Abstract
A theory that contains three fundamental constants from which one can build length, time, and mass (or force) etalons satisfies with that a necessary criterion of a “universal unified field theory.” In order to interpret such a theory physically, one has to translate it into the Galilei-Newtonian language. This leads to classical “pictures” whose compatibility is ensured by introducing appropriate measurement-theoretical principles which imply corresponding uncertainty relations. In this paper we compare different (mainly gravitational) theories from the point of view of the fundamental constants underlying each case, and of the respective uncertainty relations. Assuming Eddington's hypothesis of large cosmic numbers, it is argued in particular that in quantized general relativity one arrives at less stringent limitations on cosmology than in other conceivable approaches satisfying the principle of minimal coupling. These limitations, however, are in all cases strong enough to bar the way to quantum cosmology. Instead one is led to a Diophantean concept.
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von Borzeszkowski, H.H., Treder, H.J. Quantum cosmology and Eddington's large cosmic numbers. Found Phys 24, 1077–1088 (1994). https://doi.org/10.1007/BF02054649
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DOI: https://doi.org/10.1007/BF02054649