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Demonstrates the necessity of complex Hilbert space in quantum theory, highlighting implications for admissibility and locality.
We show that the effective quantum description reconstructed in Modal Triplet Theory must be formulated on a complex Hilbert space. Admissible basin outcomes induce an orthomodular lattice of propositions with infinite orthogonality, placing the theory within the scope of Solèr’s theorem. An admissibility-based formulation of local tomography excludes quaternionic Hilbert space, while phase-rich coherence requirements exclude real Hilbert space. The result is a rigidity theorem: complex Hilbert space is uniquely enforced by admissibility and locality.
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Peter Nero (2026) studied this question.
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