pith. sign in

arxiv: 2605.21377 · v1 · pith:OZV4QCEInew · submitted 2026-05-20 · ✦ hep-th · hep-ph· math-ph· math.MP· nucl-th

Causal UV completions of relativistic hydrodynamics

Robbe Brants This is my paper

Pith reviewed 2026-05-21 03:17 UTC · model grok-4.3

classification ✦ hep-th hep-phmath-phmath.MPnucl-th
keywords relativistic hydrodynamicscausalityUV completionsnon-hydrodynamic modeseffective field theorydissipative systemslight cone
0
0 comments X

The pith

Any stand-alone relativistic hydrodynamic effective field theory is inherently acausal and requires transient UV modes to restore causality.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that relativistic hydrodynamics cannot function as a complete causal description on its own. Pure hydrodynamic models lead to signals that propagate outside the light cone in some regimes. Adding short-lived modes from higher energy scales fixes the causality problem while ensuring the equations reduce back to standard hydrodynamics after sufficient time. This reduction works because dissipative effects decay exponentially across most of the light cone. The authors then study how the extra non-hydrodynamic modes arise and what limits they must satisfy in consistent completions.

Core claim

Any stand-alone hydrodynamic EFT is inherently acausal and therefore requires the addition of transient UV modes in order to restore causality. This is made possible by the exponential decay of dissipative hydrodynamics in a majority of the lightcone, allowing the possibility of a causal description that still reduces to the hydrodynamic one at late timescales. The paper investigates the emergence and possible restrictions of the non-hydrodynamic modes in these causal UV completions.

What carries the argument

Transient UV modes, also called non-hydrodynamic modes, that are added to the hydrodynamic equations to enforce causal signal propagation while permitting reduction to hydrodynamics at late times.

If this is right

  • Pure hydrodynamic models must be supplemented with additional degrees of freedom to avoid acausal behavior.
  • The added modes decay exponentially and therefore become negligible at late times.
  • Causal UV completions place restrictions on the spectrum and couplings of the non-hydrodynamic modes.
  • The framework applies to any out-of-equilibrium system described by relativistic hydrodynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar causality requirements may apply to other effective theories in high-energy physics that truncate at low energies.
  • Numerical implementations of relativistic fluid dynamics could incorporate these modes to improve early-time accuracy.
  • The approach suggests a general pattern for completing effective descriptions when causality is at stake.

Load-bearing premise

Dissipative hydrodynamics decays exponentially in a majority of the lightcone, which permits a causal description that still reduces to hydrodynamics at late timescales.

What would settle it

An explicit construction of a causal hydrodynamic theory with no transient modes, or a concrete calculation showing superluminal propagation in a regime where hydrodynamics applies without UV corrections.

read the original abstract

Relativistic hydrodynamics successfully provides an effective field theory description for the low energy regime of many out-of-equilibrium systems. On the other hand, in this paper we proof that any stand-alone hydrodynamic EFT is inherently acausal and therefore requires the addition of transient UV modes in order to restore causality. This is made possible by the exponential decay of dissipative hydrodynamics in a majority of the lightcone, allowing the possibility of a causal description that still reduces to the hydrodynamic one at late timescales. We then investigate the emergence and possible restrictions of the non-hydrodynamic modes in these causal UV completions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims to prove that any stand-alone relativistic hydrodynamic EFT is inherently acausal, requiring the addition of transient UV modes to restore causality. This follows from the exponential decay of dissipative hydrodynamics in a majority of the lightcone, which permits causal completions that reduce to hydrodynamics at late times. The authors then analyze the emergence and restrictions of non-hydrodynamic modes in such UV completions.

Significance. If rigorously established, the result would clarify why hydrodynamic EFTs in relativistic systems cannot stand alone and must incorporate transient modes, with relevance to applications in heavy-ion physics and out-of-equilibrium QFT. The focus on non-hydrodynamic modes offers concrete guidance for constructing causal models. The paper's strength lies in framing the problem via lightcone properties rather than ad-hoc parameters, though verification of the decay assumption is needed for the claim to hold.

major comments (2)
  1. [Main derivation (following the abstract statement on exponential decay)] The assertion that dissipative hydrodynamics exhibits exponential decay in a majority of the lightcone (invoked to justify the late-time reduction and inherent acausality) is not derived for general constitutive relations, arbitrary transport coefficients, or nonlinear terms. This property is load-bearing for the central claim but appears assumed rather than proven from the hydrodynamic equations, leaving open counterexamples where the decay fails.
  2. [Core proof section on acausality] The proof of inherent acausality for any stand-alone EFT relies on lightcone properties and the decay argument, but without explicit steps showing how acausality emerges independently of specific choices (e.g., first-order parabolic equations), the generality remains unclear. This affects the conclusion that transient UV modes are always required.
minor comments (2)
  1. [Abstract] The abstract contains a grammatical error: 'we proof' should read 'we prove'.
  2. [Introduction and notation] Notation for lightcone coordinates and mode classifications should be defined consistently at first use to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. The comments help clarify the presentation of our results on the acausality of standalone hydrodynamic EFTs. We address each major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: The assertion that dissipative hydrodynamics exhibits exponential decay in a majority of the lightcone (invoked to justify the late-time reduction and inherent acausality) is not derived for general constitutive relations, arbitrary transport coefficients, or nonlinear terms. This property is load-bearing for the central claim but appears assumed rather than proven from the hydrodynamic equations, leaving open counterexamples where the decay fails.

    Authors: We appreciate the referee pointing this out. The exponential decay is derived in the manuscript for the linearized hydrodynamic equations by analyzing the poles of the retarded Green's function in the complex frequency plane, showing exponential suppression in most of the lightcone for dissipative systems with positive transport coefficients. We acknowledge that this is primarily for linear theory and general nonlinear terms are not fully treated. In the revised version, we will add an appendix with the explicit derivation steps for the linear case and discuss the conditions under which the decay holds, including why counterexamples are not expected in standard relativistic hydrodynamics. revision: partial

  2. Referee: The proof of inherent acausality for any stand-alone EFT relies on lightcone properties and the decay argument, but without explicit steps showing how acausality emerges independently of specific choices (e.g., first-order parabolic equations), the generality remains unclear. This affects the conclusion that transient UV modes are always required.

    Authors: The acausality of standalone hydrodynamics follows from the fact that the effective theory lacks the necessary high-frequency modes to enforce causality, leading to superluminal propagation as encoded in the hydrodynamic constitutive relations. This is shown using the lightcone structure: without transient modes, the response function has support outside the light cone. We will revise the core proof section to include a more detailed, step-by-step argument that demonstrates this for general hydrodynamic EFTs, independent of the specific form (parabolic or otherwise), by focusing on the absence of UV completions. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on stated lightcone decay property without self-referential reduction

full rationale

The paper states that it proves stand-alone hydrodynamic EFTs are acausal by invoking the exponential decay of dissipative modes in a majority of the lightcone, which permits causal UV completions that match hydrodynamics at late times. This framing presents the decay as an enabling physical property rather than a quantity defined in terms of the acausality result or obtained by fitting parameters to the target conclusion. No self-citation chains, uniqueness theorems imported from prior author work, or ansatze smuggled via citation are indicated as load-bearing for the central claim. The subsequent investigation of non-hydrodynamic modes builds on the stated reduction without equations that equate the output to the input by construction. The derivation therefore remains self-contained against the paper's own premises.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard domain assumptions about hydrodynamics as an EFT and introduces transient UV modes as a postulated completion without independent experimental evidence.

axioms (1)
  • domain assumption Relativistic hydrodynamics provides a successful effective field theory description for the low energy regime of out-of-equilibrium systems
    Directly stated in the opening sentence of the abstract as background.
invented entities (1)
  • transient UV modes no independent evidence
    purpose: Restore causality to otherwise acausal hydrodynamic EFTs while allowing reduction to hydrodynamics at late times
    Introduced in the abstract as the required addition to fix the acausality problem.

pith-pipeline@v0.9.0 · 5617 in / 1208 out tokens · 52098 ms · 2026-05-21T03:17:07.417752+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · 6 internal anchors

  1. [1]

    New theories of relativistic hydrodynamics in the LHC era

    W. Florkowski, M. P. Heller and M. Spalinski,New theories of relativistic hydrodynamics in the LHC era, Rept. Prog. Phys.81(2018), no. 4 046001 [arXiv:1707.02282]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  2. [2]

    Andersson and G

    N. Andersson and G. L. Comer,Relativistic fluid dynamics: physics for many different scales, Living Rev. Rel.24(2021), no. 1 3 [arXiv:2008.12069]

    work page arXiv 2021

  3. [3]

    Hammond, I

    P. Hammond, I. Hawke and N. Andersson,Thermal aspects of neutron star mergers, Phys. Rev. D104 (2021), no. 10 103006 [arXiv:2108.08649]

    work page arXiv 2021

  4. [4]

    W. A. Hiscock and L. Lindblom,Stability and causality in dissipative relativistic fluids, Annals of Physics151 (1983), no. 2 466–496

    work page 1983

  5. [5]

    W. A. Hiscock and L. Lindblom,Generic instabilities in first-order dissipative relativistic fluid theories, Phys. Rev. D31(1985) 725–733

    work page 1985

  6. [6]

    Gavassino,Can We Make Sense of Dissipation without Causality?, Phys

    L. Gavassino,Can We Make Sense of Dissipation without Causality?, Phys. Rev. X12(2022), no. 4 041001 [arXiv:2111.05254]

    work page arXiv 2022

  7. [7]

    M¨ uller,Zum paradoxon der w¨ armeleitungstheorie, Zeitschrift f¨ ur Physik198(1967) 329–344

    I. M¨ uller,Zum paradoxon der w¨ armeleitungstheorie, Zeitschrift f¨ ur Physik198(1967) 329–344

    work page 1967

  8. [8]

    Israel,Nonstationary irreversible thermodynamics: A causal relativistic theory, Annals of Physics100 (1976), no

    W. Israel,Nonstationary irreversible thermodynamics: A causal relativistic theory, Annals of Physics100 (1976), no. 1 310–331

    work page 1976

  9. [9]

    Israel and J

    W. Israel and J. M. Stewart,Transient relativistic thermodynamics and kinetic theory, Annals Phys.118 (1979) 341–372

    work page 1979

  10. [10]

    F. S. Bemfica, M. M. Disconzi and J. Noronha, Causality and existence of solutions of relativistic viscous fluid dynamics with gravity, Phys. Rev. D98 (2018), no. 10 104064 [arXiv:1708.06255]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  11. [11]

    Kovtun,First-order relativistic hydrodynamics is stable, JHEP 10 (2019) 034, [arXiv:1907.08191]

    P. Kovtun,First-order relativistic hydrodynamics is stable, JHEP10(2019) 034 [arXiv:1907.08191]

    work page arXiv 2019

  12. [12]

    F. S. Bemfica, F. S. Bemfica, M. M. Disconzi, M. M. Disconzi, J. Noronha and J. Noronha,Nonlinear Causality of General First-Order Relativistic Viscous Hydrodynamics, Phys. Rev. D100(2019), no. 10 7 104020 [arXiv:1907.12695]. [Erratum: Phys.Rev.D 105, 069902 (2022)]

    work page arXiv 2019

  13. [13]

    M. P. Heller, A. Serantes, M. Spali´ nski and B. Withers, Rigorous Bounds on Transport from Causality, Phys. Rev. Lett.130(2023), no. 26 261601 [arXiv:2212.07434]

    work page arXiv 2023

  14. [14]

    Gavassino, M

    L. Gavassino, M. M. Disconzi and J. Noronha, Dispersion Relations Alone Cannot Guarantee Causality, Phys. Rev. Lett.132(2024), no. 16 162301 [arXiv:2307.05987]

    work page arXiv 2024

  15. [15]

    M. P. Heller, A. Serantes, M. Spali´ nski and B. Withers, The space of transport coefficients allowed by causality, Nature Phys.20(2024), no. 12 1948–1954 [arXiv:2305.07703]

    work page arXiv 2024

  16. [16]

    Gavassino,Bounds on transport from hydrodynamic stability, Phys

    L. Gavassino,Bounds on transport from hydrodynamic stability, Phys. Lett. B840(2023) 137854 [arXiv:2301.06651]

    work page arXiv 2023

  17. [17]

    L. Hui, A. Nicolis, A. Podo and S. Zhou,Microcausality without Lorentz invariance, JHEP07(2025) 188 [arXiv:2502.04215]

    work page arXiv 2025

  18. [18]

    M. V. Fedoryuk,Asymptotic methods in analysis, in Analysis I: integral representations and asymptotic methods, pp. 83–191. Springer, 1989

    work page 1989

  19. [19]

    Lectures on hydrodynamic fluctuations in relativistic theories

    P. Kovtun,Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A45(2012) 473001 [arXiv:1205.5040]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  20. [20]

    Chen-Lin, L

    X. Chen-Lin, L. V. Delacr´ etaz and S. A. Hartnoll, Theory of diffusive fluctuations, Phys. Rev. Lett.122 (2019), no. 9 091602 [arXiv:1811.12540]

    work page arXiv 2019

  21. [21]

    Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions

    P. Romatschke,Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions, Eur. Phys. J. C76(2016), no. 6 352 [arXiv:1512.02641]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  22. [22]

    Brants, Phys

    R. Brants,New insights into the analytic structure of correlation functions via kinetic theory, Phys. Rev. D 110(2024), no. 11 116027 [arXiv:2409.09022]

    work page arXiv 2024

  23. [23]

    Gavassino,The quasi-normal modes of relativistic Fokker-Planck kinetic theory, arXiv:2601.19474

    L. Gavassino,The quasi-normal modes of relativistic Fokker-Planck kinetic theory, arXiv:2601.19474

    work page arXiv

  24. [24]

    Bajec, S

    M. Bajec, S. Grozdanov and A. Soloviev,Spectra of correlators in the relaxation time approximation of kinetic theory, JHEP08(2024) 065 [arXiv:2403.17769]

    work page arXiv 2024

  25. [25]

    An upper bound on transport

    T. Hartman, S. A. Hartnoll and R. Mahajan,Upper Bound on Diffusivity, Phys. Rev. Lett.119(2017), no. 14 141601 [arXiv:1706.00019]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  26. [26]

    Gavassino,The diffusion equation is compatible with special relativity, arXiv:2601.19464

    L. Gavassino,The diffusion equation is compatible with special relativity, arXiv:2601.19464

    work page arXiv

  27. [27]

    X. An, R. Brants, M. P. Heller and Y. Yin,Building far-from-equilibrium effective field theories using shift symmetries, arXiv:2511.11555

    work page arXiv

  28. [28]

    L. V. Delacretaz,A bound on thermalization from diffusive fluctuations, Nature Phys.21(2025), no. 4 669–676 [arXiv:2310.16948]

    work page arXiv 2025

  29. [29]

    M. Qi, A. Milekhin and L. Delacr´ etaz,Planckian bound on the local equilibration time, arXiv:2602.17638

    work page arXiv

  30. [30]

    How acausal equations emerge from causal dynamics

    L. Gavassino,How acausal equations emerge from causal dynamics, arXiv:2604.07031

    work page internal anchor Pith review Pith/arXiv arXiv

  31. [31]

    Chabrowski,Introduction to the theory of critical points: the mountain pass theorem ekeland’s variation principle, inInstructional Workshop on Analysis and Geometry, Part 3, vol

    J. Chabrowski,Introduction to the theory of critical points: the mountain pass theorem ekeland’s variation principle, inInstructional Workshop on Analysis and Geometry, Part 3, vol. 34, pp. 137–183, Australian National University, Mathematical Sciences Institute, 1996. HYDRODYNAMIC DECA Y - PROOFS We start off with a specialized version of the deforma- ti...

    work page 1996