Temporal Order from Asymmetric Entanglement: Propagation and Emergent Causality

This work investigates how temporal order and causal structure can emerge from quantum dynamics without assuming a pre-existing background notion of time. Pre­vious studies showed that asymmetric entanglement can generate internally coherent oscillations (”relational ticks”) that serve as a local, operational signature of time for the entangled subsystem. Here we extend this framework to address a fundamental question: can such locally generated ticks propagate to neighbouring systems?Using a minimal asymmetric two-qubit pair as the fundamental temporal element, we demonstrate two key results. The first is that entanglement asymmetry produces a stable internal beat frequency. The second is when these pairs are coupled along a finite quantum chain, the resulting temporal density propagates outward in a clear, finite-speed light-cone structure. Numerical simulations using a Lieb–Robinson style half-maximum criterion reveal a bounded signalling speed v∗, confirming that temporal influence spreads only within a causal cone.Importantly, this finite propagation speed arises directly from local quantum in­teractions and does not require any relativistic postulates, Lorentz symmetry, or a predefined time coordinate. In the coarse-grained limit, the temporal density exhibits wave-like behaviour with a characteristic speed approaching v∗, suggesting a pathway from microscopic entanglement asymmetry to macroscopic causal order.These results support a concrete mechanistic model in which time emerges from movement, causality emerges from locality, and a finite propagation speed arises nat­urally from asymmetric entanglement alone. This provides a plausible route by which relativistic causal structure may originate from the dynamics of quantum correlations.