Curiel, Erik (2014) Measure, Topology and Probabilistic Reasoning in Cosmology. [Preprint]
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Abstract
I explain the difficulty of making various concepts of and relating
to probability precise, rigorous and physically significant when
attempting to apply them in reasoning about objects
(e.g., spacetimes) living in infinitedimensional
spaces, working through many examples from cosmology. I focus on
the relation of topological to measuretheoretic notions of and
relating to probability, how they diverge in unpleasant ways in the
infinitedimensional case, and are even difficult to work with on
their own. Even in cases where an appropriate family of spacetimes
is finitedimensional, and so admits a measure of the relevant sort,
however, it is always the case that the family is not a compact
topological space, and so does not admit a physically significant,
well behaved probability measure. Problems of a different but still
deeply troubling sort plague arguments about likelihood in that
context, which I also discuss. I conclude that most standard forms
of argument used in cosmology to estimate the likelihood of the
occurrence of various properties or behaviors of spacetimes have
serious mathematical, physical and conceptual problems.
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Item Type:  Preprint  

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Keywords:  cosmology probability infinitedimensional spaces measure theory topology anthropic arguments typicality  
Subjects:  Specific Sciences > Physics > Cosmology Specific Sciences > Mathematics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Relativity Theory 

Depositing User:  Dr. Erik Curiel  
Date Deposited:  19 Oct 2014 15:26  
Last Modified:  16 Sep 2015 13:04  
Item ID:  11071  
Subjects:  Specific Sciences > Physics > Cosmology Specific Sciences > Mathematics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Relativity Theory 

Date:  2014  
URI:  http://philsciarchive.pitt.edu/id/eprint/11071 
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