About PrincipleSim

Most virtual labs approximate physical phenomena using simple quadratic approximations or pre-rendered sprites. PrincipleSim takes the opposite path: Zero hardcoded animations.

Every trajectory, waveform, and spectrum is solved in real time from first principles:

• Classical Mechanics: Lagrangian dynamics \(\frac{d}{dt}\frac{\partial L}{\partial \dot{q}} - \frac{\partial L}{\partial q} = 0\) solved via classical 4th-order Runge-Kutta, Symplectic Verlet orbital integrators, and complete elliptic integrals \(K(k)\).
• Electrodynamics: Full-wave Maxwell equations solved via Yee staggered-grid 2D Finite-Difference Time-Domain (FDTD).
• Quantum Physics: Time-dependent Schrödinger equation \(i\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi\) solved via split-step Fourier unitary operators with norm conservation \(|\Delta| < 10^{-14}\).
• Atomic & Molecular: NIST Atomic Spectra Database benchmarks, Edlén dispersion for air wavelengths, and exact matrix diagonalization of spin-Hamiltonians.
• Physics-Informed AI: Neural networks with forward-mode automatic differentiation trained directly on PDE residuals.

Inspired by traditional Japanese aesthetic principles (間 (Ma) — intentional space, 墨 (Sumi) — rich contrast, and 落款 (Rakkan) — uncompromising authorial seal), our laboratory apparatuses feature calibrated verniers, micrometer barrels, laser photogates, and real-time phase space portraits.

Every instrument includes experimental uncertainties, realistic jitter, viva voce oral examination questions, and instant CSV export for Departmental physics laboratory coursework.