Reply to comment on: Observation of the quantum equivalence principle for matter-waves

Barak Trok; Chiara Marletto; David Groswasser; Ivette Fuentes; Maxim Efremov; Or Dobkowski; Peter Skakunenko; Roger Penrose; Ron Folman; Vlatko Vedral

Reply to comment on: Observation of the quantum equivalence principle for matter-waves

T0 review · 0 major / 3 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A closed matter-wave interferometer necessarily measures gravity, even without levitation.

desk verdict A technically sound reply that vindicates the QGI's g-sensitivity; the apparent g-dependence of the closing condition cancels, so the rebuttal holds. read the letter →

arxiv 2504.21626 v1 pith:6JBYV3YI submitted 2025-04-30 quant-ph cond-mat.quant-gasgr-qcphysics.atom-ph

Or Dobkowski , Barak Trok , Peter Skakunenko , Yonathan Japha , David Groswasser , Maxim Efremov , Chiara Marletto , Ivette Fuentes

show 4 more authors

Roger Penrose Vlatko Vedral Wolfgang P. Schleich Ron Folman

This is my paper · ORCID

classification quant-phcond-mat.quant-gasgr-qcphysics.atom-ph PACS 03.75.Dg04.80.Cc

keywords quantumGalileointerferometerequivalenceprincipleKennardphaseT^3uniformgravitationalfieldlevitationconditionclosingatominterferometry

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This reply defends the claim that the Quantum Galileo Interferometer (QGI) measures a uniform gravitational field, against a recent comment asserting the phase arises purely from magnetic forces. The authors show that the comment ignored essential terms in the action and implicitly applied a levitation condition. They derive the interference term both with and without levitation, finding it always contains g, provided the interferometer loop is closed by a g-dependent condition. The result matters because it settles whether a uniform gravitational field is observable in principle and clarifies how an external reference frame makes gravity measurable.

What carries the argument

The central object is the interference term I, defined as the overlap between the two branches' unitary evolutions. Its phase is the difference of two Kennard phases: one from the uniform gravitational field acting on the ballistic wave packet and one from the residual acceleration of the reference wave packet. The closing condition (B8), T = 2p0/(m_i Δa + m_g g), makes |I| = 1 and is exactly what forces g to enter the phase through the timing of the momentum kicks.

What would settle it

Measure the interference signal while scanning the interferometer time T around the closing value for a fixed kick velocity; Eq. (5) predicts |I| = 1 exactly only at T = 2p0/(m_i Δa + m_g g), and the phase should follow the predicted $T^{3}$ law. A deviation outside experimental uncertainties would refute the claim.

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Extended reading notes

Core claim

The paper's central claim is that the interference term of the QGI is I = exp[i/(24ℏ)(1 − 2(m_g/m_i)(g/a)) m_i $a^{2}$ $T^{3}$] when the interferometer loop is closed, and that this depends explicitly on the gravitational acceleration g. The expression holds even when the levitation condition m_i a = m_g g is not satisfied, as long as the closing condition T = 2p0/(m_i Δa + m_g g) is used to fix the time or the kick velocity. In the levitated case Δa = 0, the phase reduces to the original QGI result. The derivation uses Feynman propagators and the Kennard phase, avoiding semiclassical ambiguities that led the comment astray.

Load-bearing premise

The claimed g-sensitivity holds only if the interferometer is closed in space-time via the condition T = 2p0/(m_i Δa + m_g g), which links the kick velocity to the gravitational field.

Editorial extensions

If this is right

The QGI phase, Eq. (6), grows as T^3 and explicitly contains g, so the same device can be used to monitor local gravitational acceleration.
Because the phase depends on the ratio m_g/m_i, the experiment provides a direct route to testing the equivalence principle in quantum superposition.
Since levitation and catapulting need not be magnetic, optical or electric versions of the QGI would also measure g under the same closing condition.
The closing condition tells an experimenter exactly how to adjust the interferometer time or kick velocity in order to operate as a gravity sensor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the residual acceleration Δa is deliberately made nonzero, the phase acquires a term quadratic in Δa, which could be used to amplify or cancel the gravitational contribution in systematic studies.
The argument generalizes to any T^3 interferometer: any closed loop comparing two uniform accelerations retains a g-dependent Kennard phase when an external frame exists, which may settle similar controversies in other configurations.
A direct test of the correction would be to recompute the comment's action including the magnetic potential and catapult pulses; a complete calculation should reproduce Eq. (A10), showing that the omission, not the physics, removed g.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Short version: the authors are right. The comment's claim that g factors out of the QGI phase only works if you ignore the levitation condition and the catapult action terms. This reply fixes that by calculating the full propagator including the residual acceleration, and the algebra checks out. The new piece is Eq. (6), showing the phase is proportional to (1 - 2(m_g/m_i)(g/a)) a^2 T^3, so g is manifestly there. I re-derived the substitution and the apparent g-dependence in the closing condition cancels: T = 2p0/(m_i a). So the experimenter can fix T and p0 without knowing g and still get a g-dependent phase. That's the key point and it survives.

The propagator calculation in Appendix B is clean and self-contained. The normalization cancels, the z' integral gives a delta function, and the Kennard phases are correct. Appendix A gives the action calculation in the comment's notation, which is useful for anyone who still thinks in semi-classical terms. The citation pattern is fine; the representation-free approach is a known tool from prior work, not a self-serving reference.

Where the paper is weaker: Section IV is mostly philosophy, and it reads like a blog post. The analogy with Newton's apple is cute but doesn't resolve the genuine interpretational question of whether 'measuring g' with an external lab frame conflicts with the EEP. That section could be tightened or cut; it doesn't affect the technical result. Also, the paper claims sensitivity to g in the absence of levitation, but only when the closing condition is met. Off closure, |I| is not 1 and the simple phase expression breaks down. That's not a flaw here because the comment assumed closure too, but it's worth remembering when generalizing.

Bottom line: this is a sound, incremental reply to a specific criticism. It doesn't reshape the field, but it settles the technical dispute in the authors' favor. The math is reproducible and I couldn't find a load-bearing error. I'd send it to peer review; the referee should focus on the scope conditions and maybe ask for a cleaner presentation of Section IV. If I were still working in atom interferometry I'd want this in the record.

Recommendation: accept with minor revisions, mainly making clear that the closing condition is g-independent and the phase result holds under closure.

Referee Report

0 major / 3 minor

Summary. The manuscript is a reply to a comment [2] that claimed the measured phase shift in the Quantum Galileo Interferometer (QGI) can be calculated purely from the magnetic field gradient and therefore does not measure gravity. The reply argues that this claim follows from an incomplete action calculation and a misinterpretation of the Einstein Equivalence Principle. The main technical content is a propagator calculation (Appendix B) giving the interference term I = exp[-i/(24ℏ)(m_g^2g^2/m_i - m_i(Δa)^2)T^3], with Δa = a - (m_g/m_i)g, under the closing condition T = 2p0/(m_iΔa + m_gg). The reply then rewrites this in terms of a as Eq. (6), exhibiting an explicit dependence on g. A complementary action calculation in Appendix A and a discussion of the lab frame as an external reference are also provided.

Significance. If correct, this settles the technical dispute in favor of the original paper: the QGI phase is sensitive to the uniform gravitational acceleration g both when the levitation condition holds and when it does not. The derivation is self-contained, uses no fitted parameters, and the apparent g-dependence of the closing condition cancels on substitution (T = 2p0/(m_i a)), so the experimenter can enforce closure using a and p0 alone. The reply also correctly identifies omitted terms in the comment's action calculation. The philosophical discussion of the equivalence principle is not needed for the central result but does not undermine it.

minor comments (3)

[Appendix A, Eq. (A9)] The sign in Eq. (A9) is inconsistent with Eq. (A10) and Eq. (A13). Substituting Fmag = m_i a and m_g g0 = m_i \bar{g} into Eq. (A9) gives the negative of Eq. (A10); since Eq. (A10) and Eq. (A13) agree with the main-text result, Eq. (A9) appears to contain an overall sign error and should be corrected.
[Sections II-III and Appendix A] The time variable T is used with different meanings in different parts of the manuscript. In the main text and Appendix B, T is the interval between the two catapult pulses and the closing condition is T = 2p0/(m_i a), whereas in Appendix A the total interferometer time is 2T and the closing condition is v0 = (Fmag/m_i)T. This notational mismatch makes it unnecessarily difficult to compare Eq. (5) with Eq. (A13) and should be clarified.
[Section IV] The discussion of the Einstein Equivalence Principle in Section IV is broader than the technical derivation and asserts rather than formalizes the claim that a uniform gravitational field is observable from an external frame. This does not affect the mathematical result, but the reply would be strengthened by clearly separating the interpretive remarks from the derivation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase calculation is self-contained; self-citations are to established methods, not to the target result.

full rationale

Walking the derivation, the interference term Eq. (5) is obtained by evaluating Eq. (3) with the standard linear-potential propagators (B3)-(B4), and the normalization constant is used, not fitted. The interference term is an output of a direct calculation, not an input. The closing condition T = 2p0/(miΔa + mgg) (Eq. B8) initially looks g-dependent, but substituting the definition Δa = a - (mg/mi)g gives T = 2p0/(mia), which is independent of g. Thus no hidden calibration of g enters through the timing; the experimenter can enforce closure using only a and p0, and Eq. (6) then follows algebraically. The citations to the representation-free approach [4,5] and to the propagator technique [3] supply computational methods that are independently established and are not used as a substitute for the calculation, which is reproduced in Appendix B and cross-checked by the action calculation in Appendix A. The central claim of g-sensitivity is derived from Hamiltonians that explicitly contain mggz; showing that the resulting phase depends on g is the content of the calculation, not a circular redefinition. No fitted parameter is renamed as a prediction, and no uniqueness claim is imported from self-citation. The only limitation is that the simple phase expression applies when the closing condition is satisfied, but that is an explicit experimental assumption, not a circular step. Overall, the reply is self-contained with respect to its central claim, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central derivation rests on standard non-relativistic quantum mechanics (linear-potential propagators), the physical modeling of the reference and ballistic wave packets as experiencing constant accelerations, and the experimental constraints of levitation and closing conditions. No free parameters are fitted; all constants are physical or experimental settings.

assumptions (5)

standard math Propagator for a particle in a linear potential (Eqs. B3-B4) with Kennard phase φ = -m a^2 T^3/(24ℏ).
Standard quantum-mechanical result used to evaluate the interference term.
standard math Interference probability is given by Eq. (1) with I = ⟨ψ|U1†U2|ψ⟩.
Standard definition for an interferometer's output probability.
domain assumption The reference wave packet experiences constant acceleration a (or Δa = a - m_g g/m_i) throughout the evolution, and the catapult pulses are instantaneous.
The magnetic field gradient is treated as spatially uniform and constant over the interferometer time; the pulse duration is taken in the τ→0 limit.
domain assumption The interferometer loop is closed in position and momentum via the closing condition T = 2p0/(m_i Δa + m_g g).
The experiment demands that the two wave packets overlap at the detector; this condition introduces g into the phase and is necessary for |I|=1.
domain assumption The lab frame serves as an external reference frame for observing the effect of a uniform gravitational field.
The interpretation that the QGI measures g relies on comparing atomic motion to the lab frame, as argued in Section IV.

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Pith. "Pith review of Reply to comment on: Observation of the quantum equivalence principle for matter-waves." pith.science (2026). https://pith.science/paper/6JBYV3YI

@misc{pith2026250421626,
  author       = {Pith},
  title        = {Pith review of: Reply to comment on: Observation of the quantum equivalence principle for matter-waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6JBYV3YI}},
  note         = {Machine review of arXiv:2504.21626}
}

read the original abstract

We show that in contrast to a recent claim, the Quantum Galileo Interferometer is sensitive to a uniform gravitational field in the presence and even in the absence of the levitation condition.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

9 extracted references · 7 canonical work pages

[2]

residual acceleration

(A2) But, to get the correct phase of the ballistic wave packet, we must calculate also the action during the catapulting pulses, during which there is a magnetic potential acting on the wave packet, resulting in an acceleration akick =µ ∇Bpulse /m i for a duration τ, such that akick = v0 τ . The action during the ﬁrst pulse is given by Skick = lim τ →0 ∫...

work page
[1]

a uniform gravitational ﬁeld is unobservable

and in the comment [2], the prefactor 1 / 24 turns into 1 / 3). We emphasize that the QGI is another realization of a T 3-atom interferometer [3, 7] and measures the diﬀerence of the Kennard phases caused by the two diﬀerent acce lerations in the two arms of the interferom- eter. In the presence of the levitation condition, the acceleration of the ballist...

work page
[3]

Dobkowski et al., Observation of the quantum equivale nce principle for matter-waves, arXiv:2502.14535 (2025) 7

O. Dobkowski et al., Observation of the quantum equivale nce principle for matter-waves, arXiv:2502.14535 (2025) 7

arXiv 2025
[4]

Asenbaum and Ch

P. Asenbaum and Ch. Overstreet, Magnetic recoil interfe rometer in a uniform gravitational ﬁeld. Comment on Observation of the quantum equivalence principle for matte r-waves, arXiv:2504.15409 (2025)

arXiv 2025
[5]

Zimmermann, M

M. Zimmermann, M. A. Efremov, A. Roura, W. P. Schleich, S. A. DeSavage, J. P. Davis, A. Srinivasan, F. A. Narducci, S. A. Werner, E. M. Rasel, T 3 -Interferometer for atoms, Appl. Phys. B 123, 102 (2017)

work page 2017
[6]

W. P. Schleich, D. M. Greenberger and E. M. Rasel, A repres entation-free description of the Kasevich–Chu interferometer: a resolution of the redshift controversy, New. J. Phys. 15, 013007 (2013)

work page 2013
[7]

W. P. Schleich, D. M. Greenberger, and E. M. Rasel, Redshi ft Controversy in Atom Interferometry: Representation Dependence of the Origin of Phase Shift, Phys. Rev. Lett. 110, 010401 (2013)

work page 2013
[8]

G. G. Rozenman, M. Zimmermann, M. A. Efremov, W. P. Schlei ch, L. Shemer, A. Arie, Amplitude and Phase of Wave Packets in a Linear Potential, Phys. Rev. Lett. 122, 124302 (2019)

work page 2019

Show all 9 references

[9]

O. Amit, Y. Margalit, O. Dobkowski, Z. Zhou, Y. Japha, M. Z immermann, M. A. Efremov, F. A. Narducci, E. M. Rasel, W. P. Schleich, and R. Folman, T 3 Stern-Gerlach Matter-Wave Interferometer, Phys. Rev. Let t. 123, 083601 (2019) 8

2019

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [2]

residual acceleration

(A2) But, to get the correct phase of the ballistic wave packet, we must calculate also the action during the catapulting pulses, during which there is a magnetic potential acting on the wave packet, resulting in an acceleration akick =µ ∇Bpulse /m i for a duration τ, such that akick = v0 τ . The action during the ﬁrst pulse is given by Skick = lim τ →0 ∫...

work page

[2] [1]

a uniform gravitational ﬁeld is unobservable

and in the comment [2], the prefactor 1 / 24 turns into 1 / 3). We emphasize that the QGI is another realization of a T 3-atom interferometer [3, 7] and measures the diﬀerence of the Kennard phases caused by the two diﬀerent acce lerations in the two arms of the interferom- eter. In the presence of the levitation condition, the acceleration of the ballist...

work page

[3] [3]

Dobkowski et al., Observation of the quantum equivale nce principle for matter-waves, arXiv:2502.14535 (2025) 7

O. Dobkowski et al., Observation of the quantum equivale nce principle for matter-waves, arXiv:2502.14535 (2025) 7

arXiv 2025

[4] [4]

Asenbaum and Ch

P. Asenbaum and Ch. Overstreet, Magnetic recoil interfe rometer in a uniform gravitational ﬁeld. Comment on Observation of the quantum equivalence principle for matte r-waves, arXiv:2504.15409 (2025)

arXiv 2025

[5] [5]

Zimmermann, M

M. Zimmermann, M. A. Efremov, A. Roura, W. P. Schleich, S. A. DeSavage, J. P. Davis, A. Srinivasan, F. A. Narducci, S. A. Werner, E. M. Rasel, T 3 -Interferometer for atoms, Appl. Phys. B 123, 102 (2017)

work page 2017

[6] [6]

W. P. Schleich, D. M. Greenberger and E. M. Rasel, A repres entation-free description of the Kasevich–Chu interferometer: a resolution of the redshift controversy, New. J. Phys. 15, 013007 (2013)

work page 2013

[7] [7]

W. P. Schleich, D. M. Greenberger, and E. M. Rasel, Redshi ft Controversy in Atom Interferometry: Representation Dependence of the Origin of Phase Shift, Phys. Rev. Lett. 110, 010401 (2013)

work page 2013

[8] [8]

G. G. Rozenman, M. Zimmermann, M. A. Efremov, W. P. Schlei ch, L. Shemer, A. Arie, Amplitude and Phase of Wave Packets in a Linear Potential, Phys. Rev. Lett. 122, 124302 (2019)

work page 2019