I am not an expert on either of these fields, so take what I say with a grain of salt.
I think neither: I mean, on one side, you have loop quantum gravity, a theory of quantum gravity, they are not concerned in unifying the forces, they just want to find a way to fit gravity in the whole standard model. The way they want to formulate LQG is based around Einstein’s formulation of gravity in GR, where gravity is not a force, but a property of spacetime itself. So if you want to quantize gravity, maintaining Einstein’s geometric formulation, well, space and time need to be discrete, in the same way, energy, momentum and matter is quantized in the classical quantum mechanics. Can you imagine, space and time itself as being discrete? Apparently there is a minimum interval of time, and a minimum distance at which, for anything below that, physics doesn’t make sense.
Now this carries important consequences. If we assume LQG to be correct, then:
- There needs to be a classical limit. That is, there needs a scale at which the new theory could be approach by our current description of physics. And that is one of the main problems for LQG right now, there is some difficulty into establishing a proper semiclassical limit that in the end would correspond to Einstein’s General Relativity.
- Black Hole Entropy, Hawking Radiation (with even the hypothesis of a Planck Star inside of a Blackhole, who could solve the information paradox) and even an entire field of Loop Quantum Cosmology are fields that have had active research.
- In LQG phenomenology, we would fit LQG in realistic models and try to see if we can obtain results in experiments to reject or reinforce the hypothesis. And honestly, quantum gravity effects would be terribly small, because the Planck Length (the discrete unit of spacetime) would be just too small to be properly measured. But by observations of astrophysical effects and gravitational waves detectors, it can be possible to observe LQG effects, that would be visible at such large scales.
As for string theory, they are a theory of quantum gravity, but they are also a theory of unification or everything (so that’s a plus). And in simplest way possible, it replaces the point-like particles that are used in physics to describe interactions with strings. And it describe both how these strings move through spacetime and how they interact with each other. And the fundamental string has made vibrational modes, just like the string of a guitar, and depending on the vibrational mode, we may perceive them as different particles from a distance, including gravitons. And there is also correspondence between string theory and the quantum field theory (i.e. Anti-de Sitter/Conformal Field Theory correspondence) so you could say that string theory gives a field theory description to gravity, opposite to the geometrical description, however I am not so sure about it, since essentially a lot of what motivated them to increase the number of dimensions in ST was a geometrical description not only for gravity, but for all other fundamental forces. Accepting things as being made of strings would not be so tough for the scientific if not for the limits required for such effects to be observable. Not only is the size of the string absurdly small, but the string itself is not 4-dimensional, as we assumed our universe to be. Depending on whether you are talking of superstrings or membranes, you have either 10 or 11 dimensions in which string theory is workable and makes mathematically accurate predictions.
Now string theory itself has some characteristics going for it:
- They also provided a theoretical description for black hole entropy, and it solves the black hole information paradox, to some extent. It also has applications in quantum chromodynamics and nuclear physics. And in condensed matter theory. And that not considering the incredible mathematical contributions that may be attributed to string theory.
- And also there is phenomenology, which is to try and fit the string theory into realistic models. This is very important, because it would later allow experimentations to either confirm or dismiss string theory. And due to mathematical and theoretical difficulties (we may have run out of math), and specially because the energies required are unachievable for the time being (we definitely ran out of tech), there is currently no way to experimentally verify the validity of ST.
- And also there are issues, like the monstruous number of solutions you have, 10^500. There aren’t even that many protons in the entire universe.
One of things ST may have in its favor is its well established, mathematically beautiful foundations. I mean, many people want it to be true just because of how mathematically precise it is, how everything seems to come out of it so naturally. And also the advantage that it gives the unification that physicists daydream constantly about. And spacetime, keeps being as smooth as we always knew it. But it gives 10 extra dimensions and a gigantic number of possible solutions (and possible universes, with said solutions), making it pretty much untestable for the time being.
As for LQG, well, it has the perks of coming straight from quantum theory and general relativity, so we can still consider spacetime as being 4-dimensional, I am not sure if that has changed. And it comes a unique perspective of a quantization of spacetime itself. And it does tackle only quantum gravity, but changing the nature of spacetime will definitely cause a shake-up to the cores of modern physics. On the same way that Quantum Theory and Special Relativity shook it about a century ago. Physicists would be just as excited with how physics could change if that were to be true. But it does have some flaws. For one, it doesn’t make any experimental predictions that we can’t explain by the Standard Model or General Relativity. However with the technology we currently have, we can observe such phenomenons through astrophysical observations and gravitational wave detections. So a sufficiently large dataset could be used, and LQG has an advantage over ST in this.. And well, there is no semiclassical limit to a continuous description of spacetime (GR).
However recently, as efforts to String Theory have dwindling, there seems to be a renewed interest in LQG. So yeah, there is a lot of room for mathematical development in LQG. I would love to know in the future, how developments in each would have gone, and I hope to personally work on it.
Quora to the rescue! Dude, this question is way beyond my pay grade.
Thanks for sharing.
