In what way is M-Theory different from Loop Quantum Gravity?

[nuclearhead]

I have been reading about M-Theory and LQG, and from what I read they are actually very similar.

It seems that just a a string-world sheet is the same as a sum of an infinite number of Feynman diagrams, a membrane would be the sum of an infinite number of graphs or networks. Or as Susskind suggested, 0-branes connected by strings. Which if you draw it looks a lot like a network of points and lines.

In M-Theory there are not separate membranes (since any two can be connected by an infinitely thing tube of zero energy) just one big one. And presumably the lowest energy state where the membrane has lowest surface area it would simply collapse to a network of thin tubes like a network. The only thing that would differentiate this infinitely thin tube from nothing at all would be the charge or spin it carried.

Some people suggest that we live 'on' that membrane. So that the Universe 'is' this membrane.

On the other hand LQG suggests that space-time can be described by spin networks. That the Universe 'is' this network.

So two theories both described in terms of an infinite sum of networks. Albeit in string theory the network might be more "stringy" and in 10 dimensions and have supersymmetry.

I don't know how particles arise in LQG, but equally I'm not entirely sure how strings arise in M-Theory, presumably as charged loops in the membrane which preserve charge and spin.

So really when everyone says these are completely different theories I am confused because they seem remarkably similar. What do you think?

 

[ohwilleke]

I won't presume to identify all of the differences, but one of the most important ones is the number of dimensions of space-time. In M-theory, there are 10 or 11 dimensions of space-time, a number that is assumed a priori as an axiom of M-theory (to grossly oversimplify, all the good stuff is confined to a 4 dimensional space-time brane and the other 7 dimensions that dilute gravity into a much weaker force than the other three fundamental Standard Model forces which unify in string theory at higher dimensions). These dimensions are infinitely smooth and continuous, and space-time is perfectly local. Non-local connections would have to entail highly warped topologies of the relevant branes (i.e. macroscopic wormholes associated with extremely massive phenomena like black holes and the Big Bang singularity).

In Loop Quantum Gravity, and kindred theories, an a priori axiomatic assumption is made concerning how many other nodes a particular node in space-time can be linked to, and our four dimensional space-time that is approximately smooth and continuous at all scales much greater than the Planck length emerges naturally from this relationship. But, at the Planck scale, space-time is not infinitely smooth and continuous, the number of dimensions of space-time is defined in a non-obvious way that can be ill defined or take values impossible in M-theory, and space-time is not perfectly local, just approximately local. For example, in LQG, a particular point on Earth could be directly connected to a point in Alpha Centuri, but because the point is tiny and all other points nearby would connect only to Earth, this connection could not be used as a wormhole for macroscopic objects.

Another huge difference is that M-theory is, in concept, at least, a theory of everything that explains all of the fundamental forces and particles, including but not limited to a theory of quantum gravity. In contrast, Loop Quantum Gravity is a quantum alternative to general relativity, but does not purport to describe the other three fundamental forces or the fundamental particles of the Standard Model, by itself. Cutting edge work in Loop Quantum Gravity proposes ways for the Standard Model particles and forces to operate within a Loop Quantum Gravity space-time, but does not itself supply those parts of a theory of everything.

So far as I know, there is no definitive resolution of the "is" or "of" debate to which you allude (i.e. are fundamental particles and/or strings mere excitations of the background or are the separate entities that live in the background) in either M-theory or LQG, although the notion of fundamental particles as excitations of space-time are in my opinion more natural in LQG than in M-theory.