This hypothesis sets the stage for our theoretical model (Section 2), where we define a nonlinear dynamical equation governing the information field I(x,t)I(x,t), and explore its implications through simulation and experimental design.
II. Theoretical Model and Formulation
A. Governing Equation: Nonlinear Information Field Dynamics
At the heart of the Blink Universe model lies the proposition that spacetime and geometry can emerge from the nonlinear dynamics of an abstract information field, denoted as I(x,t)I(\vec{x}, t)I(x,t), propagating through a structured or responsive medium (e.g., a spin lattice, quantum vacuum, or optical condensate). The evolution of this information field is governed by a generalized nonlinear wave equation, inspired by analogies to the Gross--Pitaevskii equation, nonlinear Schrdinger equation, and Klein-Gordon-type field equations in driven-dissipative systems:
I+Ic22I+I2I=B(x,t)\ddot{I} + \gamma \dot{I} - c^2 \nabla^2 I + \lambda |I|^2 I = B(\vec{x}, t)I+Ic22I+I2I=B(x,t)
Term-by-term description:
I\ddot{I}I: Represents the inertial or second time derivative of the information field, capturing wave-like propagation and oscillatory dynamics.
I\gamma \dot{I}I: A dissipative term, representing loss or damping, consistent with coupling to an underlying reservoir (as occurs in spin-lattice systems or lossy optical cavities). The sign and magnitude of \gamma control the stability and the resonance profile.
c22I-c^2 \nabla^2 Ic22I: The spatial dispersion term, analogous to the Laplacian in wave equations, allowing spatial information to propagate and interfere. The parameter ccc represents the effective information propagation velocity---akin to the speed of sound in the medium.
I2I\lambda |I|^2 II2I: A nonlinear self-interaction term, enabling amplitude-dependent modulation and pattern formation. It is responsible for phenomena such as self-focusing, soliton generation, or chaos depending on the sign and magnitude of \lambda.
B(x,t)B(\vec{x}, t)B(x,t): An external information pulse or "blink"---an impulsive, spatially and temporally localized forcing function that seeds the excitation of the system. This acts as the initial "trigger" mimicking the birth of a localized spacetime bubble.
This equation draws its strength from physical analogies while preserving mathematical generality. It can be tuned to emulate:
Spinor condensates, where III is a complex order parameter for spin orientation.
Magnon condensates, where III encodes collective spin-wave amplitudes.
Optomechanical fields, where III couples to photon-phonon interactions in microcavity systems.
Quantum fluids, where III behaves similarly to a superfluid wavefunction under driven-dissipative constraints.
Assumptions and Interpretations:
The field III may be real or complex, depending on whether phase information is considered part of the encoded structure (we consider the complex case to allow rich phase topologies).
The system is non-Hermitian, due to the presence of damping \gamma and driving BBB; this allows for resonance-induced symmetry breaking and topological defect formation.
The nonlinearity \lambda may evolve dynamically or vary spatially, allowing for inhomogeneous responses---akin to metric fluctuations or curvature formation in analog spacetime.
The governing equation is dimensionally consistent, and its parameters can be adapted to specific platforms---such as spin-lattice chains, opto-mechanical arrays, or BEC analogs. In subsequent subsections, we will explore numerical simulations, scaling laws, and topological implications that follow from this foundational equation.
B. Dimensional Analysis and Scaling
Energy, Length, and Frequency Scaling Laws
