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It is not the case that In models that do not exclude violations of λ-independence, controllable probabilistic dependence is not a necessary condition for superluminal signaling.
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Reasons For
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Reason for 1 of 2
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1.
Controllable probabilistic dependence remains a necessary condition for *operationally meaningful* superluminal signaling, since uncontrollable correlations cannot transmit information between agents.
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2.
Violations of λ-independence introduce hidden variable conspiracies that, by definition, remove the experimenter's ability to freely choose measurement settings, thereby undermining the signaling channel itself.
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Reason for 2 of 2
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1.
Maudlin's analysis in 'Quantum Non-Locality and Relativity' establishes that superluminal signaling requires a controllable cause, and λ-independence violations merely redescribe pre-existing correlations rather than generating new causal pathways.
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2.
A model permitting λ-independence violations conflates epistemic inaccessibility of hidden variables with genuine causal influence, making the alleged 'signaling' explanatorily vacuous by Fine's criterion of causal relevance.
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Reasons Against
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Reason against
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1.
The necessary and sufficient conditions for superluminal signaling differ across models depending on whether λ-independence violations are excluded.
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2.
In models that permit violation of λ-independence, superluminal signaling can occur through mechanisms other than controllable probabilistic dependence.
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