The Unexpected Resurgence of Weyl Geometry in late 20th-Century Physics

  • Erhard ScholzEmail author
Part of the Einstein Studies book series (EINSTEIN, volume 14)


Weyl’s original scale geometry of 1918 (“purely infinitesimal geometry”) was withdrawn by its author from physical theorizing in the early 1920s. It made a surprising comeback, however, in the last third of the 20th century in several different contexts: scalar-tensor theories of gravity, foundations of space-time theories, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open window for research on the foundations of physics even after the turn into the new millenium.



This paper owes its existence to David Rowe’s initiative in several respects. He encouraged me to present heterodox ideas on Weyl-geometric methods in cosmology at the conference and invited me to rethink the case after a cool reception of the talk by the other participants. That gave me the chance to place my views in the wider range of recent attempts to use Weyl-geometric methods in physics. After an interruption of several years, an earlier first draft of this paper (Scholz 2011b) had be to be rewritten completely for the final version of this book. The new version overlaps nicely with the wider ambit of the investigations of the interdisciplinary group Epistemology of the LHC with center at Wuppertal and supported generously by the DFG/FWF. This group offers the chance for a close communication between historians and philosophers of science and collegues from the elementary particle community. H. Cheng, F. Hehl, J. Miritzis, C. Romero, D. Rowe, A. Trautman, S. Walter gave helpful hints for the final version of the paper.


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Authors and Affiliations

  1. 1.University of WuppertalDepartment C, Mathematics and Natural Sciences, and Interdisciplinary Center for Science and Technology StudiesWuppertalGermany

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