Geometric Phase without Time: A Universal Correction in Matter-Wave Interference

Uwe Becker

Jörg Geisbauer

This is Part II of the series The Geometry of Phase. It provides a strictly conservative, phase-geometric reconstruction of de Broglie matter waves from the invariant proper-time action of massive matter. No new physics is introduced. The central claim is that the de Broglie matter wave is the frame-dependent spatial expression of the invariant proper-time phase of massive matter. The paper serves as the clean bridge between the phase-first interference account of Part I and the exploratory curvature-coupled extensions of Part III. It remains deliberately conservative and identifies the proper-time action phase as the invariant core of massive matter-wave phase. Related works: Part I: Phase-First Quantum Interference (DOI: 10.5281/zenodo.20687982) Part III: Phase Meets Curvature (DOI: 10.5281/zenodo.20683956)

Jörg Geisbauer

This paper explores a possible bridge between quantum matter-wave phase and spacetime curvature. The conservative starting point is the established relation between relativistic action, proper time, and quantum phase: for massive matter, the accumulated phase is determined by the proper-time integral along a worldline. In curved spacetime, this makes matter-wave phase sensitive to the metric geometry. Building on this relation, the paper asks whether matter-wave phase may acquire additional curvature-dependent contributions beyond the standard proper-time action phase. Such a contribution would not replace quantum mechanics or general relativity. Instead, it would represent a controlled covariant correction that becomes physically meaningful only if it produces calculable and falsifiable deviations in matter-wave interferometry, precision clock comparisons, gravitational redshift tests, or related high-precision experiments. The central proposal is that quantum phase, proper time, and spacetime curvature may be linked through a deeper action-geometric structure. In this view, phase is not treated merely as a formal parameter on a fixed background, but as a possible probe of how matter samples spacetime geometry. The paper does not claim a completed theory of everything. It identifies a concrete research direction: new physics may appear as measurable curvature-dependent corrections to phase accumulation. This work is Part III of the series The Geometry of Phase. Parts I and II reconstructed quantum interference and de Broglie matter waves from a phase-first perspective within standard physics. The present paper extends that line of thought toward curvature-coupled matter-wave phase and possible experimentally testable deviations. This manuscript is intended as a conceptual and exploratory foundations paper. It separates established reconstruction from speculative extension and provides a mathematical starting point for future tests of curvature-coupled quantum phase.

R. Citro, O. Durante

Andrii Stafeiev

Xuguang Yue, Shujuan Liu, Biao Wu +1 more

Ultra-cold atomic gases provide a new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science 315 1556 (2007)]. Our theory paves the way to experimentally study various types of ultra-cold atomic gases with the means of matter wave interference.