The paper argues that certain low-energy effective field theories, described by local, Lorentz-invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction arises from the signs of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation is superluminal fluctuations around non-trivial backgrounds, making local, causal evolution impossible and implying an IR breakdown of the effective theory. Such theories cannot arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy usual analyticity properties. This conclusion applies to the DGP brane-world model and models of electroweak symmetry breaking with negative anomalous quartic couplings. Experimental support for the DGP model or negative anomalous quartic couplings would indicate superluminality and macroscopic non-locality, falsifying local quantum field theory and perturbative string theory. The paper shows that the positivity of certain higher-dimensional operators is necessary for consistency, and violations lead to superluminal propagation and causality violations. The IR face of the problem is that the wrong sign of these operators leads to superluminal propagation, making it impossible to define a Lorentz-invariant time-ordering of events. The UV face is that analyticity and unitarity imply positivity constraints on low-energy amplitudes. The paper provides examples, including the DGP model and the Goldstone model, showing that the positivity of coefficients is necessary for consistency. The paper concludes that the positivity constraints provide a powerful tool for identifying what physics can and cannot arise in the landscape, and that violations would signal a crisis for macroscopic locality, causality, and analyticity.The paper argues that certain low-energy effective field theories, described by local, Lorentz-invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction arises from the signs of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation is superluminal fluctuations around non-trivial backgrounds, making local, causal evolution impossible and implying an IR breakdown of the effective theory. Such theories cannot arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy usual analyticity properties. This conclusion applies to the DGP brane-world model and models of electroweak symmetry breaking with negative anomalous quartic couplings. Experimental support for the DGP model or negative anomalous quartic couplings would indicate superluminality and macroscopic non-locality, falsifying local quantum field theory and perturbative string theory. The paper shows that the positivity of certain higher-dimensional operators is necessary for consistency, and violations lead to superluminal propagation and causality violations. The IR face of the problem is that the wrong sign of these operators leads to superluminal propagation, making it impossible to define a Lorentz-invariant time-ordering of events. The UV face is that analyticity and unitarity imply positivity constraints on low-energy amplitudes. The paper provides examples, including the DGP model and the Goldstone model, showing that the positivity of coefficients is necessary for consistency. The paper concludes that the positivity constraints provide a powerful tool for identifying what physics can and cannot arise in the landscape, and that violations would signal a crisis for macroscopic locality, causality, and analyticity.