GWT-2 – Gronau World Theory Particle Physics, Natural Constants, and Cosmology in Relative Space Thomas GronauIndependent Researcher, Broderstorf (Steinfeld), Germanygronauworldtheory@gmail.com | ORCID: 0009-0006-8614-4508Version 2.0 | 2026 | DOI: 10.5281/zenodo.20775111 There is no matter. There never was. What we call matter – a stone, a star, a human being – is not a substance that fills space. It is space: a stable curvature pattern of space itself. This is the central statement of the Gronau World Theory, and GWT-2 turns it into hard, testable physics. The quantitative evidence is overwhelming: from a single geometric fact – that our space is three-dimensional – this work derives the masses of all particles, the mixing angles, the coupling constants, the constants of nature, and the expansion of the cosmos. Most of the predictions are parameter-free and accurate to better than one per cent. We do not live in a three-dimensional space. We live in a spatial dimensional progression (2D → 3D → 4D → 5D → ···), and everything that exists – galaxies, atoms, living beings – is curvature of space within this progression. Mass is curvature (M ≡ K). Energy is curvature (E ≡ K). There are no “things in space” – there is only space that is curved. This is not a refinement of the existing picture of the world. It replaces it – as deeply as general relativity replaced Newton a century ago. GWT-2 comprises 21 chapters with 299 formal results, each honestly marked as either a theorem (with complete proof) or a hypothesis (numerically strong, derivation not yet complete). Keywords: Gronau World Theory, relative space, extrinsic curvature, dimensional progression, mass formula, unification of gravity and quantum mechanics, ontological quantum mechanics, natural constants, neutrino mixing, Higgs mechanism, Hubble tension, quantum entanglement, quantum tunnelling The Historic Step Four achievements of the Gronau World Theory each touch the foundations of physics. 1. The unification of gravity and quantum mechanics. For a hundred years the two great theories of physics have been incompatible. In relative space they are not. Both follow from the same geometric principle – the curvature of space within the dimensional progression. Gravity and the quantum are two views of one curvature dynamics. 2. A new quantum mechanics, derived directly from the ontology. Since 1926 the Schrödinger equation has computed the right numbers, but physics never said what it computes. GWT-2 answers this: quantum mechanics is the curvature dynamics of relative space. The Schrödinger equation turns out to be an approximation of a deeper, exact description – not a postulate, but a consequence of what space is. 3. The constants of nature, derived directly from the ontology. The fine-structure constant, the gravitational constant, the particle masses – in the Standard Model these are free parameters, measured but unexplained. In GWT-2 they follow from the geometry of three-dimensional space. The fine-structure constant, for example, is 1/α = (2/3)(E₄³ − E₃²) − Δ = 137.036, built from the number of rotation planes of the dimensional stages. 4. The cosmos without dark matter. The same gravitational formula – developed in stages (DFT, VFT, …) up to the exact ∞FT limit – describes the rotation curves of spiral galaxies, the dynamics of galaxy clusters and gravitational lensing correctly, without any dark matter. Roughly a quarter of the universe, which the standard picture must fill with an unknown substance, simply is not needed: the missing gravity is the extrinsic curvature of space itself. It was these galactic rotation curves that first revealed the decisive fact – that the curvature of space does not stop at the fourth dimension but continues without end (3D → 4D → 5D → ···). The heavens themselves showed that the dimensional progression is infinite, and that is why the exact ∞FT description became necessary. This also explains why Einstein’s space-time works so well where it does. Put simply, gravity does not travel through 3D space – it takes the shortcut through the higher dimensions. In the solar system the difference between a purely radial curvature and the full curvature across all three coordinate planes is tiny, so space-time gives excellent results. On the scale of spiral galaxies that difference becomes visible and the error shows openly; on the scale of galaxy clusters the space-time prediction is simply wrong. The GWT does not overturn general relativity – it locates it precisely as the small-scale approximation of a deeper geometry: Scale Space-time Reason Solar system good Tangential curvatures small Spiral galaxies poor Strong deviations Galaxy clusters very poor Massive discrepancy Gravitational lensing fails Wrong predictions And beneath all four lies the deepest statement of all: there is no matter. A human being is a stable curvature pattern of space. This is not a metaphor. It is the literal content of the theory, and the numbers confirm it. A New Description of Reality In the GWT the spinor describes how space curves. A particle is a stable oscillation of space between adjacent dimensional stages. 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 reaches into the fourth spatial dimension – we see only its 3D projection (4D rest position). This is why a quark can never be observed in isolation (confinement): an isolated 4D curvature pattern has no stable 3D projection. The three generations are three different positions of the spinor oscillation 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: there is no fourth plane. 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 said what this equation actually computes. All its names and interpretations were borrowed from the spacetime picture. The GWT gives the first answer. Its quantum mechanics is the first that operates in the correct ontology: it describes the curvature dynamics of relative space – what actually happens in reality. Formally it reproduces the Schrödinger equation, which means the Schrödinger equation is a truncation of GWT quantum mechanics – an approximation, extremely accurate at atomic scales but an approximation nonetheless. The deeper ∞FT construction includes all embedding dimensions and provides the exact, closed mathematical form of the theory. The structure is complete; a concrete calculation evaluates this form to a finite order, so a small residual remains – which is why even the ∞FT predictions carry the per-cent-level deviations shown below. The form is exact; its numerical evaluation can be carried ever further. In this version the programme is carried explicitly into two phenomena that had previously resisted a clear physical picture. Quantum entanglement becomes a single shared curvature mode: the correlations express the wholeness of one mode, not a signal passing between separated parts. Quantum tunnelling becomes the penetration of a curvature pattern through a sub-cutoff region, with a transmission factor and a generation hierarchy that follow from the very same geometric quantities as the mass formula. From Particle Physics to Cosmology GWT-2 reaches beyond particle physics. The base curvature K₀(t) that fixes all particle masses also evolves with cosmic expansion. This yields: Time-dependent natural constants: G(t) = G₀ · a(t)2γ evolves with the scale factor, with γ ≈ 0.01224 derived parameter-free. A parameter-free Hubble tension: ΔH₀/H₀ ≈ −8.3% follows from dim = 3 alone – without dark energy and without extra parameters. Exactly constant dimensionless couplings: α, the mass ratios and κ⊥ are topologically protected and exactly time-independent – consistent with quasar measurements (Δα/α 2 should deviate systematically from ΛCDM. Relation to GWT GWT-2 is the quantitative branch of the Gronau World Theory. It rests on the ontological foundation laid by the main GWT series: Version Date Content DOI V1.0 Nov 2025 Ontological foundation, fundamental equations 10.5281/zenodo.17672882 V2.0 Nov 2025 8 spiral galaxies, 3 clusters, 5 lensing systems 10.5281/zenodo.17704764 V3.0 Dec 2025 New quantum mechanics – DFT to ∞FT 10.5281/zenodo.17778008 V4.0 Dec 2025 Matter structure, (3+3+1) sector structure 10.5281/zenodo.17789748 The main GWT series achieved three things: it recognised that relative space and the dimensional progression exist; it unified gravity and quantum mechanics from one geometric principle, yielding a new exact quantum mechanics that contains Schrödinger as a truncation; and it showed that dark matter does not exist – rotation curves, clusters and gravitational lensing follow from extrinsic curvature alone. GWT-2 builds on this foundation and makes the physics of relative space quantitative. Key Results (Selection) GWT Tag Quantity GWT Experiment Dev. GWT-K1 κ⊥ (bare) 3/11 = 0.2727 – exact GWT-K2 κ⊥ (effective) 0.2700 – exact GWT-α 1/α 137.036 137.036 <0.01% GWT-M4 r₂ = mμ/mₑ E₄³ − E₃² = 207 206.768 0.11% 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-PMNS-δ CP phase δ 195.3° ~195°
Thomas Gronau (Sat,) studied this question.