Is space discrete?

[fredrik]

I looked at Loll's desktop gravity a little closer and it strikes me that the key seems to be how to properly interpret and use the path integral, how to make the partitions etc.

 

Loll's seems to me to admit that while she doesn't do any fool proof reasoning, the main point is that they can at least make a REAL non-perturbative calculation. And indeed the result of the dimensionaly reduction from 4 to 2 is interesting. Dynamical dimensionality is I think right on target.

 

I don't know if this is explained elsewhere but regardless of wether it works or not, the methods to compute the pathintegrals comes out at somewhat ambigous also from the physical point of view.

 

I want to see more progress in refining the nice ideas behind the path integral but I've got a feeling that the formalism is still not finished.

 

Loll doesn't specify the relation to the observer in the paper. This makes me feel something is missing, or Loll is taking the hypotetical view of an omnipresent obeserver with infinite storage capacity and processing power.

 

Since it seems like mathematical strucutre and the physical structure are generally different things, the question is if Loll in this simulation are observer the properties of the possibly redundant mathematical structure, or if he is making hypotethical observations of the physical structure?

 

Consider a real observer, trained in the now possibly 2D planck domain, how and why would he induce the crazy idea of two extra dimensions? It is easier to picture dimensional reduction, but don't we also need to explain real dimensional formation?

 

Martin, are you aware what of this that has been done in the non-string world in the context of dynamical dimensionality?

 

I'd expect something like phase changes and excessive information capacity condenses and collapses dimensions in order to maximize information content / storage capacity. Similarly uncertainty and crazy dynamics should select and grow new dimensions. The obvious challange how to do that in a no-cheating way without throwing out unitarity.

 

/Fredrik

[Yuri Danoyan]

In the Book P.Fraenkel, Yehoshua Bar-Hillel, FOUNDATIONS OF SET THEORY, North-Holland, 1958 you can read following :

"The bridging of the chasm between the domains of the discrete and the continuous,or between arithmetic and geometry, is one of the most important - may, the most important - problem of the foundations of mathematics....Of course, the character of reasoning has changed, but,as always, the difficulties are due to the chasm between the discrete and the continuous - that permanent stumbling block which also plays an extremly important role in mathematics, philosophy,and even physics."

 

This is present day problem or not to comparision of 1958 ?