Geometric Determinism in Quantum Mechanics: Wavefunction Collapse as a Hydrodynamic Lock-in Mechanism within a Superfluid Vacuum Field AUTHORS: Barbu, Ilie (Independent Researcher); DATE: December 6, 2025

ABSTRACT

Contemporary physics faces a conceptual deadlock: The Copenhagen Interpretation of Quantum Mechanics postulates that fundamental reality is probabilistic and undetermined until measurement. This paper challenges this view, arguing that the deadlock stems from neglecting the propagation medium. Starting from a calculated Vacuum Energy Density of \rho_{\text{vac}} \approx 10^{26} \text{ kg/m}^3, we propose a deterministic hydrodynamic model. We demonstrate that "superposition" is not a state of multiple existence, but a rapid dynamic scanning of phase space by a pressurized soliton. The "Collapse" of the wavefunction is redefined as a mechanical phenomenon of "Geometric Impedance Matching" (Lock-in): under the hydrostatic pressure of the vacuum, the particle is forced to instantaneously occupy the single spatial configuration that minimizes the local system tension. This model eliminates the probability paradox, suggesting that the Universe operates not on chance, but on geometric necessity and pressure equilibrium.  

1. INTRODUCTION: THE CRISIS OF CURRENT INTERPRETATION

For over a century, physics has accepted a painful compromise: the mathematical precision of quantum formalism (Schrödinger equation) comes at the cost of abandoning local realism. It is tacitly accepted that at the micro-level, cause and effect are suspended in favor of pure chance (Born rule). This paper proposes that quantum paradoxes are not intrinsic to nature but are the result of missing information about the Background Medium. Treating the vacuum as abstract (empty) geometry makes it impossible to explain the causal mechanism of collapse. Reintroducing a Superfluid Vacuum resolves the discontinuity between the micro (quantum) and macro (relativistic) worlds.

2. THEORETICAL FOUNDATION: VACUUM HYDRODYNAMICS

2.1. The Particle as a Vortex (Soliton)

We define the elementary particle not as a point object, but as a topological soliton stabilized in an inviscid fluid. Its stability is maintained by the balance between the external vacuum pressure (P_{\text{vac}}) and the centrifugal force of the internal spin.

2.2. Vacuum Pressure as a Forcing Agent

The medium exerts continuous pressure on matter. In accordance with the generalized Bernoulli Principle for quantum superfluids:

P_{\text{local}} + \frac{1}{2}\rho_{\text{vac}}v^2 + V_{\text{potential}} = \text{Constant}

Any discontinuity in geometry (a "hole" or electric potential) creates a pressure gradient (\nabla P). This gradient is the actual physical force guiding system evolution. 

3. WAVEFUNCTION COLLAPSE: GEOMETRIC REINTERPRETATION

The central "Measurement Problem" asks: Why does a spatially extended wavefunction suddenly reduce to a point?

3.1. Superposition as Geometric Scanning

The wavefunction \Psi does not represent abstract probability, but a description of the particle's hydrodynamic trajectory. In an unperturbed state, the soliton oscillates, effectively "feeling" or scanning the geometry of the surrounding system.

3.2. The "Key-in-Lock" Mechanism

Measurement introduces a geometric constraint (the measuring apparatus creates a potential template). Collapse is not a random choice, but a process of Tension Minimization.

The Macroscopic System (Vacuum + Apparatus) possesses a specific energetic "hole" (a geometry of minimum impedance).

Vacuum Pressure (10^{26} \text{kg/m}^3 equivalent) pushes the particle.

The particle inevitably and instantaneously slips ("Clicks") into the geometric configuration that perfectly matches the potential shape, akin to a key entering a lock or water filling a crack.

Partial Conclusion: The measurement result is predetermined by local spacetime geometry and the vacuum tension configuration. There is no randomness, only hidden geometric complexity.

4. ELIMINATING PROBABILITY: TOP-DOWN CAUSALITY

Quantum probability (|\Psi|^2) is not ontological. It is a statistical measure of vacuum density distribution.

Where the flux line density is high -> The probability of finding the particle is high.

The particle does not "roll the dice." The particle is transported by vacuum currents to the point of maximum stability. We introduce the concept of Hydrodynamic Top-Down Causality: The Pressure of the Whole (Universe/System) dictates the position of the Part (Particle). The system does not tolerate pressure "voids"; it forcefully fills them.

5. IMPLICATIONS FOR QUANTUM COMPUTING AND AI

If collapse is a geometric matching function rather than a probabilistic one, future technology must abandon the "brute force" approach. Optimal algorithms should be Topological, constructing geometric "negatives" of the sought solution, allowing information to naturally "collapse" toward the correct answer with minimal energy consumption.

6. FINAL CONCLUSION

Abandoning causality in the 1920s was a strategic error caused by the refusal to accept a dense physical medium. Reintegrating Vacuum Energy Density as the main actor demonstrates that quantum mechanics is a branch of Advanced Hydrodynamics. Reality is strictly deterministic, governed by precise geometric architecture, where "probabilities" are merely the shadow of our ignorance regarding the vacuum's shape. It is time to step off the path of "Probability" and onto the path of "Deterministic Geometry."