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<title>[2408.02790] Einstein Against Singularities: Analysis versus Geometry</title>
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<meta property=og:title content="Einstein Against Singularities: Analysis versus Geometry">
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<meta property=og:description content="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.">
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<meta name=citation_title content="Einstein Against Singularities: Analysis versus Geometry"><meta name=citation_author content="Norton, John D."><meta name=citation_doi content=10.31389/pop.91><meta name=citation_date content=2024/08/05><meta name=citation_online_date content=2024/08/05><meta name=citation_pdf_url content=http://arxiv.org/pdf/2408.02790><meta name=citation_arxiv_id content=2408.02790><meta name=citation_abstract content="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.">
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<h1>Physics &gt; History and Philosophy of Physics</h1>
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<strong>arXiv:2408.02790</strong> (physics)
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[Submitted on 5 Aug 2024]</div>
<h1 class="title mathjax"><span class="descriptor sf-hidden">Title:</span>Einstein Against Singularities: Analysis versus Geometry</h1>
<div class=authors><span class="descriptor sf-hidden">Authors:</span><a href="https://arxiv.org/search/physics?searchtype=author&amp;query=Norton,+J+D">John D. Norton</a></div> <div id=download-button-info class=sf-hidden hidden>View a PDF of the paper titled Einstein Against Singularities: Analysis versus Geometry, by John D. Norton</div>
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<span class="descriptor sf-hidden">Abstract:</span>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.
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<span class=primary-subject>History and Philosophy of Physics (physics.hist-ph)</span>; General Relativity and Quantum Cosmology (gr-qc)</td>
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<td class="tablecell arxivid"><span class=arxivid><a href=https://arxiv.org/abs/2408.02790>arXiv:2408.02790</a> [physics.hist-ph]</span></td>
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<td class="tablecell arxivdoi"> <a href=https://doi.org/10.48550/arXiv.2408.02790 id=arxiv-doi-link>https://doi.org/10.48550/arXiv.2408.02790</a><div class=button-and-tooltip>
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<td class="tablecell label">Journal&nbsp;reference:</td>
<td class="tablecell jref">Philosophy of Physics 2(1) (2024) 13:1-73</td>
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<td class="tablecell doi"><a href=https://doi.org/10.31389/pop.91 data-doi=10.31389/pop.91 class="link-https link-external" rel="external noopener nofollow">https://doi.org/10.31389/pop.91</a>
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<h2>Submission history</h2> From: John D. Norton [<a href=http://arxiv.org/show-email/21c5dec5/2408.02790>view email</a>] <br> <strong>[v1]</strong>
Mon, 5 Aug 2024 19:13:41 UTC (4,871 KB)<br>
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