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I recently came across Karch and Randall's 2005 paper ``Relaxing to three dimensions''

http://arxiv.org/abs/hep-th/0506053 that uses brane theory to propose an explanation for why we see 3+1 dimensions, assuming we begin with the 10 of string theory. From the abstract:

``We show that under conventional (but higher-dimensional) FRW evolution, a universe filled with equal NUMBERS of branes and antibranes will naturally come to be dominated by 3-branes and 7-branes.'' (caps mine)

The basic idea is the relaxation principle, which states:

``that the branes with the biggest filling fraction in the end-point of the universe's cosmological evolution are the most likely branes to be relevant to the state in which we live''

My question is this: what is the definition of ``filling fraction'', and what does ``most likely'' mean? It seems to me that she is saying that 3-branes are simply more numerous than other branes, and defining the likelihood of p-branes as being proportional to the number of p-branes (well, I suppose measure might be more appropriate than number). This definition of `likeliness' of branes makes no reference to, say, the wavefunction of a brane, so she is using a classical (not quantum) concept of probability.

OTOH, I might be completely missing something. Comments?

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# Lisa Randall's relaxation principle

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