Experiments

The institute develops these tools for internal validation of Morphological Physics' reach across physical domains. They are functional rather than polished, but we enjoy them enough to share. Each demonstrates Morphological Physics operating in a different physics regime, with validation against the discipline's standard reference results.

Quantum Physics

Morphological Physics' reach into molecular electronic structure, optical interference, and confined quantum systems.

2026
Replaces
Density Functional Theory

Molecular Morphology

Featured Experiment

Energy levels, wavefunctions, and the full inter-level coupling matrix of a molecule, computed analytically from the shape of its electron-density boundary. One eigenvalue solve, no Hartree-Fock, no self-consistent field, no functional. Integrals and derivatives are part of the same calculation — how the spectrum moves when the shape moves is a computable quantity.

Reproduces benzene's e₂ᵤ HOMO degeneracy, lobe pattern and coupling from boundary symmetry alone.

visualization
2026
Replaces
Finite Element eigensolvers

Quantum Confinement

Electron eigenstates on bounded 2D regions

The 2D quantum dot is the textbook problem: an electron confined to a bounded region, its energy levels found by solving Schrödinger's equation on that region. Morphological Physics treats this as a special case of a generalized eigenvalue problem on arbitrary boundary shapes — the case where the overlap matrix reduces to identity. The same machinery that produces the circular dot's Bessel-function spectrum extends to ellipses, polygons, and irregular boundaries without modification.

Eigenvalue spectrum and ordering match analytical references across available shapes.

visualization
2025
Replaces
Fraunhofer approximation

Double Slit

Electron Interference Beyond the Small-Angle Limit

Morphological Physics derives the full interference pattern from slit boundary geometry — without the small-angle approximation textbook quantum mechanics relies on, and with per-slit amplitude computed from physical conductance rather than assumed equal. Agreement with the standard Fraunhofer formula is exact where the approximation holds; measurable divergence appears for N≥3 slits, near-field geometry, and visibility. Fringe spacing matches λL/d to all reported digits; the same calculation reproduces the scale of Tonomura's 1989 electron biprism observations.

Reproduces λL/d fringe spacing exactly; consistent with Tonomura (1989) scale observation.

visualization

Classical Physics

The three classical validations of General Relativity using only Newtonian methods.

2026
Replaces
Riemannian geometry

Mercury Perihelion

GR validation via Newtonian methods

In 1916, Einstein's first quantitative test of general relativity explained the 43-arcsecond-per-century anomaly in Mercury's perihelion precession that Newtonian gravity could not. Morphological Physics recovers the same number through classical methods alone — no metric tensor, no Christoffel symbols, no curved spacetime.

Matches the observed 43.0″ per century to within measurement precision.

visualization
2026
Replaces
Riemannian geometry

Light Deflection

GR validation via Newtonian methods

In 1919, Eddington's solar-eclipse expedition measured starlight bending around the Sun by 1.75 arcseconds — twice the Newtonian prediction and exactly what general relativity required. Morphological Physics recovers the full deflection through classical methods alone, without invoking the curvature of spacetime that the eclipse measurement was thought to demand.

Matches the 1919 measurement of 1.75″ at the solar limb.

visualization
2026
Replaces
Riemannian geometry

GPS Time Dilation

GR validation via Newtonian methods

Operational GPS depends on a relativistic correction: clocks on orbiting satellites run faster than clocks on Earth's surface by 38 microseconds per day, and without correcting for the difference, position errors would grow by roughly ten kilometers per day. Morphological Physics derives the correction through classical methods alone — and produces the Schwarzschild radius along the way, as a byproduct of the simplification rather than the foundation of the derivation.

Matches the 38 µs/day correction GPS receivers apply in operational use.

visualization

Transport Phenomena

Analytical solutions to flow and diffusion on irregular bounded domains.

2026
Replaces
Finite Element Navier-Stokes

Fluid Flow

Viscous duct flow

Steady laminar flow through arbitrary duct cross-sections, computed analytically from the boundary shape. Pick a shape — circle, ellipse, polygon, irregular — and the experiment renders the velocity field alongside computed values for average velocity, volumetric flow rate, and peak-to-average ratio, compared side-by-side against published references.

Matches published references across all benchmark shapes.

visualization

Statistical Inference

Density estimation and distribution modeling derived from Morphological Physics' analytical foundations.

2026
Replaces
Kernel Density Estimation

Density Modeling

Density as a feature of a distribution

A distribution of data has many features: its mean, its variance, its support, its density. The Intrinsic Density Function is a closed-form analytical model of the density feature, constructed from observed data without an assumed parametric form. It is unbiased at every sample size — a combination KDE's bias-variance tradeoff makes impossible. Because the model is closed-form, the mean of 100 such models is itself a density model — and samples drawn from that mean are drawn from an analytical object, not from a numerical kernel sum. The cumulative distribution comes from an exact integral rather than numerical quadrature. None of these operations is available with kernel density estimation or other numerical methods.

Unbiased at every sample size and convergent in the sample limit — properties no numerical density estimator can achieve simultaneously.

visualization
2026
Replaces
Kernel Density Estimation / Gaussian mixture models

Multi-dimensional Modeling

Multi-dimensional modeling and comparison

The Intrinsic Density Function extends to multiple dimensions — current implementation effective through roughly 12 to 15. The framework computes Fisher-Rao, Weighted L² (intrinsic Hellinger distance which is metrically equivalent to the Fisher-Rao distance), Statistical Energy, and a new intrinsic Distribution Distance — all analytical, all preserving the symmetry d(A,B) = d(B,A) that MCMC sampling destroys.

Recovers 2D unimodal and bimodal distributions; Fisher-Rao distance computed without MCMC.

visualization
2026
Replaces
von Mises-Fisher

Spherical Modeling

Distribution comparison on the hypersphere

On the hypersphere — the natural setting for statistical shape analysis and directional data — the framework's distribution comparison machinery extends without dimensional limit. The Intrinsic Density Function fits a vMF sample; samples drawn from the fitted IDF are then compared back to the original via Distribution Distance, whose null distribution is derived to be normal. The hypothesis test produces an analytical p-value, no bootstrap, no permutation. The two samples are not statistically significantly different — the framework's model captures the parametric ground truth.

IDF-resampled vMF data statistically indistinguishable from the parametric original; p-value computed analytically from the derived normal null distribution.

visualization
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