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Summary of the research’s main findings and contribution

This manuscript explores the possibility that quantum coherence may be limited not only by environmental decoherence, but also by intrinsic quantum dynamics and spacetime geometry. The author introduces several characteristic scales related to particle motion, wave-packet spreading, oscillatory behavior, and spacetime curvature, and discusses their possible relevance to ultracold atoms, neutron interferometry, nanomechanical resonators, and astrophysical systems.

The manuscript’s main strength is its attempt to organize several physical ideas within a single conceptual framework. It presents the topic in a concise and accessible way and may help stimulate discussion about the distinction between environmental decoherence, wave-packet dynamics, spatial localization, and interference visibility.

At present, however, the manuscript does not yet demonstrate that the proposed quantities represent fundamental limits on quantum coherence. Several of them appear to describe characteristic scales of localization, propagation, or experimental visibility rather than an actual loss of coherence. The work could become a useful conceptual contribution after substantial clarification of its definitions, derivations, physical interpretation, and relationship to existing literature.

Major issues

1. Quantum coherence is not defined quantitatively

The manuscript repeatedly refers to coherence persistence and coherence loss, but it does not define how coherence is measured. The author should specify whether coherence refers to interference visibility, off-diagonal elements of a density matrix, purity, phase stability, or another experimentally measurable quantity.

This distinction is essential because a wave packet may spread during unitary evolution while remaining fully coherent. The manuscript should therefore connect each proposed characteristic scale to a clearly defined coherence observable.

2. Wave-packet spreading should not be identified automatically with decoherence

The discussion appears to treat spatial spreading as an intrinsic loss of coherence. However, wave-packet spreading is a standard consequence of unitary quantum evolution and does not by itself imply decoherence or a transition to classical behavior.

The author should distinguish clearly between:

• spatial delocalization,

• loss of interference visibility,

• phase uncertainty,

• environmental decoherence,

• transition to classical-looking motion.

A specific physical model showing how spreading affects a measurable interference signal would substantially strengthen the paper.

3. The proposed velocity scales require clearer physical interpretation

The manuscript introduces several characteristic velocities and interprets them as boundaries between quantum and classical behavior.

These scales may be useful dimensional estimates, but their interpretation depends on the experimental configuration, observation time, initial state, detector resolution, and preparation procedure. They should not be presented as universal transition thresholds unless this claim is supported by a more general derivation.

The author should explain which scale applies to which physical process and whether the different velocity quantities describe independent mechanisms or closely related estimates.

4. The energy–time uncertainty argument needs a more rigorous explanation

The derivation based on energy–time uncertainty is too brief. The author should define the meaning of the relevant time interval, explain how energy uncertainty is related to velocity uncertainty, and state the assumptions about the particle’s momentum distribution.

Energy–time uncertainty does not have exactly the same mathematical status as position–momentum uncertainty. The manuscript should acknowledge this and provide an operational interpretation of the time scale being used.

5. The critical-frequency claim is insufficiently supported

The manuscript proposes a characteristic frequency and associates it with the persistence of quantum phase coherence.

However, the physical meaning of the associated length scale is not clearly defined, and the connection between frequency and coherence is not derived from a specific oscillator model. The discussion also appears to combine different concepts, including thermal occupation, phase coherence, spatial confinement, and quantum behavior.

The author should separate these concepts and demonstrate the proposed frequency criterion within a clearly specified physical system.

6. Spacetime curvature is not yet connected to measurable coherence loss

The manuscript introduces curvature-related length scales and interprets them as possible coherence limits.

A geometric curvature scale is not automatically a quantum coherence length. The manuscript needs a physical mechanism connecting spacetime curvature with a measurable change in coherence. This could involve gravitational phase differences, proper-time differences between paths, tidal effects on an extended wave packet, or modifications of propagation in curved spacetime.

Until such a derivation is provided, the curvature-based interpretation should be presented as a hypothesis or heuristic proposal rather than an established result.

7. The vector-potential discussion should be reformulated

The section on magnetic fields introduces an effective velocity and states that interference is degraded under a particular condition.

This claim is not sufficiently derived, and its physical interpretation is unclear. In addition, magnetic vector potentials can produce observable phase shifts rather than simply degrade interference.

The discussion should be reformulated using gauge-invariant observables, such as measurable phase differences or interference visibility in a specific experimental configuration.

8. Experimental applications require quantitative validation

The manuscript mentions several experimental platforms but provides only brief qualitative statements.

The paper would be improved by including numerical examples using realistic values for mass, system size, observation time, temperature, coherence time, and detector resolution. These calculations should be compared with established experimental results and known environmental decoherence mechanisms.

Such comparisons are necessary to determine whether the proposed scales provide new predictive information or mainly reproduce familiar dimensional estimates.

9. The literature review is too limited

The reference list contains only three foundational sources.

The manuscript covers several mature fields, including wave-packet dynamics, quantum coherence measures, matter-wave interferometry, nanomechanical resonators, energy–time uncertainty, and quantum theory in curved spacetime. A substantially broader literature review is required.

The author should clearly distinguish between standard results, dimensional estimates, newly introduced definitions, original predictions, and speculative extensions.

Minor issues

1. Several mathematical symbols appear to be missing or incorrectly rendered in the PDF.

2. The notation for system size, wavelength, curvature scale, and coherence scale should be defined consistently.

3. The type of density used in the curvature discussion should be specified clearly.

4. Terms such as “quantum behavior,” “classical-like trajectories,” and “coherence persistence” should be replaced by more precise and measurable descriptions.

5. The assumptions behind each argument should be stated explicitly, including whether the treatment is nonrelativistic, single-particle, Gaussian, freely evolving, and interaction-free.

6. The wording in the abstract suggests a higher level of mathematical rigor than is currently demonstrated. A more cautious formulation would be appropriate unless full derivations are added.

7. The conclusion should clearly separate established physical results from proposed interpretations and future research directions.

8. The presentation would benefit from a table summarizing each proposed scale, its physical meaning, assumptions, domain of validity, and measurable consequence.

Overall recommendation

The manuscript presents an interesting interdisciplinary idea and offers a potentially useful way of organizing several characteristic quantum and geometric scales. Its concise structure and broad physical motivation are positive features.

However, major revision is required before the proposed quantities can be interpreted as intrinsic limits on quantum coherence. The most important improvement would be to define a quantitative coherence observable and demonstrate, in at least one explicit physical model, how the proposed scales affect that observable.

Competing interests

The author declares that they have no competing interests.

Use of Artificial Intelligence (AI)

The author declares that they used generative AI to come up with new ideas for their review.