01 Science — the Bell test
Measure the impossible agreement.
Two detectors, one source, four angles. Statistics past S = 2 rule out every pre-written script — and you can run the test in this page.
01Feel — the apparatus, at rest
Two answers, given apart, that agree too well.
A source emits pairs. Each detector picks an angle and returns +1 or −1. Compare the answer streams and a pattern appears that no shared script, however clever, could have written in advance.
One number, S, condenses the whole experiment. Every local story tops out at 2. The pairs reach 2.828. That gap is the phenomenon.
02Touch — 512 pairs per round
Put your hands on the apparatus.
Run rounds, switch the source to a local hidden-variable model and watch S fall back under 2, verify the transcript chain, then fetch a signed pulse from the live beacon and recompute it here.
Run the Bell test yourself.
Two peers seed a CHSH ritual; every round re-derives from those seeds and chains by SHA3-256. Verify the chain, then fetch a signed pulse from the live beacon and verify that too.
PEER A — · PEER B — · FUSED SHA3-256 —
S = —
awaiting rounds
- E(a,b)
- —
- E(a,b′)
- —
- E(a′,b)
- —
- E(a′,b′)
- —
- PAIRS
- 0
a 0° · a′ 45° · b 22.5° · b′ 67.5° — CHSH-optimal settings, one round = 512 pairs, settings switched per pair.
Honesty note: your browser cannot hold entangled photons — this bench samples the exact quantum statistics (E = cos 2(a−b)) versus a genuine local hidden-variable model (λ uniform, deterministic outcomes). The point it proves is mathematical and real: no local model crosses 2; quantum statistics do. Every signed pulse below carries a backend label — today’s beacon pulses say local-sim, and the verifier shows it. When hardware pulses ship, that label is how you will know.
Recompute a signed beacon pulse in this browser
Your browser fetches one pulse, recomputes its SHA3-256 self-commitment from the raw bytes, checks the hash-chain link, and re-derives the CHSH Bell-violation flag exactly as the signer did.
This button is the only network request this instrument ever makes — one GET to https://quantumentanglement.io/pulse/latest, a QERYX-owned origin, and only when you press it.
Press FETCH & VERIFY to pull the latest signed pulse from the beacon and recompute it here.
Until you run the downloadable verifier, a passing widget means self-consistent and chain-linked — not yet signature-authenticated. The bytes are identical; only the lattice-signature math is deferred.
03Understand — the exact formulas running above
Read the math the bench computes.
Three steps: the statistics of a pair, the CHSH sum, and the reason no local model crosses 2. These are the exact formulas running above.
P(same outcome) = cos²(a − b) E(a, b) = 2·P(same) − 1 = cos 2(a − b)
a and b are the two detector angles. E runs from −1 (always opposite) to +1 (always the same). The bench samples outcomes with exactly these probabilities.
S = E(a, b) − E(a, b′) + E(a′, b) + E(a′, b′) a = 0° a′ = 45° b = 22.5° b′ = 67.5° E(a, b) = cos 45° = +0.707 E(a, b′) = cos 135° = −0.707 E(a′, b) = cos 45° = +0.707 E(a′, b′) = cos −45° = +0.707 S = 0.707 − (−0.707) + 0.707 + 0.707 = 2√2 ≈ 2.828
Four correlations, one sum. At the CHSH-optimal settings the quantum statistics reach 2√2 — the Tsirelson bound, the most any quantum system can score.
fix every answer in advance: A, A′, B, B′ ∈ {−1, +1}
A·(B − B′) + A′·(B + B′) = ±2 one bracket is 0, the other ±2
⟨S⟩ ≤ 2 an average of ±2 terms
If both answers exist before measurement, the four-term combination is ±2 for every single pair, so its average can never exceed 2. The instrument calls a violation only when S − 3σ > 2 — three standard errors past the bound.
Why is the window between 2 and 2.828 the signature?
Below 2, a local model suffices. Between 2 and 2√2 is the quantum band. Past 2√2 no quantum system can go — so a reading beyond it means the sampler itself is broken, and the instrument flags exactly that.
What makes the transcript trustworthy?
Every round re-derives deterministically from the two peer seeds via SHAKE256, and rounds chain by SHA3-256. VERIFY CHAIN regenerates the whole transcript from the seeds alone — steering by either peer and editing after the fact both surface as a broken chain.
- J. S. Bell, "On the Einstein Podolsky Rosen paradox," Physics 1, 195 (1964)
- J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Phys. Rev. Lett. 23, 880 (1969)
- B. S. Cirel'son, "Quantum generalizations of Bell's inequality," Lett. Math. Phys. 4, 93 (1980)
04In QERYX — above the hybrid floor, never below
Follow the binding into the protocol.
Every session key is bound to a CHSH-verified, Tsirelson-window-validated Bell-game transcript both peers seed and any auditor can verify — and to an operator-signed transcript from real quantum processors where the v2 lane is active.
Today the transcript lane is v1: a dual-peer deterministic CHSH ritual (SHAKE256) — the same math this page runs. The operator-signed quantum-processor lane is v2; it ships in the client and activates per deployment.
Bell-binding sits above the X25519 + ML-KEM-1024 hybrid floor, never below it. Breaking a session requires breaking both X25519 and ML-KEM-1024.
Precision note This is not QKD. Not quantum networking. Not quantum teleportation. We do not violate the no-communication theorem. We bind a key-derivation function to a verifiable physical measurement no classical adversary can fabricate in advance.
05The record — the questions we get asked hardest
The honest questions.
Does my phone measure entangled photons?
No. Your browser samples the exact quantum statistics — E = cos 2(a−b) — against a genuine local hidden-variable model. The point it proves is mathematical and real: no local model crosses 2; quantum statistics do. The instrument carries this note on its face.
How will I know when hardware pulses ship?
Every signed beacon pulse carries a backend label and the
verifier displays it. Today's pulses say local-sim; a
hardware pulse announces itself in the same field, on the same signed
record.
Why 2.828 and never more?
2√2 is the Tsirelson bound — the ceiling quantum mechanics itself obeys. Stronger-than-quantum correlations are mathematically consistent yet never observed in nature; a bench reading past the window is reported as a sampler fault, never as a discovery.