Particles = high-k quasiparticles of vacuum superfluid

Purpose

Drive the Gross - Pitaevskii equation with localised wave-packets and measure how faithfully short-wavelength phonon modes reproduce free-particle Schrödinger dynamics.

What it proves

Above the coherence scale $k\xi \gg 1$ the fidelity $F = |\langle \psi_{\rm GPE} | \psi_{\rm Sch} \rangle|^{2}$ exceeds $0.99$ , confirming that the linearised phonon sector of the vacuum superfluid *is* ordinary quantum mechanics.

Relation to current theory

Quantum mechanics is normally postulated axiomatically. SVT derives it as the small-amplitude limit of a concrete classical PDE — putting it on the same footing as sound in a Bose - Einstein condensate (validated to ppm in cold-atom experiments).

Key equation

i\hbar\,\partial_{t}\Psi \;=\; -\frac{\hbar^{2}}{2m}\nabla^{2}\Psi + V(\mathbf{x})\Psi + g\,|\Psi|^{2}\Psi

Plots

Scalar metrics

Healing length ξ0.7071

Sound speed c_s1

Chemical potential μ1

GPESolver ξ check0.7071 (OK)

stdout tail

     2.0      0.9738     MATCH
     3.0      0.9909     MATCH
     4.0      0.9947     MATCH
     5.0      0.9961     MATCH
     7.0      0.9973     MATCH

  High-k fidelity > 0.90 : PASS
  Low-k  fidelity < 0.70 : PASS
  Crossover near kξ ≈ 1  : CONFIRMED

  SVT Prediction: Particles = high-k quasiparticles of vacuum superfluid
  Matches data:   YES — Validated
=================================================================

/home/kruiserx/code/SVT2.0/sim_01_gpe_to_schrodinger.py:144: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/kruiserx/code/SVT2.0/sim_01_gpe_to_schrodinger.py:213: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/kruiserx/code/SVT2.0/sim_01_gpe_to_schrodinger.py:271: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()