Fields & Spacetime

The model behind the image

Use the animation to ask a question, the measurements to compare outcomes, and the equations to understand the model. A visually convincing result is not by itself evidence of numerical or physical accuracy.

How to investigate

Choose a question and write your prediction.
Change one parameter while holding the others fixed.
Compare the live measurements and revisit your prediction.
Read the equations, units, assumptions, and limitations.
Save control settings or export a measurement snapshot to document your trial.

Model types and mathematical levels

The level indicates the mathematics used in the explanation, not a barrier to trying the experiment. Conceptual uses qualitative relationships; Algebra uses equations, ratios, and graphs; Calculus introduces derivatives, integrals, or differential equations.

Analytical models evaluate a stated mathematical solution.
Numerical models approximate evolution using finite steps and resolution.
Statistical models generate outcomes whose individual results fluctuate.
Geometric models explore prescribed surfaces, projections, or slices.
Teaching approximations and schematic models emphasize a relationship without resolving every physical process.

Experiment model directory

Open an experiment for its live equations, control units, implementation notes, and limitations. Formula panels remain in standard mathematical notation in every language.

Checks and known limitations

The September 2026 review compared all 37 worlds and the 43 modes in the added collections. Corrections in this edition address the Bell statistic and preparation handling, Rutherford energy and charge scaling, wormhole launch constraints, collider idle state, Roche and GPS wording, the capped fission recurrence, flyby orientation, and lensing normalization.

These checks support specific statements about the implemented models. They do not certify research accuracy, full parameter-range convergence, or experimental calibration.

Tests cover selected invariants and limits, including collision momentum, orbital geometry, quantum-state normalization, relativistic clock rates, electric-field gradients, magnetic motion, induction, and wave propagation. The release validation record identifies the checks actually run.

Release validation record · Original audit and reproduction evidence

Critical or chaotic trajectories can depend strongly on initial conditions and numerical resolution.
Finite grids, softened forces, and absorbing boundaries change the ideal continuum problem.
The gas and wind models are simplified numerical systems; neither is a calibrated three-dimensional fluid experiment.
Collider events, stellar stages, galaxy formation, and several diagrams are explicitly illustrative.
Bell error estimates are approximate. Manual settings, small samples, and simulated data do not constitute a loophole-free physical Bell experiment.
Quantum tunneling regional probabilities are instantaneous values, not automatically final transmission and reflection coefficients.

Scientific references

These independent educational resources provide background. Their inclusion does not imply affiliation or endorsement.

Version history

3.0 · September 2026: Fields & Spacetime identity; experiment-level discovery; subject and level filters; guided investigations; prediction notes; reproducible control links; measurement snapshots; shared model documentation; targeted mathematical corrections.

2.3: 37 worlds, the added experiment collections, consistent thumbnail accents, and 18 offline language options.

Accessibility

Navigation, filters, language settings, and form controls support keyboard use. Reduced-motion preferences pause home animations. Light and dark themes, visible focus outlines, and language direction are supported. Canvas and 3D scenes remain primarily visual; this collection has not been certified for complete nonvisual access. Readouts and model explanations provide text alternatives where available.

Saved data and experiment records

Favorites, visit history, prediction notes, and appearance preferences stay in browser storage when available. Clear history removes navigation history and favorites. Prediction notes can be erased in their text boxes; clearing site data removes all local preferences. Opening an experiment records a visit, not mastery.

Control links reproduce supported input values. They do not serialize an evolving trajectory, random outcomes, arbitrary drawing, or camera state. Measurement CSV files preserve visible text and units at a single capture time; they are not raw solver time series.

Report a discrepancy

Use “Report a discrepancy” at the bottom of an experiment to download a report containing the experiment, input settings, visible measurements, and your description. Include what you expected, what happened, and steps to reproduce it. Send the file to the person maintaining your copy; this offline edition has no configured contact address and sends nothing automatically.

Credits and licensing

This edition builds on the existing local experiment collection. Existing source notices are retained. Three.js and OrbitControls are bundled locally under their included MIT license. No blanket redistribution license for the entire collection is asserted here; consult the individual source notices before redistribution.

Bundled Three.js license · Project documentation

Translations are machine-assisted. English is the reference text. The collection is independent and is not affiliated with MIT, PhET, or the other reference providers.