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Von Euklids Elementen zur zehnten Dimension: Geometrie und Topologie von Raum und Zeit

Von Euklids Elementen zur zehnten Dimension: Geometrie und Topologie von Raum und Zeit

          
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About the Book

Wenn man in der Nacht zum Sternenhimmel aufschaut, so blickt man in eine unendliche Weite. Ist unser Universum tatsächlich unendlich groß? Alles was wir aus unserer Erfahrung kennen ist endlich. Etwas, was eine unendliche Ausdehnung hat, können wir nicht begreifen. Aber auch die Vorstellung eines Weltraums mit endlichem Volumen führt zu Problemen: Das Universum müsste dann einen Rand haben. Wie könnte ein solcher Rand aber aussehen und was liegt hinter der Grenze? Ein weiteres Problem kommt hinzu: Unser Blick in den Himmel ist ein Blick in die Vergangenheit. Das Licht der Sterne hat Tausende von Jahren gebraucht, um uns zu erreichen. Wie sieht der Raum da draußen heute aus? Macht es überhaupt Sinn, von einem heutigen Ereignis auf einem fremden Stern zu sprechen? Vielleicht gibt es den Himmelskörper und den umgebenden Raum gar nicht mehr. Fragen dieser Art beschäftigen Philosophen, Physiker und Mathematiker seit Jahrtausenden. Und obwohl wir inzwischen eine Fülle von Informationen gesammelt haben, gibt es noch keine endgültigen Antworten. Das vorliegende Buch befasst sich mit der Natur von Raum und Raumzeit aus der Sicht eines Mathematikers. Es zeigt, dass die Mathematik Modelle sowohl von endlichen als auch unendlichen Räumen bereitstellt, ohne sich in Widersprüche zu verwickeln. Es beschreibt, dass man mit logischen Mitteln Rückschlüsse sowohl auf die globale Gestalt als auch auf lokale Eigenschaften des Universums ziehen kann, wenn man bestimmte Axiome als wahr annimmt. Das Buch folgt damit der Tradition von Euklid, welcher als erster solche Raum-Axiome in systematischer Weise präzisierte. Ausgehend von der euklidischen Geometrie wird ein Bogen gespannt bis zu den Mannigfaltigkeiten, welche vielen physikalischen Theorien als Basis dienen. Dabei lassen wir uns nicht von der Fragestellung nach der wahren Natur des Raumes leiten, sondern fragen uns: Welche Modelle des Universums sind aus logischer Sicht möglich? So werden wir uns in die Gedankengänge eines zwei


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Product Details
  • ISBN-13: 9783751900201
  • Publisher: Books on Demand
  • Publisher Imprint: Books on Demand
  • Height: 210 mm
  • No of Pages: 390
  • Spine Width: 20 mm
  • Weight: 467 gr
  • ISBN-10: 3751900209
  • Publisher Date: 10 Jun 2020
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Sub Title: Geometrie und Topologie von Raum und Zeit
  • Width: 148 mm


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