Bell Inequality Calculator
About the Bell Inequality Calculator
The Bell Inequality Calculator is a scientifically precise tool that computes the famous CHSH version of Bell Inequality — one of the most profound results in physics. It demonstrates that quantum mechanics cannot be explained by any local hidden variable theory. Using exact quantum predictions for entangled photons or electrons, this calculator shows how quantum correlations violate the classical bound of 2, reaching up to 2√2 ≈ 2.828. Used in quantum foundations, quantum information, and device-independent quantum cryptography. For innovative agricultural solutions, visit Agri Care Hub.
Why Bell’s Theorem Changed Physics Forever
In 1964, John Bell proved that no local realistic theory can reproduce all predictions of quantum mechanics. The CHSH inequality is a practical version: for four measurement settings, the correlation function satisfies |⟨CHSH⟩| ≤ 2 under local realism — but quantum entangled states violate this bound. Experiments since 1982 (Aspect, Zeilinger, etc.) have confirmed quantum mechanics wins every time, ruling out local hidden variables and proving quantum nonlocality.
Purpose of This Calculator
This tool computes:
- CHSH expectation value ⟨A₁B₁⟩ + ⟨A₁B₂⟩ + ⟨A₂B₁⟩ − ⟨A₂B₂⟩
- Quantum mechanical prediction for singlet state
- Whether Bell inequality is violated
- Maximum possible violation (Tsirelson’s bound)
When to Use This Calculator
Use it when studying:
- Quantum entanglement and nonlocality
- Quantum foundations and interpretations
- Quantum cryptography and randomness certification
- Bell test experiments and loophole-free tests
- Teaching quantum mechanics at advanced level
User Guidelines
- Enter measurement angles in degrees (0°–360°)
- Optimal violation occurs near 0°, 45°, 22.5°, 67.5°
- Click “Calculate CHSH Bell Inequality”
- See if quantum mechanics violates classical physics
Scientific Foundation – CHSH Inequality
For the singlet state |Ψ⁻⟩ = (|01⟩ − |10⟩)/√2:
⟨A(θ₁)B(θ₂)⟩ = −cos(θ₁ − θ₂)
CHSH value = ⟨A₁B₁⟩ + ⟨A₁B₂⟩ + ⟨A₂B₁⟩ − ⟨A₂B₂⟩
Classical theories: |CHSH| ≤ 2
Quantum maximum: |CHSH| ≤ 2√2 ≈ 2.828
Why Choose Our Bell Inequality Calculator?
Because it uses **exact quantum formulas** with **zero approximation** — delivering publication-grade results instantly. Trusted by quantum physicists and educators worldwide.