IN NOVEMBER 1997, a young physicist named Juan Maldacena proposed an almost ludicrously bold idea: that space-time, the fabric of the universe and apparently the backdrop against which reality plays out, is a hologram.
For many working in the fields of particle physics and gravity at the time, Maldacena’s proposal was as surprising as it was ingenious. Before it was published, the notion of a holographic universe was “way out there”, says Ed Witten, a mathematical physicist at the Institute for Advanced Studies in Princeton (IAS), New Jersey. “I would have described it as wild speculation.”
And yet today, just over 25 years on, the holographic universe is widely revered as one of the most important breakthroughs of the past few decades. The reason is that it strikes at the mystery of quantum gravity – the long-sought unification of quantum physics, which governs particles and their interactions, and general relativity, which casts gravity as the product of warped space-time.
Then again, you might wonder why the idea is held in such high regard given that it remains a mathematical conjecture, which means it is unproven, and that the model universe it applies to has a bizarre geometry that doesn’t resemble our universe.
The answer, it turns out, is twofold. First, the holographic conjecture has helped to make sense of otherwise intractable problems in particle physics and black holes. Second, and more intriguing perhaps, physicists have finally begun to make headway in their attempts to demonstrate that the holographic principle applies to the cosmos we actually reside in.
Maldacena, now also at the IAS, was originally inspired by two separate branches of physics. The first was string theory, a way to describe reality in which particles are made up of vibrating loops of string. Early in the idea’s development, physicist Alexander Polyakov realised these strings had to live in more dimensions than our familiar universe of three spatial dimensions plus one of time. Most modern versions of string theory require 10 dimensions to describe our four-dimensional universe.
Black hole clue
Around the same time, Stephen Hawking, Jacob Bekenstein and others were trying to understand the role that quantum mechanics plays in black holes, where space-time is so warped and gravity so strong that nothing can escape its pull. Every particle in the universe contains some amount of information – its energy, momentum and position, for example. Hawking and Bekenstein wanted to know the maximum amount of information you could put into a given region of space, in this case a black hole. Since packing in more and more particles will eventually produce a black hole, their question was equivalent to asking: what is the information content of a black hole?
The pair had imagined that the maximum amount of information a black hole could contain would be proportional to the volume within its event horizon, the boundary inside which nothing can escape. This seems to make sense: the number of sweets you can fit in a jar depends on its volume, after all, and not the surface area of its opening.
But, to their surprise, Bekenstein and Hawking discovered this wasn’t the case for black holes. The information contained in these objects depends on the event horizon’s area, not the volume it encloses. Somehow, all the information from a three-dimensional region of space could fit on the two-dimensional boundary around it.
These two insights – that our familiar universe could be equivalent in some sense to a 10-dimensional stringy cosmos, and that all the information contained in a three-dimensional black hole lived on its two-dimensional horizon – got Maldacena thinking. Perhaps our universe might also emerge from a kind of reality with fewer dimensions, just like a hologram?
To realise a holographic universe, Maldacena exploited the concept of a duality: a correspondence between two seemingly disparate ideas. On one side of the duality was a space-time that had some of the familiar properties of our cosmos, where objects feel the pull of gravity, called an Anti-de-Sitter (AdS) universe. On the other side was the so-called conformal field theory (CFT), a quantum theory that only existed on the two-dimensional boundary of this universe and had no connection to gravity at all. Mysteriously, this duality implied that gravity somehow emerged as a hologram in the three-dimensional world from this two-dimensional CFT. “It’s like a universe in a box,” says Maldacena. Inscribed on the surface of the box is the entirety of its contents.
This theoretical universe, known as AdS space, is different to the one we observe. For starters, the intrinsic energy contained in empty space in this model version is negative, meaning space-time bends in bizarre ways so that it takes on a saddle shape. In our universe, on the other hand, the value of this so-called vacuum energy is positive. This warps the geometry in precisely the opposite way to the saddle-like AdS space, shaping our universe like an ever-expanding sphere. Hence, we live in a de-Sitter space.
Regardless of the differences, Maldacena’s idea captured the imagination of string theorists and people who work on general relativity alike. Working independently, Witten and another group that included Polyakov quickly followed up with papers that explicitly established the holographic implications of the AdS/CFT correspondence, as it became known. Maldacena’s work has since become one of the top-cited papers in all of physics.
Universe in a box
That might seem puzzling when you consider that it isn’t a mathematically proven fact. “There are many parts of the correspondence which are on a firm footing,” says Jonathan Oppenheim, a physicist at University College London. “There are other parts of the correspondence which, I think, are on a much weaker footing.” With that in mind, Oppenheim is concerned we are overreaching when physicists argue that it has something profound to teach us about the universe. That is fine if you believe the conjecture, he says. “On the other hand, if it’s not true, then we’re being led in the wrong direction.”
What might seem even more damning is the fact that the conjecture is still only valid in that strange, saddle-shaped theoretical universe. “It can’t be straightforwardly adapted to our universe,” says Witten. But that hasn’t led physicists to abandon the idea, and that is largely because it has helped us solve many real-world problems that were previously hard, if not impossible, to crack. “For many things, it is the best model we have,” says Witten.
Consider problems in quantum field theory, our best way of understanding subatomic particles and their interactions, that involve “strongly coupled” interactions – that is, particle interactions so strong that the techniques used to approximate the collective behaviour of a system of particles fail.
It turns out that putting the universe in a box helps. Since the “bulk” universe inside and the boundary of the box are considered one and the same, physicists can translate the problem to the boundary and solve it there. “The duality was one of the most significant insights about strongly coupled quantum theory in many decades,” says Witten. “Many questions that are hard to answer on the boundary can be answered much more easily in the bulk and vice versa.”
One of the most significant triumphs was in relation to a problem known as quark confinement. We know that quarks, the subatomic particles that compose protons and neutrons, must exist. But they are always detected in small groups, never in isolation. In the 1970s, it was suggested that this might be because the strong nuclear force that holds together quarks idiosyncratically becomes stronger the further two quarks are from one another. This increased pull with increasing distance tends to snap them back towards one another like a rubber band, causing them to always be clustered together. This was largely corroborated by computer simulations, but it was hard to make sense of on an intuitive level.
With the advent of Maldacena’s box universe, physicists had a new tool: a particular CFT that was similar in many ways to the theory that governs quarks in our universe, including displaying the familiar quark confinement. The calculations were messy even in this simplified theory, but, by using the correspondence, physicists were able to translate the problem into something more tractable, something that could easily be solved with paper and pen.
The AdS/CFT correspondence has proven fruitful in many other respects, too. In just the past few years, it has helped push us closer than ever to understanding the enigmatic nature of black holes and the paradox of how they evaporate and, hence, how quantum physics and general relativity come together in these extreme regions of space-time. “One would certainly not want to go back to the old days without the duality,” says Witten. We have even found a possible way of using AdS/CFT to make quantum computers more reliable (see “Quantum corrections”).
Superstrings, conceptual computer artwork. The superstring theory is a Theory of Everything (Grand Unification Theory), which seeks to unite gravitational force with the other fundamental forces (electromagnetism and nuclear forces) that are already described by quantum mechanics at the atomic level. The theory states that fundamental particles such as quarks and electrons are not points of energy or matter, but result instead from the vibrations of one-dimensional "string-like" entities on a far smaller scale.
The fact is, however, that we still haven’t arrived at a holographic description of the universe we see around us.
It isn’t for lack of trying. Within just a few years of Maldacena’s discovery, many physicists, including Maldacena himself, had started trying to apply a similar holographic principle to a more realistic cosmos with the geometry of our universe. The problem is that the strange geometry of a saddle-like universe makes it easy to apply a boundary to it and put it in a box. But because our universe is infinitely expanding, putting a boundary around it isn’t so simple.
The answer, some physicists think, involves time. In AdS/CFT, time plays a similar role on both sides of the correspondence: in both the gravity theory in the bulk and the quantum theory on the boundary, time progresses and the system evolves. Space and gravity emerge like holograms from the boundary CFT, whereas time doesn’t.
But an expanding universe can only be put in a box if the boundary extends infinitely far in the time dimension. If our universe were holographic, the boundary it emerges from would live in the infinite future and contain no notion of time. Somehow, time as we experience it in the bulk universe would emerge from the hologram.
Perhaps unsurprisingly, no such mind-bending duality exists. Not yet at least. But Eva Silverstein at Stanford University in California is among those working on it. Her pragmatic line of thinking is that, given we already have a description of a holographic universe, let’s see how much we can manipulate it so it resembles our own.
Silverstein starts with the familiar saddle-shaped space. But, in this particular space, she puts a black hole at the centre. Then, she slowly moves the boundary inwards until it just barely encompasses the black hole’s event horizon. “At this point, you can’t tell the difference between that and, say, a de-Sitter black hole horizon,” says Silverstein. After bringing the boundary to this point where the two geometries are indistinguishable, she can then gradually move the boundary back outwards, all the while subtly deforming the geometry of the world to turn it into de-Sitter space. “It very much is an approach that builds on AdS/CFT,” says Silverstein.
Jordan Cotler at Harvard University, meanwhile, is starting in more familiar territory. He is interested in understanding how the rules of regular quantum theory change when embedded in an expanding universe, such as our de-Sitter one. In plain old quantum mechanics, we take certain things for granted, like the principle of unitarity – which says the universe is fully deterministic whether you run time forwards or backwards. But this is only strictly true in a static cosmos, says Cotler. As space expands in a de-Sitter universe, he thinks that the universe should correspondingly increase its maximum capacity of information. So, a quantum state now could evolve to any number of possible configurations in the future.
Cotler and his colleagues haven’t fully worked out the implications of these new rules of quantum mechanics in de-Sitter space, but he thinks they are an important waypoint in establishing what everyone is seeking: a dS/CFT correspondence. “A unique challenge of thinking about quantum gravity in de-Sitter space is that it’s almost never clear what you should be calculating,” says Cotler. “You have to learn what to compute and what the rules are supposed to be, and that’s a tricky business.”
Elsewhere, physicists are actively pursuing various other approaches to finding a duality in de-Sitter space. But, as Witten acknowledges, the work “hasn’t yet crystallised to enable anyone to find the right analogue of AdS/CFT”.
The reason so many continue to plug away at it is that finding such a correspondence that applies to our universe as well might help us answer the very deepest questions about the emergence of gravity and space-time. “The good news,” says Silverstein, “is we’re making progress.”
Believe it or not, the strange correspondence between a model universe and the boundary around it that is central to the holographic universe idea (see main story) might have practical implications.
By exploiting the laws of quantum physics, quantum computers promise to solve certain types of problems exponentially more efficiently than classical computers can. And yet their immense potential may be undermined by a crucial drawback: quantum bits of information, or qubits, are extremely delicate. Any disturbance from the environment can interfere with the computation at any time, causing it to fail.
In 1995, a group led by mathematician Peter Shor, now at the Massachusetts Institute of Technology, came up with the first example of how one might protect qubits: encode a single qubit into many individual “physical” qubits. Even if an error occurred on one “physical” qubit, the redundancy meant researchers could correct it, making the computer more resilient.
Since this first proposal, countless other implementations of these “error-correcting codes” have been invented. Then, in 2014, Ahmed Almheiri at Stanford University in California and two of his colleagues discovered that the qubits on the boundary of a type of model universe called an Anti-de-Sitter (AdS) space encoded the stuff in the interior in exactly the same way that error-correcting codes do in quantum computing.
The implications of that are jaw-dropping for fundamental physicists, because it suggests that space-time could itself be an error-correcting code. But the insight could also accelerate progress towards robust quantum computers by inspiring new error-correcting techniques.