Can Loop Gravity and String Theory be Compared Fairly?

[marcus]

How do you balance the Loop and String programs?

They have each advanced unevenly in different respects, so trying for a fair objective comparision involves weighing "bundles" of different advantages and drawbacks, taking account, as well, of rates of progress on various fronts.

I should say that in my view what we traditionally require of a physics theory is that it be compact well-defined unambiguously predictive and testable.

So I have never called LQG a theory until 2010. And I do not think of String as a theory.
I agree with David Gross that "We do not know what string theory is." And since a theory is a human artifact, if we do not know what it is then it does not exist.

Until last year I always referred to LQG as an "approach". And I apply that same rule evenhandedly to String.

In comparing the Loop and String programs, the salient change we need to take account of is that Loop now has a preeminent compact testable formulation. It has become an actual physics theory.

The most adequate presentation and definition is in these two draft papers:
1939 October 2010 which is how I try to remember http://arxiv.org/abs/1010.1939
3660 February 2011 which is how I try to remember http://arxiv.org/abs/1102.3660

If you want to make pronouncements about Loop you need to give those two papers a thorough reading. One is titled "A Simple Model" and the other is called "Lectures on Loop Gravity".

That's where I'm coming from. On that basis I will try to balance the different bundles of advantage and drawback.

What about you? How do you see the comparison between the two research programs...or the two general approaches, Loop and String? Different people may have different ways to sort the matter out.

 

[marcus]

Over the years I have usually tried to avoid making comparisons between the two programs, largely because it seems to me that string-minded folks are sensitive about this and tend to get irritated. But I'm making an exception here in part because we got started on a comparison discussion in another thread:
https://www.physicsforums.com/showthread.php?t=471770

That got me wondering, can we get anything constructive out of this kind of discussion? Are there issues that actually need clarification---that it will benefit us to clarify?

And in fact that other thread showed me a place where I think clarification will be helpful.
It is about the various indications that GR is recovered.

It is not correct to say that the various perturbative string formulations recover GR, but there are strong indications. Because on certain fixed (flat or curved) geometries one gets a spin-2 particle.

Likewise in the LQG case there are substantial indications, some 6 of them are listed starting on page 5 of "A Simple Model", but as yet no rigorous proof that the LQG theory recovers GR as a background independent nonperturbative theory of dynamical geometry---in other words that it recovers full GR.

In neither case does one as yet fully recover GR, but in both cases there are indications.
So I encourage you to WEIGH them as best you can. Read the 1939 October paper's section V "Relation with GR" and try to judge how persuasive the evidence is. Also you could sample the 3660 February paper's section IV "Derivations," that begins on page 11.