Relation to Existing Physical Theories

Quantum Mechanics

In standard quantum mechanics, a system is described by a state vector $\lvert \Psi(t) \rangle$ in a Hilbert space. Its evolution obeys the Schrödinger equation:

$$ i\hbar \frac{d}{dt} \lvert \Psi(t) \rangle = \hat{H} \lvert \Psi(t) \rangle. $$

Drift Theory does not modify this equation. Instead, it introduces a separate experiential manifold $\mathcal{X}$ and a trajectory $X(t)$ governed by

$$ dX_t = -\nabla \Phi(X_t)\,dt - \alpha e(t) \nabla \Psi(X_t;C)\,dt + \sqrt{2D(1+\kappa e(t))}\,dW_t. $$

The two descriptions operate at different levels: the Hilbert-space dynamics of $\lvert \Psi(t) \rangle$ describe physical evolution, while the drift dynamics of $X(t)$ describe the structure of lived experience.

Many-Worlds Interpretation

In the Everett interpretation, the universal wavefunction branches into many non-interacting "worlds". Drift Theory can be viewed as a coarse-grained mapping from such branches into an experiential manifold $\mathcal{X}$, where each point $x$ represents a macro-level experiential version.

The novelty of Drift Theory lies in modeling a continuous path through nearby experiential versions, rather than emphasizing discrete branching alone. Emotional intensity and commitments bias which nearby coarse-grained region is most likely to be inhabited over time.

General Relativity and Wormholes

General relativity describes spacetime geometry using a metric tensor $g_{\mu\nu}$, satisfying Einstein's field equations

$$ G_{\mu\nu} = 8\pi G \, T_{\mu\nu}. $$

Spacetime wormholes, when they exist as solutions, are geometric structures in this metric. Drift Theory uses the term "wormhole" for a different object: a high-curvature segment of the experiential trajectory $X(t)$ in $\mathcal{X}$ during periods of strong affect.

$$ e(t) > e_c, \quad \max_{t \in [t_1, t_2]} \frac{\lVert \ddot{X}(t) \rVert}{\lVert \dot{X}(t) \rVert} > K_c. $$

Physical wormholes and experiential wormholes live in different spaces: spacetime vs. experiential configuration space. There is no formal conflict as long as this distinction is maintained.