TN3: Quantum-Pointer Hamiltonian Realisation of the Bell-Singlet Correlation
Zayn Blore
This technical note gives an explicit quantum-pointer measurement construction for the two-qubit Bell singlet within the finite-dimensional geometric framework used in Constraint-Surface Dynamics. Technical Note 2 previously showed, at the probability-functional level, that the singlet state gives the standard correlation E(a,b) = -a · b. The present note supplies the corresponding system-apparatus construction. It uses the standard von Neumann measurement Hamiltonian, with two qubits coupled to two finite-dimensional pointer sectors, and shows how the measurement interaction separates the four pointer branches associated with outcomes s,t = ±1. The pointer-sector projectors define the operational outcome sectors for each measurement context. In the strong-readout limit, their branch weights reproduce the standard singlet probabilities P_st(a,b) = (1 - st a · b)/4, giving E(a,b) = -a · b. The local marginals remain equal to 1/2, so operational no-signalling follows by direct marginal summation. The role of this note is compatibility and architectural closure. It does not introduce a new measurement Hamiltonian, does not derive the Born rule independently, and does not rely on Fubini-Study Voronoi volumes or isotropy-to-linearity arguments. Instead, it shows that the standard quantum-pointer measurement model embeds cleanly into the finite-dimensional geometric reconstruction. In the CSD interpretive layer, outcomes are treated as context-indexed sectors rather than Bell-local factorised hidden-variable assignments. The note should be read downstream of Paper B and Technical Note 2, and as preparation for the later Lean formalisation target assigned to LF3.
•May 16, 2026•0 citations