{"id":"d8043a57-1551-4923-84f8-a304ef288d8b","arxiv_id":"2505.02026","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper proposes two viscoelastic fluid models for DSR phonons, but sign errors make the derived dispersions opposite to the claimed DSR relations.","lead":"A theory paper adds special forces to a fluid so that its sound waves follow the energy-momentum rules of doubly special relativity. The equations contain sign errors, so the claimed DSR dispersions do not actually follow from the models.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central construction relies on an imaginary force term iγ∇²v in the real hydrodynamic equations; no real velocity potential can satisfy it, so the phonon models lack a physical substrate.","rationale":"The reader's rejection is sound, and the most robust reason is the imaginary force term, not the sign errors. The sign of the iγ terms in Eqs. (3) and (16) depends on the Fourier convention: with the standard e^{-iEt} convention the signs are indeed opposite to the claimed DSR corrections, but a coherent e^{+iEt} convention would make both Eqs. (3) and (16) algebraically match Eqs. (1) and (17). Since the paper never fixes the convention, the sign criticism is less decisive. The imaginary force is decisive because it is a structural contradiction with real-valued hydrodynamics, independent of any Fourier convention. Equation (8) is presented as a real linearized Euler equation for the velocity potential; inserting Φ1=iγ∇²ψ1 makes the equation complex. Requiring real ψ1 leaves no nontrivial solutions; allowing complex ψ1 removes the physical interpretation of ρ1 and φ1 as density and potential fluctuations. The paper's appeal to rheological 'storage viscosity' misunderstands the status of complex viscosity: it is a frequency-domain response function, and a real time-domain version is a memory integral. Therefore, the central claim that phonons in a fluid obey DSR1/DSR2 rests on an equation that no real fluid satisfies. This is a load-bearing unsupported premise, and the preprint should be rejected or majorly revised. My verdict is unchanged from the reader's REJECT.","tokens_in":7289,"tokens_out":14163,"duration_ms":138857,"concrete_test":"Symbolic consistency check: impose ψ1,ρ1 real in Eqs. (7)-(8) with Φ1 = iγ∇²ψ1. The imaginary part of Eq. (8) gives ∇²ψ1=0; combining with Eq. (7) yields ∂_T ρ1=0, i.e., no propagating phonons. Then rerun the derivation with a real causal viscoelastic term, e.g., ∂_Tψ1 = -P1/ρ0 - φ1 - ∫_0^t K(t-t') ∇²ψ1(t') dt', and compute the resulting dispersion; if no causal K reproduces Eq. (1), the claimed DSR realization cannot be achieved by a physically realizable hydrodynamic model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the definition Φ1 = iγ∇²ψ1 (just after Eq. (12)) and its nonlinear counterpart iγ∇²v in Eq. (14), presented as a 'storage viscosity' — a reactive, non-dissipative viscoelastic force. This is not a legitimate time-domain force for a real fluid. In the linearized Euler equation (8), ∂_Tψ1 = -P1/ρ0 - φ1 - iγ∇²ψ1, the left side is real if ψ1 is the physical velocity potential, while the right side contains the purely imaginary term -iγ∇²ψ1. For nonzero γ and nontrivial ψ1 the equation has no real solution; forcing the imaginary part to vanish gives ∇²ψ1=0, which through Eq. (7) kills the density dynamics. If ψ1 is instead taken complex, the continuity equation (7) makes ρ1 complex, so no real density fluctuation exists, and the real part of the velocity potential obeys an equation coupled to the imaginary part, not Eq. (3). The paper's rheological justification invokes the complex viscosity of viscoelastic fluids, but that object is defined in the frequency domain; a causal time-domain constitutive relation is necessarily a convolution (memory) integral, not a bare iγ∇²v term. The Conclusion's own admission of 'oversimplified description of viscoelastic effects' does not repair this: the simplification is not quantitative but structural, removing the real-fluid interpretation. Without this term, Eqs. (3) and (16) are not derived from hydrodynamics, and the DSR claim collapses.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript claims to construct two hydrodynamic models in which phonons obey doubly special relativistic (DSR) kinematics. The first model adds a repulsive dipolar interaction and a purely imaginary 'storage viscosity' term iγ∇²v to the Euler equation, purportedly yielding the Amelino-Camelia (DSR1) dispersion relation up to O(E³/E_p³). The second model replaces this term with an elastic restoring force iγ'ψ, purportedly yielding the Magueijo-Smolin (DSR2) relation. The analogue Planck scale is identified with viscoelastic parameters. Section II contains the algebraic construction, and Section III summarizes the two models and discusses idealizations. The paper is written as a Letter and includes references to the analogue gravity and DSR literature.","tokens_in":7683,"tokens_out":7344,"duration_ms":71280,"significance":"If the reported construction were sound, it would be a noteworthy extension of the analogue gravity program, showing that DSR-type modified dispersion relations can emerge from non-Newtonian fluid mechanics and potentially offering a condensed-matter testbed for DSR phenomenology. The paper has strengths: it states clear target relations, builds on established analogue gravity concepts, and explicitly identifies the parameters that control the putative Planck scale. However, the central hydrodynamic derivation relies on an imaginary force term with no real-fluid time-domain realization, and the dispersion algebra does not reproduce the claimed DSR relations. As a result, the promised significance is not achieved by the present manuscript.","major_comments":[{"comment":"The dispersion relation obtained from Eq. (3) does not match DSR1. Fourier transforming Eq. (3) with ∂_T → -iω and ∇² → -k² gives ω² = c_s²k² + Ω₀² - γωk², i.e., in energy-momentum variables E² = c_s²p² + m²c_s⁴ - (c_s²p²E)/E_p (using γ = ℏc_s²/E_p). The correction is negative, whereas the DSR1 relation (1) requires E² ≈ c_s²p²(1 + E/E_p) + m²c_s⁴, i.e., a positive correction. Thus Eq. (3) yields a subluminal modification, not the Amelino-Camelia relation claimed in the abstract and Section III.","section":"Section II, Eq. (3)"},{"comment":"The claimed reduction to DSR2 is not supported by the equations. Fourier transforming Eq. (16) gives ω² = c_s²k² + Ω₀² + γ'ω, or E² = c_s²p² + m²c_s⁴ + ℏγ'E, with a positive correction proportional to ℏE. The paper's Eq. (17) instead states E² = c_s²p² + m²c_s⁴(1 - γ'E/(m²c_s⁴)), which has a negative correction with a different coefficient. The rescaling (18) only redefines c_s and m; it cannot flip the sign of the γ' term or change its coefficient from ℏγ'E to the form in Eq. (17). The claimed equivalence at linear order therefore fails.","section":"Section II, Eqs. (16)-(18)"},{"comment":"The term iγ∇²v is not a legitimate time-domain force in a real fluid. In the linearized Euler equation (8), setting Φ₁ = iγ∇²ψ₁ makes the right-hand side imaginary for a real velocity potential ψ₁; the only real solution is ∇²ψ₁ = 0, which suppresses density dynamics via Eq. (7). If ψ₁ is instead taken complex, the continuity equation (7) forces ρ₁ to be complex, contradicting the interpretation of ρ₁ as a real density fluctuation. A causal viscoelastic constitutive relation is necessarily a memory convolution in the time domain; the frequency-domain storage modulus cannot be transplanted into the real-time Euler equation as a bare imaginary coefficient. This is a structural, not quantitative, problem: without this term, Eq. (3) is not derived from the hydrodynamics.","section":"Section II, Eq. (14) and the storage-viscosity paragraph"},{"comment":"The matching of the dispersion relations is achieved by reverse engineering: the parameters γ and γ' are fixed a posteriori to reproduce the target DSR Planck scale (γ = ℏc_s²/E_p and E_p = 2m²c_s⁴/γ'), and the dipolar strength β sets the mass term. The statement that DSR 'naturally emerges' is therefore true by construction rather than by prediction. To support the claim of a physical analogy, the paper would need an independent identification of the viscoelastic parameters—e.g., from a rheological measurement—that did not presuppose the DSR scale.","section":"Section III, Discussion and Conclusions"}],"minor_comments":[{"comment":"The text says 'Substituting these expressions into Eq. (2)' but the substitution is into the continuity equation (4), not the DSR2 dispersion relation (2).","section":"Section II, after Eq. (4)"},{"comment":"Equation (5) is called the linearized continuity equation but contains the second-order term ρ₁v₁; the linearized equation should read ∂_tρ₁ + ∇·(ρ₀v₁) = 0.","section":"Section II, Eq. (5)"},{"comment":"For γ = 0, Eqs. (14)-(15) reduce to the Euler equations for an inviscid fluid, not to the Navier-Stokes equations; Navier-Stokes would require a real viscous term η∇²v.","section":"Section II, Eq. (14)"},{"comment":"The equivalence of the rescaling (18) to the new barotropic law P' = (1 + γ'/4βρ₀)P is stated without derivation; this step should be shown explicitly or removed.","section":"Section II, text near Eq. (18)"}],"recommendation":"reject","confidential_remarks":"The manuscript is clearly written and engages a real literature, but the central construction is not viable: the imaginary viscosity term is not a physical time-domain force and the dispersion algebra contains sign and coefficient errors that the claimed rescalings cannot fix. I do not see a repair within the scope of a short Letter; the model would require a fundamentally different viscoelastic formulation and a corrected derivation. Hence rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the construction as written doesn't do what it claims. The sign errors are real, and the iγ∇²v term isn't a legitimate time-domain force for a real fluid. But the underlying idea is not silly, and the paper is clearly written and well placed in the analogue-gravity literature.\n\nWhat's new: the specific mapping of the DSR1 and DSR2 dispersions to a storage-viscosity term and an elastic restoring force is, as far as I know, not in the cited literature. That is a real conceptual suggestion. The paper also does a clean job of setting up the linearized hydrodynamics and connecting the effective Planck scale to the viscoelastic parameters.\n\nThe soft spots are load-bearing. First, Eq. (3) gives a subluminal correction of the wrong sign; for p² = E²/c_s² it produces E² = c_s²p² + ... − ℏ E³/E_p, whereas DSR1 has a plus. Second, Eq. (16) with Φ₁ = iγ'ψ₁ yields E² = c_s²p² + Ω₀² + γ'E; the printed Eq. (17) has the opposite sign. You can't fix that with the rescaling in (18); that rescaling just renames c_s and m and doesn't remove the sign mismatch. Third, and more fundamentally, the force iγ∇²v (or iγ∇²ψ₁) in a real-fluid Euler equation has no real solution for real ψ₁; a complex velocity potential forces a complex density, so the model is not a fluid in any ordinary sense. Rheological 'storage viscosity' is a frequency-domain object; a causal time-domain constitutive law is a convolution, not a bare imaginary term. The Conclusion's note about an 'oversimplified description' doesn't address this structural problem.\n\nWhat should happen: I'd reject this version. The idea might be salvageable if the author can find a real constitutive model (e.g., a relaxational viscoelastic response) whose low-frequency/linearized limit gives the desired dispersion with the correct sign, but that requires substantial rewriting. As is, the derivation fails on its own terms.\n\nAudience: someone working on analogue gravity and DSR phenomenology might get a useful idea out of the mapping, but they should treat the equations with suspicion.\n\nRecommendation: don't desk-reject out of hand—send to a referee who can check the signs and the constitutive question. But the referee should understand the paper is currently not correct.","headline":"Current version fails on its own equations, but the DSR-to-hydrodynamics mapping is a genuinely new idea worth a corrective rewrite.","tokens_in":8208,"tokens_out":5922,"would_cite":false,"duration_ms":57607,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Phonons in tailored fluids can reproduce doubly special relativity","keywords":["doubly special relativity","phonons","analogue gravity","dispersion relation","viscoelastic fluids","storage viscosity","Planck scale","hydrodynamic analogue"],"falsifier":"Measure the complex shear modulus of a candidate viscoelastic fluid: if its real (dissipative) part is non-negligible at the phonon frequencies, or if its response violates the causality relations linking real and imaginary parts, the purely imaginary storage force needed for the DSR1 model cannot be physical. Alternatively, a direct search for the predicted dispersion $E^2=c_s^2p^2(1+E/E_p)+m^2c_s^4$ in a real fluid's phonon spectrum would fail if the linear-in-$E/E_p$ correction is absent.","tokens_in":7021,"feed_emoji":"🌊","tokens_out":13713,"duration_ms":123558,"temperature":0.7,"pith_summary":"This paper constructs two hydrodynamic models in which the collective sound waves (phonons) obey the deformed energy-momentum relations of doubly special relativity (DSR), with the fluid's viscoelastic parameters playing the role of the Planck scale. The first model adds an elastic storage term to the Euler equation and yields the DSR1 dispersion relation to order $E^3/E_p^3$; the second adds an elastic restoring force and yields the DSR2 relation after a rescaling of sound speed and mass. The demonstrations use the standard analogue-gravity setup of a barotropic, irrotational, inviscid fluid, extended with repulsive dipolar interactions that give the phonons a rest mass. If the constructions hold, quantum-gravity-inspired kinematics could be simulated in ordinary fluids rather than requiring Planck-scale physics.","feed_headline":"Phonons in tailored fluids can reproduce doubly special relativity","feed_subtitle":"Storage viscosity gives the DSR1 law; elastic restoring forces give the DSR2 law, with a tunable sonic Planck scale.","key_machinery":"The argument is carried by the two linearized interaction potentials added to the Euler equation. The first, $\\Phi_1=i\\gamma\\nabla^2\\psi_1$, is called the storage-viscosity term: it is meant to represent momentum storage without dissipation, and its convective derivative supplies the $-i\\gamma\\partial_T\\nabla^2\\psi_1$ term in the modified Klein-Gordon equation. The second, $\\Phi_1=i\\gamma'\\psi_1$, is an elastic restoring force analogous to a spring, and it leads to the DSR2 dispersion after redefining the sound speed and the phonon mass. The dipolar potential $\\varphi_1$ satisfying the Poisson equation $\\nabla^2\\varphi_1=-\\beta\\rho_1$ provides the rest frequency $\\Omega_0=\\sqrt{\\beta\\rho_0}$, and the analogue Planck frequency for the DSR2 model is $\\Omega_p=(4\\beta\\rho_0+\\gamma')/(2\\gamma')$.","core_discovery":"The central discovery is that two simple additions to the fluid momentum equation turn the usual acoustic Lorentz-invariant phonon dispersion into the two canonical DSR laws. With a reactive storage term $\\Phi_1=i\\gamma\\nabla^2\\psi_1$ in the linearized Euler equation, the phonon wave equation becomes $\\partial_T^2\\psi_1=c_s^2\\nabla^2\\psi_1-\\Omega_0^2\\psi_1-i\\gamma\\partial_T\\nabla^2\\psi_1$, whose dispersion is the DSR1 relation $E^2\\simeq c^2p^2(1+E/E_p)+m^2c^4$ at order $E^3/E_p^3$. With a spring-like restoring term $\\Phi_1=i\\gamma'\\psi_1$ instead, the dispersion becomes the DSR2 relation after the rescalings $c_s^2\\to c_s^2(1-m^2c_s^4/E_p)$ and $m^2\\to m^2(1-m^2c_s^4/E_p)$, with $E_p=2m^2c_s^4/\\gamma'$. In both models the rest mass comes from a repulsive dipolar interaction $\\nabla^2\\varphi_1=-\\beta\\rho_1$, and the analogue Planck scale is fixed by the viscoelastic coefficients $\\gamma$ and $\\gamma'$ together with $\\beta$ and the background density.","pith_inferences":["The same design strategy should extend to other deformed dispersion relations: replacing the storage and restoring potentials with other interaction kernels would generate families of phonon laws with different high-energy corrections.","If a photon-fluid or atomic-condensate analogue is built, one could probe DSR predictions such as deformed boosts or an energy-dependent speed of sound; the fluid would be the first experimental system where a Planck-like scale is a tunable knob rather than a fixed constant.","A rheological consistency test follows from the model itself: a purely imaginary, frequency-independent viscosity would violate causality because the real and imaginary parts of any passive linear response are linked by integral relations, so the construction can be made fully physical only if a constitutive model produces a reactive force that is imaginary in the linearized equation but still cau","Because the DSR1 realization is stated only to order $E^3/E_p^3$, measuring the next-order term in the phonon dispersion would distinguish the analogue model from exact DSR1 and reveal the underlying microscopic cutoff."],"forward_implications":["A fluid with engineered dipolar and viscoelastic interactions would display phonon dispersions identical to DSR1 and DSR2 near its sonic Planck scale, making Planck-scale kinematics accessible in a tabletop system.","The analogue Planck scale is not fixed by atomic discreteness but by rheological parameters, so it can in principle be tuned across many orders of magnitude.","The two models show complementary deformations: the DSR1 relation can be read as an energy-dependent inertial mass, while the DSR2 relation corresponds to an energy-dependent rest mass; a fluid analogue could switch between the two by changing one interaction term.","The full nonlinear equations (continuity, Euler, and Poisson equations with either $\\Phi=i\\gamma\\nabla^2\\psi$ or $\\Phi=i\\gamma'\\psi$) provide a concrete starting point for numerical or experimental study of analogue DSR kinematics."],"supporting_citations":[{"why":"defines the DSR1 energy-momentum relation that the storage-viscosity model is built to reproduce.","marker":"[7]"},{"why":"defines the DSR2 relation that the elastic-restoring-force model reproduces after rescaling.","marker":"[8]"},{"why":"establishes the acoustic analogue of Lorentz invariance for phonons in barotropic irrotational inviscid fluids.","marker":"[30]"},{"why":"provides the acoustic black hole framework that motivates analogue dispersion modifications.","marker":"[31]"},{"why":"supplies the fluid-mechanics equations and the conventional viscous term against which the storage term is contrasted.","marker":"[32]"},{"why":"shows how a massive Klein-Gordon equation arises in an analogue spacetime, supporting the use of interactions to give phonons mass.","marker":"[33]"},{"why":"supports the claim that suitably shaped dipolar interactions endow phonons with a rest mass in photon fluids.","marker":"[36]"},{"why":"supplies the rheological notion of storage modulus used to justify the imaginary viscosity term.","marker":"[41]"}],"fun_headline_variants":["Phonons in fluids mimic DSR with tailored viscosity terms","Acoustic analog: fluid phonons obey Amelino-Camelia and Magueijo-Smolin","Viscoelastic fluids turn phonons into doubly special relativity","Phonon hydrodynamics reproduces both DSR1 and DSR2 laws"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The construction assumes that a fluid can exert a purely reactive imaginary viscous force $i\\gamma\\nabla^2 v$ with no dissipative counterpart and no constitutive model, so that the linearized Euler equation can contain an imaginary term while the velocity potential remains real.","fun_headline_variants_meta":{"raw":{"variants":["Phonons in fluids mimic DSR with tailored viscosity terms","Acoustic analog: fluid phonons obey Amelino-Camelia and Magueijo-Smolin","Viscoelastic fluids turn phonons into doubly special relativity","Phonon hydrodynamics reproduces both DSR1 and DSR2 laws"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000291,"raw_usage":{"total_tokens":1694,"prompt_tokens":935,"completion_tokens":759,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":551,"completion_tokens_details":{"reasoning_tokens":676}},"tokens_in":551,"tokens_out":759,"duration_ms":7609,"temperature":1.0,"reasoning_tokens":676,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:05:55.640553+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the complex shear modulus of a candidate viscoelastic fluid: if its real (dissipative) part is non-negligible at the phonon frequencies, or if its response violates the causality relations linking real and imaginary parts, the purely imaginary storage force needed for the DSR1 model cannot be physical. Alternatively, a direct search for the predicted dispersion $E^2=c_s^2p^2(1+E/E_p)+m^2c_s^4$ in a real fluid's phonon spectrum would fail if the linear-in-$E/E_p$ correction is absent.","supporting_citations":[{"cited_title":"The DSR1 energy-momentum relation at O(E3/E 3 p) is E2 ≃c2p2 ( 1 + E Ep ) +m2c4 (1) where E is the total energy of a particle with momentum p and rest mass m","cited_arxiv_id":null,"evidence_quote":"defines the DSR1 energy-momentum relation that the storage-viscosity model is built to reproduce."},{"cited_title":"Amelino-Camelia, Doubly-special relativity: first r esults and key open problems","cited_arxiv_id":null,"evidence_quote":"defines the DSR2 relation that the elastic-restoring-force model reproduces after rescaling."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the acoustic black hole framework that motivates analogue dispersion modifications."},{"cited_title":"Visser, Acoustic black holes: horizons, ergospheres and Hawking ra diation","cited_arxiv_id":null,"evidence_quote":"supplies the fluid-mechanics equations and the conventional viscous term against which the storage term is contrasted."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"shows how a massive Klein-Gordon equation arises in an analogue spacetime, supporting the use of interactions to give phonons mass."},{"cited_title":"Girelli, S","cited_arxiv_id":null,"evidence_quote":"supports the claim that suitably shaped dipolar interactions endow phonons with a rest mass in photon fluids."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the rheological notion of storage modulus used to justify the imaginary viscosity term."}],"review_version":1}