Manchak, JB and Barrett, Thomas William (2026) Classical Heraclitus Spacetimes and the Equivalence of Local and Global Structure. [Preprint]
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Abstract
In any spacetime theory, a model is Heraclitus if no distinct points share the same local structure. Heraclitus models are known to exist in general relativity. Here, we present three examples of Heraclitus models within the classical spacetime context: (i) a geometrized classical spacetime (with curved derivative operator), (ii) a classical cosmological model whose underlying spacetime is Galilean (with flat derivative operator), and (iii) a classical cosmological model whose underlying spacetime is Leibnizian (with no derivative operator). The third example is of special interest since it shows a sense in which non-rigid Leibnizian spacetime can be "rigidified" by adding matter. This means Leibnizian spacetime+matter can be more deterministic than Leibnizian spacetime itself. We close with a general theorem which holds in any spacetime theory: Heraclitus models have the same local structure if and only if they have the same global structure.
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| Item Type: | Preprint | |||||||||
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| Keywords: | Spacetime, Heraclitus, Leibniz, Determinism | |||||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Cosmology General Issues > Determinism/Indeterminism Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | JB Manchak | |||||||||
| Date Deposited: | 28 Apr 2026 22:17 | |||||||||
| Last Modified: | 28 Apr 2026 22:17 | |||||||||
| Item ID: | 29388 | |||||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Cosmology General Issues > Determinism/Indeterminism Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 2026 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/29388 |
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