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It is not the case that Decoherence selects preferred bases relative to a choice of system-environment partition, which is not determined by the formalism itself.
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Reasons For
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Reason for
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1.
Effective Hamiltonians and interaction strengths in realistic systems naturally suppress certain bases; the partition follows, not precedes.
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2.
If preferred bases are truly underdetermined, the same system should decohere into incompatible bases simultaneously—contradicting empirical stability.
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3.
The formalism's symmetries and conservation laws constrain viable partitions; they are not arbitrary human conventions but theory-immanent constraints.
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Reasons Against
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Reason against
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1.
The Schrödinger equation is partition-agnostic; it treats all degrees of freedom identically, so partitions require external specification.
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2.
Different system-environment cuts produce empirically distinct decoherence rates, showing the partition choice has real physical consequences.
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3.
Natural partitions (macroscopic vs microscopic) emerge pragmatically from measurement contexts, not from mathematical structure alone.
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