Theory of Everything: Matter–Antimatter Asymmetry in DRUMS

1. Symmetry at the Superfluid Level

At the fundamental level, DRUMS allows symmetric excitation modes corresponding to matter and antimatter:

\[ \Psi_{\pm} = \sqrt{\rho} e^{\pm i\theta} \]

The \(+\) and \(-\) phase windings correspond to matter and antimatter states, respectively.

The cubic magnetic substrate introduces a directional bias in phase evolution due to anisotropic coupling:

\[ \Delta E = E_{+} - E_{-} \neq 0 \]

This arises because phase winding interacts differently with substrate orientation:

\[ E_{\pm} \sim \int \left( \frac{\hbar^2}{2m} |\nabla \theta|^2 \pm \alpha \, \mathbf{B}_{\rm sub} \cdot \nabla \theta \right) dV \]

The coupling term \(\alpha \, \mathbf{B}_{\rm sub} \cdot \nabla \theta\) breaks symmetry between matter and antimatter.

Weak bosons couple to chiral modes of the superfluid:

\[ \mathcal{L}_{\rm weak} \sim g \, \bar{\Psi} \gamma^\mu (1 - \gamma^5) \Psi \, W_\mu \]

In DRUMS, this chirality emerges from preferred rotational direction of vortex modes relative to the substrate.

As a result, decay rates differ:

\[ \Gamma_{matter} \neq \Gamma_{antimatter} \]

Over cosmological time, the small energy difference leads to exponential amplification:

\[ \frac{dn}{dt} \sim -\Gamma_{ann} n^2 + \Delta \Gamma \, n \]

Where \(\Delta \Gamma\) encodes asymmetry. Solution yields:

\[ n(t) \propto e^{\Delta \Gamma t} \]

This naturally produces a matter-dominated universe.

CP violation parameters should correlate with measurable anisotropies in underlying field structure.
Weak decay asymmetries should show directional dependence relative to large-scale structure.
Analog superfluid systems with imposed lattice anisotropy should reproduce matter-antimatter imbalance.