A 2025 atom-chip experiment (the Quantum Galileo Interferometer) observed the quantum phase of a freely falling matter wave — the de Broglie-gauge phase, proportional to T3T^{3} — and found it consistent with applying the equivalence principle (EP) in the quantum domain. The experiment opens onto, and leaves unresolved, a scientifically substantive question: which of the proposed quantum formulations of the EP actually hold. In particular, no experiment has tested clock-based quantum formulations of the EP, in which the interfered object is a spatially delocalized quantum clock whose internal evolution samples proper time along both arms; and no experiment has reached the active-gravity regime (coherent superpositions of 10910^{9}–101010^{10} amu masses with ~1 1\,s coherence) where gravitationally induced collapse, the quantization of gravity, and possible tensions with the quantum EP become testable. The open problem is to extend experimental quantum-EP testing from the gauge phase to quantum-clock formulations, with the massive-particle regime as the long-term horizon.

Background

Einstein's equivalence principle (EP) — roughly, that all bodies fall with the same acceleration regardless of mass or composition, and that no local non-gravitational experiment distinguishes free fall from absence of gravity — underlies the metric description of general relativity and is verified to high precision for classical bodies. In quantum mechanics, free fall acquires a genuinely new signature: the phase of a matter wave. When one wave packet of an interferometer is held fixed in the laboratory while the other falls freely, the predicted relative phase scales as T3T^{3}, where TT is half the interferometer time — in contrast to the familiar T2T^{2} scaling of light-pulse atom interferometers (devices that split and recombine atomic wave packets using photon recoil). This T3T^{3} phase, called the phase of a freely falling object or the de Broglie-gauge phase, has long been predicted to be a consequence of applying the EP to quantum systems. An atom-chip experiment (a chip carrying current-carrying wires that produce magnetic traps and gradients near a Bose–Einstein condensate, an ultracold coherent cloud of atoms) realized this geometry in 2025 using a Stern–Gerlach interferometer (SGI) — an interferometer whose beam splitters are magnetic-field gradients acting on the atomic spin, requiring no light pulses at all — in what the authors call a Quantum Galileo Interferometer (QGI), where one wave packet is levitated by a magnetic force balancing gravity while the other is in free fall. The measured phase confirmed the predicted T3T^{3} behavior, and the authors concluded that, in this low-energy regime, the EP may be applied to the quantum domain. The interpretation of this measured phase is itself contested: Asenbaum and Overstreet argued in a 2025 comment that the observed phase is a magnetic recoil phase — inversely proportional to inertial mass and independent of gravitational mass, analogous to recoil phases in light-pulse interferometers — while the authors' reply maintains that the Quantum Galileo Interferometer is sensitive to a uniform gravitational field with and without the levitation condition. This exchange concerns the already-completed measurement, not the open directions below, but it sharpens the requirement that future quantum-EP protocols have a frame-independent interpretation. Beyond this gauge-phase test, the paper's outlook identifies deeper open directions. First, more elaborate quantum formulations of the EP have been proposed but not tested: Zych and Brukner showed that the Einstein EP requires the rest mass-energy that constitutes a system's inertia, its weight, and its internal Hamiltonian to be equivalent, and that in quantum mechanics internal energy is an operator — so for a delocalized quantum system the EP acquires operator-valued content that classical formulations do not capture. A 'quantum clock' is an atom or molecule whose internal degrees of freedom (e.g., hyperfine or optical states) evolve periodically and can serve as a clock reading proper time; putting such a clock into a spatial superposition in an interferometer allows tests of the universality of clock rates (one facet of local position invariance, the EP requirement that clock rates be independent of position in a gravitational field) in a regime inaccessible to classical clocks. The only clock-in-SGI experiment to date demonstrated that a clock can act as a which-path witness, but did not test the EP. Protocols for a true clock-based quantum-EP test — for example an atom-interferometric universality-of-clock-rates test whose signature again scales as T3T^{3} — exist in theory but have not been realized. Second, the experiment probed only the passive role of mass (how a body responds to gravity). When mass plays an active role — the source of gravity — new physics may appear: the Diósi–Penrose conjecture (Penrose's proposal that a superposition of mass distributions is unstable, with a gravitationally driven collapse of the wave function, the lifetime being set by the gravitational self-energy of the difference between the superposed mass distributions) and the question whether gravity is quantum at all, as addressed by the proposed Bose–Marletto–Vedral-style experiments that would witness gravitationally induced entanglement between two massive particles in superposition. The source paper notes that probing this regime requires coherent superpositions of masses of order 10910^{9}–101010^{10} atomic mass units persisting for about a second — several orders of magnitude beyond the most massive molecular interferometry superpositions (~25 25\,kDa) to date — and that such an interferometer could reveal tensions between active-mass gravitational effects and the quantum EP. Technical obstacles along this path are quantified in the source: on an atom chip, the magnetic-field curvature that lenses and distorts the wave packets scales as I/r3I/r^{3} (current over distance to the chip) while the useful gradient scales only as I/r2I/r^{2}, so increasing the splitting while suppressing curvature is technologically hard; and the present phase measurement is limited by systematics including the kick-to-hold current ratio (0.5%–1% sensitivity), ambient magnetic gradients (∼0.68 \sim0.68\,G/cm), second-order Zeeman accelerations (aSOZ≈0.10 a_{\mathrm{SOZ}}\approx0.10\,m/s2^{2}, i.e. spin-dependent shifts quadratic in magnetic field that mimic accelerations), and residual non-trajectory phase contributions (up to ∼1 \sim1\,rad).

Problem Statement

The problem is to extend experimental tests of the equivalence principle in the quantum domain beyond the already-measured de Broglie-gauge (T3T^{3}) phase, mapping which proposed quantum formulations of the EP actually hold. It has two linked components serving this single objective: (1) Near-term core — realize a matter-wave interferometric test in which the interfered object is a delocalized quantum clock, i.e. an atom whose internal-state evolution reads proper time along each arm, so that the universality of clock rates (local position invariance) is tested for a spatially superposed clock, for example by adapting the T3T^{3}-scaling universality-of-clock-rates protocol of Di Pumpo et al. to an atom-chip Stern–Gerlach realization — the test of the "more complex formulations suggested for the equivalence principle in the quantum domain" that clock-wave-packet manipulation opens. (2) Long-term horizon — extend to the active-gravity regime, i.e. coherent spatial superpositions of masses of order 10910^{9}–101010^{10} atomic mass units with coherence times of order 1 1\,s (for example, nanodiamonds in a Stern–Gerlach interferometer), where the Diósi–Penrose gravitationally induced collapse conjecture, the quantization of gravity, and possible tensions between active-mass gravitational effects and the quantum EP become experimentally accessible. Component (1) constitutes the completion boundary of this problem window — a concrete, quantified interferometric scheme that realizes the universality-of-clock-rates test at the design level for a spatially superposed clock in an atom-chip Stern–Gerlach interferometer (species and internal states, state preparation, splitting and levitation, phase readout, and a systematic-error budget covering the atom-chip geometry: magnetic-field curvature and lensing, kick-to-hold current ratio, ambient gradients, second-order Zeeman accelerations, and non-trajectory phases); component (2) is the long-term extension toward which component (1) is a milestone.

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