Beyond Quantum Mechanics: Local QM Space-Time Algebra Prediction of the Singlet State

Abstract

I derive the quantum mechanical prediction − a · b for the singlet spin state using local measurement functions within the Space-Time Algebra (STA) framework. I establish a compact and computationally tractable STA representation of the two-particle singlet state, Ψ = 1 2 ( I σ 2 ( 1 ) − I σ 2 ( 2 ) ) , which is simpler than previously published forms but is not required for the correlation calculation. The analysis shows that STA naturally generates both scalar dot-product terms ( a · s 1 ) and ( s 2 · b ) and bivector wedge-product terms ( a ∧ s 1 ) and ( s 2 ∧ b ) from local spin-detector interactions, whereas standard quantum mechanics retains only the scalar contributions through expectation-value projection. Because the standard quantum formalism represents correlations via operator expectation values, the antisymmetric (cross-product) contributions are averaged out at the level of observables. In contrast, the STA formulation keeps these bivector terms explicit in the intermediate geometric products, raising the question of whether potentially meaningful geometric structure is being hidden by the quantum averaging procedure. I verify the analytical derivation using computational simulations in Mathematica with a Clifford algebra package, confirming that local measurement functions reproduce the standard quantum correlation − cos θ , where θ is the angle between measurement directions a and b . The correlation − a · b is the scalar coordinate of 3-sphere rotors.