#### marcus

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What I suspect is a major paper by Ashtekar (and others) appeared in arXiv this month----on June 9.

Mathematical structure of loop quantum cosmology

Ashtekar, Bojowald, Lewandowski

arXiv:gr-qc/0304074

http://www.arxiv.org/abs/gr-qc/0304074

Here is the concluding paragraph:

"We conclude with a general observation. The way in which the big-bang singularity is resolved has potentially deep implications on questions about the origin of the universe. For instance, the question of whether the universe had a beginning at a finite time is now ‘transcended’. At first, the answer seems to be ‘no’ in the sense that the quantum evolution does not stop at the big bang. However, since space-time geometry ‘dissolves’ near the big-bang, there is no longer a notion of time, or of ‘before’ or ‘after’ in the familiar sense. Therefore, strictly, the question is no longer meaningful. The paradigm has changed and meaningful questions must now be phrased differently, without using notions tied to classical space- times. A similar shift of paradigm occurred already with the advent of general relativity. Before Einstein, philosophers argued that the universe could not have a finite beginning because, if it did, one could ask what there was before. However, this question pre-supposes that space-time is an eternal, passive arena and matter simply evolves in it. With general relativity, we learned that space and time are ‘born with matter’, whence the question of ‘what was there before’ is no longer meaningful. Loop quantum cosmology brings about a

further shift of paradigm, weeding out certain questions that seemed meaningful in classical general relativity and requiring that they be replaced by more refined questions, formulated in the context of quantum space-times."

Mathematical structure of loop quantum cosmology

Ashtekar, Bojowald, Lewandowski

arXiv:gr-qc/0304074

http://www.arxiv.org/abs/gr-qc/0304074

Here is the concluding paragraph:

"We conclude with a general observation. The way in which the big-bang singularity is resolved has potentially deep implications on questions about the origin of the universe. For instance, the question of whether the universe had a beginning at a finite time is now ‘transcended’. At first, the answer seems to be ‘no’ in the sense that the quantum evolution does not stop at the big bang. However, since space-time geometry ‘dissolves’ near the big-bang, there is no longer a notion of time, or of ‘before’ or ‘after’ in the familiar sense. Therefore, strictly, the question is no longer meaningful. The paradigm has changed and meaningful questions must now be phrased differently, without using notions tied to classical space- times. A similar shift of paradigm occurred already with the advent of general relativity. Before Einstein, philosophers argued that the universe could not have a finite beginning because, if it did, one could ask what there was before. However, this question pre-supposes that space-time is an eternal, passive arena and matter simply evolves in it. With general relativity, we learned that space and time are ‘born with matter’, whence the question of ‘what was there before’ is no longer meaningful. Loop quantum cosmology brings about a

further shift of paradigm, weeding out certain questions that seemed meaningful in classical general relativity and requiring that they be replaced by more refined questions, formulated in the context of quantum space-times."

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