Loop Quantum Gravity seems to be the leading alternative to String theory/M theory. Both build upon the smallest of metrics…the Planck Scale.
M/Strings apply Planck Scale to the particles of matter and energy, where Quantum Loop Gravity applies Planck Scale to Spacetime.
The Theory of General Relativity posits a four dimensional manifold of space and time, distorted by mass, to produce Gravity.
Applying the rules of 4d GR to five dimensions produces gravity AND electromagnetism, as per Kaluza Klein theory.
Adding dimensions 6 and 7 gives rise to the Weak Nuclear Force, and going up to 11 dimensions gives the Strong Nuclear Force.
This is Supergravity…precursor to String/M Theory.
Can you “add dimensions” to Quantum Loop Gravity and end up getting electromagnetism and nuclear forces?
Not so far as anyone’s figured out. Loop quantum gravity is a theory only of gravity, not a unification with anything else. Which may be a feature, not a bug: There’s no inherent reason why everything must be unifiable, and maybe it isn’t.
Well, yes and no. Kaluza Klein can give you something that behaves classically (i.e., non-quantumly) like electromagnetism, but you can’t reproduce QED with it. Which, given that QED is the most precisely tested theory in the history of science, is a nonnegligible drawback.
Although there is no inherent reason that all physical mechanisms must be part of a unifed system of rules, it would seem awkward and strange if they weren’t. Ever since Michael Faraday discoverd that electricity and magnetism were two expressions of the same force, we’ve found symmetry in physical forces and mechanisms wherever we’ve looked. In general relativity, gravity is an emergent property of the curvature of spacetime, and it seems like underneath the field theories for the other forces should be an analagous plenum controlling the expression of those forces.
That’s putting it mildly. Any theory that cannot produce the same results as QED can be assumed to be incomplete if not completely wrong.
Well, I guess the idea would be to take the classical Kaluza-Klein theory, and apply loop quantization methods to hopefully get a quantum theory of gravity and electromagnetism, and perhaps even the other forces.
The problem with this is that the traditional loop quantization really only works in four spacetime dimensions, for technical reasons I don’t understand well enough to try and explain. There has been some work trying to find a different path towards quantizing higher-dimensional gravity theories, most notably supergravity, but I’m not aware that much has come from this. (Here is the first in a series of papers by Thomas Thiemann et al. attempting to develop this formalism.)
Supergravity isn’t necessarily a Kaluza-Klein theory. It’s a gauge theory in which the supersymmetry (which roughly exchanges fermions for bosons and vice versa) is gauged. Supersymmetry contains the Poincaré symmetry, which is essentially the symmetry of special relativity—symmetry under translations, rotations, and Lorentz boosts. Gauging this symmetry—letting it depend on the spacetime point—yields a theory of gravity of which general relativity is a special case.
You can also compactify a higher-dimensional supergravity theory in order to reduce the effective dimension, and this is indeed then a type of Kaluza-Klein theory, but sugra in itself doesn’t necessarily imply compactification.
Also, while sugra is in some historical sense a precursor to string theory, the relationship between string theories and supergravity is more complicated: for instance, 11D-sugra contains two dimensional membranes, and if you compactify it on a circle, the membranes may ‘wrap around’ the compact dimension, yielding a stringy degree of freedom, which in fact behaves like strings in type IIA string theory. So in this sense, although one might think of supergravity as a kind of low-energy limit of string (or M) theory, one also gets string theory out as a particular kind of limit of supergravity.