Benefits and Flaws of Loop Quantum Gravity
As with string theory, loop quantum gravity is passionately embraced by some physicists and dismissed by others. The physicists who study it believe that the predictions (described in the preceding section) are far better than those made by string theory.
One major argument in support of LQG is that it’s seen by its adherents as a finite theory, meaning that the theory itself doesn’t inherently admit infinities. These same researchers also tend to dismiss the flaws as being the product of insufficient work (and funding) devoted to the theory. String theorists, in turn, view them as much a victim of groupthink as critics view string theorists.
The benefit of a finite theorem
One major benefit of loop quantum gravity is that the theory has been proved finite in a more definitive sense than string theory has. Lee Smolin, one of the key (and certainly most high profile) researchers of LQG, describes in his book The Trouble with Physics three distinct ways that the theory is finite (with string theorist objections in parentheses):
The areas and volumes in loop quantum gravity are always in finite, discrete units. (String theorists would say this isn’t a particularly meaningful form of finiteness.)
In the Barrett-Crane model of loop quantum gravity, the probabilities for a quantum geometry to evolve into different histories are always finite. (This sounds just like unitarity, which is a property of string theory and all quantum field theories.)
Including gravity in a loop quantum gravity theory that contains matter theory, like the Standard Model, involves no infinite expressions. If gravity is excluded, you have to do some tinkering to avoid them. (String theorists believe this claim is premature and that there are substantial problems with the proposed LQG models that yield this result.)
Some questions exist (largely brought up by loop quantum gravity theorists) about whether string theory is actually finite — or, more specifically, over whether it has been rigorously proved finite.
From the theoretical side of things, the loop quantum gravity people view this uncertainty as a major victory over string theory. (String theorists would argue that the statements above still don’t prove that LQG can’t result in an infinite solution when experimental data is put into the theory.)
Some of the flaws of loop quantum gravity
Many of the flaws in loop quantum gravity are the same flaws in string theory. Their predictions generally extend into realms that aren’t quite testable yet (although LQG is a bit closer to being able to be experimentally tested than string theory probably is).
Also, it’s not really clear that loop quantum gravity is any more falsifiable than string theory. For example, the discovery of supersymmetry or extra dimensions won’t disprove loop quantum gravity any more than the failure to detect them will disprove string theory.
The only discovery that I think LQG would have a hard time overcoming would be if black holes are observed and Hawking radiation proves to be false, which would be a problem for any quantum gravity theory, including string theory.
The biggest flaw in loop quantum gravity is that it has yet to successfully show that you can take a quantized space and extract a smooth space-time out of it. In fact, the entire method of adding time into the spin network seems somewhat contrived to some critics, although whether it’s any more contrived than the entirely background-dependent formulation of string theory remains to be seen.
The quantum theory of space-time in loop quantum gravity is really just a quantum theory of space. The spin network described by the theory cannot yet incorporate time.
Some, such as Lee Smolin, believe that time will prove to be a necessary and fundamental component of the theory, while Carlo Rovelli believes that the theory will ultimately show that time doesn’t really exist, but is just an emergent property without a real existence on its own.