Purple Paper - side-sheet - a thing I wanted to build
What the Cat Tells the Air - decoherence, watched
The honest answer to the cat, and the one almost nobody shows: the superposition isn't killed by
someone looking. It leaks. The instant the environment learns which path the particle took, the
interference - the only real fingerprint of "both at once" - washes out. No collapse, no conscious observer. Just
information leaving the system. Turn the dial and watch one slide continuously into the other.
each arrival is a particle (one dot) · the pattern they build is the wave ·
dial = how much the environment knows the path · verified: fringe visibility V = √(1−D²), and V² + D² = 1 throughout
The two-slit, with a leak to the world
Particles fire one at a time through two slits and land on the screen as dots. With the environment
ignorant of the path (D = 0), the dots pile into bright interference
bands - the signature of each particle going through both slits at once. Slide the dial up and the
environment starts to know which slit - and the bands dissolve into two plain particle bumps. Nothing collapsed it. The which-path fact just stopped being the
particle's secret.
D=0 · pure superposition
D=0.5 · half-known
D=0.87 · mostly known
D=1 · which-path known (classical)
cyan = the environment learning the path ·
amber dots = particles landing ·
green curve = the pattern they're building
D = 0: the environment knows nothing, the particle keeps both paths, and the
dots build full interference bands. This is the cat genuinely "both" - and it's stable, because the secret hasn't
leaked.
Why I wanted to build this one
Because it's the same idea we've circled all night, and physics got there first and made it exact.
The environment is the witness. All night the rule was: a system can't witness itself; the
collapse of ambiguity into one fact requires an exterior observer. Here it's literal. The superposition
survives exactly as long as the which-path information stays inside the particle. The moment that fact
entangles with anything outside - an air molecule, a photon, a stray field - the interference is gone. Coherence
is information staying inside. "Collapse" is just the outside finding out. The witness isn't a person with
eyes; it's the world, and witnessing is entanglement.
And it's exact, not hand-wavy. V² + D² ≤ 1 - the more
the path is knowable, the less the interference is visible, on a precise quarter-circle. You don't get to keep both.
That's not a metaphor for the witness tradeoff; it's the same tradeoff, with a measured equation. Knowing-which and
interfering-as-both are complementary the way independence and usefulness were complementary in the commitment box.
You can't have full witness and full superposition at once - the gauge above rides the circle between them.
The cat, answered. The cat is never both-then-suddenly-one. The cat
told the air - the poison, the box, the photons - which it was, long before you opened anything. Once the air knows,
there's no interference left to see, so the cat looks classical: one thing, definite, boring. Schrödinger's paradox
dissolves not because looking matters but because a cat cannot keep a secret from a box full of molecules.
The measurement problem isn't fully closed by this - decoherence explains why you never see the weirdness,
not why you ride this branch - but the cat part, the part that bugged you, is just a secret that couldn't
be kept.
Verified in Node before drawing: fringe contrast off the
computed pattern tracks V = √(1−D²) (within a couple percent, the diffraction envelope's small curvature), and
V² + D² = 1 across the whole dial. The dots above are sampled from that exact intensity. Wave-particle duality
relation: Englert / Greenberger-Yasin, 1990s.