DRUMS Theory · Fast Radio Bursts in DRUMS

To Text Summary

1. Superfluid Plasma Representation

In DRUMS, cosmic plasma is a coherent superfluid field described by:

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

The velocity field is given by:

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

2. Excitation and Phase Collapse

Fast radio bursts are modeled as rapid phase collapses of localized regions. The phase dynamics are governed by:

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

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

                        "The FRB is a phase avalanche — a sudden, coherent collapse of a region of the superfluid plasma field."
                    

3. Nonlinear Coherence Threshold

Define energy density threshold ρ_th:

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

This triggers synchronized oscillation across the region. The threshold marks the point at which the superfluid's nonlinear interactions overcome the damping term γ, allowing a coherent collapse rather than a gradual decay.

4. Radiated Field

The emitted electromagnetic field corresponds to the time derivative of the phase:

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

The spatial coherence of the phase field gives narrow spectral emission. The burst is not a random noise event but a coherent, synchronized emission from a macroscopic region.

5. Frequency Determination

The characteristic frequency is determined by the size of the coherent region L:

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

For typical interstellar medium parameters, this yields GHz frequencies — exactly the observed range.

6. Dispersion Measure

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 same superfluid coherence that produces the burst also determines how its signal is spread by the intervening medium.

7. Burst Duration

The emission timescale arises from phase relaxation:

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

Short spatial extent yields millisecond durations — perfectly matching FRB observations.

8. Repetition and Memory

Regions with residual coherence can trigger repeated bursts:

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

This explains repeating FRBs naturally. The superfluid phase field has memory: a region that has collapsed once may still retain enough coherence to collapse again.

"Repeating FRBs are not a different class of object — they are regions where the phase field partially recovers between collapses."

9. Energetics

The total energy emitted scales as:

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

This matches observed burst energies (~10³⁸–10⁴⁰ erg) for reasonable plasma parameters. The burst energy is determined by the size of the collapsing region and the local superfluid density.

10. Final Interpretation

Within DRUMS, Fast Radio Bursts emerge naturally from:

Localized phase collapse in the superfluid plasma field
Coherent emission due to nonlinear synchronization
Frequency and duration set by region size and sound speed
Dispersion arising from propagation through coherent field channels
Repeating bursts due to residual phase memory

No exotic astrophysical mechanisms are required; the phenomenon is a direct consequence of coherent superfluid dynamics. The same superfluid that gives rise to emergent gravity, the CMB anomalies, and the cosmic web also produces the brightest millisecond flashes in the radio sky.

                        "Every FRB is a measurement of the superfluid's coherence length and its nonlinear response to accumulated phase stress."
                    

Conclusion: FRBs as Superfluid Phase Avalanches

In the DRUMS framework, Fast Radio Bursts are not exotic magnetar flares or unknown cataclysmic events. They are phase avalanches in the superfluid plasma field — sudden, coherent collapses of regions that have accumulated excess phase stress. The burst's frequency, duration, energy, and dispersion are all direct consequences of the superfluid's properties and the geometry of the collapsing region.

This interpretation resolves the major puzzles of FRB astrophysics: why bursts are so bright (coherent emission from a macroscopic region), why they are so short (small collapse size), why they appear in the GHz range (sound speed over region size), and why some repeat (residual phase memory). No separate population of objects is required; any region of the superfluid plasma field that exceeds the coherence threshold can produce an FRB.

In this reading, the FRB sky is not a catalog of exotic objects but a map of the superfluid's stress distribution. Each burst marks the location and scale of a phase collapse, providing a new window into the coherence properties of the universe's fundamental medium. The fact that FRBs are observed across cosmic distances is not a coincidence — it is a direct probe of the superfluid's coherence length and its variation with redshift.