Abstract
If all the fundamental constants x of physics were expressed in one set of units (e.g., mks) and then used as pure numbers in one overall histogram, what shape would that histogram have? Based on some invariances that the law should reasonably obey, we show that it should have either an x−1 or an x−2 dependence. Empirical evidence consisting of the presently known constants is consistent with an x−1 law. This is independent of the system of units chosen for the constants. The existence of the law suggests that the fundamental constants may have been independently and randomly chosen, at creation, from it, and hence that at the next “big bang” randomly a different set will be produced. Also, because of the law, the number 1.0 has an interesting cosmological property: it is the theoretical median of all the fundamental constants. Finally, as a practical matter, the law predicts that current methods of evaluating the fundamental constants are biased toward overly large numbers. A correction term is given for each of three kinds of noise.
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Frieden, B.R. A probability law for the fundamental constants. Found Phys 16, 883–903 (1986). https://doi.org/10.1007/BF00765336
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DOI: https://doi.org/10.1007/BF00765336