Quantum gravity


• A relatively promising theory (and which, in some aspects, uses the same kind of concepts as those I defend here), is the one called “loop quantum gravity” [1]. This theory however involves (to my humble opinion) some “defects” of which it is not obvious they would be avoidable.

• This theory “persists” in considering that quantized space-time a priori exists ; it then adds to that some interactions (in the form equivalent to some Feynman's diagrams) by weighting some nodes of the graphs ; theses interactions influence space-time that contains them, but this one can exist without them.

I think that on the contrary must be considered a theory where space-time is only one of the properties following from interactions (Feynman's diagrams) and nothing else : without interactions there is no space-time.



• When the loop quantum gravity considers (as example) a photon that propagates in quantized space-time, it describes this one as a local modification of the graphs representative of space-time (what may be visualized, in a very simplified way, à l'aide the first of the above diagrams).

I think on the contrary that the graphs of space-time are much more tangled (and this in a fundamental way, that is not only due to the unavoidable simplification for the visualization) : what we consider as “neighbour” at the macroscopic level (and thus what is at “small distance” according to the space-time metric) is not necessarily “neighbour” at the “microscopic” level, and reciprocally.

Two points, some millions of light-years away according to the meaning of our macroscopic metric, but connected by a photon (or any massless particle), are at null distance in the meaning of elementary interactions. The space itself proceeds from a multitude of interactions a large number of which are between “very distant” points (rather according to the second of the above diagrams) and which “large distance” correlations (including some E.P.R. type effects) cause the phenomena such as inertia.

It does not look to me as indispensable to add whatever else in order to bring in an inertial effect... and thereby I am convinced that there is nothing to add : the only diagrams to be considered would be those of interactions that happen in space-time (Feynman's diagrams) and the gravitation would be only an effect of their multiple large distance correlations.

• Another approach, which falls into the same defects, is the one evoked under the name of “euclidean quantum gravity” [2] : in order to search for a limit structure describing space-time, one must avoid to start from preexisting space-time polyhedrons.

• The interpretation may be moreover complicated by some a priori connected to the usual concepts. Let us consider as example the motion of a particle, from a point A up to a point B, thus going in the neighbourhood of a zone with “high density of interaction” (in the following symbolic diagrams, the detail of the particle's interactions during the motion is not specified) [3].


If one considers a “local” reasoning, one may conclude that a motion which passes round the zone would be caused by an attraction : the motion starts aside (without any previous intent to reach B), then the attraction deviates it and causes it to finally reach B. If one considers a “global” reasoning, one may conclude in favour of a kind of repulsion : among the ways which comes globally from A to B, the more likely are those which don't cross the interaction zone and are in such a manner “rejected” (in the same way as the magnetic field lines are “rejected” by the supraconductors).

• Of course, in so far as it is not evident to find what topology to associate with a so tangled hank, one can try to represent it (by a kind of renormalization) by means of a “dual” theory, each graph of which represents locally the global effect of large distance correlations in the initial theory. It would thus be more or less to the loop quantum gravity that would probably look like such a dual theory. But in this case, if it is probable that this would allow a best “connection” with our macroscopic description, it would not be on the contrary representative of microscopic elementary diagrams.

It must be noticed elsewhere that, in despite of the analogy for “the absence of gravitation”, the point of vue considered here seems to me as devoid of direct relation with the kind of “dual” theory which has been propound with extrapolation to the “border” of extra dimensions [4] (but maybe that my incredulity is not independent of the doubts that cord theories inspire to me).

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References :

1. see as example :  “Des atomes d'espace et de temps”, L. Smolin, Pour la Science n° 316, february 2004.

2. see as example : “L'univers quantique auto-organisé”, J. Ambjorn, J. Jurkiewicz et R. Loll, Pour la Science n° 371, september 2008.

3. though the studied concepts are in a large part different, some researches about communications in networks will perhaps provide important ideas in this way ; see as example :  “Double clustering and graph navigability”, O. Sandberg, <http://fr.arxiv.org/abs/0709.0511>, september 2007.

4. see as example :  “La gravité est-elle illusion ?”, J. Maldacena, Pour la Science n° 339, january 2006.




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