Chua, Eugene Y. S. and Callender, Craig (2025) The Toll of the Tolman Effect: On the Status of Classical Temperature in General Relativity. [Preprint]
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Text (Preprint of 14 July 2025. Please cite published version when available.)
2507.10529v1.pdf - Accepted Version Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (8MB) |
Abstract
The Tolman effect is well-known in relativistic cosmology but rarely discussed outside it. That is surprising because the effect -- that systems extended over a varying gravitational potential exhibit temperature gradients while in thermal equilibrium -- conflicts with ordinary classical thermodynamics. In this paper we try to better understand this effect from a foundational perspective. We make five claims. First, as Tolman knew, it was Einstein who first discovered the effect, and furthermore, Einstein's derivation helps us appreciate how robust it is. Second, the standard interpretation of the effect in terms of 'local temperature' leads to the breakdown of much of classical thermodynamics. Third, one can rescue thermodynamics by using Einstein's preferred interpretation in terms of the 'wahre Temperatur' -- what we'll call global temperature -- but it too has some costs. Fourth, the effect is perhaps best understood in terms of clocks as opposed to energy loss. Fifth, inspired by a proposal of Einstein's elsewhere, we sketch an interpretation of the effect in terms of a third novel temperature, which we call the 'wahre-local temperature'. On this view, temperature -- and thermodynamics -- is defined only in relation to local clocks. In sum, we view the fragmentation of temperature in thermodynamics as a natural and expected result of the fragmentation of time in general relativity.
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| Item Type: | Preprint | |||||||||
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| Additional Information: | Accepted for publication at The British Journal for the Philosophy of Science. Preprint of 14 July 2025. Please cite published version when available. | |||||||||
| Keywords: | thermodynamics, general relativity, consilience, Einstein, time, temperature | |||||||||
| Subjects: | General Issues > Natural Kinds Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics General Issues > Theory Change |
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| Depositing User: | Dr. Eugene Y. S. Chua | |||||||||
| Date Deposited: | 16 Jul 2025 14:06 | |||||||||
| Last Modified: | 16 Jul 2025 14:06 | |||||||||
| Item ID: | 25948 | |||||||||
| Subjects: | General Issues > Natural Kinds Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics General Issues > Theory Change |
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| Date: | July 2025 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/25948 |
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