Borotschnig, Hermann (2026) From One Clock to Programmable Coordinates: A Material Layer for Coordinate Freedom in General Relativity. [Preprint]
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Abstract
In general relativity, any valid coordinate chart may describe a given spacetime region, yet material reference frames used to visualize this freedom - such as Einstein's "reference mollusk," a deformable reference body equipped with arbitrarily running clocks - can directly display only charts adapted to their built-in protocol. This contribution introduces an elementary enhancement that lifts that restriction: each observer in a seed congruence carries a programmable device that computes and displays four coordinate values as functions of the four seed coordinates. Several consequences follow. A single observer swarm can directly display charts not adapted to its underlying congruence, including light-cone coordinates with two null and two spacelike basis directions, Painlevé-Gullstrand coordinates inside the Schwarzschild horizon with four spacelike basis directions, and Kruskal-Szekeres coordinates with two null directions. Coordinate directions need not mirror observer motion: observers travel on timelike worldlines while the displayed coordinates may have null or spacelike basis directions. The same physical swarm can display multiple charts during deployment. Standard coordinates and special constructions can be programmed, including harmonic coordinates or coordinates built from curvature invariants. The metric is then reconstructed in the displayed coordinates by standard local-inertial measurements, keeping three layers manifestly distinct: the material reference apparatus, the coordinate labels it displays, and the metric subsequently reconstructed in those labels.
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| Item Type: | Preprint | ||||||
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| Keywords: | General relativity; Coordinate freedom; Reference frames; Observer congruence; Programmable coordinates; Material reference frames | ||||||
| Subjects: | General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Relativity Theory General Issues > Theory/Observation |
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| Depositing User: | Hermann Borotschnig | ||||||
| Date Deposited: | 03 May 2026 16:25 | ||||||
| Last Modified: | 03 May 2026 16:25 | ||||||
| Item ID: | 29450 | ||||||
| Subjects: | General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Relativity Theory General Issues > Theory/Observation |
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| Date: | 2 May 2026 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/29450 |
Available Versions of this Item
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From Mollusk to Swarms of Observers: A Fully General, Observer-Based Operational Framework for General Relativity. (deposited 18 Jul 2025 13:34)
- From One Clock to Programmable Coordinates: A Material Layer for Coordinate Freedom in General Relativity. (deposited 03 May 2026 16:25) [Currently Displayed]
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