An artistic impression of a black hole and its accretion disk. Illustration: XMM-Newton, ESA, NASA
- In 1997, physicist Juan Maldacena found a way to bridge mathematical theories with and without gravity — a feat that remains a notoriously complex problem to this day.
- Maldacena’s paper — which has become the most-cited physics paper in history — has also been hailed as a major mathematical victory for string theory.
- His work gave rise to the possibility that an entity that exists in a number of dimensions can be described by another entity that exists in a fewer number of dimensions.
- This is closely related to the holographic principle, which states that when we view our 3D universe, we are actually viewing physical information encoded on a distant 2D surface.
Twenty-five years ago, in 1997, the Argentine physicist Juan Martin Maldacena published what is the most quoted physics paper in history (more than 20,000 to date). In the paper, Maldacena described a “bridge” between two theories that describe how our world works, but separately, without meeting. These are the field theories, which describe the behavior of energy fields (such as the electromagnetic fields) and subatomic particles, and the general theory of relativity, which treats gravity and the universe on the largest scale.
Field theories have many types and properties. One is a conformal field theory: a field theory that does not change when it undergoes a conformal transformation — that is, a theory that preserves angles, but not lengths related to the field. As such, conformal field theories are: Said to be “mathematically well behaved”.
In relativity, space and time are united in the spacetime continuum. This continuum can occur in many possible spaces. Some of these spaces have the same curvature everywhere and come in three forms (roughly, universes of certain “shapes”): the Sitter space, Minkowski space, and anti-de Sitter space. the Sitter space has positive curvature everywhere – like a sphere (but is empty of any matter). Minkowski space has no curvature anywhere – that is, a flat surface. Anti-de Sitter space has negative curvature everywhere – like a hyperbola.
Because these shapes are related to the way our universe looks and works, cosmologists have their own way of understanding them. If the spacetime continuum exists in Sitter space, the universe would have a positive cosmological constant† Likewise, Minkowski space holds a cosmological constant of zero and anti-de Sitter space a negative cosmological constant. Studies by various space telescopes have shown that our universe is a positive cosmological constantmeaning it’s roughly a de Sitter space (but not exactly because our universe has matter).
In 1997, Maldacena found evidence suggesting that a description of quantum gravity in anti-de Sitter space in N dimensions is the same as a conformal field theory in N – 1 dimensions. This one AdS/CFT Correspondence was an unexpected but monumental discovery that linked two kinds of theories that had hitherto refused to cooperate.
The wire science had a chance to interview Maldacena about his past and current work in 2018, in which he also provided further insights into AdS/CFT.
In his paper, Maldacena showed that in a very specific case, the quantum gravity in anti-de Sitter space in five dimensions was the same as a specific conformal field theory in four dimensions. He hypothesized that this equivalence would hold not only for the limit case, but for the entire theories. The correspondence is therefore also called the AdS/CFT. named suspect† Physicists have so far not proven this to be the case, but there is circumstantial evidence from many results that indicates that the conjecture is true.
Nevertheless, the finding was also hailed as a major mathematical victory for string theory. This theory is an important candidate for a theory that can unite quantum mechanics and general relativity. However, we have found no experimental evidence for the many claims of string theory.
Nevertheless, thanks to the correspondence, (mathematical) physicists have found that some problems that are difficult on the ‘AdS’ side are much easier to crack on the ‘CFT’ side, and vice versa – all they had to do was cross Maldacena’s ‘ ‘bridge’! This was another sign that the AdS/CFT correspondence was not just a math trick, but could be a legitimate description of reality.
So how could it really be?
The holographic principle
In 1997, Maldacena proved that a string theory in five dimensions was the same as a conformal field theory in four dimensions. However, gravity in our universe exists in four dimensions – not five. So the correspondence came close to providing a unified description of gravity and quantum mechanics, but not close enough. Nevertheless, it raised the possibility that an entity that exists in a number of dimensions can be described by another entity that exists in a certain number of dimensions one less number of dimensions.
In fact, the AdS/CFT correspondence did not lead to this possibility, but mathematically realized it. The sense of possibility had existed for many years until then, as the holographic principle. Dutch physicist Gerardus ‘t Hooft first proposed it, and American physicist Leonard Susskind brought it firmly into the realm of string theory in the 1990s. A way of expressing the holographic principle, in the words of the physicist: Matthew Headrickis therefore:
“The universe around us, which we’re used to thinking is three-dimensional, is actually two-dimensional on a more fundamental level, and everything we see that’s happening around us in three dimensions is actually happening in two-dimensional space. ”
This “two-dimensional space” is the “surface” of the universe, which is infinitely distant from us, where information is encoded describing everything that happens in the universe. It’s a mind-boggling idea. “Information” here refers to physical information, such as, to use one of Headrick’s examples, “the positions and velocities of physical objects.” When beholding this information from the infinitely distant surface, we are apparently beholding a three-dimensional reality.
I repeat, this is a mind-boggling idea. We have so far no evidence that the holographic principle is a true description of our universe – we just know that it is could describe our reality, thanks to the AdS/CFT correspondence. That said, physicists have used the holographic principle to study and understand black holes.
In 1915, Albert Einstein’s general theory of relativity provided a set of complicated equations to understand how mass, the spacetime continuum, and gravity are related. Within a few months, physicists Karl Swarzschild and Johannes Droste, followed in subsequent years by the likes of Georges Lemaître, Subrahmanyan Chandrasekhar, Robert Oppenheimer, and David Finkelstein, began to realize that one of the exact solutions of the equations (i.e., non-approximate) indicated the existence of a point mass around which space is completely wrapped, preventing even light from escaping from within this space to the outside. This was the black hole†
Because black holes were exact solutions, physicists assumed they had no entropy — that is, the insides showed no disorder. Had there been such a disorder, it would have appeared in Einstein’s equations. It didn’t, so QED. But in the early 1970s, Israeli-American physicist Jacob Bekenstein noticed a problem: If a system with entropy, such as a container of hot gas, was thrown into the black hole, and the black hole has no entropy, where does it come from? it then? go entropy? It had to go somewhere; otherwise, the black hole would violate the second law of thermodynamics – that the entropy of an isolated system, such as our universe, cannot decrease.
Bekenstein argued that black holes must also have entropy, and that the amount of entropy is proportional to the area of the black hole, ie the area of the event horizon. Bekenstein also found that there is a limit to the amount of entropy that a given volume of space can contain, and that all black holes can be described by just three observable attributes: their mass, electric charge and angular momentum. So if a black hole’s entropy increases because it swallowed some hot gas, this change should manifest as a change in one, some, or all of these three attributes.
All things considered, when some hot gas is thrown into a black hole, the gas would fall into the event horizon, but the information about its entropy may appear to be encoded on the black hole’s surface, from an outside observer’s point of view. and away from the event horizon. Note here that the black hole, a sphere, is a three-dimensional object, while its surface is a flat, curved plate and therefore two-dimensional. That is, all the information needed to describe a 3D black hole could, in fact, be encoded on its 2D surface.
Doesn’t this remind you of the AdS/CFT correspondence? For example, consider a fifth-dimensional anti-de Sitter space that contains a black hole. We can use the correspondence to show that the entropy of the theory describing the boundary of this space exactly matches the entropy of the black hole itself. This would realize ‘t Hooft and others’ conjecture – except here the information is not encoded on the event horizon, but on the boundary of fifth-dimensional space itself.
This is just one example of the broader context in which the AdS/CFT correspondence resides. For more examples and other insights, read Maldacena’s interview with The wire science†
The author is grateful Nirmalya Kajuric for discussion and feedback on this article.