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Dueling Arrows of Causality, Causal Uncertainty and Quadratic Gravity

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Quadratic gravity is a renormalizeable theory of quantum gravity which is unitary, but which violates causality by amounts proportional to the inverse Planck scale. To understand this, I will first discuss the arrow of causality in quantum field theory (with a detour concerning the arrow of time), and then discuss theories with dueling arrows of causality. But the causality violation might be better described by causality uncertainty. This is discussed both in quadratic gravity and in the effective field theory of general relativity.