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It is not the case that Nonseparability of Hamiltonians is a mathematical feature of the formalism, not a metaphysical fact about ontological parts and wholes.
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Reasons For
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Reason for
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1.
If Hamiltonians describe actual physical interactions, their mathematical structure constrains what ontologies are coherent or permissible.
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2.
Distinguishing 'mere formalism' from 'metaphysical fact' requires independent access to reality—a distinction physics cannot justify.
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3.
Nonseparability produces empirically distinct predictions; formalism affecting observable outcomes suggests it tracks real structure.
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Reasons Against
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Reason against
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1.
Mathematical formalism can represent physical systems without committing to specific ontologies about parts, wholes, or composition.
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2.
Nonseparability arises from our coordinate choice and basis selection, which are conventional tools rather than fundamental reality.
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3.
Multiple mathematically equivalent formulations of quantum mechanics exist, suggesting formalism underdetermines metaphysical conclusions.
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