Emotional Wave Dynamics: A Phase-Field Model of Social Emotional Contagion

# Update Summary (v1.1) This version refines the theoretical framing of Emotional Wave Dynamics to improve internal consistency with the IPCSALT/UPF framework and later recoverability-focused work. Key revisions include: Reframing “phase transition” language into phase regime / amplification balance, avoiding claims of irreversible collapse or direct prediction. Clarifying the role of the phase temperature T_phase as a relative diagnostic index of amplification dominance, rather than a forecasting threshold. Removing policy-prescriptive and deterministic interpretations, and strengthening the interpretive, structural focus of the model. Harmonizing terminology related to the Dark Field, shielding, and damping to emphasize background influence and modulation, not causal determinism. Minor textual revisions across Sections 4–6 to align tone with a pre-diagnostic, phase-dynamic analysis. No core equations were altered.These updates position this paper as a foundational, interpretive model of collective emotional wave dynamics, intended to support later work on filter bubbles, recoverability, and diagnostic phase geometry. Emotional Wave Dynamics (EWD) proposes a phase-field framework in which emotions are modeled not as isolated psychological states but as waves propagating through a social consciousness field.This work explains how individual affect becomes large-scale emotional contagion, why societies rapidly polarize, and how stable communities transition into chaotic regimes. Modern societies experience accelerated emotional spread, unpredictable collective behavior, and recurring phase shifts between stability and disorder.Psychology and sociology provide essential qualitative insights, but a unified quantitative model capable of describing emotional propagation, collective trauma, and stabilization mechanisms has been missing. This paper introduces a mathematical formulation within the IPCSALT–UPF framework that describes emotions as phase-field waves on a social consciousness manifold.The EWD model formalizes: emotion-specific propagation speed v_k directional phase vectors shaped by relational structure v_k,ij environmental stress ΔEenv as a projection of historical trauma stored in the Dark Field ΦDark nonlinear personal shields S_i generated by self-cohesion, recovery energy, and love-based stabilizing fields The model introduces a phase transition temperature, Tphase, distinguishing harmonious, unstable, and chaotic social regimes.Mathematically, destructive emotions such as fear propagate much faster than constructive ones ( αfear≫αlove ).Conversely, love functions as a Higgs-like stabilizing mechanism, providing effective mass and coherence to the social phase field at minimal energetic cost. Emotional Wave Dynamics offers a unified mathematical language for analyzing emotional contagion, collective trauma, polarization, and systemic collapse.It further proposes intervention strategies involving algorithmic modulation, recovery energy E_R, and cultural adjustment factors.The framework establishes the theoretical foundation for future empirical validation using large-scale affective datasets and computational social simulations. This work is an exploratory contribution situated within the IPCSALT–UPF phase-based meta-framework.