# [[releases/2025/Infomatics]] # 6. Interaction Strength as an Emergent Consequence of Dynamics **(Operational Framework v2.5)** A fundamental aspect of physical theories involves quantifying the strength of interactions. Standard physics employs dimensionless coupling constants, like the fine-structure constant (α ≈ 1/137) for electromagnetism, which lack a first-principles explanation and rely on potentially artifactual constants like $\hbar$. Infomatics proposes a more parsimonious and fundamental approach: **interaction strengths are not independent constants but emerge directly as calculable consequences of the underlying π-φ geometry and the dynamics governing transitions between stable resonant states (Î)** characterized by indices $(n, m)$. Infomatics rejects the fundamental status of empirically fitted coupling constants like α, viewing them as effective parameters valid only within the standard model’s interpretive framework (which depends on $\hbar$). Instead, interactions are understood as transitions between stable $(n, m)$states (Section 3). The **probability amplitude** for a specific allowed transition, $(n_i, m_i) \rightarrow (n_f, m_f)$involving mediator $(n_{\gamma}, m_{\gamma})$, is **determined entirely by the fundamental π-φ dynamics** governing the informational field I and its potential contrast κ. This transition amplitude, which operationally replaces standard vertex factors involving $\sqrt{\alpha}$, must be **calculated** using the Infomatics action principle (with action scale $\phi$) applied to the π-φ Lagrangian (to be fully formulated in Phase 3). The result of this calculation will be a dimensionless complex number whose magnitude depends only on the geometric properties encoded in the indices $(n_i, m_i), (n_f, m_f), (n_{\gamma}, m_{\gamma})$and the fundamental constants π and φ. The **observable probability (P)** of the interaction is proportional to the squared magnitude of this calculated amplitude, integrated over relevant phase space factors (also derived from π-φ geometry). This probability corresponds to the **effective coupling strength ($\alpha_{eff}$)** measured experimentally. Based on numerical consistency and potential geometric interpretations involving ratios of scaling areas ($\sim \phi^2$) to cyclical volumes ($\sim \pi^3$) explored iteratively (see Appendix A), it is **hypothesized that the result of this π-φ calculation for the squared amplitude of fundamental electromagnetic interactions will scale as:** $\text{Calculated } |Amplitude_{EM}|^2 \propto \frac{\phi^4}{\pi^6} $ *(The precise dimensionless proportionality constant must emerge from the detailed Phase 3 calculation).* This leads directly to an effective electromagnetic coupling strength: $\alpha_{eff} \propto P \propto |Amplitude_{EM}|^2 \propto \frac{\phi^4}{\pi^6} \approx \frac{1}{140.3} $ This provides a potential **geometric origin for the observed strength of electromagnetism**, deriving its approximate magnitude from π and φ without needing α as an input. The framework predicts that rigorous calculation using the action scale $\phi$and this geometrically derived interaction probability will reproduce experimental observations currently interpreted using $\hbar$and the empirical $\alpha_{measured} \approx 1/137$. As discussed previously (Appendix A), the small numerical difference is expected to be reconciled by differing dynamical coefficients ($C_{inf}$vs $C_{std}$) arising from the distinct $\phi$-based versus $\hbar$-based theoretical frameworks. In conclusion, Infomatics operationally eliminates fundamental coupling constants. Interaction strengths are emergent consequences of the state-dependent transition probabilities calculated directly from the fundamental π-φ dynamics. The observed strength of electromagnetism is hypothesized to arise from specific geometric factors ($\phi^4/\pi^6$) inherent in these dynamics. This approach enhances parsimony and grounds all interactions within the core geometric principles, pending the full Phase 3 derivation of the dynamic equations and the resulting transition amplitudes. *(Detailed iterative reasoning in Appendix A).* ---