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- W4384264791 abstract "We show that linear superpositions of plane waves involving a single-valued, covariantly stable dispersion relation $omega(k)$ always propagate outside the lightcone, unless $omega(k) =a+b k$. This implies that there is no notion of causality for individual dispersion relations, since no mathematical condition on the function $omega(k)$ (such as the front velocity or the asymptotic group velocity conditions) can serve as a sufficient condition for subluminal propagation in dispersive media. Instead, causality can only emerge from a careful cancellation that occurs when one superimposes all the excitation branches of a physical model. This is shown to happen automatically in local theories of matter that are covariantly stable." @default.
- W4384264791 created "2023-07-14" @default.
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- W4384264791 date "2023-07-12" @default.
- W4384264791 modified "2023-10-18" @default.
- W4384264791 title "Dispersion relations alone cannot guarantee causality" @default.
- W4384264791 doi "https://doi.org/10.48550/arxiv.2307.05987" @default.
- W4384264791 hasPublicationYear "2023" @default.
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