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Rezeptions- und Wirkungsgeschichte

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Author
Jürgen Jost
Published in
Bernhard Riemann - Über die Hypothesen, welche der Geometrie zu Grunde liegen
Publisher
Springer Berlin Heidelberg

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Abstract

Riemanns Text war äußerst wirkmächtig, nicht nur in der Mathematik selbst, sondern auch in der Physik und der Philosophie. Zunächst reagierte der führende deutsche Physiker Hermann Helmholtz mit Überlegungen, wie die Geometrie des Raumes empirisch festgestellt werden könnte. Weil er von der freien Beweglichkeit starrer Maßstäbe ausging, schloss er, dass der physikalische Raum eine konstante Krümmung besitzen müsse. Die Überlegungen von Helmholtz waren ein wesentlicher Ausgangspunkt für die Theorie der Symmetriegruppen von Sophus Lie. Die Riemannsche Geometrie wurde die mathematische Grundlage der Allgemeinen Relativitätstheorie von Albert Einstein. Dieser brachte in seinen berühmten Feldgleichungen die Riccikrümmung des Raumes mit der Verteilung physikalischer Massen in Verbindung. Die Riemannsche Geometrie liefert auch die mathematische Sprache der Quantenfeldtheorie. Allerdings ist die mathematische Vereinigung von Gravitations- und Quantentheorie noch unbekannt.

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previous chapter Präsentation des Textes
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Title
Rezeptions- und Wirkungsgeschichte
Author
Jürgen Jost
Copyright Year
2025
Publisher
Springer Berlin Heidelberg
Book
Bernhard Riemann - Über die Hypothesen, welche der Geometrie zu Grunde liegen

Print ISBN: 978-3-662-70871-2

Electronic ISBN: 978-3-662-70872-9

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-662-70872-9_5

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