Temporal-Causal Unity as an Operational Framework for Collective Dynamics: Causal-Progress Clocks, Synchronization, and Polarization

Abstract:This paper develops temporal-causal unity (TCU), a framework connecting a process-philosophical thesis -- time is the ordered unfolding of causal change -- to an operational model of cognitive and social dynamics. The framework deliberately separates three claims: an interpretive thesis about becoming, a measurable causal-progress coordinate, and a stochastic network model. Causal progress is defined by $\tau(t)=\int_0^t\lambda(s\mid\mathcal H_s)\,{\rm d}s$, where the nonnegative event intensity $\lambda$ must be specified independently of the outcome. Agents carry an orientation phase and an activation amplitude; weighted interaction, heterogeneous drift, external input, anchoring, and diffusion govern their evolution in $\tau$. First- and second-harmonic order parameters separate consensus from bipolar polarization. For the all-to-all noisy Kuramoto special case with Lorentzian drift width $\Delta$, synchronization begins at the conditional threshold $K_c = 2(\Delta + D)$, not at a universal constant. Reproducible numerical illustrations illustrate (not empirically demonstrate) this threshold, causal-clock curve collapse, and the consensus-polarization distinction. Six historical episodes are treated as scope probes rather than validation data. The paper derives falsifiable hypotheses and an out-of-sample protocol for comparing causal-progress and chronological-time models. TCU is therefore offered as a disciplined bridge between process ontology and complex-systems modeling, not as a replacement for spacetime physics or as an empirically established identity between time and causation.

Physics and Society (physics.soc-ph); Artificial Intelligence (cs.AI)

arXiv:2607.18620 [physics.soc-ph]

(or arXiv:2607.18620v1 [physics.soc-ph] for this version)

https://doi.org/10.48550/arXiv.2607.18620 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.