Giovanelli, Marco (2024) 'The Tensor Calculus Knows Physics Better Than the Physicist': Bachelard on the Role of 'Covariant Differentiation' in Relativity Theory.
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Abstract
Gaston Bachelard's 1929 La valeur inductive de la relativité is arguably his most overlooked work. This paper argues that, nevertheless, it represents a noteworthy contribution to the early history of the philosophical interpretation of general relativity. In particular, Bachelard deserves recognition for identifying the central importance of the comma-goes-to-semicolon rule, referenced in modern textbooks: The principle of general relativity demands that fundamental laws of nature be expressed by tensor equations, substituting ordinary derivatives (commas) with covariant derivatives (semicolons). The equivalence principle might be taken as the claim that this formal change in non-gravitational laws directly leads to the discovery of gravitational laws. The paper concludes that, among early professional philosophers working on relativity, Bachelard uniquely grasped the "inductive value" of this heuristic device: "tensor calculus knows physics better than the physicist does", as Langevin once put it.
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| Item Type: | Published Article or Volume | ||||||
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| Keywords: | Gaston Bachelard; General relativity; tensor calculus; Covariant derivative | ||||||
| Subjects: | Specific Sciences > Mathematics > History of Philosophy General Issues > History of Philosophy of Science Specific Sciences > Physics > Relativity Theory |
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| Depositing User: | Dr. Marco Giovanelli | ||||||
| Date Deposited: | 18 Apr 2026 19:01 | ||||||
| Last Modified: | 18 Apr 2026 19:01 | ||||||
| Item ID: | 29242 | ||||||
| Official URL: | https://doi.org/10.1016/j.shpsa.2026.102134 | ||||||
| DOI or Unique Handle: | 10.1016/j.shpsa.2026.102134 | ||||||
| Subjects: | Specific Sciences > Mathematics > History of Philosophy General Issues > History of Philosophy of Science Specific Sciences > Physics > Relativity Theory |
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| Date: | 2024 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/29242 |
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'The Tensor Calculus Knows Physics Better Than the Physicist': Bachelard on the Role of 'Covariant Differentiation' in Relativity Theory. (deposited 17 Mar 2025 16:03)
- 'The Tensor Calculus Knows Physics Better Than the Physicist': Bachelard on the Role of 'Covariant Differentiation' in Relativity Theory. (deposited 18 Apr 2026 19:01) [Currently Displayed]
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