Theory of Everything: Fast Radio Bursts in the DRUMS Framework

1. Superfluid Plasma Representation

In DRUMS, cosmic plasma is a coherent superfluid field:

\[ \Psi(\mathbf{x},t) = \sqrt{\rho(\mathbf{x},t)} e^{i\theta(\mathbf{x},t)} \]

The velocity field is:

\[ \mathbf{v} = \frac{\hbar}{m} \nabla \theta \]

Fast radio bursts are modeled as rapid phase collapses of localized regions:

\[ \frac{\partial^2 \theta}{\partial t^2} + \gamma \frac{\partial \theta}{\partial t} - c_s^2 \nabla^2 \theta = 0 \]

When nonlinear interaction exceeds a threshold, the region undergoes coherent emission.

Define energy density threshold \(\rho_{th}\):

\[ \rho(\mathbf{x},t) > \rho_{th} \Rightarrow \text{Coherent Emission} \]

This triggers synchronized oscillation across the region.

The emitted electromagnetic field corresponds to time derivative of phase:

\[ \mathbf{E}(t) \propto \frac{\partial \mathbf{v}}{\partial t} = \frac{\hbar}{m} \frac{\partial}{\partial t} \nabla \theta \]

The spatial coherence gives narrow spectral emission.

Characteristic frequency determined by size of coherent region \(L\):

\[ \nu \sim \frac{c_s}{L} \]

For typical interstellar medium parameters, this yields GHz frequencies.

Propagation through the medium adds dispersion:

\[ \text{DM} = \int_0^d n_e(l) \, dl \]

DRUMS explains observed dispersion as density integral along coherent field channels.

The emission timescale arises from phase relaxation:

\[ \tau_{FRB} \sim \frac{L}{c_s} \]

Short spatial extent yields millisecond durations.

Regions with residual coherence can trigger repeated bursts:

\[ \theta(t+\Delta t) \approx \theta(t) + \delta \theta \]

Explains repeating FRBs naturally.

Total energy emitted:

\[ E_{FRB} \sim \rho L^3 c_s^2 \]

Matching observed burst energies (~10^{38}–10^{40} erg) for reasonable plasma parameters.

Within the DRUMS framework, Fast Radio Bursts emerge naturally from:

No exotic astrophysical mechanisms are required; the phenomenon is a direct consequence of coherent superfluid dynamics.