The Echochamber.
Specimen HYLA-Ψ-2301 is held in an equal superposition of two call states — calling and silent — until someone looks. This is not an animation of that idea. The chamber computes the specimen's Wigner function on a live grid, in your browser, and every observation below is a genuine sample from the Born rule — and every one of them is anchored to the provenance ledger the moment it happens. The frog is a picture; the state is not.
What the chamber holds.
A superposition of coherent states on a ring in phase space — the same object trapped-ion labs build one photon at a time. Here it is computed in closed form, cross terms kept.
Two call states at once
The specimen's call states are coherent states set apart in phase space. The lobes in W(x,p) are the states; the ripples between them are interference, and they only exist because the cross terms are kept. Drop them and you have an ordinary frog that is simply either calling or not.
Negativity is the witness
Between the lobes, W dips below zero — something no classical probability distribution can do. Push decoherence κ up and watch the fringes die while the lobes survive: the parts stay, the betweenness goes, and the specimen becomes a mixture.
Measurement, honestly
Observing draws one sample from the marginal P(x) — the real distribution, not a coin flip over two labels. Repeat it and the tally converges to the curve it came from. That is the Born rule, executed rather than illustrated.
How to read it.
This is the same state the chamber above renders. Change it here and the chamber changes with it.
Wigner W(x,p)
— gridLime is probability, blue is impossible
Bright lime regions are where a position–momentum measurement is likely to land. The blue fringes are negative regions — quantum interference with no classical reading. A frog that were merely calling or silent would show two plain lobes and nothing between them.
α sets the distance between call states
Larger α pushes the states apart and packs the interference fringes tighter — structure finer than ħ, which is exactly what makes these states hard to keep alive in a real lab.
κ is the environment listening in
Photon loss damps the cross terms first, and distant states lose their fringes fastest. At κ near 1 the specimen is classical: still two lobes, no longer one frog.
Study terminal.
Six numerical studies run against the live state — Kolmogorov–Smirnov on the sampler, Wehrl entropy against Lieb's bound, Mandel Q, Fisher information, ZN symmetry, sub-Planck scaling. Nothing precomputed; each run declares a pass condition before it executes.