Lessons from the role of non-relativistic causal models in the history of QFT?

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There are a number of cases in the history of particle physics in which analogies to non-relativistic condensed matter physics models guided the development of new relativistic particle physics models. This heuristic strategy for model construction depended for its success on the causal structure of the non-relativistic models and the fact that this causal structure is not preserved in the relativistic models. Focusing on the case of spontaneous symmetry breaking, the heuristic role of representations of causal structure and time in the non-relativistic models will be examined. I will reflect on whether the use of non-relativistic causal models to construct relativistic quantum field theory models offers methodological lessons for the shift from definite causal structures in pre-general relativistic quantum theories to indefinite causal structures in quantum gravity.