On the Ostrogradski Instability; or, Why Physics Really Uses Second Derivatives

British Journal for the Philosophy of Science 73 (1):23-46 (2022)
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Abstract

Candidates for fundamental physical laws rarely, if ever, employ higher than second time derivatives. Easwaran sketches an enticing story that purports to explain away this puzzling fact and thereby provides indirect evidence for a particular set of metaphysical theses used in the explanation. I object to both the scope and coherence of Easwaran's account, before going on to defend an alternative, more metaphysically deflationary explanation: in interacting Lagrangian field theories, it is either impossible or very hard to incorporate higher than second time derivatives without rendering the vacuum state unstable. The so-called Ostrogradski instability represents a powerful constraint on the construction of new field theories and supplies a novel, largely overlooked example of non-causal explanation in physics.

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Noel Swanson
University of Delaware

References found in this work

The metaphysics within physics.Tim Maudlin - 2007 - New York: Oxford University Press.
Causality and properties.Sydney Shoemaker - 1980 - In Peter van Inwagen (ed.), Time and Cause. D. Reidel. pp. 109-35.
Principles of Mathematics.Bertrand Russell - 1903 - New York,: Routledge.

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