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How Lorentz Boosts Reshape Relaxation Spectra
1University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
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In relativity, relaxation processes are often assumed to undergo time dilation under Lorentz boosts. We show that this intuition fails generically. Because of relativity of simultaneity, Lorentz boosts can split a single relaxation mode into a continuum of excitations, with a width set by the maximal signal propagation speed. Focusing on linearized relativistic (kinetic or rheological) theories with an Onsager-type symmetry, we derive rigorous bounds on relaxation spectra in arbitrary inertial frames, expressed solely in terms of rest-frame spectral data at zero wave number. As a consequence, nonhydrodynamic gaps, maximal relaxation rates, and the convergence radii of hydrodynamic modes obey nontrivial Lorentz-covariant constraints. These results provide a unified framework for understanding how relativity constrains relaxation dynamics in many-body systems.
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