New Constraints on Varying Alpha

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I briefly present some current theoretical motivations for time or space variations of the fundamental constants of nature and review current key observational results. I focus on the fine-structure constant, and particularly on measurements using quasars and the cosmic microwave background. I also compare various observational results to the simplest model-building expectations.
8 pages, review talk at the XXXIX Rencontres de Moriond (La Thuile, March 2004), to appear in the proceedings

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