I am a student just beginning a study of LQG and I would appreciate some comment on a few questions and intuitions that I have as I enter the subject.(adsbygoogle = window.adsbygoogle || []).push({});

My background is more in mathematics than in physics, and my perspective on space has been guided more by topology than by the concerns of HEP, and perhaps this bias affects how I view the discussions here concerning string theory and LQG. But here goes...

My first issue deals with time. My tendency is to view the universe as a single space, which appears 4-dimensional, and I think of time primarily as an aspect of our perspective on the manifold. That is, I feel very uncomfortable accepting probability as an intrinsic aspect of the space and prefer to think of it in terms of information. GR seems compatible with this perspective. Does LQG invariably treat space as a 3-dimensional set of nodes whose connections vary with time in lock step? Is the choice of a 3-D slice an arbitrary convention or do we have to bring back the idea that the universe actually has well defined instants?

I come to this discussion with the idea that quantizing space by discrete nodes is one thing, and saying that different possible states all exist at the 'same time' is another. Am I wrong to seperate the issues?

Also, I am somewhat familiar with the process of triangulation of a topological space to represent it with a polyhedron. In this process every node in the sapce will have the same number of vertices stemming from it, and the number is fininte for finite dimensional polyhedra. Is this is in any way related to LQG? Do the nodes in LQG have a given number of vertices, or perhaps every node is connected to every other node?

Finally, one of the things I find fascinating about GR is the possbility of a gravitational geon, that is, a particle that is nothing but curved space attracting itself. Does LQG limit us to saying that particles are actors playing out in the stage of space, or does it allow for the concept that particles and space are actually two manifestations of the same stuff?

mike

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# Time in LQG

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