SPACETIME ≡ ENERGY EVOLUTION
Unifying physics from a single geometric postulate, without free parameters.
Methodological Pillars
1. NO ONTOLOGICAL COMMITMENTS
▼This model makes no claims about the "existence" of space, particles, or fields as independent entities. Instead, all phenomena are treated as observer-dependent energetic projections. Physics is derived from the relational structure between observers, governed by the foundational Energy Symmetry Law: $$\Delta E_{A \rightarrow B} + \Delta E_{B \rightarrow A} = 0$$ This ensures that energy is always conserved and redistributed in any interaction, never created or destroyed.
2. EPISTEMIC HYGIENE
▼WILL Geometry enforces a disciplined refusal to introduce unjustified assumptions or hidden parameters. The guiding principle is: Nothing is assumed. Everything is derived. All physical quantities, including space, time, mass, and energy, must emerge directly from relational geometry and causal structure, eliminating the need for arbitrary constants or abstract entities.
3. STRICT RELATIONALISM
▼All physical quantities are defined purely by their relations to one another, not by absolute properties or external frames. The framework disallows all background structures, even asymptotic ones, which are often implicitly used in other theories. Energy itself is not a substance but a differential invariant of state transitions within the WILL framework.
4. ZERO FREE PARAMETERS
▼The framework introduces no free parameters. All measurable quantities and fundamental "constants"—from the cosmological density parameter \( \Omega_\Lambda \) to the equation of state \(w = -1\)—emerge as necessary consequences of the geometric and algebraic closure of the system. They are not fitted to data, but are derived from first principles.
5. STRUCTURAL DYNAMICS
▼The system is not described by differential equations of motion evolving in time. Instead, its evolution is dictated by a closed network of algebraic relations that enforce a perpetually balanced configuration. Any change in one parameter necessitates a coordinated shift in all others to maintain geometric self-consistency. What we perceive as "dynamics" is this ordered succession of balanced states. The framework thus inverts the classical paradigm: Time does not drive change — change defines time.
6. GEOMETRIC NECESSITY
▼There is only one valid configuration for a system at any moment: the one where all projectional constraints are satisfied. Everything else is not forbidden—it is geometrically and topologically undefined. The universe does not "choose" a path that minimizes action; it simply exists in the state of perfect balance. Causality is internal, coherence is enforced, and the laws of physics are an inevitable consequence of the system's self-consistency.
Key Results
Solving the Galactic Rotation Problem
This framework provides a novel solution to the galactic rotation problem using only the observed baryonic matter. Testing on the SPARC dataset (175 galaxies) shows a strong fit (RMSE = 23.05 km/s) without invoking dark matter and without free parameters.
Test with Interactive CalculatorOne Input Cosmology
The entire standard cosmological model is replaced by an algebraic system that requires only one input parameter to set the scale (e.g., $H_0$). All other quantities, including the cosmic energy budget ($\Omega_{\Lambda} \approx 2/3$), are predictions of the model, with NO adjustable parameters.
Explore with Interactive CalculatorGetting Started
The Core Geometry
All physics emerges from two related projections, β and κ, defined by separate angles on the unit circle. Use the slider to control κ and observe the relationships.
Geometric Relations
κ (Potential)
0.800
β (Kinetic)
0.566
θG (from κ)
53.13°
θS (from β)
55.55°
Tc = cos(θG)
0.600
Lc = sin(θS)
0.825
The Three Domains of WILL
The geometric framework is applied across three core domains of physics, providing novel solutions to long-standing problems. Click each pillar to learn more.
⚡ Relativity Reimagined
▼Derives SR & GR from geometry, inherently avoiding singularities.
Unifies SR & GR: Reproduces standard results via trigonometric re-parameterization.
Solves Singularities: The geometric limit `κ² ≤ 1` naturally prevents infinite densities.
Defines Local Energy: Provides an algebraic field equation: `κ² = R_s/r`.
🌌 Cosmology without Dark Forces
▼Explains cosmic observations without Dark Matter or Dark Energy.
Dark Energy is Geometric: Explained as "accumulated projectional loss," not a substance.
Predicts Cosmic Budget: Derives `Ω_Λ = 2/3` and `Ω_m = 1/3` from first principles.
Explains Galaxy Rotation: Models rotation curves without dark matter halos (Median RMSE: 20.1 km/s).
⚛️ Quantum Mechanics from Geometry
▼Replaces wave-function probability with deterministic geometric constraints.
No Wave Functions: Atomic physics emerges from pure geometric constraints.
Derives Fine Structure Constant: Shows `α` is the kinetic projection for hydrogen's ground state.
Predicts Hydrogen Spectrum: Replicates the energy level formula `E_n = -α²m_e c²/(2n²)`.