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

Mass Gap for the Gribov-Zwanziger Lattice Measure: A Non-Perturbative Proof

Authors: Lluis Eriksson
Comments: 13 Pages.

We prove that the quadratic Gribov-Zwanziger measure on a d-dimensional periodic lattice (d ≥ 2) with gauge group SU(N_c) exhibits a mass gap, uniformly in the lattice size L. The gluon propagator at zero momentum satisfies D(0) ≤ C_d,Nc/g² for all L ≥ 2 and all coupling g > 0. In the thermodynamic limit, m_gap = g[(d-1)N_cI₁/d²]^1/2, where I₁ = ∫ d^dk/(2π)^d 1/k̂² is a finite lattice constant (I₁ ≈ 0.155 in d = 4). For SU(3) at β = 6 the predicted mass scale is m_gap ≈ 0.6 GeV, in quantitative agreement with lattice Monte Carlo measurements. The proof combines four ingredients: strict log-concavity of the measure (Bhatia's matrix inequality), dimensional reduction to a fixed finite-dimensional zero-mode sector (Prékopa's theorem), an exact computation of the effective Hessian at the origin, and a 1/N scaling argument that renders the effective potential asymptotically quadratic. No perturbative expansion in the coupling constant is employed.
Category: Quantum Physics

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

Authors: Lluis Eriksson
Comments: 15 Pages.

We establish three results for the SU(Nc) lattice Yang-Mills mass gap. First, the function U → -Re Tr U is strictly geodesically convex on Bπ/2(I) ⊂ SU(Nc), with an explicit Riemannian Hessian. Second, the orbit space B = A/G has Ricci curvature RicB ≥ Nc/4, giving a spectral gap λ1(ΔB) ≥ Nc/4 uniform in lattice size, making rigorous an argument of Mondal. Third, and most importantly, we prove that the Yang-Mills-Faddeev-Popov potential is not geodesically convex at the trivial vacuum in zero-mode directions, for any value of the coupling in d ≥ 3. This shows that convexity-based methods — Brascamp-Lieb, Bakry-Émery, Dobrushin, Prékopa — cannot establish the mass gap through the Hessian of the full potential. We argue that the physical mass gap O(e-c/g²) requires the global topology of B, accessible via the Witten-Helffer-Sjöstrand framework.
Category: Quantum Physics

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

Authors: Lluis Eriksson
Comments: 11 Pages.

We establish four results toward the SU(N_c) lattice Yang-Mills mass gap. First, the Wilson potential on the gauge orbit space B=A/G is Morse-Bott with critical manifold M_flat (the flat connections), and we derive the Born-Oppenheimer effective Hamiltonian on M_flat. Second, we prove that the Faddeev-Popov obstruction identified in Paper II applies to the path integral but not to the Hamiltonian on B: since V_pot = S_YM >= 0 has non-negative Hessian at its minimum, the Bakry-Emery framework gives an unconditional mass gap m >= c(L,N_c,d) g^2 > 0 for each fixed lattice size L. Third, we show that the physical mass gap m ~ exp(-C/g^2) follows if the spectral gap at Balaban's terminal renormalization scale is bounded below. We identify this as the single remaining step toward the Yang-Mills Millennium Problem on the lattice.
Category: Quantum Physics

The Yang—Mills Mass Gap on the Lattice: a Self-Contained Proof

Authors: Lluis Eriksson
Comments: 6 Pages.

We prove that SU(N_c) lattice Yang-Mills theory in d=4 dimensions with Wilson action at sufficiently weak coupling has a positive mass gap m >= c(N_c) exp(-C(N_c)/g^2) > 0 in lattice units, uniformly in the lattice size L up to the correlation length. The proof is self-contained modulo Balaban's constructive renormalization group (Comm. Math. Phys., 1984-1989) and combines three ingredients proved here: (i) a Ricci curvature bound Ric_B >= N_c/4 for the gauge orbit space, via O'Neill's submersion formula; (ii) a Holley-Stroock spectral gap estimate at Balaban's terminal renormalization scale; (iii) a transfer-matrix trace identity, with controlled errors from the non-nearest-neighbor couplings in Balaban's effective action, showing that the physical mass gap is approximately scale-invariant under the renormalization group.
Category: Quantum Physics

The Yang—Mills Mass Gap on the Lattice: a Self-Contained Proof Via Witten Laplacian and Constructive Renormalization

Authors: Lluis Eriksson
Comments: 10 Pages.

We prove that SU(Nc) lattice Yang—Mills theory in d = 4 dimensions with Wilson action at sufficiently weak coupling has a positive mass gap mgap ≥ c(Nc) · e−C(Nc)/g2 > 0 in lattice units, uniformly in lattice sizes L ≤ C0 eC/g2 . The proof is self-contained modulo Balaban’s constructive renormalization group and combines: (i) a Ricci curvature bound RicB ≥ Nc/4 for the gauge orbit space, treating its orbifold singularities; (ii) a Witten Laplacian semiclassical spectral gap estimate at Balaban’s terminal scale, using the Morse—Bott structure of the Wilson potential with all hypotheses of the Helffer—Sjöstrand theory explicitly verified; and (iii) a transfer-matrix trace identity with controlled errors from nonlocal temporal couplings.
Category: Quantum Physics

Yang-Mills Existence and Mass Gap: A Framework via Anomaly Algebra, Gradient-Flow Spectral Methods, and Quantum Information

Authors: Lluís Eriksson
Comments: 34 Pages.

We present a rigorous framework for the Yang-Mills mass gap problem, combining three independent lines of argument.Result A (Unconditional). A new MaxEnt Clustering-Recovery Bridge: for any lattice gauge state with finite correlation length xi, the Petz recovery fidelity satisfies 1-F <= C e^{-r/xi}. This is proved via maximum-entropy truncation on gauge-invariant algebras, a convergent polymer expansion, and the Fawzi-Renner theorem.Result B (Unconditional on the lattice, conditional for all couplings). For SU(N) lattice gauge theory (T=0, theta=0, d=3+1, N>=2): the algebraic phase exclusion, using the projective commutation relation of 1-form symmetry operators, unconditionally excludes the trivially gapped symmetric phase. Combined with Perron-Frobenius non-degeneracy and Gauss-law constraints, this forces the theory into the confined phase at strong coupling. The extension to all couplings relies on a single hypothesis: the absence of a bulk phase transition. Under this hypothesis, the uniform lattice mass gap Delta >= m_0 > 0 holds for all lattice spacings.Result C (Conditional). Under the same hypothesis, the continuum limit of SU(N) Yang-Mills theory in d=3+1 exists as a Euclidean QFT satisfying all Osterwalder-Schrader axioms (OS0-OS4), with exponential clustering rate m_0 > 0 (mass gap).Result D (Gradient Flow Reduction). Independently of the anomaly argument, we prove that the mass gap in d=4 is equivalent to a concrete spectral condition on the gradient flow beta-function being strictly negative for all g > 0, combined with a Tauberian regularity condition.The proof architecture uses three main tools: (1) the algebraic structure of higher-form symmetry anomalies on the lattice, (2) backward error analysis of the lattice gradient flow combined with a new spectral calibration, and (3) the MaxEnt bridge from quantum information theory. Exact diagonalisation of Z_2 lattice gauge theory on lattices up to 12 qubits and Z_3 clock models confirms all quantum-information predictions of the framework. This paper contains one explicitly stated hypothesis (absence of bulk phase transition) that is not proven. All conditional results are clearly marked.
Category: Quantum Physics

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

Authors: Lluis Eriksson
Comments: 18 Pages.

We establish a conditional reduction of the Yang-Mills mass gap problem to a concrete spectral inequality involving the gradient flow.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, and reducing 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 three ingredients: (1) a spectral representation of the gradient flow energy E(t) and a monotonicity identity R'(t) = -2 Var_t(lambda) <= 0 for the ratio R(t) = F(t)/E(t); (2) the Komargodski-Schwimmer a-theorem constraining the IR behaviour; and (3) a gradient flow Poincare inequality connecting functional inequalities to exponential clustering of correlators.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 (R(t) < 2/t for g > 0). We identify the non-perturbative obstruction (the indefiniteness of the Weitzenbock curvature term) as the precise technical barrier to closing the argument in d=4. This paper is a companion to the author's paper on anomaly algebra and quantum information methods for the mass gap. The two approaches are complementary and independent.
Category: Quantum Physics