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It is not the case that Modal interpretations assign definite properties via preferred observables determined by the reduced density matrix of each subsystem independently.
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Reasons For
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Reason for
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1.
Reduced density matrices themselves contain basis ambiguity; eigenbases aren't physically privileged without independent justification for 'preferredness'.
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2.
Subsystem independence creates coherence problems: entangled systems have correlated properties, yet independent density matrices don't capture these correlations.
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3.
The approach struggles with contextuality—same observable may require different preferred bases in different measurement contexts, undermining determinateness claims.
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Reasons Against
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Reason against
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1.
Reduced density matrices capture all observable facts about subsystems; using them avoids spurious preferred basis choices external to physical structure.
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2.
Modal interpretations preserve standard quantum mechanics predictions while providing determinate properties, solving measurement problem without collapse.
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3.
Subsystem independence respects locality: properties of distant systems needn't depend on each other's density matrices, supporting relativistic intuitions.
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