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Non-classical correlations resulting from entangled quantum systems havesparked debates about the compatibility of quantum theory and relativity, andabout the right way to think about causation. Key to a causal theory is thatsuperluminal signalling is forbidden, which holds in quantum theory. In Bellscenarios, relativistic causality principles like no superluminal signallingare often assumed to follow from the standard no-signalling constraints oncorrelations. We explore the connections between a range of relativisticprinciples, including no superluminal signalling and no causal loops, andconstraints on correlations that can arise with arbitrary interventions, withinmulti-party Bell scenarios. This includes standard no-signalling conditions andproposed relaxations allowing phenomena like jamming, where it was suggestedthat superluminal signalling and causal loops remain impossible. Using ourrecent framework combining relativistic principles with causal modelling, weshow that any theory (classical or non-classical) allowing jamming must rely oncausal fine-tuning and superluminal causal influences. Additionally, we showthat jamming theories can lead to superluminal signalling in certainsituations, highlighting limitations for their physicality. However, weidentify cases where jamming correlations avoid superluminal signalling undergeneral interventions, demonstrating that standard no-signalling constraintsare not necessary for this purpose. We also show that these constraints areinsufficient to rule out superluminal signalling and are neither necessary norsufficient for ensuring no causal loops under general interventions. Finally,we derive necessary and sufficient conditions for ruling out superluminalsignalling and operationally detectable causal loops, solidifying ourunderstanding of relativistic causality principles in information processingtasks in space-time.

The standard no-signalling constraints in Bell scenarios are neither  sufficient nor necessary for preventing superluminal signalling with general  interventions