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REVIEW 2 major objections 4 minor 51 references

Matter interferometers could sense the cosmic neutrino background through potential-energy differences between their two arms, but the predicted phase shifts of 10^-22 to 10^-14 rad are orders of magnitude below any planned sensitivity.

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2026-08-03 20:48 UTC pith:O6KSIA4W

load-bearing objection Useful sensitivity estimate for CNB in matter interferometers; the negative conclusion holds, but the non-relativistic Stodolsky benchmarks are inflated by ~1/β due to the chirality-helicity mismatch. the 2 major comments →

arxiv 2511.18245 v2 pith:O6KSIA4W submitted 2025-11-23 hep-ph astro-ph.COhep-ex

Detection prospects for the Cosmic Neutrino Background using matter interferometers

Chrisna Setyo Nugroho , Martin Spinrath This is my paper
classification hep-ph astro-ph.COhep-ex PACS 13.15.+g03.75.Dg95.35.+d14.60.Pq
keywords cosmic neutrino backgroundmatter interferometerMSW effectStodolsky effectatom interferometryneutrino detectionlepton asymmetrydark Stodolsky effect
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether matter interferometers—devices that split atoms or neutrons into two paths and measure the phase difference when they recombine—could detect the relic neutrinos from the Big Bang, the cosmic neutrino background (CNB). The authors show that the CNB changes the energy of the interfering particles through two weak-interaction potentials: the standard matter potential behind the MSW effect and the spin-dependent Stodolsky potential. Under benchmark assumptions about neutrino densities and asymmetries, they find phase shifts of about 10^-22 rad for the MSW-type channel and 10^-14 rad for the Stodolsky channel. Since current interferometers resolve phases near 10^-2 rad and even ambitious future proposals reach only 10^-10 rad, the paper concludes that direct CNB detection with matter interferometers is out of reach for now—though the same formalism applied to fermionic dark matter gives signals that could be larger and more accessible.

Core claim

The central claim is that a fermionic matter interferometer experiences a phase difference ΔΦ = (V2 − V1)T/ℏ from the cosmic neutrino background, where V2 − V1 is the difference in weak-interaction potential energy along the two arms. The paper derives the potentials from the low-energy Standard Model Hamiltonian, separating them into a scalar potential, a pseudo magnetic field, and a spin-spin interaction for both Dirac and Majorana neutrinos, in relativistic and non-relativistic limits. With benchmark inputs—a terrestrial CNB density asymmetry rν ≈ 10^-8 from diffraction near the Earth's surface, a lepton asymmetry Δν ≈ 1 cm^-3, and coherent addition over Nc = 10^8 atoms—the MSW-type phase

What carries the argument

The central object is the effective CNB–matter potential, written as a sum of a scalar potential, a pseudo magnetic field coupling to the target's magnetic moment, and a spin-spin interaction (eqs. 3.16 and 3.27). The load-bearing identity is the interferometer phase formula ΔΦ = (V2 − V1)T/ℏ, which converts a potential-energy difference between two spatially or spin-separated arms into an observable phase. The potential expressions for Dirac and Majorana neutrinos (eqs. 3.12–3.13 and 3.25–3.26) carry the derivation, and the benchmark numbers in Sec. 4 turn them into predictions.

Load-bearing premise

The spin-independent prediction depends on a tiny asymmetry (about one part in 10^8) in the local density of relic neutrinos near the Earth's surface; if that asymmetry does not exist, the two interferometer arms feel identical potentials and the predicted phase shift drops to zero.

What would settle it

A matter interferometer with phase resolution better than 10^-14 rad that measures a spin-dependent phase shift matching the Stodolsky prediction would directly falsify the paper's conclusion that the CNB is unobservable. Alternatively, an independent measurement of the terrestrial relic-neutrino density gradient finding rν to be zero or much smaller than 10^-8 would collapse the MSW-channel benchmark, while confirming a gradient much larger than 10^-8 would revive it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The CNB-induced MSW-type phase shift in matter interferometers is at most about 10^-20 rad for atoms, more than ten orders of magnitude below current 10^-2 rad sensitivity.
  • The Stodolsky (spin-dependent) channel is larger—up to about 10^-12 rad for atoms—but still roughly three orders of magnitude below the most optimistic future proposals.
  • No phase difference arises unless the neutrino background is asymmetric; with symmetric densities both arms sit in identical potentials and the effect vanishes.
  • Applied to fermionic dark matter, the same formalism yields a 'Dark Stodolsky' phase shift that could reach about 10^-10 rad for light dark matter near 10 keV, potentially within reach of future atom interferometers.
  • The gap between benchmark predictions and projected sensitivities defines a concrete target that future matter interferometers would need to reach to observe the CNB.

Where Pith is reading between the lines

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

  • The paper's negative result could be inverted into a bound: a null interferometer measurement at a given phase resolution would translate into an upper limit on the product rν Δν (for the MSW channel) or on the lepton asymmetry Δν (for the Stodolsky channel), constraining new physics that generates large cosmological lepton asymmetries.
  • Because the effective pseudo-magnetic field depends on the target's axial coupling in a species-specific way, a future detection of the Stodolsky phase could be cross-checked by comparing different target species (electron, neutron, 87Sr, 87Rb), providing a fingerprint of weak axial interactions rather than a spurious systematic.
  • The assumption that neutrino magnetic moments are aligned with their momenta is an idealization; any misalignment would suppress the Stodolsky phase further, so the quoted 10^-14 rad benchmark is likely an optimistic ceiling for the spin channel.
  • Spin-echo neutron interferometers, which separate spin states rather than spatial paths, avoid the diffraction-gradient suppression and might reach the Stodolsky benchmark sooner than generic atom-interferometer projections; a purpose-built apparatus optimizing for long interrogation times and large coherent atom numbers would be the most direct experimental follow-up.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper considers the detection of the Cosmic Neutrino Background using fermionic matter interferometers. Starting from the SM low-energy neutrino interaction Hamiltonian, it derives effective potentials in both relativistic and non-relativistic limits, recasts them as scalar potentials, pseudo-magnetic fields, and spin-spin interactions, and then identifies two measurement channels: an MSW-type vector channel that relies on a terrestrial density asymmetry r_nu, and a Stodolsky-type axial channel that relies on a lepton/spin asymmetry Delta_nu. Under benchmark assumptions (r_nu ~ 1e-8, Delta_nu ~ 1 cm^-3, coherent atom number N_c ~ 1e8, T ~ 1 s), the paper estimates phase differences of order 1e-22 rad for the MSW channel, and 1e-14 rad for neutrons / 1e-12 rad for atoms in the Stodolsky channel. These are compared to current sensitivities (~0.01 rad) and future projections (1e-6 to 1e-10 rad), leading to the conclusion that direct CNB detection with matter interferometers is unlikely. A brief extension to fermionic dark matter is also given.

Significance. The paper provides a clear, self-contained formalism and a useful set of benchmark estimates for a novel detection channel. The central negative conclusion is robust to order-of-magnitude uncertainties in the speculative input parameters: even if the Stodolsky channel were as large as quoted, it still falls short of the most optimistic future sensitivities. The paper does not fit any free parameter to the target phase, and the input asymmetries are externally motivated, so the result is genuinely predictive rather than circular. The explicit Dirac/Majorana comparison and the recasting in terms of pseudo-fields and spin-spin interactions are useful for future work. However, two quantitative issues affect the quoted benchmarks: the treatment of non-relativistic chiral neutrinos in the Stodolsky channel and the use of a coherence factor N_c as a signal enhancement. Both issues make the predicted signals smaller, so they strengthen the overall conclusion, but they require correction before the numerical claims can be taken at face value.

major comments (2)
  1. [Sec. 4, Eqs. (4.13)-(4.20), (4.31)-(4.32)] The all-non-relativistic Stodolsky estimates assume that the relic neutrinos populate only helicity s_k=-1 (Dirac) or have a full helicity asymmetry n(-1)-n(+1)=Delta_nu (Majorana). For a left-chiral neutrino of velocity beta, the helicity expectation value is -beta, not -1: the chiral state is a superposition with probabilities (1+beta)/2 and (1-beta)/2 for the two helicities. The helicity-weighted densities that enter the axial spin-dependent terms are therefore beta times the lepton-number asymmetry, not the full Delta_nu. Consequently the spin-dependent phase differences in Eqs. (4.31)-(4.32) are overestimated by a factor ~1/(2 beta), i.e. by two to three orders of magnitude for beta=7.7e-4 or for beta~1e-2 relevant to m~0.05 eV neutrinos. The vector MSW channel is unaffected because it is driven by the lepton-number asymmetry. The central conclusion is strengthened, but the quoted a
  2. [Sec. 4, before Eq. (4.25), Eqs. (4.25)-(4.32)] The phase differences are multiplied by N_c/1e8, effectively treating an ensemble of N_c atoms or neutrons as a single coherent object. In a standard atom or neutron interferometer with independent particles, each particle acquires the same single-particle phase Delta_Phi; the measured fringe phase is Delta_Phi, and the benefit of N particles is a sqrt(N) improvement in phase sensitivity, not an N-fold enhancement of the signal. The quoted benchmarks of ~1e-14 rad for neutrons and ~1e-12 rad for atoms in the Stodolsky channel therefore appear to be overestimated by N_c unless a genuine BEC/collective-coherence regime is assumed. The authors should justify N_c for each device class, or quote per-particle phase shifts and treat N_c as a potential sensitivity gain of sqrt(N_c).
minor comments (4)
  1. [Sec. 3, Eq. (3.2)] The central potential formula is imported from Ref. [5] without derivation. Since the present paper uses a different spin-vector convention and extends the result to Majorana neutrinos and non-relativistic targets, a derivation or a more explicit statement of the correspondence with Ref. [5] would improve reproducibility.
  2. [Sec. 4, Eqs. (4.25)-(4.32)] The benchmark inputs r_nu and Delta_nu are highly uncertain and flavor-dependent, but the paper treats them as flavor-universal single numbers. A short discussion of how the final estimates scale with flavor-dependent or smaller values would help the reader see which conclusions are robust.
  3. [Fig. 2 caption] The caption refers to '87St' in the text; this should be '87Sr'.
  4. [Sec. 5] The summary quotes the Stodolsky phase differences as 'of the order of 1e-14 for neutrons and 1e-12 for atoms'. These numbers already include the N_c factor; please state that explicitly and, in light of the major comments, re-evaluate the quoted ranges.

Circularity Check

0 steps flagged

No significant circularity: all numerically load-bearing inputs are external (standard weak couplings, external density/asymmetry estimates, experimental sensitivities), and the phase-difference predictions follow by direct substitution into standard potential formulas.

full rationale

The paper's claimed derivation is self-contained in the relevant sense: the central phase-difference formulas, Eqs. (4.25)-(4.32), are obtained by inserting (i) standard SM neutral-current couplings from Eqs. (4.1)-(4.5), (ii) externally motivated CNB density asymmetries r_nu (from refs. [16-19]) and lepton asymmetries Delta_nu (from ref. [4]), and (iii) assumed benchmark velocities and polarizations, into the general potential expressions derived in Sec. 3. No parameter is fitted to the predicted phase difference, and no target quantity is defined in terms of the paper's own output. The authors' self-citations ([8]-[11]) are contextual references to their earlier work on related CNB detection ideas and are not load-bearing for the numerical results; the key asymmetries come from independent groups. The 'practical Majorana-Dirac confusion theorem' [36] is also an external result, not a self-citation. The weakest points are openly stated assumptions (flavor-universal r_nu, aligned magnetic moments, Delta_nu ~ 35 cm^-3), but stating an assumption is not circular. Even the skeptic's helicity-factor objection, if correct, would be a physical underestimation issue, not a circularity: it would change the size of a predicted effect without making the prediction equivalent to its input. The benchmarks are genuinely predictive given their stated assumptions, so the circularity score is 0.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

The paper's claims rest on standard weak-interaction theory plus a chain of cosmological and experimental inputs. The most uncertain inputs are the lepton asymmetry, the terrestrial diffraction asymmetry, the spin-alignment assumption, and the coherence count; the paper is transparent that these are assumptions, but they set the scale of every quoted phase.

free parameters (5)
  • Δν (lepton/spin asymmetry) = benchmark 1 cm^-3; bound |Δν|≲35 cm^-3
    Sets the size of both MSW and Stodolsky potentials; chosen at the upper end of [4]; no measurement currently fixes it.
  • rν (terrestrial asymmetry from diffraction) = ~1e-8, flavor-universal
    Taken from refs. [16-19]; required to create a potential difference between surface and underground arms for the MSW channel.
  • |β0| (nonrelativistic neutrino velocity) = 7.7e-4
    Approximated by the galactic virial velocity at the Sun; affects NR phase formulas by factors (1+|β0|) or |β0|.
  • Nc (coherent atom count) = 1e8 for neutrinos, 1e6 for DM
    Assumed number of atoms/nucleons contributing coherently to the phase; uncertainty here is order-of-magnitude and scales ΔΦ linearly.
  • cosθ_v (angle between relativistic and NR species) = 0.67
    Set by assuming relativistic neutrinos follow the CMB dipole and NR neutrinos follow the Cygnus/virial direction (Eq. 4.16); affects the Stodolsky A11 combination.
axioms (7)
  • domain assumption Standard Model low-energy effective weak Hamiltonian with V,A couplings (Eq. 3.1)
    The paper computes all potentials from this interaction; any new physics in the neutrino sector would change the result.
  • domain assumption CNB exists with Tν≈1.95 K and n0≈56 cm^-3 today
    Standard cosmological prediction used as the input background.
  • domain assumption Terrestrial diffraction asymmetry rν≈1e-8 exists and is flavor-universal
    Taken from refs. [16-19]; central to the MSW phase estimate.
  • ad hoc to paper A large lepton asymmetry Δν is present, with Dirac densities n(+1)≈0≈nbar(−1), Eq. (4.13)-(4.15)
    Needed to make the background asymmetric; in the SM this asymmetry is tiny.
  • ad hoc to paper Nonrelativistic neutrino magnetic moments align with momentum: μk/|μk| ≈ βk/|βk|
    Used to evaluate spin-dependent terms; stochastic distortions are neglected.
  • domain assumption All Nc atoms act as one coherent wave function because the CNB de Broglie wavelength is ~0.1 cm
    Cites [8,41]; if the atomic cloud is larger than the wavelength, coherence is reduced.
  • standard math Parallelogram interferometer with constant potential gradient, Eq. (2.2), daily/annual modulations neglected
    Geometry and time-independence assumptions for the phase formula.

pith-pipeline@v1.3.0-alltime-deepseek · 18199 in / 22538 out tokens · 212138 ms · 2026-08-03T20:48:39.103873+00:00 · methodology

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read the original abstract

In this paper we discuss how the Cosmic Neutrino Background can affect the measured phase difference in a matter interferometer. This phase is proportional to a difference in potential energies along the two interferometer paths. The relevant potentials here are the well-known neutrino matter potential and a potential related to the Stodolsky effect. We show how they can be rewritten in terms of scalar potentials, pseudo magnetic fields and spin-spin interactions. Unfortunately, current technology is unlikely to detect this effect and we discuss prospects for the future. We also briefly comment on fermionic Dark Matter which can give rise to very similar effects which can easily be larger than the neutrino case.

Figures

Figures reproduced from arXiv: 2511.18245 by Chrisna Setyo Nugroho, Martin Spinrath.

Figure 1
Figure 1. Figure 1: Simplified sketch of a matter interferometer. At the points A and C, that is at t = 0 and t = 2 T a π/2 pulse is applied which acts as a beam splitter or merger. At B1 and B2 a π pulse is applied which leads to an inversion of the ground and excited state. application, namely to look for the CNB using matter interferometers. But the physics we discuss here can also apply to certain types of DM as we will m… view at source ↗
Figure 2
Figure 2. Figure 2: Dependence of |∆Φ| in an electron, neutron 87St and 87Rb interferometer with T = 1 s for the four cases we discuss. Here we plot the effect of the neutrino-matter potential depending on the combined parameter rν ∆ν in 10−8/cm3 . The electron and neutron, and the 87St and 87Rb lines almost overlap. The current sensitivity taken here is 0.01 rad inspired from results on measuring the gravitational Aharonov-B… view at source ↗
Figure 3
Figure 3. Figure 3: Dependence of |∆Φ| in an electron, neutron 87St and 87Rb interferometer with T = 1 s for the four cases we discuss. Here we plot the effect of the Stodolsky potential depending on the parameter ∆ν in 1/cm3 . The 87St and 87Rb lines almost overlap. The current sensitivity taken here is 0.01 rad inspired from current results from the spin-echo neutron interferometry result [33]. For the future prospects we t… view at source ↗
Figure 4
Figure 4. Figure 4: Dependence of |∆Φ| for the DM case with T = 1 s and GDM = 10 GF . Here we plot the effect of the DM-matter potential and the Dark Stodolsky potential depending on the DM mass. For more details, see main text. Another issue is that without detailed model assumptions we cannot estimate the size of nDM(±1) or even the average orientation of ⃗µDM, i.e., how well it aligns with the DM momentum direction. In ter… view at source ↗

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