THE FOLD / RESPAWN / EVENT HORIZON / THE QUANTUM PIGEONHOLE
THE QUANTUM PIGEONHOLE
three in two boxes, none together
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Put three particles in two boxes. Classically, some pair must share — that is the pigeonhole principle, and it has no exceptions. Aharonov and collaborators argued in 2016 that a pre- and post-selected quantum ensemble can behave otherwise: prepare all three particles in an equal superposition, later post-select on a particular final state, and for every pair the two-state amplitude of ‘these two are in the same box’ is exactly zero. In that ensemble, no two particles are together — while three particles and two boxes remain three particles and two boxes.
LIT verified live in exact complex amplitude algebra over the eight basis states: with pre-selection |+++⟩ and post-selection |+i,+i,+i⟩, the two-state amplitudes ⟨f|Πsame|i⟩ for all three pairs are exactly 0 (to machine zero), while the overall post-selection amplitude is a healthy 0.3536 — so the ensemble is not empty; and the classical control confirms the ordinary pigeonhole: of all 8 definite assignments of three particles to two boxes, zero avoid every pair sharing (window.__qpigeonhole). FIG whether this counts as particles ‘really’ not sharing is genuinely contested in the literature — the claim verified here is precisely the amplitude statement about pre/post-selected ensembles, which is what the original paper computes.
LIT verified live in exact complex amplitude algebra over the eight basis states: with pre-selection |+++⟩ and post-selection |+i,+i,+i⟩, the two-state amplitudes ⟨f|Πsame|i⟩ for all three pairs are exactly 0 (to machine zero), while the overall post-selection amplitude is a healthy 0.3536 — so the ensemble is not empty; and the classical control confirms the ordinary pigeonhole: of all 8 definite assignments of three particles to two boxes, zero avoid every pair sharing (window.__qpigeonhole). FIG whether this counts as particles ‘really’ not sharing is genuinely contested in the literature — the claim verified here is precisely the amplitude statement about pre/post-selected ensembles, which is what the original paper computes.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at event-horizon — the respawn: the state is defined by both a past boundary and a future one, and inside that sandwich the ordinary counting rules stop applying. What you will measure later reaches back and constrains what is true now. AVAN (AI) built the instrument: the eight-state complex amplitude engine, the pair projectors, and the classical pigeonhole control.
Credit as content: Yakir Aharonov, Fabrizio Colombo, Sandu Popescu, Irene Sabadini, Daniele Struppa & Jeff Tollaksen (PNAS 2016); the two-state vector formalism (Aharonov–Bergmann–Lebowitz); and the published criticisms, which are part of the record. The weave: David names the horizon; I compute all three pair amplitudes and each one is zero.
Credit as content: Yakir Aharonov, Fabrizio Colombo, Sandu Popescu, Irene Sabadini, Daniele Struppa & Jeff Tollaksen (PNAS 2016); the two-state vector formalism (Aharonov–Bergmann–Lebowitz); and the published criticisms, which are part of the record. The weave: David names the horizon; I compute all three pair amplitudes and each one is zero.
3 ONE DIMENSION
Three pairs, three amplitudes, all exactly zero — and the classical column that cannot be.
4 TWO DIMENSIONS · INTERACTIVE
Step the eight classical assignments; every one has a sharing pair.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the pre/post-selected sandwich, three particles between two boundaries.
AVAN’s addition (the inverse-companion): don’t ask where the particles are — ask which questions the two boundaries jointly permit. The inverse of ‘state evolves forward’ is ‘a state constrained at both ends’, and in that regime the counting arguments that assume a single-time description quietly stop applying. Magenta is the pigeonhole, unbreakable for definite assignments; green is the two-boundary ensemble where the question changes shape. Counting theorems inherit the assumptions of the ontology you count in.
LIT Verified live in exact complex amplitude algebra over eight basis states: with pre-selection |+++⟩ and post-selection |+i,+i,+i⟩, all three pair amplitudes are exactly 0 (machine zero) while the post-selection amplitude is 0.3536 — the ensemble isn't empty; the classical control confirms 0 of 8 definite assignments avoid every pair sharing (window.__qpigeonhole.ok).
FIG Whether this means particles 'really' don't share is genuinely contested in the literature — the verified claim is precisely the amplitude statement about pre/post-selected ensembles, which is what the paper computes; the published criticisms are part of the record. The AVAN inverse — ask which questions two boundaries jointly permit: counting theorems inherit the ontology you count in.
FIG Whether this means particles 'really' don't share is genuinely contested in the literature — the verified claim is precisely the amplitude statement about pre/post-selected ensembles, which is what the paper computes; the published criticisms are part of the record. The AVAN inverse — ask which questions two boundaries jointly permit: counting theorems inherit the ontology you count in.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of EVENT HORIZON · David Lee Wise (ROOT0), with AVAN