Recent Quantum Galileo Interferometer experiments compare two coherent wave packets of the same atom: one following a ballistic free-fall trajectory and the other magnetically held in the laboratory frame. Their measured relative phase agrees with the standard prediction, whose idealized leading dependence is cubic in the free-fall time (T³). This paper develops a structure-first interpretation of that result within Harmonic Physics. On this reading, intrinsic phase relations constrain the paths that can be jointly resolved, observer-level geometry describes their organization, and recombination makes the differential phase accessible without creating the underlying distinction. The experiment supports a reproducible path-dependent phase relation and the consistency of quantum evolution with the equivalence principle in the tested regime. It does not uniquely confirm Harmonic Physics, establish that gravity is non-dynamical, or directly test objective-collapse mechanisms. A distinct empirical test would require an independently defined phase-relational quantity and a reproducible residual beyond the complete standard interferometer model and its known systematics. The paper therefore presents the experiment as a clear interpretive case for structure-first ordering and as a platform for future discriminating tests.
Recent Quantum Galileo Interferometer experiments compare two coherent wave packets of the same atom: one following a ballistic free-fall trajectory and the other magnetically held in the laboratory frame. Their measured relative phase agrees with the standard prediction, whose idealized leading dependence is cubic in the free-fall time (T³). This paper develops a structure-first interpretation of that result within Harmonic Physics. On this reading, intrinsic phase relations constrain the paths that can be jointly resolved, observer-level geometry describes their organization, and recombination makes the differential phase accessible without creating the underlying distinction. The experiment supports a reproducible path-dependent phase relation and the consistency of quantum evolution with the equivalence principle in the tested regime. It does not uniquely confirm Harmonic Physics, establish that gravity is non-dynamical, or directly test objective-collapse mechanisms. A distinct empirical test would require an independently defined phase-relational quantity and a reproducible residual beyond the complete standard interferometer model and its known systematics. The paper therefore presents the experiment as a clear interpretive case for structure-first ordering and as a platform for future discriminating tests.
The unification of quantum theory and the general theory of relativity, describing gravity, is one of the most important challenges in science. Einstein's general theory of relativity is based on the principle of equivalence and has been confirmed to great accuracy for large bodies. However, in the quantum domain, the equivalence principle has been predicted to take a unique form involving a gauge phase, which is equal, in the context of a measurement on Earth, to the quantum phase of a free-falling wave packet relative to its counterpart wave packet which is static in Earth's frame. To measure this phase, we realize a novel cold-atom interferometer in which one wave packet stays static in the laboratory frame while the other is in free fall. The observed relative phase of the wave packets confirms the predicted phase and shows that, in our low energy regime, the equivalence principle may be applied to the quantum domain. Our observation constitutes a fundamental test of the interface between quantum theory and gravity. The new interferometer also opens the door for further probing of the latter interface, as well as to searches for new physics.
Recent experimental developments provide important empirical context for phase-based approaches to physical dynamics. The direct measurement of quantum phase accumulation during free fall using a Quantum Galileo Interferometer (QGI) reported by Dobkowski et al., Science Advances (2026) DOI: 10.1126/sciadv.adj8028, demonstrates that gravitational dynamics can be directly encoded in a measurable phase evolution. Independently, the realization of magnetic-free non-reciprocity through parametric phase modulation reported by Estep, Sounas, Soric, and Alù, Nature Physics (2014) DOI: 10.1038/nphys3134, demonstrates that the relative temporal phase of spatially distributed resonators ( for ) can generate synthetic angular momentum and modify collective dynamics. These results do not validate the Universal Applied Time (UAT) or Unified Principle of Causality (UPC) frameworks. Both experiments were developed and interpreted within established frameworks. Nevertheless, they provide robust experimental precedents for treating discrete phase geometry and temporal modulation as primary experimental variables. Within this context, this work analyzes the eight-coil rotational matrix developed under the UAT/UPC program as an exploratory macroscopic platform. The system implements a synthetic rotational configuration with discrete phase increment , where physical coil opposition is replaced by controlled phase relationships. For eight ideal equal-amplitude components, . Any measured residual must therefore be decomposed into instrumental, phase, frequency, electronic, and potentially structural contributions. During development, a candidate residual was identified under phase/frequency confrontation, alongside a central-coil RMS scale . Both values are treated strictly as candidate invariants requiring independent reproduction. This work explicitly defines the falsification protocol (ideal signals, real channels, random permutation, phase inversion, and frequency variation ) and the hypotheses : residual explained by systematics vs : persists after controls. The detector, calibration code and methodology are documented in the 8+1 coil report. Related identifiers: UAT: 10.5281/zenodo.17729221 UPC: 10.5281/zenodo.18210808 Resonant Hunter v8.4: 10.5281/zenodo.18446712 8+1 Coil Rotational Detector & Calibration: 10.5281/zenodo.19646349 Alù et al. (2014): 10.1038/nphys3134 Dobkowski et al. (2026): 10.1126/sciadv.adj8028
Quantum Tests of the Universality of Free FallIn the process of formulating a "theory of everything" that aims to provide a self-contained model of modern physics by unifying all four fundamental interactions, two theoretical frameworks have yielded important contributions: quantum mechanics, which can explain the nature of physics at the most microscopic length scales such as the origin of spectra of electrons bound in atomic systems, and Einstein's general relativity, that conveys our understanding of gravity over the largest distances across the universe.Although no theory of "quantum gravity", that is consistent over all energy scales, exists to date, certain modifications may enable a reconciliation of quantum mechanics and general relativity.These approaches allow for violations of the universality of free fall (UFF), that among Lorentz invariance and local position invariance constitute Einstein's equivalence principle.The UFF states that all bodies, located at the same space-time point, experience the same acceleration in a gravitational field independently of their composition.Because of its central role in modern physics the UFF has been tested extensively in many experiments, most of which utilized classical test masses.Quantum mechanical tests of the UFF differ from classical ones in various aspects such as the coherence length and spin polarization of the test masses.In this thesis, the first inertial-sensitive matter wave interferometer comparing the free fall of two different elements, 87 Rb and 39 K, was realized.This quantum test of the UFF yielded an Eötvös ratio 𝜂 Rb,K = (0.3 ± 5.4) × 10 -7 , and was limited by statistical uncertainty.In this work, an existing apparatus for rubidium interferometry was extended to the use of potassium and the first inertial-sensitive potassium matter wave interferometer with a resolution to gravitational acceleration of 𝜎 K = 3 × 10 -6 m/s 2 after 4096 s integration has been demonstrated.A description of the experiment including the technical realization and the techniques used is provided.Specifically, the challenges imposed by the use of potassium, which in comparison to rubidium has a smaller mass and lower hyperfine energy splitting, are examined.The thesis furthermore discusses an assessment of the systematic effects influencing the dual species measurement and presents future strategies to further improve the performance of the apparatus.As a preliminary result, it was possible to improve the potassium short-term sensitivity to gravitational acceleration to 𝜎 K = 2.1 × 10 -5 m/s 2 / √ Hz.The results of this thesis pave the way for exciting future experiments to be performed in large-scale apparatuses and in space.
The Einstein equivalence principle (EEP) links the universality of free fall, local Lorentz invariance, and local position invariance to the geometric description of gravity. In quantum systems, however, internal energy is represented by an operator and may occupy coherent superpositions; consequently, equality of classical mass parameters is not sufficient to establish equivalence at the operator level. This work develops a compact operator-level Quantum Equivalence Principle (QEP) residual and performs a literature-based experimental cross-validation using independent high-precision experiments. The theoretical basis follows the operator formulation of Zych and Brukner and its relativistic extension by Das, Fridman, and Lambiase. The quantum weak equivalence sector is tested using the 87Rb Bragg atom-interferometry experiment of Rosi et al., which compared two hyperfine internal-energy eigenstates and a coherent superposition, finding Eotvos ratios consistent with zero and constraining the off-diagonal quantum-WEP parameter to 5 x 10^-8. A classical diagonal WEP benchmark is supplied by the final MICROSCOPE result, eta(Ti,Pt) = [-1.5 +/- 2.3(stat) +/- 1.5(syst)] x 10^-15. The local Lorentz-invariance sector is cross-checked using fast 7Li+ optical clocks, which verified relativistic time dilation at 2 x 10^-10 accuracy, while the local-position-invariance sector is cross-checked using millimetre-scale 87Sr optical-clock gravitational-redshift measurements with fractional-frequency uncertainty 7.6 x 10^-21. Finally, published 2025 gravitational-wave QEP bounds are evaluated, with GW190814 providing the intervals [-0.59,0.54], [-0.40,0.37], and [-0.19,0.17] for WEP-, LLI-, and LPI-associated mass-energy differences, respectively. No statistically significant violation is identified in any analyzed sector. The combined evidence supports operator-level QEP consistency over laboratory quantum superpositions, relativistic clock kinematics, gravitational redshift, precision free fall, and strong-field gravitational-wave phenomenology, while also isolating the remaining experimental gap: direct off-diagonal tests of quantum LLI and quantum LPI.
Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift when considering the atom as a clock operating at the Compton frequency associated with the rest mass. We analyze this claim in the frame of general relativity and of different alternative theories. We show that the difference of "Compton phases" between the two paths of the interferometer is actually zero in a large class of theories, including general relativity, all metric theories of gravity, most non-metric theories and most theoretical frameworks used to interpret the violations of the equivalence principle. Therefore, in most plausible theoretical frameworks, there is no redshift effect and atom interferometers only test the universality of free fall. We also show that frameworks in which atom interferometers would test the redshift pose serious problems, such as (i) violation of the Schiff conjecture, (ii) violation of the Feynman path integral formulation of quantum mechanics and of the principle of least action for matter waves, (iii) violation of energy conservation, and more generally (iv) violation of the particle-wave duality in quantum mechanics. Standard quantum mechanics is no longer valid in such frameworks, so that a consistent interpretation of the experiment would require an alternative formulation of quantum mechanics. As such an alternative has not been proposed to date, we conclude that the interpretation of atom interferometers as testing the gravitational redshift is unsound.
The search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.