  Processes with an indefinite causal structure may violate a causal
inequality, which quantifies quantum correlations that arise from a lack of
causal order. In this paper, we show that when the inequalities are analysed
with a Gaussian-localised field theoretic definition of particles and labs, the
causal indeterminacy of the fields themselves allows a causal inequality to be
violated within the causal structure of Minkowski spacetime. We quantify the
violation of the inequality and determine the optimal ordering of observers.
