Bell Inequality Violations from Non-Injective Projection

  Violations of Bell inequalities are commonly interpreted as evidence for either nonlocal dynamics or the failure of classical realism.
  In this work, we show that Bell-type correlations can arise without invoking superluminal influences, retrocausality, or local hidden variables, provided that the mapping between underlying configurations and observable outcomes is non-injective.

  We study a class of effective models in which multiple underlying states correspond to the same observable description.
  Such non-injective projections generically induce non-factorizable joint probability structures at the level of observables, even when the underlying description itself is fully local and deterministic.
  As a result, the statistical assumptions required to derive Bell inequalities are violated at the effective level, while locality is preserved at the underlying level.

  Within this framework, quantum correlations emerge as structural features of projected descriptions rather than as signatures of nonlocal causation.
  We clarify the precise assumption of Bell’s theorem that fails in this setting and show how classical behavior is recovered in regimes where the effective projection becomes approximately injective, suppressing nonlocal correlations through decoherence and environmental coarse-graining.

  Our results suggest that Bell inequality violations need not reflect a fundamental nonlocality of nature, but may instead indicate intrinsic information loss induced by non-injective mappings between underlying configurations and observable descriptions.