Satellite Bell Test: Distance-Independent Quantum Nonlocality at 1200 km — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Abstract

FINDING: Quantum nonlocality (Bell violation) is distance-independent — satellite Bell tests confirm violation of the CHSH inequality at 1200 km, saturating toward the Tsirelson bound 2√2, with no decay attributable to separation. | MATH: CHSH parameter S ≤ 2 (local hidden variables) vs. S_max = 2√2 ≈ 2.828 (quantum/Tsirelson). Quantum correlation E(a,b) = -cos(a-b) for singlet state; S = |E(a,b) - E(a,b') + E(a',b) + E(a',b')|. Maximal violation at measurement angles a=0°, a'=45°, b=22.5°, b'=67.5°. | CONNECTION: 2√2 = 2·√2 is the diagonal of a 2×2 square (side 2), i.e. the space diagonal of a unit cube scaled — a root-system constant of the B₂/C₂ lattice. The angle set {0°, 22.5°, 45°, 67.5°} partitions 90° into four equal 22.5° steps = 90/4, a base-4 (dyadic) subdivision, not golden. No 0.618/1.618 ratio appears in the optimal CHSH angles; the geometry is square/cubic (√2), not pentagonal (φ). | DEPTH: 7 Notes on the remaining findings (lower relevance, extracted for completeness): Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23830940

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Satellite Bell Test: Distance-Independent Quantum Nonlocality at 1200 km — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Publisher

Abstract

DOI: 10.5281/zenodo.23830940

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Satellite Bell Tests Confirm Distance-Independent Quantum Nonlocality at Tsirelson Bound 2√2 — E8 Intelligence Research

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FINDING: Satellite Bell tests confirm Tsirelson bound 2√2 as distance-independent — quantum nonlocality persists across 1200 km with no attenuation of correlation strength | MATH: CHSH inequality |S| ≤ 2 (classical local hidden variables); quantum maximum |S| = 2√2 ≈ 2.8284; measured S values in satellite experiments ~2.5–2.7 (limited by detector efficiency, not distance); no distance-dependent decay term observed | CONNECTION: 2√2 = 2 × √2 is the operator norm of the tensor product of two Pauli observables; it arises from the geometry of the Bloch sphere (real projective plane RP²) — specifically from the maximum of ⟨A₁B₁⟩ + ⟨A₁B₂⟩ + ⟨A₂B₁⟩ − ⟨A₂B₂⟩ over projective measurements. The ratio 2√2/2 = √2 ≈ 1.414 is the quantum-to-classical gap, not a Fibonacci/φ ratio. However, √2 is the diagonal of the unit square and appears in the octahedral/cubic root system B₃ normalization. No direct link to 0.618, 1.618, or base-60 in the Tsirelson bound itself | DEPTH: 7 --- FINDING: Bell nonloca Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Satellite Bell tests confirm Tsirelson bound 2√2 as distance-independent — quantum nonlocality persists across 1200 km with no attenuation of correlation strength | MATH: CHSH inequality |S| ≤ 2 (classical local hidden variables); quantum maximum |S| = 2√2 ≈ 2.8284; measured S values in satellite experiments ~2.5–2.7 (limited by detector efficiency, not distance); no distance-dependent decay term observed | CONNECTION: 2√2 = 2 × √2 is the operator norm of the tensor product of two Pauli observables; it arises from the geometry of the Bloch sphere (real projective plane RP²) — specifically from the maximum of ⟨A₁B₁⟩ + ⟨A₁B₂⟩ + ⟨A₂B₁⟩ − ⟨A₂B₂⟩ over projective measurements. The ratio 2√2/2 = √2 ≈ 1.414 is the quantum-to-classical gap, not a Fibonacci/φ ratio. However, √2 is the diagonal of the unit square and appears in the octahedral/cubic root system B₃ normalization. No direct link to 0.618, 1.618, or base-60 in the Tsirelson bound itself | DEPTH: 7 --- FINDING: Bell nonloca Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Oct 31, 20260 citations

FINDING: Bell inequality tests reveal quantum nonlocality; new rules unify entanglement geometry; ballistic electron experiment proposed. | MATH: Bell inequality:

|E(a,b) - E(a,c)| \leq 1 + E(b,c)

(CHSH form:

S = |E(a,b) + E(a,b') + E(a',b) - E(a',b')| \leq 2

; quantum violation up to

2\sqrt{2} \approx 2.828

). Ratio

2.828/2 = 1.414 = \sqrt{2}

. | CONNECTION:

\sqrt{2}

is the diagonal of a unit square, linking to 2D orthogonal basis rotations; no direct golden ratio or base-60 link. Crystallographic symmetry:

\sqrt{2}

appears in square lattice (root system

A_1 \times A_1

D_2

). | DEPTH: 6 — foundational but no new geometric constants; advances understanding of quantum vs. classical correlation boundaries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

FINDING: Bell inequality tests confirm quantum non-locality; new generalized rules (Buscemi) unify entanglement tests via device-independent frameworks. MATH: CHSH inequality:

S = E(a,b) + E(a,b') + E(a',b) - E(a',b') \leq 2

(local hidden variables); quantum violation max

S = 2\sqrt{2} \approx 2.828

. Bell's original inequality:

P(\vec{a},\vec{b}) - P(\vec{a},\vec{c}) \leq 1 + P(\vec{b},\vec{c})

. Buscemi's unification: replaces measurement settings with quantum inputs, yielding semi-device-independent bounds—generalizes to

S_q \leq 2\sqrt{2}

for qubits, but for higher-dimensional systems, Tsirelson bounds scale as

2\sqrt{d}

for maximally entangled states. CONNECTION: The maximal quantum violation

2\sqrt{2}

relates to the golden ratio via

2\sqrt{2} = 2 \times 1.414

, and

1.414^2 = 2

—a Pythagorean doubling. More directly, the CHSH bound

2\sqrt{2}

appears in the geometry of the square (diagonal/side ratio), linking to 45° rotations in 2D lattice symme Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com