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Physics > History and Philosophy of Physics
arXiv:2408.02790 (physics)
[Submitted on 5 Aug 2024]
Einstein Against Singularities: Analysis versus Geometry
John D. Norton
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Einstein identified singularities in spacetimes, such as at the Schwarzschild radius, where later relativists only find a coordinate system assigning multiple values to a single spacetime event. These differing judgments derive from differences in mathematical methods. Later relativists employ geometrical structures to correct anomalies in the coordinate systems used in analytic expressions. Einstein took the analytic expressions to be primary and the geometrical structures as mere heuristics that could be overruled if physical assumptions required it. Einstein's non-geometric methods had a firm base in the history of mathematical methods. They continued the non-geometric orientation of Christoffel, Ricci and LeviCivita. Einstein's insistence that singularities must be eliminated marked a departure from earlier tolerance of singularities. It was founded upon his longterm project of eliminating arbitrariness from fundamental physical theories. However, Einstein was willing to theorize with singularities only temporarily if they were the least arbitrary approach then available.
Subjects:	History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc)
Cite as:	arXiv:2408.02790 [physics.hist-ph]
 	(or arXiv:2408.02790v1 [physics.hist-ph] for this version)
 	
https://doi.org/10.48550/arXiv.2408.02790
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Journal reference:	Philosophy of Physics 2(1) (2024) 13:1-73
Related DOI:	
https://doi.org/10.31389/pop.91
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Submission history
From: John D. Norton [view email]
[v1] Mon, 5 Aug 2024 19:13:41 UTC (4,871 KB)

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