Quantum mechanics takes the phase of a state to lie on a continuous U(1), with relative phases varying smoothly and no preferred value. This paper formulates and bounds a minimal departure: a discrete ℤₙ substructure marking N preferred directions, encoded in one parameter p that vanishes for standard theory. To first order, a two-branch interferometer scanned in relative phase φ develops sidebands at (N−1)φ and (N+1)φ of relative amplitude p/2N, locked to a fixed frame — an N-fold fringe anisotropy, a broken phase-rotation symmetry. Its isotropic part is a visibility loss, degenerate with decoherence; the anisotropic harmonics are falsifiable. The most precise phase metrology reads a freely winding phase in which the modulation averages away and is blind to p; the bound comes instead from Josephson current–phase sinusoidality and matter-wave phase linearity, giving p ≲ 10⁻¹. A dedicated fixed-frame search could improve this by orders of magnitude.
Quantum mechanics takes the phase of a state to lie on a continuous U(1), with relative phases varying smoothly and no preferred value. This paper formulates and bounds a minimal departure: a discrete ℤₙ substructure marking N preferred directions, encoded in one parameter p that vanishes for standard theory. To first order, a two-branch interferometer scanned in relative phase φ develops sidebands at (N−1)φ and (N+1)φ of relative amplitude p/2N, locked to a fixed frame — an N-fold fringe anisotropy, a broken phase-rotation symmetry. Its isotropic part is a visibility loss, degenerate with decoherence; the anisotropic harmonics are falsifiable. The most precise phase metrology reads a freely winding phase in which the modulation averages away and is blind to p; the bound comes instead from Josephson current–phase sinusoidality and matter-wave phase linearity, giving p ≲ 10⁻¹. A dedicated fixed-frame search could improve this by orders of magnitude.
This work presents a minimal, experimentally testable deviation from standard two-path interference. The deviation arises from an underlying discrete phase structure and appears as a small first-harmonic bias in the interference fringe. The predicted effect does not introduce higher harmonics or alter the qualitative form of the fringe. Instead, it manifests as a coupled visibility rescaling and phase offset that can be absorbed into standard sinusoidal fits. For this reason, the deviation is not directly visible at the level of fringe shape alone. To distinguish the effect from conventional systematics, a phase-cycling discriminator is introduced. Under controlled quarter-phase shifts, the residual is predicted to exhibit a structured quadrature rotation that is not generically reproduced by noise, detector imbalance, or calibration drift. A set of null-control conditions is provided to isolate this behavior experimentally. A characteristic magnitude for the effect is estimated under a class of structural assumptions, yielding a candidate scale on the order of 10−410^{-4}10−4, with a more strongly suppressed regime near 10−710^{-7}10−7. These values lie near the sensitivity threshold of high-precision interferometric measurements. The result is a concrete, falsifiable prediction: either a stable first-harmonic residual with the specified phase-cycling structure is observed, or the corresponding parameter regime is constrained. This document isolates the observable prediction and experimental test, independent of the broader theoretical framework from which it is derived.
This note proposes a simple, falsifiable interferometric test for structured deviations from standard two-path interference. In conventional interference, the observed intensity is described by a single effective phase parameter: I(ϕ)=P1+P2+2P1P2cosϕ, and deviations are typically attributed to visibility loss or phase offset. The present protocol tests for a different class of behaviour: phase-locked deviations that depend on the internal structure of the phase profile applied to one arm of the interferometer. A controlled phase modulation of the form ϕ(x)=n⋅f(x)\phi(x) = n \cdot f(x) ϕ(x)=n⋅f(x) is introduced in one arm, where nn n indexes the complexity of the imposed phase structure. The resulting interference signal is measured as a function of the global phase and decomposed into quadrature components: In(ϕ)=Cn+Vn[Ancosϕ+Bnsinϕ]. A deviation metric is defined relative to the baseline (flat-phase) case: Δn=(An−A0)2+(Bn−B0)2. The testable prediction is that, if structured phase-dependent effects are present, then: the baseline satisfies Δ0≈0\Delta_0 \approx 0 Δ0≈0; the deviation Δn\Delta_n Δn increases systematically with the imposed phase structure, and the deviation remains phase-locked in the quadrature basis and cannot be absorbed into a simple phase offset. The protocol includes explicit control conditions to distinguish such behaviour from conventional effects: symmetric modulation of both arms should eliminate the deviation; random phase noise should reduce visibility but not produce systematic scaling in Δn\Delta_n Δn; and phase referencing is required to resolve the quadrature structure. The outcome is binary. If no structured deviation is observed, the hypothesis is falsified. If a phase-locked, structure-dependent deviation is observed, then the standard interference model is incomplete under these conditions. This proposal is intentionally model-independent. While motivated by broader work on structured phase transport in discrete systems, the experimental test does not rely on that framework and can be evaluated directly.
Experimental Signatures and Falsifiability of Phase Ontology: How a Phase-Primary Framework Can Be Tested (Phase Ontology — Part VII) completes the Phase Ontology series by translating its core claims into concrete, falsifiable expectations. While Parts I–VI argue that phase coherence is physically real and that spacetime is an emergent projection of stable phase relations, this paper makes the scientific demand explicit: the framework must constrain what should be observed in the laboratory—not merely reinterpret existing results. The paper outlines a set of testable signatures that should appear if measurement is genuinely a phase-locking process, if coherence is a physical resource that can be preserved or dispersed, and if detectors and environments are active material participants rather than generic sources of noise. Key experimental arenas include: (1) detector-dependent phase-locking thresholds (e.g., interferometry where small, controlled detector-material changes produce disproportionate shifts in localization/fringe behavior), (2) coherence capacity and delayed classicality (engineered environments that produce non-linear regime changes rather than only smooth decoherence), (3) entanglement under structured phase environments (sensitivity to structured phase modulation beyond standard loss/noise parameters), (4) precision clocks as phase probes (searching for residual coherence-environment dependencies beyond known systematics), and (5) macroscopic coherence bridge regimes in superconducting and mesoscopic networks where topology and coupling geometry should matter in structured ways. Crucially, the paper states what falsification would look like in practice: if across multiple platforms detector variations yield no structured threshold effects, coherence isolation produces only fully predictable smooth behavior, entanglement responds solely to standard channel parameters, and precision clocks show no reproducible residual coherence-structure dependence, then Phase Ontology remains an interpretation but loses its claim to be an empirically distinct physical framework. A staged experimental program is proposed, moving from tabletop interferometry to progressively more demanding coherence and clock tests.
Abstract Optical Michelson–Morley experiments constrain anisotropy in vacuum light propagation with extraordinary precision, but they do not automatically exclude residual preferred-frame effects in the matter sector. Because matter waves are dispersive, a preferred constitutive frame can remain effectively hidden in optical null tests while producing an anisotropic phase signature in matter-wave interferometry. In this work we derive the corresponding interferometric observable for a class of preferred-frame kinematical models in which wave propagation is isotropic in a distinguished frame (F_0), while laboratory observables are reconstructed in a moving frame (F'). Starting from a phase-based constitutive map between the preferred frame and the laboratory frame, we derive the induced transformations of frequencies, wave vectors, energies, and momenta, and formulate the experimentally relevant observable as the phase difference accumulated between two constrained interferometric branches. For a symmetric horizontal light-pulse Mach–Zehnder geometry and a preparation protocol with fixed laboratory frequency at the beam splitter, the leading preferred-frame contribution takes the form S(θ,t) = A₂ β²_lab(t) cos(2θ) + O(β⁴_lab) This identifies a clean quadrupolar target signal with natural sidereal and seasonal modulation. The paper clarifies the respective roles of propagation, laser, and diffraction phases, and shows why the effect is not trivialized by the local exactness of the phase differential. The coefficient (A_2) should be interpreted as a propagation-level kinematic coefficient of the model rather than as a complete instrument-specific forecast. The result provides a concrete falsifiable target for testing whether residual preferred-frame effects could persist in the dispersive matter sector despite optical null results. Matter-wave interferometry therefore emerges here as a direct empirical probe of constitutive preferred-frame kinematics rather than as a simple extension of optical isotropy tests.
This work develops a relativistic variational framework based on phase invariance. Starting from relativistic wave-phase invariance, the relation -ħ δΦ = δE δt - δp·δx is obtained, together with the limiting cases δt = 0 ⇒ ħ δΦ = δp·δx and δx = 0 ⇒ -ħ δΦ = δE δt. The framework associates a given phase with a family of admissible variation configurations rather than with a unique localized classical configuration. This motivates the global operator Λ = |L><L|, acting as Λ|C> = <L|C>|L> = α|L>. A first falsifiable experiment is proposed to test history dependence. Two photon ensembles are prepared through different controlled histories and restored to the same final operational state before entering the same interferometer. Standard state-based quantum mechanics predicts P_A(x) = P_B(x), while the history-sensitive framework allows the possibility of a residual difference ΔP(x) = P_B(x) - P_A(x) ≠ 0. Numerical simulations were then performed using the phase relation above. The simulations confirm that a common global phase leaves coherent probabilities unchanged, whereas relative-phase changes can strongly modify constructive and destructive interference. A four-dimensional scan over (δE, δt, δp, δx) reveals continuous phase-matching families satisfying δE δt - δp·δx = 2πnħ, n ∈ Z. Using the muonium ground-state hyperfine scale, a characteristic phase period of approximately 224 ps is obtained, indicating experimentally relevant phase sensitivity on tens-to-hundreds of picoseconds timescales. A second experiment is therefore proposed: a phase-controlled muonium-antimuonium conversion test. A Ramsey-type microwave sequence controls the relative phase θ = ΔE T / ħ + φ_RF, while the normalized conversion rate R(θ) = N_antiMu(θ) / N_Mu,initial(θ) is measured. The decisive candidate signature is a reproducible residual dependence dR/dθ ≠ 0, after standard coherent dynamics, population-transfer effects, magnetic-field effects, decoherence, and instrumental systematics have been excluded. The simulations do not by themselves prove a new interaction or a single underlying field, but they provide a quantitative phase-matching structure and motivate two experimentally falsifiable tests of the framework.
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.