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Consistency between strong/M-theory and LQG

  1. Nov 27, 2007 #1
    Consistency between string/M-theory and LQG

    Is there a reason that LQG and other QG theories cannot be consistent with string/M-theories? My naive understanding is that the former theories approach the problems of QG and unification from the perspective of quantising GR, while the latter start from QFT. If both are rigorously defined purely from well-tested aspects of GR and QFT respectively then presumably they may both provide complementary descriptions of the same physics. On the other hand if either or both is built on unproven postulates then one, or both of them may be incorrect. I'd be interested to hear the views of some QG and string theory experts....
    Last edited: Nov 27, 2007
  2. jcsd
  3. Nov 27, 2007 #2


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    GR and QFT don't mix.

    People have different ways of explaining the incompatibility (and of implicitly assigning the blame) You may get several different views on this---it might be an interesting discussion.

    I don't claim to speak with authority, dante, but maybe I can say a few things to lay a groundwork.

    You are perfectly right that most non-string QG approaches start off by taking the basic lessons of GR seriously, that is their point of departure.
    And string thinkers' point of departure is more particle physics and QFT. So the incompatibility is there right at the start.

    Different people, will say this differently and disagree passionately about what seems almost to be mere language issues, even insisting on basically different meanings for certain words. I want to start the ball rolling. the idea is to try to say what is so different between GR and QFT.

    GR is dynamical geometry. The gravitational field is an equivalence class of metrics. For simplicity let's forget that we identify equivalent metrics and just say the gravitational field is the metric, which describes the geometry.
    Points in spacetime have no physical existence, the fundamental entity is the field. This is admittedly hard to grasp but that is how it is, and GR works.

    GR starts with a shapeless manifold---a continuum without geometry---and it arrives at various spacetime shapes as solutions of the main GR equation. One geometry is Minkowski space. This is the metric which you get by assuming no matter exists. Minkowski geometry is the flat, matterless, solution of GR. This is the geometry assumed in special relativity.

    I guess if someone asks what is special about special relativity, you could say that it is General Relativity specialized to the case where there is no matter in the universe (and zero cosmological constant) so you get only the flat metric as a solution.


    Traditionally, QFT is based on some static choice of geometry---typically Minkowski space. For the most part this is an excellent approximation because space is, indeed, approximately empty. QFT is called "relativistic" but it is so only in the special relativity sense of being constructed with special rel (Poincaré) symmetry on flat (Minkowski) space.

    Of course this doesnt appeal to relativists (the GR people) because they like to build theories with no prior choice of fixed geometry. They want geometry to be dynamic.

    QFT methodology is traditionally perturbative, which in the case of gravity would mean that you start with a flat geometry and perturb it slightly, with a little tickle, or ripple, or dimple. It is an analytical tool. Perturbative analysis works excellently with all the standard particles and forces except gravity.

    The idea of perturbative analysis is successive approximation. As long as you start with a known solution and study a small ripple in it, then the approximations get better and better. You can improve them in a series, term by term. I think it goes back to the 18th century, or perhaps to Archimedes.

    But it doesnt work with Einstein gravity. the successive approximations don't get better. It seems you can't study GR as little ripples on flat Minkowski space. It is a fundamentally non-perturbative theory.

    Particle theorists normally react to this by saying that GR must be wrong.
    It must be possible to replace GR by some more fundamental theory. As it stands, they tend to regard GR as merely an effective theory----one that applies in certain limited contexts and gives a useful approximation where it applies.

    I suppose the basic division is in how you imagine the replacement. Relativists think in terms of a geometric theory in which you don't make a prior choice of static background geometry at the outset. For them, the goal is more like a quantized GR----a quantum dynamics from which spacetime emerges. And lately they have been trying to see how space, time, and MATTER as well can emerge from some fundamental microscopic description. How matter could arise as a facet of geometry. So relativists probably visualize a new theory resembling General Relativity in some basic ways, only better.

    Particle theorists probably visualize a new theory looking more like the QFT they are familiar with---a fixed Minkowski stage with particles dancing on it.

    Anyway, dante, people describe the contrast in various ways and I've sketched one perspective on it. I'm saying that the root difference actually goes back to the two historical sources GR and QFT.
    Last edited: Nov 27, 2007
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