Lock Model: Vibrational Dynamics of Space as the Origin of Gravity, Matter, and Dark Energy

This work presents the Lock Model, a theoretical framework that reinterprets dark matter and dark energy as emergent geometric phenomena—arising not from exotic substances, but from the vibrational dynamics of a three-dimensional spatial membrane M³, embedded in a higher-dimensional pluripotential quantum field. In this model, time is not a fundamental dimension, but an emergent property resulting from the oscillatory patterns of space itself.

Updated: August 27, 2025: "[The foundation of this spatial membrane is directly linked to the Quantum Cycle Model of Form (MCCF), a structural framework in which material manifestation arises from symbolic, fractal configurations within a dynamic quantum field. According to the MCCF, the electron — with its symmetric configuration {1,1,1,1,1,1} — represents the minimal stable form, emerging when the field achieves a threshold of structural coherence. However, the space that precedes this activation is not empty: it is composed of sub-threshold configurations where 0<∣nk∣<1, forming a dense, fractal network of latent symbolic structures. This network constitutes what is traditionally termed dark matter — not as a particle, but as the very fabric of space.

We define the spatial membrane M³ in its pre-material state through the occupation vector n = (n1, n2, n3, n4, n5, n6), where each component satisfies 0.1 ≤ nk ≤ 0.9. This representation corresponds to fractional configurations of the membrane, distinct from both the full saturation of a minimal particle (such as the electron, described by n = (1,1,1,1,1,1)) and from the vacuum. For instance, a perfectly symmetric configuration n = (0.5,0.5,0.5,0.5,0.5,0.5) yields an approximate structural energy of E ≈ 0.2184 MeV, which lies below the minimal constant εf = 0.511 MeV. Such configurations define the universal pre-matter structure, identifiable with the substrate of dark matter in the model. With appropriate funding, a third book could be developed to unify both works, making it clear that the membrane is composed of pre-matter or dark matter.]"

August 28, 2025: For a concise visual explanation, watch the video here: https://www.youtube.com/watch?v=-zJwNIFFyBY

Within this framework, the pre-material, oscillating membrane is the source of all physical dynamics:

• Local vibrational modes generate additional gravitational effects, replicating those attributed to dark matter.

• Global resonances drive the accelerated expansion of the universe, replacing the need for a fixed cosmological constant.

• Stars and massive bodies act as active resonators, perturbing the membrane through plasma oscillations, magnetic dynamics, and mass ejections, generating observable spatial deformations.

The dynamics are governed by a scalar field ϕ\phiϕ, satisfying a modified Klein–Gordon equation in an expanding universe. This formulation provides a unified explanation for gravitational lensing, galactic rotation curves, and cosmic acceleration — all as expressions of spatial tension, curvature, and resonance, rather than as effects of unseen mass or energy.

A key falsifiable prediction of the model is the existence of interference rings in gravitational lensing patterns, which could confirm or refute this vibrational framework by 2027.

This geometric and resonant view of the cosmos — where form precedes physics, and the universe emerges from a fractal quantum field — aims to broaden the frontiers of theoretical cosmology. It is not a replacement for existing theories, but a deeper structural layer from which they may naturally arise.

Version 6: This version corrects formatting issues in the references section (removal of markdown-style asterisks and application of proper italics for book and journal titles).

Version 5: From versions 1 through 4, only formatting corrections were made, without altering the conceptual content of the document. However, in version 5, I identified a significant issue in the translation of Appendices 9.8 and 9.9 from Spanish to English. The AI translation in that case was based on conventional existing models rather than the intended perspective of the Lock Model, which is geometric and vibrational in nature. As a result, some concepts were incorrectly represented or even reversed. I apologize for this error.

Version 5 is now presented with those specific sections corrected to properly reflect the Lock Model’s definition of time. It is important to emphasize that the concepts of time discussed in the conclusions have not been modified—they remain consistent with the original formulation. Only the misinterpreted points in the aforementioned appendices have been revised.

Lock G., Luis Antonio. Lock Model (Spanish version), Zenodo. https://zenodo.org/records/15705242

For academic inquiries or collaboration opportunities, please contact:
📧 ing.luislock@gmail.com