialist at the University of California at Santa Barbara and Jorge Santos, Ph.D. from the Horowitz group, applied the principle of holographic dualism to cuprates. They derived a formula for the conductivity of approximately two-dimensional metals, studying the properties of what would correspond to them in 3D: an electrically charged black hole of unusual shape.

In cuprates, a swarm of strongly correlated electrons moves along a fixed atomic lattice. Modeling metals with holographic dualism required the reconstruction of the equivalent of this lattice in the structure of the corresponding black hole, or rather, to give its horizon a waviness.

“When it comes to black holes, you need Gary,” says Zaanen.

To determine the conductivity of the cuprates, Horowitz and Santos had to study the features of the interaction of light with the complex horizon of their black hole. The equation was too complicated to solve head-on, so they found approximate solutions using a computer. In their first work on this approach, written together with David Tong, a physicist at the University of Cambridge, and published in July 2012 in the Journal of High Energy Physics, they derived a formula that corresponds to the conductivity of cuprates at high temperatures for alternating current. In the new work, they expanded the calculations to those temperatures at which cuprates become superconducting, that is, conduct current without resistance, and again showed a good approximation to the experimental data on the conductivity of real cuprates.

“It surprises me that such a simple model of gravity can reproduce any property of real material,” said Horowitz. “It inspires us to work further.”

The accuracy of the model in some important cases fails, for example, for alternating currents of ultrahigh frequency, but Sachdev says that, considering how simple the “wrinkled black hole” model turned out to be, “the best could not be expected.” The inclusion of more microscopic details of cuprates in the structure of a black hole, in his opinion, will deepen their congruence.

Hartnol, who recently used the principle of holographic dualism to model metal-dielectric transitions in materials with strong correlation, hopes to use the results of Horowitz and Santos, having solved their equations precisely. “They have input and output data; we would like to unpack them and understand important intermediate steps, ”he said. This will help to understand why the conductivity formula appears from the black hole model, and will give an understanding of the corresponding forces working inside the cuprates.

New dualism

Understanding the physics of cuprates can have important practical implications. Most metals pass into the superconducting state when the temperature drops to a state close to absolute zero. But for not quite clear reasons, cuprates exhibit superconductivity at much more affordable temperatures, which makes them useful for use in various devices, from high-power electrical cables to ship engines. But cuprates are fragile and expensive, so the creation of improved versions of this material can lead to a significant breakthrough in various technologies, from vehicles with magnetic cushion to more efficient electrical networks.

They have the potential to advance fundamental physics. If holographic dualism gives accurate predictions of the behavior of cuprates and other materials with a strong correlation, these materials can be considered, in fact, like black holes in higher dimensions.

“If we had a model that reproduces all the properties of a material, it could be considered as its theory — very unusual, but, thanks to dualism, it would be the equivalent of any theory working on the border with ordinary particles,” said Horowitz. “And that might be a much simpler approach.”


Computer representation of the black hole horizon used in the study to model cuprates

Holographic dualism has something in common with wave-wave dualism, which led to the development of quantum mechanics. At the beginning of the 20th century, the light, previously considered a wave, in some studies behaved mysteriously, if only it was not considered as particles; the behavior of electrons, considered to be particles, sometimes did not make sense if they were not considered as waves. “The corpuscle-wave dualism, when it was first proposed, came as a surprise - since these were two seemingly different concepts, and we learned that they represent the same thing,” said Horowitz. Holographic dualism is “more complicated, but it has the same properties,” he says. “You have two, at first glance, completely different objects that appear to be equivalent.”

But how does holographic dualism fit into our understanding of nature? Is the analogy with one-dimensional strings from the pond real? According to physicists, not necessarily. In fact, the strings are generally not included in the calculations of the properties of the black hole of Horowitz and Santos, which they used to model cuprates. But these discoveries really lead to the fact that “all these theories, which seemed to us to be different, are connected with each other,” said Maldacena. “This shows that string theory is not divorced from the rest of physics.”

According to physicists, string theory may simply turn out to be the best mathematical language for working with certain aspects of reality.

“Physics has traditionally been subject to reductionism. She wants to take something complicated and understand what parts it consists of, ”explains Hartnol. “But for this approach there is no unique way: in some cases electrons can be fundamental building blocks, and in others, the joint excitation of electrons turns out to be more fundamental than any of them individually.”

“We are trying to find the right fundamental parts to describe these strange phases of matter,” he says. “These could be strings in a higher dimension.”

Physicists interpret the meaning of the fact that particles in strange brittle metals mathematically correspond to strings and unusual black holes that theoretically exist in a higher dimension, and holographic dualism helps them “think differently in laboratories about riddles,” says Zaanen. - Perhaps it's not just a different way of thinking; the point is to see real and beautiful facts. ”