{"id":"63e135f4-517e-44bb-8dde-22864f3f0bff","arxiv_id":"2506.04736","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Earth's gravity shifts HOM interference through an effective time delay from the photon phase, not the geodesic travel time, and the proposed difference-signal probe could make the effect detectable in a terrestrial laboratory.","lead":"This paper studies how Earth's gravity changes the pattern of two-photon Hong-Ou-Mandel interference in a laboratory-scale interferometer. It argues that gravity acts on the quantum phase of photons rather than on their travel time, and it proposes a new probe that could make tiny gravitational effects visible in tabletop experiments.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sec. 6.1's claim that Ref. [26] supports the wave perspective rests on an unverified sign conversion; if the observed delay direction matches the particle formula (75) rather than (76), the central experimental support collapses.","rationale":"The theoretical derivation of δt = -δT at first order is algebraically consistent and does not depend on the minimally-coupled scalar approximation, which only affects amplitude transport at higher order. The load-bearing weakness is therefore not the quantum-state construction itself but the empirical claim that Ref. [26] discriminates between the two perspectives. The reader's verdict was already CONDITIONAL, partly due to reliance on reinterpreting a single prior experiment; my concern sharpens that condition to a specific sign conversion that can be checked directly. I do not see a reason to change the verdict before that check, since the theoretical prediction still stands and the experiment may well confirm the wave picture once the conventions are carefully mapped. The internal 10^3 vs 10^4 loop inconsistency noted by the reader is real but does not threaten the central claim, which is the wave-versus-particle distinction and its experimental support. Hence UNCHANGED, with the condition made explicit: verify the sign mapping to Ref. [26] before treating the experimental support as established.","tokens_in":32094,"tokens_out":13363,"duration_ms":157803,"concrete_test":"Re-analyze Ref. [26]'s data with explicit sign conventions: (i) determine from their Fig. 3 which direction of T they call 'positive photon delay' when the platform rotates clockwise and the coupler is on the counterclockwise path; (ii) rewrite their Eq. (8) in the form P = 1/2[1 - exp(-ζ²(T + s·4Aω/c²)²)] and extract s; (iii) compare the sign of the observed dip shift with s = +1 (wave, Eq. 76) versus s = -1 (particle, Eq. 75). If the data yields s = -1, the claim that Ref. [26] supports the wave perspective is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that HOM interference in a terrestrial gravitational field is governed by the effective time delay (wave perspective) rather than the relativistic time delay (particle perspective) is supported theoretically by the first-order identity δt = -δT, which is robust under eikonal quantization. The empirical pillar, however, is the reinterpretation of the rotating-platform experiment of Ref. [26] in Sec. 6.1. With the paper's convention A·ω = -Aω (Eq. 74), the leading Sagnac term in (58) gives δT = +4Aω/c², so the wave-perspective coincidence probability (76) has its dip at T = -4Aω/c², while the particle-perspective formula (75) has it at T = +4Aω/c². The paper states that the measured photon delay was positive and increasing with rotation speed and asserts this matches (76), but it never demonstrates that Ref. [26]'s sign convention for 'positive delay' corresponds to this orientation. The paper even acknowledges that Ref. [26] constructed their state using the relativistic time delay and calls the agreement a 'coincidence'; a more natural reading is that the experimentalists' data matched their own (particle-perspective) formula, which would support the opposite conclusion. Without a step-by-step mapping of Ref. [26]'s setup and sign conventions to Eqs. (75) and (76), the experimental support for the wave perspective is not established. (Also, Eq. (75) as printed has a '+' before the exponential, which would produce an anti-bunching peak rather than the HOM dip; assuming a typo, the intended contrast is between dips at ±4Aω/c².)","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies how Earth's gravitational field enters the Hong-Ou-Mandel coincidence probability in a terrestrial laboratory. It computes, to second order in the metric perturbation, a 'relativistic time delay' from the null geodesic equation (the particle perspective) and an 'effective time delay' from the eikonal phase of a minimally coupled massless scalar field (the wave perspective). The central theoretical result is that these two delays differ: at first order they differ by a sign, δt = −δT, and at second order they differ by additional terms. The paper then applies these delays to a rectangular interferometer in two configurations, one isolating frame-dragging effects and one isolating redshift effects, estimates loop numbers needed for detection, proposes difference observables P_HOM and P_QB, and revisits the rotating-platform experiment of Ref. [26], claiming that it supports the wave perspective.","tokens_in":32419,"tokens_out":6501,"duration_ms":83139,"significance":"If the central claim is correct, the paper makes a crisp and falsifiable statement: in a terrestrial HOM experiment the coincidence dip shifts in opposite directions depending on whether one uses the null-geodesic time delay or the phase-derived effective delay, and the wave picture is the experimentally relevant one. The analytic derivations are detailed and parameter-free: no free parameter is fitted to the target result, the metric inputs are specified, and the explicit first- and second-order expressions, including the auxiliary Appendix D relation between phase and time delay, are a useful resource. The proposed observables P_HOM and P_QB, together with the concrete loop-number estimates in Sec. 5.3, are genuine experimental predictions. However, the experimental pillar of the paper, the reinterpretation of Ref. [26] in Sec. 6.1, rests on a sign-convention mapping that is not established, and the quantum-state construction in Sec. 3.2 contains an assumption about phase-only gravitational effects that is not derived from the field expansion. These issues do not invalidate the formal derivation, but they do affect the strength of the paper's main claim.","major_comments":[{"comment":"The claim that Ref. [26] supports the wave perspective is not established. With the convention A·ω = −Aω in Eq. (74), the leading Sagnac term of Eq. (58) gives an effective delay δT1−δT2 = +4Aω/c², so the wave-perspective formula (76) has its dip at T = −4Aω/c². The particle-perspective formula, after correcting the typographical plus sign in Eq. (75), has its dip at T = +4Aω/c². The paper never maps the sign convention used for 'positive photon delay' in Ref. [26] onto this coordinate choice, so the statement that the measured positive delay matches Eq. (76) rather than Eq. (75) is unsupported. In addition, Eq. (75) as printed, with a '+' before the exponential, is an anti-bunching peak rather than an HOM dip. Because Ref. [26] constructed its state using the relativistic time delay, a natural reading is that the data matched the particle-perspective formula; the authors must provide a step-by-step conversion of Ref. [26]'s setup and sign conventions to Eqs. (75) and (76), or soften the claim that the experiment selects the wave picture.","section":"Sec. 6.1"},{"comment":"The central step of the wave-perspective calculation is the replacement of e^{iωt} by e^{−iS'} in the two-photon state. This assumes that the gravitational effect on the coincidence probability is fully captured by the eikonal phase, with amplitude transport, normalization prefactors, and possible polarization-dependent curvature couplings neglected. The Wronskian condition (35) fixes the normalization of each mode, but it does not guarantee that frequency- and path-dependent amplitude factors are irrelevant at the order of the first-order time delay. Because the sign difference δt = −δT is the paper's central claim, the authors should either derive Eq. (49) from the field expansion (34) while tracking the amplitude α'_k explicitly, or state clearly that this is an additional assumption and assess its effect on the sign conclusion. As written, Eq. (49) is an ansatz rather than a derived consequence of the quantized scalar field.","section":"Sec. 3.2"},{"comment":"The photon is modeled as a massless minimally coupled scalar field, while the authors note that actual transverse Maxwell modes obey a conformally coupled wave equation and differ from Eq. (33). In the exterior of Earth the Ricci scalar vanishes, so the ξRφ term alone does not distinguish the two, but the vector nature of the Maxwell field introduces additional curvature couplings that are not estimated. If such couplings contribute to the coincidence probability at order c^{−2}, the pure phase-shift description in Eq. (49) would need modification. The authors should quantify this correction or state more explicitly that the scalar model is a leading-order proxy whose quantitative accuracy for the sign claim remains to be checked.","section":"Sec. 3.2"}],"minor_comments":[{"comment":"The definition of the gravitational potential U appears twice, in Eq. (19) and again in Eq. (20); one of the two should be removed.","section":"Sec. 2.2"},{"comment":"The conclusions refer to Figs. 5(d), 6(c), and 6(f), but the displayed figures contain only panels (a)-(c); the figure references should be updated to match the actual panels.","section":"Sec. 7"},{"comment":"Equation (E.20) contains a doubled comma before the equation tag; this should be corrected.","section":"Appendix E"},{"comment":"The symbol '⁄=' in Eq. (42a) is nonstandard and could be confused with a division sign; using the standard '\\neq' would improve readability.","section":"Sec. 3.2"}],"recommendation":"major_revision","confidential_remarks":"The formal derivation is solid and the paper has useful, falsifiable predictions. The main risk is the Sec. 6.1 experimental reinterpretation: if the sign mapping cannot be established, the wave-picture conclusion should be presented as a theoretical prediction rather than as an experimentally supported fact. The authors should also be asked to clarify the status of the phase-only ansatz in Sec. 3.2 before the central claim is accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper makes a genuine theoretical point: in HOM interference in a terrestrial gravitational field, the time delay that enters the coincidence probability is not the null-geodesic delay but an effective delay read off from the eikonal phase, and at first order these differ by a sign. The derivation is detailed and self-consistent, and the second-order calculation adds a real term (the next-to-leading-order Sagnac effect from gravitational acceleration) that earlier work missed. Second, the paper's claim that the rotating-platform experiment of Ref. [26] supports the wave perspective is not established, because the sign conventions are never mapped.\n\nThe eikonal derivation is the strongest part. The paper solves the Klein-Gordon equation order by order, shows that dt does not equal dS/(ck0), and exhibits δt = -δT explicitly. The generalization to arbitrary interferometer orientation and the differential probe P(T, ΔT1, ΔT2) are useful ideas. The authors also honestly flag that they model photons as minimally coupled scalars and defer the conformal-coupling issue.\n\nNow the soft spots. The big one is Sec. 6.1. With their Eq. (74) (A·ω = -Aω), the wave-perspective formula (76) puts the HOM dip at T = -4Aω/c², while the particle-perspective formula (75) puts it at +4Aω/c² after correcting the plus sign in (75), which as printed gives an anti-bunching peak rather than the HOM dip. The paper says Ref. [26] measured a positive delay and concludes this matches (76). But a positive measured delay would match the particle-perspective dip at +4Aω/c², not the wave-perspective dip at -4Aω/c², unless Ref. [26]'s convention for 'positive delay' is the opposite. The paper never demonstrates that. So the experimental support for the central conclusion is shaky.\n\nThere is also a consistency slip: Sec. 7 says the redshift effect needs 10^3 loops, but Eq. (73) requires 10^4. Minor, but it should be fixed.\n\nThe central theoretical distinction between δt and δT stands, and the paper deserves a serious referee. But the broader conclusion that the wave picture is 'more adequate' should be stated conditionally until the sign mapping is sorted out.\n\nWho is this for: people working on quantum optics in curved spacetime, and relativists interested in Sagnac-type effects in tabletop experiments. Worth engaging with, but as a draft it needs a major revision focused on Sec. 6.1 and the sign conventions. Send it to review; don't desk-reject.","headline":"Solid eikonal derivation showing a real first-order sign difference between the relativistic and effective time delays in HOM interference, but the experimental support for the wave perspective rests on an unmapped sign convention and needs major revision.","tokens_in":32951,"tokens_out":4243,"would_cite":false,"duration_ms":48742,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C25","83C47","81V80"],"pacs":["04.25.Nx","04.80.Cc","42.50.Ar"],"model":"deepseek-v4-flash","headline":"In HOM interference, Earth's gravity acts through the wave phase: the effective time delay from the phase shift, not the null-geodesic delay, controls the coincidence probability.","keywords":["Hong-Ou-Mandel interference","gravitational redshift","frame dragging","Sagnac effect","eikonal phase","proper reference frame","quantum field theory in curved spacetime","Lense-Thirring effect"],"falsifier":"Rotate the HOM platform in both directions and measure the coincidence dip versus the coupler delay $T$. The wave picture gives $P^c=\\frac{1}{2}[1-e^{-\\zeta^2(T+4A\\omega/c^2)^2}]$ and the particle picture gives $\\frac{1}{2}[1+e^{-\\zeta^2(T-4A\\omega/c^2)^2}]$, so with the area $A$ and angular velocity $\\omega$ known, the direction of the dip's shift settles which time delay enters.","tokens_in":31836,"feed_emoji":"🌍","tokens_out":9253,"duration_ms":88595,"temperature":0.7,"pith_summary":"This paper argues that in Hong-Ou-Mandel interference inside Earth's gravitational field, the coincidence probability is set by the effective time delay obtained from the phase shift of the photon wave, not by the relativistic time delay obtained from null geodesics. At first order the two delays are opposite in sign, and at second order they differ by several additional terms, so the two pictures predict different interference patterns. Re-examining the rotating-platform HOM experiment, the paper concludes that its outcome supports the wave picture. The paper also derives the frame-dragging and redshift time delays for an arbitrarily oriented rectangular interferometer, isolates one effect per photon-path scenario, and proposes the difference of two HOM patterns as a practical probe.","feed_headline":"Gravity enters HOM interference as a wave phase, not a particle delay","feed_subtitle":"The rotating-platform experiment already picks the wave picture; a next-order Sagnac term becomes testable.","key_machinery":"The load-bearing object is the eikonal phase replacement: the mode function is written as $u_{\\vec k}=N\\alpha'_{\\vec k}\\,e^{-i\\omega(\\bar t+\\delta T+\\delta^{(2)}T)}e^{ik\\int_O dl}$, with the effective delays $\\delta T$ and $\\delta^{(2)}T$ obtained by expanding the Klein-Gordon eikonal equation in the laboratory-frame metric. These effective delays are contrasted with the null-geodesic delays $\\delta t$ and $\\delta^{(2)}t$ from the null interval; the paper shows the two are related through a coefficient vector $\\Lambda^0_\\alpha$ rather than by a simple division of phase by frequency. The minimally-coupled massless scalar field is canonically quantized in the proper reference frame, and the two-photon state is built directly from the integrated phases.","core_discovery":"The paper's central claim is that the correct way to put a terrestrial gravitational field into a two-photon HOM state is to replace the Minkowski phase $e^{i\\omega t}$ by the eikonal phase $e^{-iS'}$ of a mode function satisfying the Klein-Gordon equation. The resulting effective time delays $\\delta T$ and $\\delta^{(2)}T$ enter the coincidence probability as $P^c(T+\\delta T_1-\\delta T_2+\\cdots)$, whereas the particle-picture delays $\\delta t$ and $\\delta^{(2)}t$ enter with opposite sign at first order and with a different composition at second order. The paper shows this distinction is physical: the rotating-platform HOM experiment shifts its coincidence dip in the direction predicted by the wave picture. It further identifies a next-to-leading-order Sagnac term, arising from the coupling of rotation and acceleration, that previous work omitted and that is comparable in size to the Thomas, geodetic, and Lense-Thirring contributions. It estimates that roughly $10$ loops suffices for the leading Sagnac effect and $10^4$ loops for the gravitational-acceleration redshift effect at current $\\sim 10^{-18}\\,\\mathrm{s}$ timing precision.","pith_inferences":["If phase-derived delays are the correct description, then gravitational \"time delays\" in quantum interferometry are not simply coordinate propagation delays; operational time definitions in quantum clock or quantum communication networks may need to track phase shifts rather than geodesic delays.","Because real photons are conformally coupled whereas the paper uses a minimally-coupled scalar field, redoing the same two-scenario calculation for the Maxwell field would test whether the sign separation between the wave and particle pictures survives at second order.","The same difference-probe technique could be adapted to large-area fiber Sagnac interferometers or satellite-to-ground HOM links, where the loop-count amplification is replaced by physical area or baselines.","Planning note: the paper gives two different loop-number estimates for the gravitational redshift experiment ($10^3$ in the conclusions, $10^4$ in Sec. 5.3); an experimental design would need to resolve that discrepancy."],"forward_implications":["If the wave picture is right, the HOM coincidence dip is controlled by phase-derived effective delays, so the \"time delay\" inferred from a HOM dip in a gravitational field is not the geodesic arrival-time difference between the two arms.","The next-to-leading-order Sagnac effect is comparable to the Thomas, geodetic, and Lense-Thirring effects and should be included in terrestrial Sagnac interferometer analyses.","About $10$ loops in a roughly $10\\,\\mathrm{m}$ interferometer brings the leading Sagnac delay to the $\\sim 10^{-18}\\,\\mathrm{s}$ level, and about $10^4$ loops brings the gravitational-acceleration redshift delay to the same level.","The proposed difference observables $P_{\\mathrm{HOM}}$ and $P_{\\mathrm{QB}}$ need only $\\sim 10^{-12}\\,\\mathrm{s}$ temporal resolution, making gravitational effects observable without resolving the tiny dip shift directly."],"supporting_citations":[{"why":"Original Hong-Ou-Mandel experiment whose Gaussian spectral profile and coincidence formula the paper uses.","marker":"[22]"},{"why":"Rotating-platform HOM experiment whose observed dip direction the paper uses to favor the wave perspective.","marker":"[26]"},{"why":"Prior wave-perspective treatment of frame dragging and redshift in HOM interference that the paper generalizes and corrects.","marker":"[24]"},{"why":"Earlier terrestrial interferometer analysis that omitted the next-to-leading-order Sagnac coupling identified here.","marker":"[44]"},{"why":"Satellite-terrestrial HOM predictions whose probes and bandwidth dependence the paper compares with its own.","marker":"[23]"},{"why":"Reference-frame relations used to connect the laboratory and geocentric metrics.","marker":"[37]"},{"why":"Proper reference frame metric and Fermi-Walker transport used to set up the laboratory coordinates.","marker":"[47]"},{"why":"Current $\\sim 10^{-18}\\,\\mathrm{s}$ timing precision used to estimate the required number of loops.","marker":"[67]"}],"fun_headline_variants":["Wave picture wins in gravitational HOM interference","Gravity shifts HOM dip: wave phase over particle delay","Next-order Sagnac effect testable in HOM interference","HOM experiment picks wave phase for gravity","Rotating platform HOM: gravity as wave phase"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument rests on the assumption that the gravitational effect on the two-photon state is fully captured by replacing the flat-space phase with the eikonal phase of a minimally coupled massless scalar field, so that amplitude transport, normalization, and polarization or conformal-coupling corrections can be neglected at the orders considered.","fun_headline_variants_meta":{"raw":{"variants":["Wave picture wins in gravitational HOM interference","Gravity shifts HOM dip: wave phase over particle delay","Next-order Sagnac effect testable in HOM interference","HOM experiment picks wave phase for gravity","Rotating platform HOM: gravity as wave phase"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000652,"raw_usage":{"total_tokens":3038,"prompt_tokens":1042,"completion_tokens":1996,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":658,"completion_tokens_details":{"reasoning_tokens":1920}},"tokens_in":658,"tokens_out":1996,"duration_ms":14447,"temperature":1.0,"reasoning_tokens":1920,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:35:58.049535+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rotate the HOM platform in both directions and measure the coincidence dip versus the coupler delay $T$. The wave picture gives $P^c=\\frac{1}{2}[1-e^{-\\zeta^2(T+4A\\omega/c^2)^2}]$ and the particle picture gives $\\frac{1}{2}[1+e^{-\\zeta^2(T-4A\\omega/c^2)^2}]$, so with the area $A$ and angular velocity $\\omega$ known, the direction of the dip's shift settles which time delay enters.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Original Hong-Ou-Mandel experiment whose Gaussian spectral profile and coincidence formula the paper uses."},{"cited_title":"Restuccia, et al., Phys","cited_arxiv_id":null,"evidence_quote":"Rotating-platform HOM experiment whose observed dip direction the paper uses to favor the wave perspective."},{"cited_title":"Brady and Stav Haldar, Phys","cited_arxiv_id":null,"evidence_quote":"Prior wave-perspective treatment of frame dragging and redshift in HOM interference that the paper generalizes and corrects."},{"cited_title":"Bosi, et al., Phys","cited_arxiv_id":null,"evidence_quote":"Earlier terrestrial interferometer analysis that omitted the next-to-leading-order Sagnac coupling identified here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Satellite-terrestrial HOM predictions whose probes and bandwidth dependence the paper compares with its own."},{"cited_title":"Gersl, Universe 3, 24 (2017)","cited_arxiv_id":null,"evidence_quote":"Reference-frame relations used to connect the laboratory and geocentric metrics."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proper reference frame metric and Fermi-Walker transport used to set up the laboratory coordinates."},{"cited_title":"Lyons, et al., Sci","cited_arxiv_id":null,"evidence_quote":"Current $\\sim 10^{-18}\\,\\mathrm{s}$ timing precision used to estimate the required number of loops."}],"review_version":1}