String Theory Meets Loop Quantum Gravity

Two candidates for the “theory of everything”, long considered incompatible, may be two sides of the same coin.

Eighty years have passed since physicists realized that the theories of quantum mechanics and gravity are incompatible, and the mystery of their combination remains unsolved. Over the past decades, researchers have studied this problem in two different ways — through string theory and quantum gravity — which their practitioners consider to be incompatible. But some scientists argue that to advance it is necessary to combine efforts.

Among attempts to unify quantum theory and gravity , string theory attracted the most attention. Its premise is simple: everything consists of small strings. Strings may be closed or open; they can vibrate, stretch, combine, or decay. And in this diversity lie the explanations of all observable phenomena, including matter and space-time.
')
Loop quantum gravity (PCG), on the contrary, gives less importance to the matter present in space-time, and concentrates more on the properties of space-time itself. In PCG theory, spacetime is a network. The smooth background of Einstein's theory of gravity is replaced by nodes and links that are assigned quantum properties. Thus, the space consists of individual pieces. PCG is mainly engaged in the study of these pieces.

This approach has long been considered incompatible with string theory. In fact, their differences are obvious and profound. For a start, the PCG studies pieces of space-time, and string theory examines the behavior of objects in space-time. These areas share technical problems. String theory needs 10 dimensions in space; PCG in higher dimensions does not work. String theory assumes the presence of supersymmetry, in which all particles have yet to be discovered partners. Supersymmetry is not peculiar to PCG.

These and other differences divided the community of theoretical physicists into two camps. “Conferences are divided,” said Dordzh Pullin , a physicist at the University of Louisiana and co-author of the textbook on PCG . - Petlevik ride on loop konfy, string players - on string. They now do not even go to conferences on "physics". I think it is very regrettable. ”

But some factors can move these camps closer. New theoretical discoveries have revealed possible similarities between the PCG and string theory. The new generation of string theorists went beyond the bounds of string theory and began to search for methods and tools that could be useful for creating the “theory of everything”. And the recent paradox with the loss of information in black holes made everyone feel more modest.

Moreover, in the absence of experimental evidence for string theory or PCG, a mathematical proof that they are two sides of the same coin would be an argument that physicists, in search of a "theory of everything", are moving in the right direction. The combination of PCG and string theory would make the new theory unique .

Unexpected connection

Attempts to solve some of the problems of the PCG led to the first unexpected connection with string theory. Physicists who study PCG do not have a clear understanding of how to move from pieces of a network of space-time to a large-scale description of space-time, which coincides with Einstein's GR, our best theory of gravity. Moreover, their theory cannot be reconciled with the special case in which gravity can be neglected. This is a problem that lies in wait for any attempt to use space-time piece by piece: in SRT, the linear dimensions of an object decrease depending on the movement of the observer relative to the object. Compression also affects the size of pieces of space-time, which are perceived differently by observers moving at different speeds. This discrepancy leads to problems with the central principle of Einstein's theory - that the laws of physics do not depend on the speed of the observer.

"It is difficult to introduce discrete structures without experiencing problems with SRT," says Pullin. In his work, written in 2014 with colleague Rudolfo Gambini, a physicist at the Republican University of Uruguay in Montevideo, Pullin writes that bringing the PCG into line with the SRT inevitably leads to the appearance of interactions similar to those present in string theory.

The fact that these two approaches have something in common has seemed likely to Pullin since the fruitful discovery made in the late 1990s by Juan Malcadena , a physicist at the Institute for Advanced Study in Princeton, New Jersey. Maltsadena in the anti-Desitter space-time (AdS) aligned the theory of gravity and conformal field theory (CFT) on the space-time boundary. Using the AdS / CFT approach, gravity theory can be described using a more comprehensible field theory.

The full version of dualism is still a hypothesis, but it has a well-understood limiting case that string theory has nothing to do with. Due to the fact that the strings in this case do not play a role, it can be used in any theory of quantum gravity. Pullin sees here a point of contact.


PCG as an artist

Hermann Verlinde , a theoretical physicist at Princeton University, who often works with string theory, believes it plausible that PCG methods can shed light on the gravitational side of dualism. In a recent paper, he described a simplified AdS / CFT model in two dimensions for space and one for time, or as physicists say, in the case of “2 + 1”. He found that the AdS space can be described using such networks that are used in the PCG. Despite the fact that the whole structure is still working in “2 + 1”, it offers a new look at gravity. Verlinde hopes to generalize the model for more dimensions. “They looked at PCG too narrowly. My approach includes other areas. In an intellectual sense, this is a look into the future, ”he said.

But even if we succeed in combining the methods of PCG and string theory, in order to move forward with the AdS space, the question remains: how useful would such a combination be? The AdS space has a cosmological constant negative (this number describes the geometry of the Universe on a large scale), while our Universe has a positive one. We do not live in the mathematical construction described by the AdS space.

Verlinde's approach is pragmatic. “For example, for a positive cosmological constant we may need a new theory. Then the question is how different it will be from this one. AdS is the best hint to the structure we are looking for, and we need to do some trick to arrive at a positive constant. ” He believes that scientists do not waste time with this theory in vain: "Although AdS does not describe our world, it will give us lessons that will lead us in the right direction."

The union on the territory of the black hole

Verlinde and Pullin point to another possibility of uniting the communities of string theory and the PCG: the mysterious fate of information falling into a black hole . In 2012, four researchers from the University of California drew attention to the contradiction in the dominant theory. They argued that if a black hole allowed information to escape from it, it would destroy the thin structure of empty space around the horizon of a black hole, and create a high-energy barrier - a “firewall”. But such a barrier is incompatible with the equivalence principle underlying UTO, which states that the observer cannot tell whether he has crossed the horizon. This incompatibility brought indignation to the ranks of string theorists, who believed that they understood the connection of black holes with information, and who were forced to seize their notebooks again.

But this problem is important not only for string theorists. “The whole controversy surrounding firewalls was mostly in the string theorists community, which I don’t understand,” Verlinde said. “The questions of quantum information, entanglement, and the construction of mathematical Gilbert space are what the PCG specialists worked on.”

At this time, an event unnoticed by most string specialists occurred - the fall of the barrier erected by supersymmetry and additional measurements. The Thomas Thiemann group at the University of Erlangen-Nuremberg (Germany) extended the PCG to higher dimensions and included supersymmetry in it - and these concepts used to be the territory exclusively of string theory.

Recently, Norbert Bodendorfer, a former Timann student working at the University of Warsaw, applied loop quantification from the PCG to the AdS space. He argues that the PCG is useful for working with the AdS / CFT duality in cases where string theorists cannot perform gravity calculations. Bodendorfer believes that the gap between the PCG and the strings disappears. “Sometimes I got the impression that string theorists are very poor at PCG and do not want to talk about it,” he said. - But more young specialists demonstrate open views. They are very interested in what happens at the junction of the regions. ”

“The biggest difference is in how we define our questions,” says Verlinde. “The problem is more sociological, not scientific, unfortunately.” He does not think that the two approaches conflict: “I have always considered string theory and the PCG as parts of the same description. PCG is a method, not a theory. This is a method of thinking about quantum mechanics and geometry. This is a method that string theorists can use and already use. These things are not mutually exclusive. "

But not everyone is sure about it. Moshe Rozali [ Moshe Rozali ], a string theorist from the University of British Columbia, retains skepticism about the PCG: “I don’t work on a PCG because she has problems with the CTO,” he says. “If your approach from the very beginning is without respect for symmetries in SRT, you will need a miracle at one of the intermediate steps.” However, according to Rosalie, some of the mathematical tools that came from the PCG may be useful. “I do not think that there is a possibility of combining the PCG and string theory. But people usually need methods, and in this sense they are similar. Mathematical methods can intersect. ”

Also, not all PCG supporters are waiting for the merger of the two theories. Carlo Rovelli , a physicist from the University of Marseilles and the founder of the theory of PCG, believes in the prevalence of his theory. “The string community is no longer as arrogant as it was ten years ago, especially after a cruel disappointment with the absence of supersymmetric particles ,” he says. “It is possible that two theories may be part of the same solution ... but I think it is unlikely.” In my opinion, the string theory could not give what it promised in the 80s, and represents one of those ideas that look pretty, but do not describe the real world, which in the history of science was complete. I do not understand how people can still pin their hopes on it. ”

Pullin believes that declaring victory is premature: “Adherents of the PCG say that their theory is the only correct one. I will not subscribe to this. It seems to me that both theories are extremely incomplete. ”