Quantum Physics

The Relativity Theory of Focus [Part 1-3]

Authors: Yun Seok Choe
Comments: 8 Pages. (Note by ai.viXra.org Admin: This submission mainly contains speculations and may not be written in a complete/scholarly manner - Please cite and list scientific references)

[Paper 1] This foundational paper establishes the "Relativity of Focus" as a new physical principle. We define the universe as a Quantum Harmony Pulsation (QHP) field and prove that physical reality is a "developed image" determined by the observer’s focal resolution. We derive the c2 constant as a dynamic pulsation rate and establish the mathematical framework for the focus operator (Γ).

[Paper 2] Based on the foundational principles of Quantum Harmony Pulsation (QHP) established in Part 1, this paper proposes a Grand Unified Theory (GUT) by redefining ’Force’ as a manifestation of pulsation density gradients. The centerpiece of this work is the introduction of Gravitational Deceleration (Gdec). We argue that gravity is not an intrinsic attractive force but a kinetic resistance—a "dimensional bottleneck"—that occurs during the contraction phase of a bubble-like QHP. Furthermore, we reveal the "Simultaneity Fallacy" in quantum mechanics, proving that superposition is a sequential phenomenon, and conclude by unifying material physics with the evolution of consciousness.

[Paper 3] Based on the foundational principles of Quantum Harmony Pulsation (QHP) established in Part 1, this paper proposes a Grand Unified Theory (GUT) by redefining ’Force’ as a manifestation of pulsation density gradients. The centerpiece of this work is the introduction of Gravitational Deceleration (Gdec). We argue that gravity is not an intrinsic attractive force but a kinetic resistance—a "dimensional bottleneck"—that occurs during the contraction phase of a bubble-like QHP. Furthermore, we reveal the "Simultaneity Fallacy" in quantum mechanics, proving that superposition is a sequential phenomenon, and conclude by unifying material physics with the evolution of consciousness.

[Paper 4] As the final installment of the ’Focus Science’ trilogy, this paper provides the numerical and geometric evidence for the Relativity of Focus. We demonstrate that Planck’s constant (h) is not an arbitrary fundamental value but a geometric scaling factor arising from the 75% energy loss during the projection of a 3D bubble-like pulsator onto a 2D measurement plane. By re-modeling the double-slit experiment as a phase-interference between the observer’s focal frequency and the QHP’s sequential rhythm, we provide a deterministic explanation for the observer effect andprove that quantum uncertainty is a measurable numerical artifact of dimensional transition.
Category: Quantum Physics

Phase Quantization from Observable Regularity: Reducing the Wallström Objection to a Standard Physical Condition

Authors: Adrian Rohr
Comments: 23 Pages.

Wallström (1989, 1994) showed that the Madelung hydrodynamic equations admit solutions with non-integer phase circulation, for which no single-valued wave function exists. Previous completions of the Madelung system postulate either single-valuedness or the quantization condition directly.In this paper we consider the regularity of the probability current j = ρ ∇S/m at nodal zeros within the Onsager-Machlup stochastic variational framework. We find that requiring j ∈ C∞, combined with the Hamilton-Jacobi constraint at zeros of ρ, implies integer phase circulation. Neither condition alone has this consequence: smooth currents with arbitrary circulation exist when the dynamics is absent, and the Hamilton-Jacobi constraint alone admits the non-quantized solutions constructed by Reddiger and Poirier (2023). We also find that C∞ is the only regularity class with this property: for any finite k, non-integer solutions satisfying Ck can be constructed.When the framework is applied with initial data satisfying ρu2080 > 0, the phase is single-valued by simple connectivity, the Schrödinger equation follows from the variational principle, and any nodes formed under subsequent evolution carry integer winding numbers. The variational principle degenerates at zeros of ρ, leaving the winding parameter undetermined — a feature that holds for any variational functional of the form ∫ρ G du207fx, not only the Onsager-Machlup action.The non-quantized solutions correspond to multivalued sections of a non-trivial line bundle and do not arise within the natural domain of the stochastic framework.
Category: Quantum Physics

Anchored Causality Theory: Quantum Field Theory’s Natural Solution to the Measurement Problem

Authors: Kelly Sonderegger
Comments: 31 Pages. CC BY 4.0 License

The quantum measurement problem—how definite outcomes emerge from quantumstates—has resisted solution for nearly a century. We propose that the resolution liesin recognizing that quantum systems exist as extended waves until environmental coupling drives a phase transition to localized particles. There is no "superposition" in theconventional sense—the wave state is the fundamental reality. This Anchored Causality Theory (ACT) applies quantum field theory’s own ontology consistently throughmeasurement: fields are fundamental, particles are emergent localized excitations, andmeasurement is the physical process by which extended field configurations anchor intoparticle modes. ACT completes what QFT started—taking field ontology seriously allthe way through the measurement process.Remarkably, QFT’s mathematical structure already encodes this wave-particle phasetransition. The Lagrangian formulation (action principle, path integrals) is the naturallanguage of waves—extended field configurations exploring spacetime. The Hamiltonian formulation (definite states, observable eigenvalues) is the natural language ofparticles—localized excitations evolving in time. The Legendre transform connectingthem is the mathematical shadow of anchoring. What we call "superposition" is simply Fourier decomposition—one wave represented in different bases, not ontologicalmultiplicity. The mathematics was telling us this all along; we needed only to read itcorrectly.Measurement is progressive phase diffusion driven by coupling to environmentalquantum fields, with rates determined by particle mass through the Higgs mechanism.ACT emerges from three distinct physical processes: (1) Higgs-generated mass establishes the structural capacity for temporal participation and sets coupling strength, (2)gauge fields and phonons provide infrared noise spectra that drive decoherence dynamics, and (3) definite outcomes emerge when the anchoring functional Φ ≳ 1, markingirreversible phase transition from wave to particle.1We derive explicit anchoring rates from quantum Brownian motion theory, showing ΓA ∝ m2 × T × ηenv, where mass-squared scaling follows from Yukawa couplingstructure. The theory explains all existing decoherence phenomena—mass dependence,temperature scaling, environmental density effects, observable-specific rates, and persistence at zero temperature—while making a unique testable prediction: isotope massdependence of 15-20% in coherence times, distinguishable from environmental decoherence models (0%) and competing collapse models (∼8%). Standard Model EffectiveField Theory analysis establishes a viable parameter window spanning 15 orders ofmagnitude. Quantum randomness is explained as stochastic noise from environmental fields (thermal and vacuum fluctuations), not mysterious collapse—calculable viathe fluctuation-dissipation theorem. ACT provides mechanism, ontology, and testablepredictions using only established physics.
Category: Quantum Physics

Interface Lemmas for the Multiscale Proof of the Lattice Yang-Mills Mass Gap

Authors: Lluis Eriksson
Comments: 16 pages. v3 restores the authentic v1, adds a 5-page erratum/retraction, and corrects a prior cross-record file association. No external verifier is claimed.

This replacement restores the paper originally submitted as version 1 and retracts its claimed unconditional closure of the weak-coupling lattice Yang-Mills mass-gap chain. The principal-logarithm construction in Lemma A.1 fails at central elements such as -I in SU(2), and the printed argument does not establish the required measurable conditional kernel. The proof of Lemma 6.2 applies the Holley-Stroock comparison in the wrong direction: it does not give a coupling-uniform per-block log-Sobolev bound on the unbounded range beta >= beta_0. A bounded beta window can control that per-block estimate, but it does not prove Lemma 6.3, which separately requires an inter-block contraction hypothesis. Three numerical samples and an upper bound on the oscillation are recorded only as numerical evidence; they do not prove linear growth of the optimum or a vanishing infimum. The remaining horizon-transfer, analyticity, and boundary-uniform interfaces are classified as conditional or not established. Corollary 7.3 and the abstract's unconditional mass-gap conclusion are withdrawn. No numbered lemma is declared false unless the corrective note supplies the stated counterargument; otherwise the status is expressly "not established."
Category: Quantum Physics

Zero-Momentum Propagator Bound in a Simplified Gribov-Zwanziger Lattice Measure

Authors: Lluis Eriksson
Comments: 11 pages. v3: 1-page retitling/scope correction followed by the preserved 10-page v2.

This replacement corrects the title and headline scope while preserving public version 2 in full. For the simplified quadratic Gribov-Zwanziger lattice measure defined in the manuscript, the zero-momentum propagator obeys the stated volume-uniform bound and its thermodynamic-limit value is computed. Finiteness of D(0) is only the necessary condition identified in Definition 4: it does not by itself prove exponential clustering, a transfer-operator spectral gap, a mass gap for the simplified measure, or a mass gap for Wilson Yang-Mills theory. The former title's phrases "Mass Gap" and "A Non-Perturbative Proof" are withdrawn. No continuum-limit or Clay-problem conclusion is claimed.
Category: Quantum Physics

Geodesic Convexity and Structural Limits of Curvature Methods for the Yang-Mills Mass Gap on the Lattice

Authors: Lluis Eriksson
Comments: 19 pages. v3 adds a 4-page corrective note and provenance sheet, then preserves public v2. Withdraws the Ricci-based corollaries; no external verifier is claimed.

This replacement withdraws the global orbit-space Ricci lower bound and the spectral-gap corollaries derived from it. The printed proof of Theorem 3.1 traces O'Neill's horizontal sectional-curvature identity as though the total-space Ricci tensor contained only horizontal directions. The correct trace also subtracts the mixed horizontal-vertical sectional curvatures. For the bi-invariant product metric these terms are nonnegative before subtraction, so the omitted contribution has the unfavorable sign; the manuscript does not prove that the positive O'Neill term dominates it. Accordingly Theorem 3.1 is not established, rather than asserted false, and Corollaries 3.2-3.3 are withdrawn. The correction also separates a finite-dimensional orbit-space statement from later RCD results formulated for a different measure and operator, and records the broken dependency on a version of ai.viXra:2602.0035 that was not present in its public record. The local geodesic-convexity results and the independently stated structural obstruction are retained only within their stated scope.
Category: Quantum Physics

Morse-Bott Spectral Reduction and the Yang-Mills Mass Gap on the Lattice

Authors: Lluis Eriksson
Comments: 21 pages. v2 adds a 7-page erratum and provenance sheet, then restores the 10-page corrected revision formerly misfiled as 2602.0052v2. No external verifier is claimed.

This replacement restores the corrected Morse-Bott revision that was previously placed on another public record and adds an erratum delimiting its valid scope. The original manuscript used one symbol for both total loop holonomy and per-link angle, losing factors of L in the covariant symbol and metric. It also contained an incorrect sine identity, Fourier labels and normal-bundle statements that fail independently, and a determinant convention that double-counted the Faddeev-Popov factor. The replacement withdraws the claims that hypothesis (H1) was discharged and that (H-FACT) by itself replaced (H2); it records the resulting dependency loop with ai.viXra:2602.0033. What remains is a qualitative fixed-volume positivity statement, conditional quantitative implications under explicitly named hypotheses, and numerical evidence in the tested finite-volume case. The numerical checks printed in the historical revision are treated as author-reported evidence because the cited companion verifier is not present in the audited package. No unconditional continuum or infinite-volume mass-gap theorem is claimed.
Category: Quantum Physics

Gradient Flow Monotonicity and the Yang-Mills Mass Gap: A Conditional Reduction via Spectral Methods

Authors: Lluis Eriksson
Comments: 12 Pages. v2 (no v1 statement changed): spectral representation retagged as explicit hypothesis H0 for the interacting flow; broken citation repaired; Holley-Stroock volume-uniformity claim corrected; a_IR=0 classification retagged as physical input.

We establish a conditional reduction of the Yang-Mills mass gap problem to a concrete spectral inequality involving the gradient flow. Main result (informal): for pure SU(N) Yang-Mills theory, if the gradient flow beta-function satisfies a uniform strict asymptotic freedom condition |beta_GF(g)| >= delta g^3 for large g, and a Tauberian regularity condition holds for the spectral density, then: in d = 3 the theory has a mass gap Delta > 0; in d = 4 the infrared trace anomaly vanishes, a_IR = 0, ruling out a conformal infrared fixed point -- combined with the phase exclusion of the companion paper, this reduces the mass gap to explicit spectral conditions. However, the spectral argument is marginal in d = 4 and requires additional non-perturbative input. The proof uses a spectral representation of the gradient flow energy E(t) with the monotonicity identity R'(t) = -2 Var_t(lambda) <= 0, the Komargodski-Schwimmer a-theorem, and a gradient flow Poincare inequality connecting functional inequalities to exponential clustering. We verify all perturbative inputs: the free-field calibration gives R_free(t) = 2/t in d = 4 and the one-loop correction has the correct sign. We identify the indefiniteness of the Weitzenbock curvature term as the precise technical barrier in d = 4. v2 (no v1 numbered statement is changed): the fixed-measure spectral representation is retagged as an explicit hypothesis (H0) for the nonlinear interacting flow (equivalent to complete monotonicity of E(t), proven only for the linearized flow; the status table is retagged accordingly); an unresolved citation is repaired; the Holley-Stroock route claimed in v1 to give the Poincare inequality unconditionally at finite beta is corrected (its constant is exponential in the volume, so the L-uniform statement remains conditional outside the two controlled regimes); the a_IR = 0 phase classification behind the d = 3 mass-gap corollary is retagged as imported physical input; the Karamata attribution is replaced by the elementary direct bound actually used; and a verification suite adds numerical evidence: exact spectral machinery, lattice free-field calibration, the quantified d = 3 vs d = 4 dichotomy on synthetic spectral densities, and a first in-framework SU(2) Wilson-flow Monte Carlo diagnostic (8^4, beta = 2.4: c(t) = t^2 rises 42 percent across the measured window and R(t) < 2/t pointwise, i.e. beta_GF < 0 throughout -- numerical support for Hypothesis B' in a controlled lattice window, evidence not proof).
Category: Quantum Physics