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It is not the case that Therefore 'exact match between model states and target system states' is nomologically impossible regardless of whether discretization is eliminated.
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Reasons For
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Reason for
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1.
Perfect match may not be nomologically necessary; approximate isomorphism of relevant properties suffices for scientific purposes.
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2.
The claim conflates 'exact match' (unrealistic) with 'complete causal fidelity' (potentially achievable within physical laws).
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3.
Some quantum systems exhibit exact state correspondence in limited domains, suggesting nomological possibility isn't categorically ruled out.
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Reasons Against
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Reason against
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1.
Any model is a finite, symbolic representation while target systems contain infinite detail and continuous processes.
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2.
Physical laws permit multiple realizations of the same macroscopic state, making identical microscopic matching impossible.
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3.
The observer-model relation always introduces asymmetries that prevent the model from matching the system's complete state.
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