Emotional Wormholes and Relational Attractors

4. Emotional Wormholes as High-Curvature Transitions

In popular multiverse narratives, a "wormhole" is a sudden transition to a very different version of reality. Drift Theory reinterprets this idea within experiential state-space: a wormhole is a rapid reconfiguration of $X(t)$ driven by strong affect.

Define velocity and acceleration:

$$ \dot{X}(t) = \frac{dX}{dt}(t), \quad \ddot{X}(t) = \frac{d^2X}{dt^2}(t), $$

assuming sufficient smoothness. An interval $[t_1, t_2]$ is an emotional wormhole segment if:

• Emotional intensity exceeds a critical threshold $$e(t) > e_c \quad \text{for } t \in [t_1, t_2],$$
• The trajectory exhibits high curvature in $\mathcal{X}$: $$ \max_{t \in [t_1, t_2]} \frac{\lVert \ddot{X}(t) \rVert}{\lVert \dot{X}(t) \rVert} > K_c. $$

After such an event, external physical details may remain almost unchanged, but the subject's meaning-structure, self-understanding, and relational stance can be significantly different.

5. Relational Attractors and Stability Basins

Drift Theory also aims to capture the intuition that certain patterns—especially long-term relationships and repeated choices—seem to persist across many local variations of life.

Let $V: \mathcal{X} \times \mathcal{C} \to \mathbb{R}$ be a relational stability potential. For a given set of commitments $C$, define $V(x;C)$ such that $V$ is low when the frame $x$ reflects honored commitments (continuing a chosen relationship, living consistently with values), and high when commitments are violated.

Define a combined energy-like function

$$ U(x;C) = \lambda_{phys} \, \Phi(x) + \lambda_{rel} \, V(x;C), $$

with weights $\lambda_{phys}, \lambda_{rel} \ge 0$ expressing the relative importance of continuity versus relational stability.

In a simplified deterministic limit (neglecting noise and treating emotion intensity as slowly varying), the drift can be approximated by

$$ \dot{X}(t) = -\nabla U(X(t); C). $$

Regions where $U(x;C)$ is locally minimal form attractor basins: sets of frames that the trajectory tends to visit and revisit. Many slightly different experiential frames can share the feature of "being with the same partner in a relationship of mutual commitment," even as external details change.