*Can we craft a theory in which space and time aren’t assumed to exist?*

Over the past decades, a field of physics has developed that postulates the existence of mysterious algebraic entities called spin networks. These networks—proposed as the constituent stuff of space and time—condensed to produce the Universe as we know it. That condensation resulted in the event that we currently call the Big Bang, giving the field its name: condensate cosmology.

It may sound like an odd idea, but we already know that the Universe works in very strange ways.

The idea, technically termed “Group Field Theory (GFT) condensate cosmology,” is a branch of quantum gravity, a field of physics that aims to establish the fundamentals of what everything from light and matter to space and time is made of. It is an idea based completely in theoretical calculations—and it's totally untested for now. Condensate cosmology requires a great deal of abstract reasoning to even try to understand it.

Despite these challenges, quantum gravity has drawn a lot of attention from some of the sharpest minds in all of physics. Its ideas are bold and daring, highly creative, and extraordinarily imaginative.

## Why quantum gravity?

Quantum gravity has been formulated to tackle one of the greatest problems in all of physics: the need to unite the two great theories of the 20th century—general relativity and quantum mechanics.

The former presents a framework for understanding the world in terms of space and time, and it covers behavior over large distances. General relativity introduces the notion that time is relative and that gravity itself exists because of a curved space-time. As Einstein first realized, a ball does not fall to the Earth because it is attracted to its mass, as Newton told us; it falls because of the existence of a space-time field that permeates the Universe and curves around large objects.

Quantum mechanics is a mysterious yet incredibly accurate theory that describes the world of the very small. It tells us that both particles and fields exist in discrete units that, because of uncertainty, can only be described probabilistically. The theory also describes entanglement, the bewildering phenomenon in which physical systems can be so intertwined with one another that they lose their independent, individual reality and start obeying rules that apply to a collective.

As far as we can tell, these two theories are both right—and in conflict. Their simultaneous existence generates a paradox, meaning physics is, in a sense, in disarray. While quantum mechanics deals with reality in discrete, granular fashion, relativity tells us that space-time, and therefore gravity, is continuous and non-discrete.

One way to deal with this is to give one of the theories precedence. Since we know the world is quantum, general relativity must be an approximation of an underlying quantum description of space-time itself. And this suggests that any unification of the theories requires that gravity become discrete.

## Development of LQG

Over the past few decades, a branch of quantum gravity called Loop Quantum Gravity (LQG) has shown some potential in solving the challenge of making gravity discrete. LQG begins with Einstein's field equations, but it takes a closer look at what might be hiding beneath the surface of space-time. The mathematics produced myriad discrete geometric objects, including loops, lattices, and polygons, arranged in various constructions called spin-networks and spin foams. Together, they can describe the structure of reality itself—these geometric oddities of LQG do not exist in space and time, but rather they are space and time and therefore the very constituents of gravity itself.

While recent progress has greatly elaborated LQG, the idea has a long history. The dichotomy between general relativity and quantum mechanics became apparent during the 20th century's interwar period. This spawned approaches to quantum gravity that were developed by taking general relativity and using different methods to quantize it. But the approach to this problem changed during the 1970s and 1980s when physicists began to learn new things from semi-classical physics, according to Daniele Oriti, Heisenberg Group Leader at the Arnold Sommerfeld Centre for Theoretical Physics, Ludwig-Maximilians-Universität in Munich.

Oriti told Ars that, at that time, emerging ideas about black holes focused on using quantum mechanics to describe the matter fields around them. This work suggested that theorists might need another, more radical, approach to quantum gravity—rather than simply quantizing general relativity, a new way to understand the nature of space-time at a microscopic level might be needed.

These ideas derived from black holes suggested that the gravitational field itself is not really fundamental, regardless of whether it is classical or quantum. Instead, it became apparent that the gravitational field might be a manifestation of something more fundamental, something that does not look like a field at all and so cannot be described in standard spatio-temporal ways.

New approaches to quantum gravity, like LQG, began to emerge during this period. In the 1990s through to the 2000s, LQG gained a lot of credibility amongst a growing population of theoretical physicists. “One thing LQG achieved was a precise suggestion of how space-time could look at a more fundamental level,” says Oriti. “It was discovered that, at least according to the theory, the basic entities of space and time do not look at all like the gravitational field as we know it. In LQG we call these basic entities spin-networks, which are discrete, algebraic objects.”

## LQG as an alternative to string theory

At its core, LQG is in conflict with string theory, the particle-focussed theoretical framework that also aims at unifying general relativity and quantum mechanics. In string theory, a space-time is generally assumed—the very assumption that quantum gravity aims to explain. From the LQG perspective, space and time must emerge in a successful theory of quantum gravity, rather than being a starting component.

String theory has many strengths. Most of the work done in theoretical physics assumes a space-time, so this isn’t an issue specific to string theory. And there are good reasons for this: without a space-time framework, it is very hard to say anything about the real world. This issue actually creates problems for LQG. Since it and related approaches like group field theory do not assume a space-time, it gets hard to connect the fundamental theory back to any well-understood physics.

“That is not to say that string theorists deny the notion that space-time cannot be fundamental,” says Oriti. “When we work on quantum gravity—whatever the approach—and really talk frankly to each other, we agree on many of the main points. But for those of us who are working on quantum gravity and aiming to get at the microscopic structure of reality, we find any explicit reliance on space-time to be a conceptual and technical burden, and we tend to react negatively to its implementation.”

For their part, the string theorists often react negatively to a lot of the work done in LQG, arguing that, without a space-time, you cannot even say you are working on gravity. Both groups are right in their own way.

“I think people involved in quantum gravity, like myself, and those in string theory, are very willing to sit down and work together. There is no obvious reason why these different approaches cannot be compatible. There may even be a way that we can connect several approaches or different formalisms. We just don't know.” For example, Oriti cannot exclude the notion that, if an emergent framework of space-time arrives (whether via LQG or some related theory), it might reflect some of the ideas suggested by string theory.

## GFT condensate cosmology

According to Oriti, the field of quantum gravity now needs more radical ideas to push itself forward. That's because something new is needed to bring the ideas around LQG, which has been developed at the microscopic scale, up to the scale of the Universe as a whole. Over the past decade or so, he has led research in the direction of Group Field Theory (GFT) condensate cosmology, which proposes that the Universe as we know it came about through a kind of hydrodynamic condensation process.

“One can think of this process in GFT condensate cosmology as being analogous to steam,” he says. “Steam is a phase in which the entities which constitute all of space—or atoms of space as we call them—can find themselves condensing into water, which is our analogy for space-time.”

According to this version of LQG, once this transition takes place—at the beginning of the Universe for example—then the familiar constructs of space and time are born. Awkwardly, even speaking of a 'transition' or 'beginning' implicitly assumes the notion of time, or a process happening over time. In the context of these ideas, we must learn to forget that.

Oriti's PhD student Isha Kotecha says that a lot of their work involves thinking about classical gravitational systems in terms of statistical thermodynamics, the branch of physics that deals with heat and temperature. “There are two reasons we can think of gravity thermodynamically” she told Ars. “Firstly, the laws of classical black hole mechanics already hint at a relationship between gravity and thermodynamics, suggesting that more generally we can think of space-time as a thermodynamic system. This is what we call the thermodynamics of gravity.

“Secondly, we know that macroscopic thermodynamic systems have an underlying quantum microstructure, so for a thermodynamical space-time, a natural thing to do is to study the statistical mechanics of its fundamental quantum gravity entities,” she continued. “But how all this is related exactly is still up for grabs.”

Kotecha explains that the mathematical variables required for a hydrodynamical description of GFT condensate cosmology have statistical and thermodynamical origins. Examples of these include the number density and temperature fields of a fluid. For instance, the fluid may be colder and denser in one part than the other; in order to describe the dynamics of such systems as they evolve, one first has to be able to define these differences. This is where statistical mechanics and thermodynamics come in.

“The idea is that we need statistical techniques to describe suitable collective variables at the emergent spacetime level,” she says.

Oriti and his team have thus far successfully shown that a spin-network condensate as described by GFT can be characterized using a mathematical function that has the same features as the so-called wave-function of the Universe. In quantum cosmology, this wave function gives an indication of the probability the Universe has of having a certain shape, or geometry. That Oriti's math produces something that resembles it gives the approach some credibility. So it seems, from this point of view, that the condensate can be interpreted as representing the Universe at very large scales.

The ideas are also capable of producing a big bounce—an event where the Universe fell in on itself until it reached a point where it exploded outward again, producing our current reality. This behavior is also seen in other areas of cosmological physics, adding credence to the GFT approach.

## Putting the theory to the test

Oriti and Kotecha both suspect that any breakthrough in their field will come through cosmological observation and experimentation. The hallmark of good science, after all, is a theory that is testable. So what about the Universe might be connected to condensate cosmology?

One possibility is to introduce perturbations in the GFT’s underlying mathematics and see if they could produce something like the Cosmic Microwave Background (CMB), the electromagnetic radiation remnant produced shortly after the beginning of the Universe. If GFT’s underlying spin-networks and spin-foams can reproduce the CMB, Oriti will have a real, viable way of testing his ideas. Another way he aims to proceed is to introduce perturbations into his models that could produce gravitational waves.

The two theorists—along with many others in the field—hope that, in time, there will be important advances in one (or more than one) approach to quantum gravity. Physicists will find a universal, or at least common, feature to many approaches and a way to connect to observations and experiments. Perhaps researchers will realize that some of the observations already available can be explained by mechanisms that are common to several quantum gravity approaches.

It’s impossible to know whether any of the current ideas around LQG or GFT will achieve real success along the long road to produce a viable, testable theory. But one thing's for sure; there is merit in the search for a fundamental truth even if—for now—it lies beyond our current notions of space and time.

*Conor Purcell, PhD, is an independent author who writes on science and its role in society and culture. He was a 2019 Journalist in Residence at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Germany. He can be found on Twitter @ConorPPurcell, and you can find some of his other articles at cppurcell.tumblr.com.*

*This article was first published on Ars Technica*