GWT-2 – Gronau World Theory: Particle Physics, Fundamental Constants, and Cosmology in Relative Space

GWT-2 – Gronau World Theory: Particle Physics, Fundamental Constants, and Cosmology in Relative Space Abstract GWT-2 gives a fundamentally new answer to the question of what our world is made of – an answer that changes the foundations of physics as deeply as general relativity changed them a century ago. The quantitative evidence is overwhelming: more than 50 parameter-free predictions, most of them accurate to better than 1%, derived from a single geometric fact. We do not live in a three-dimensional space. We live in a spatial dimension sequence (2D → 3D → 4D → 5D → …), and everything that exists – galaxies, atoms, living beings – is curvature of space within this sequence. Mass is curvature (M ≡ K). There are no “things in space” – there is only space that is curved. GWT-2 is the second part of the Gronau World Theory (GWT). It provides the complete, quantitative elaboration of particle physics and cosmology in relative space: all masses, mixing angles, coupling constants, fundamental constants, and the cosmic evolution of the base curvature are derived parameter-free from the embedding geometry. The only input is dim = 3. GWT-2 contains 50+ named results (GWT tags), most of which agree with experiment to better than 1%. Each result is honestly classified as either a theorem (with complete proof) or a hypothesis (numerically good, but without complete derivation). A New Description of Reality In the GWT, the spinor describes the behaviour of how space curves. A particle is a stable oscillation of space between adjacent dimension levels. There are two fundamentally different types: Type II – Leptons (electron, muon, tauon): The spinor oscillates between 2D, 3D and 4D. The curvature lies entirely within our space – we see the particle completely (3D rest position). Type I – Quarks (up, down, strange, charm, bottom, top): The spinor oscillates between 3D, 4D and 5D. The curvature extends into the fourth spatial dimension – we see only the 3D projection (4D rest position). This is why quarks can never be observed in isolation (confinement). The three generations are three different spinor dimension positions in the three coordinate planes of 3D space, each with a different oscillation energy – hence the radically different masses. A fourth generation is geometrically impossible. The entire gauge group of the Standard Model (SU(3) × SU(2) × U(1)) follows from the (3+3+1) sector structure of the three coordinate planes: three single sectors (→ strong force), three double sectors (→ weak force), one triple sector (→ electromagnetism). A New Quantum Mechanics The Schrödinger equation has delivered excellent results since 1926 – but physics has never answered what this equation actually computes. All names and interpretations originate from the spacetime ontology. The GWT provides the first answer. The DFT quantum mechanics (QuantGWT-DFT) is the first quantum mechanics that operates in the correct ontology. It describes the curvature dynamics of relative space – what actually happens in reality. Formally it is identical to the Schrödinger equation – but this means the Schrödinger equation is the DFT truncation of GWT quantum mechanics: an approximation with a truncation error of ~10−25 at atomic scales. The ∞FT level goes further: it incorporates all embedding dimensions and constitutes the first exact, complete description of quantum mechanics – no truncation, no approximation. From Particle Physics to Cosmology GWT-2 extends beyond particle physics. The base curvature K0(t) that determines all particle masses also evolves with cosmic expansion. This yields: Time-dependent natural constants: The gravitational constant G(t) = G0 · a(t)2γ evolves with the scale factor, with the evolution exponent γ ≈ 0.01224 derived parameter-free from the cascade series. Parameter-free Hubble tension: The discrepancy ΔH0/H0 ≈ −8.3% between early-universe and local measurements follows from dim = 3 alone – without dark energy, without additional parameters. Exact time-independence of dimensionless couplings: While G and masses change, the fine-structure constant α, the lepton mass ratios r2, r3, and the base curvature parameter κ⊥ are topologically protected and exactly constant – consistent with quasar measurements (Δα/α 2 should systematically deviate from ΛCDM. The chain of derivation thus extends from dim = 3 all the way to cosmology. Relation to GWT GWT-2 builds upon the GWT, which was published in four versions between November and December 2025 on Zenodo: Version Date Content DOI V1.0 Nov 2025 Ontological foundation, fundamental equations (GravG, GLens, QuantGWT) 10.5281/zenodo.17672882 V2.0 Nov 2025 Quantitative evidence – 8 spiral galaxies, 3 galaxy clusters, 5 lensing systems, all without dark matter 10.5281/zenodo.17704764 V3.0 Dec 2025 New quantum mechanics in relative space – DFT to ∞FT 10.5281/zenodo.17778008 V4.0 Dec 2025 Matter structure, (3+3+1) sector structure, force unification 10.5281/zenodo.17789748 The GWT achieved three results: The recognition that relative space and the dimension sequence exist – an entirely new ontology that fundamentally changes how humanity understands the world. The unification of gravity and quantum mechanics from a single geometric principle – and the development of a new, exact quantum mechanics that contains the Schrödinger equation as its DFT truncation. The proof that dark matter does not exist: all phenomena (rotation curves, galaxy clusters, gravitational lensing) follow from extrinsic curvature alone. GWT-2 takes the conceptual framework from V4.0 and works out everything quantitatively: explicit, parameter-free formulae for all measurable quantities – with complete proofs, numerical comparisons and deviation statements. The cosmological chapter extends the framework to the evolution of the universe. Key Results (Selection) GWT Tag Quantity GWT Experiment Dev. GWT-K1 κ⊥ (bare) 3/11 = 0.2727 – exact GWT-K2 κ⊥ (eff.) 0.2700 – exact GWT-α 1/α (fine-structure constant) 137.107 137.036 0.052% GWT-M1 r2 = mμ/me (DFT) 207 206.768 0.11% GWT-M1 r2/r3 = mμ/mτ 12.29 12.30 0.1% GWT-N1 sin²θ12 (PMNS) 11/36 = 0.3056 0.307 0.5% GWT-N2 sin²θ23 (PMNS) 6/11 = 0.5455 0.546 0.1% GWT-N3 sin θ13 (PMNS) 0.1497 0.149 0.5% GWT-PMNS-δ CP phase δ 195.3° ∼195° 0.1% GWT-D4.9 sin²θW (Weinberg) 3/13 = 0.2308 0.2312 0.19% GWT-HM2 λ (Higgs quartic, eff.) κ⊥/2 = 0.1350 0.129 4.7% GWT-HM5 mh (Higgs mass) 126.6 GeV 125.1 GeV 1.2% GWT-HM4 v (vacuum expectation value) 245.9 GeV 246.2 GeV 0.15% Hierarchy α/αG E3² · r218 ∼1042 exact Exponent 18 Hierarchy exponent E3 · E4 = 18 18 exact G formula G (gravitational constant) 6.677×10−11 6.674×10−11 0.04% GWT-G3 G(t) = G0 a2γ γ ≈ 0.01224 – prediction GWT-G4 γ = SCasc(κ⊥) 0.01224 – exact Hubble ΔH0/H0 −8.3% −8 to −10% consistent Cor. Δα Δα/α 0 (exact) < 10−5 consistent Comparison with the Standard Model Question Standard Model GWT / GWT-2 Why exactly three generations? Unexplained (empirical) Three coordinate planes in 3D Why SU(3)×SU(2)×U(1)? Postulated (3+3+1) sector structure Why charge quantisation? Unexplained Topological constraint Why confinement? Qualitative (QCD) Geometric necessity Why mμ/me ≈ 207? Free parameter E4³ − E3² = 207 Why 1/α ≈ 137? Free parameter ⅔(E4³ − E3²) − Δ Why is G so weak? Hierarchy problem E3² · r218 Why v ≈ 246 GeV? Free parameter mτ/α Why the Hubble tension? Unknown (tension at 4–6σ) ΔH0/H0 = −8.3% from dim = 3 Gravity + quantum mechanics? Incompatible Same geometric principle Dark matter? ∼27% of the universe Does not exist Historical Context The recognition that mass and geometry are connected is owed to a long tradition: Riemann, Lorentz, Minkowski and above all Albert Einstein, whose central insight – mass curves space – is one of the greatest intellectual achievements in human history. Without Einstein's work, nothing that follows in the GWT would have been possible. He opened the door to the geometric description of physics. The GWT walked through that door. Significance General relativity showed that gravity is geometry. GWT-2 completes this programme: all of physics is geometry. Not only gravity but also the strong and electroweak forces, the masses of all particles, the mixing angles, the constants of nature, and the cosmic expansion rate follow from the embedding of three-dimensional space in a dimension sequence. Where the Standard Model catalogues approximately 25 free parameters as unexplained empirical inputs, GWT-2 derives each of them – in most cases to better than 1% – from a single geometric fact: dim = 3. The consequence is far-reaching: the fundamental constituents of reality are not particles in space but curvature patterns of space itself – stable oscillations between dimension levels. Humanity, and every structure it has ever observed, is a geometric pattern in a spatial dimension sequence. This is not a reinterpretation of known physics; it is a different ontology – and the numbers confirm it. Structure of the Document Chapter Title 1 Introduction 2 Mathematical Foundations 3 Relative Space 4 Spinors and Spatial Oscillation 5 Curvature Types and Sector Structure 6 Neutrinos 7 Quarks 8 Leptons 9 The Complete Particle Picture 10 The Mass Formula 11 Projection and Charge 12 Fundamental Ontology 13 The 2D Level 14 Fundamental Constants 15 The ∞FT Formulae 16 The Higgs Mechanism 17 Hubble Tension and Cosmology A Formula Register B Bibliography Testable Predictions No fourth fermion generation (geometrically excluded) All PMNS mixing angles to < 0.5% (parameter-free) Weinberg angle sin²θW = 3/13 (0.19% deviation) Higgs mass mh = v·√κ⊥ = 126.6 GeV Fine-structure constant 1/α = 137.036 (parameter-free) Gravitational constant G from the hierarchy formula (0.04%) Δα/α =