Put a question
under your control.
Move a parameter and see what the model predicts. Every tool includes its equation, units or dimensionless convention, assumptions and a route into the research.
These tools calculate idealized model predictions. They do not display experimental data or establish that a model applies to every physical implementation.
Download SVG ↓Penrose’s proposed lifetime
Hypothesis explorer. E_G is an entered gravitational self-energy of a mass-density difference. This is not a complete collapse model or a verified universal law.
A freely spreading quantum packet
One-dimensional free particle, initial unchirped minimum-uncertainty Gaussian. Dimensionless units: ℏ = m = 1. The plotted position density broadens under unitary evolution.
Squeezing an uncertainty ellipse
Ideal pure one-mode Gaussian squeezing with ℏ = 1. The ellipse represents one-standard-deviation widths, not a particle trajectory. Loss and technical noise are omitted.
Combine two coherent inputs
Ideal lossless balanced combiner with a chosen phase convention. Curves show input field amplitudes and their sum; the readouts give normalized power fractions in the two output ports.
Watch a vibration lose mechanical energy
Underdamped viscous oscillator: m = k = 1, x(0) = 1, v(0) = 0. Energy is calculated from displacement and velocity; it is transferred to the omitted environment.
Small-particle Rayleigh scattering
Unpolarized light, a fixed isolated particle much smaller than every selected wavelength, and fixed optical properties. The curves show relative differential cross section in the Rayleigh…
A structured beam carries a phase winding
Transverse p = 0 Laguerre–Gaussian-like mode in dimensionless waist coordinates. Opacity encodes normalized intensity; cyclic color encodes phase. Paraxial pure modes have orbital angular…
Reflection at an impedance boundary
Lossless acoustic plane waves at normal incidence between two positive real impedances. The coefficients are energy fractions; pressure-amplitude transmission can exceed one without…
The noise cost of phase-insensitive gain
Ideal quantum-limited phase-insensitive linear amplifier, coherent input, vacuum idler, quadrature vacuum variance 1/2. G is power gain. The pump supplies output energy.
Phase noise washes out fringes
Equal path populations and independent zero-mean Gaussian phase fluctuations averaged over many runs. This models the observed reduced fringe contrast; it does not identify the underlying…
Cross a waveguide cutoff
Ideal uniform vacuum rectangular guide, TE₁₀ mode, perfectly conducting walls and no loss. Below cutoff, β is imaginary and the depicted field is evanescent. Finite barrier transmission…
Rotate a quantum measurement basis
Born-rule predictions for a normalized real two-level pure state and an ideal projective measurement. Displayed bars are calculated probabilities, not experimental counts or a…
Account for a one-dimensional collision
Body 1 has mass 1 and initial velocity 1; body 2 starts at rest. An isolated one-dimensional encounter uses restitution 0 ≤ e ≤ 1. Lost translational kinetic energy becomes internal modes,…
Sweep a damped resonance
Steady-state linear oscillator with drive ratio r = ω/ω₀ and damping ratio ζ. Amplitude is normalized to the static displacement F₀/k. The finite-damping displacement peak need not occur…
Read a constant-rate decay law
Memoryless exponential survival model; time and lifetime use the same arbitrary unit. Expected survivors are calculated for an initial population of 1,000. Real quantum survival can depart…
Find the phase-locking threshold
Adler phase model with fixed detuning Δ and coupling K, integrated from φ(0) = 0.2 rad using fourth-order Runge–Kutta. Time uses a chosen unit; Δ and K have inverse-time units. This is a…
A brief push leaves a ringing response
Unit-mass, unit-frequency oscillator initially at rest, driven by one rectangular force pulse with fixed external impulse J = 1. Restoring forces act during the pulse, so residual energy…
Exchange energy between two coupled modes
Lossless reciprocal coupling between two equal-frequency modes, with constant coupling κ and detuning Δ. Normalized length units are used; κ and Δ have inverse-length units. P₁ + P₂ = 1.…