A Discrete Heuristic Model of Vacuum Memory with Fractal-like Structure: Entropy, Fourier Signatures, Bohmian Guidance and Decoherence in a Two-Slit Interferometer

We present a conceptual and computational investigation of vacuum memory within a discrete toy-model framework. In this phenomenological approach, we introduce an effective memory field that records virtual events and nonlocal couplings on a lattice, without claiming to derive a fundamental new field of nature. Using a discrete toy model, we simulate memory formation via virtual events, nonlocal links, and black-hole-like information sinks. The resulting dynamics exhibit long-range spatial correlations, curvature-induced accumulation, high-entropy retention zones, and distinct spectral features, indicating that the modeled memory field can store and organize information in a vacuum-like medium. Building on this foundation, we incorporate curvature-modulated vacuum memory fields into Bohmian particle dynamics. By varying the memory coupling strength λ, we demonstrate that memory gradients systematically bend particle trajectories toward curvature centers, illustrating an active role for structured memory in guiding quantum-like motion. We further show that when vacuum memory encodes the full quantum phase S(x, t) and particles are guided by the Bohmian relation x˙=m−1∂xS, the trajectories collapse onto a single path with machine-level precision, providing a numerical consistency check that our implementation reproduces exact pilot-wave guidance and minimal-action dynamics. Through a minimal two-site entangled-memory model, we demonstrate that coupled memory fields—without explicit particle dynamics—can spontaneously synchronize via weak informational coupling, generating robust nonlocal correlations reminiscent of entanglement. Finally, we simulate two-slit interference under vacuum memory perturbations. While random, unstructured memory preserves quantum coherence and fringe visibility, structured, phase-sensitive memory induces dephasing and suppresses interference, functioning as a phenomenological decoherence mechanism. Together, these results situate our toy model within emerging information-based views of quantum dynamics and spacetime, offering a computational platform and conceptual lens for exploring the informational dynamics of a vacuum-like medium.