Is loop quantum gravity the only theory concerning the structure of spacetime?

Question

As said in wikipedia's page

More precisely, space can be viewed as an extremely fine fabric or network "woven" of finite loops. These networks of loops are called spin networks. The evolution of a spin network over time is called a spin foam. The predicted size of this structure is the Planck length, which is approximately 10−35 meters. According to the theory, there is no meaning to distance at scales smaller than the Planck scale. Therefore, LQG predicts that not just matter, but space itself, has an atomic structure.

Throughout the years many theories were proposed for describing what matter is made of. This effort lead to the standard model, which as far as I know is currently our better understanding about the structure of matter.

Now, as I understand, loop quantum gravity is a theory that does the same for spacetime. It proposes spacetime has an atomic structure. So I believe this is a theory trying to describe the structure of spacetime, what spacetime is made of in some sense, as has been done for matter for many years.

Interestingly, it is the first time I read about a theory that tries to do so. Is loop quantum gravity the only theory that tries to describe what spacetime is made of, or in other words, the structure of spacetime? Are there any other seriously considered theory that also deals with the structure of spacetime?

I ask "seriously considered" because obviously is a possibility that some kind of theories have already been proposed but by some reason (either theoretical or experimental) have not been considered as going in the right direction. As far as I know, although still a research topic, loop quantum gravity is somehow considered as a valid way for describing quantum gravity.

Answer 1

I think the general viewpoint is that any theory of quantum gravity must have the geometry of spacetime emerge at low energy from more fundamental degrees of freedom. One argument for this emergence is the Bekenstein-Hawking entropy formula for a black hole, which says the entropy is equal to one quarter the area in Planck units. In particular, the entropy is finite, suggesting that the smooth geometry of the black hole is built up from a large but finite number of degrees of freedom in the UV theory. This is in contrast to renormalizable quantum field theories, which have infinitely many degrees of freedom at short distance.

Although I'm not an expert on loop quantum gravity, it seems like the spin foam models that appear in that theory realize these finite number of UV degrees of freedom in a very concrete way. One big open issue in this field is to actually demonstrate that these spin foams can approach a smooth geometry in an appropriate low energy limit.

String theory, and especially the AdS/CFT correspondence, provides another very useful example of a quantum gravity theory, and also gives some explanation about the fundamental building blocks of spacetime. In this case, the conformal field theory living at the boundary of Anti-de Sitter space is supposed to contain all the degrees of freedom describing the spacetime geometry. The duality exhibits a very interesting UV/IR correspondence, which means that short distance degrees of freedom in the gravitational theory correspond to long distance degrees of freedom in the CFT. So presumably the finitely many long distance degrees of freedom of the CFT describe what happens to the spacetime geometry at very short distances. Note in this case the CFT is a field theory, so really has infinitely many degrees of freedom at short distance, but again the UV/IR correspondence tells us that these are related to the infinite size of the bulk AdS space. Understanding how the CFT describes the short distance granularity of spacetime is an open and active area of research.

Answer 2

Let me adress your question at face value first. The main theory adressing the structure of spacetime is general relativity. Now it is known that for extremely small distances, this theory cannot describe the structure acurately anymore. The standard method of quantization (pertubation + renormalization) failed.

So here (Loop Quantum Gravity) LQG comes in as a canonical non-pertubative approach to quantize general relativity.

Surprisingly, an approach from a different side, as an 'extension' of the ideas of pertubative quantum field theories, called string theory seems to be applicable to this problem. The prediction of string theory to the fabric of space-time, are basically 11-dimensionality, brane-worlds, and multiverse theory.

Answer 3

I can give an example of another "promising" theory which tries to explain spacetime by "atoms" of spacetime.

The Dutch (like me) scientist Renate Loll, working at Utrecht University, is one of the major developers of Causal Dynamical Triangulation. Like LQG it's a background independent theory:

Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

This theory has, like all theories involved in the unification of GR and QFT, its drawbacks too. Otherwise, this would be the theory of quantum gravity, and until now there is no such theory. The atoms of space in CDT are called pentachorons.

So the answer to your question is:

No, QLG is not the only theory concerning the structure of spacetime.

Answer 4

I just want to supplement the @lalala answer above, and say that, afaik, string theory is not background independent, whereas loop quantum gravity is.

I should add that while both ideas are, in (very) rough outline, familiar to me, that I am far from knowing if this has significance or not, as some sources such as Lee Smolin who, as you probably know, is known for his work on LQG, states that it has, whereas the writer of this Wikipedia Background Independent article, does not see it as a serious problem.

I am in the happy position of not knowing enough about either idea to worry about it :).