This component archives the twelfth theoretical preprint of the Redefined Mass unified field theory. This paper resolves the physical origins of fundamental quantum constants and wave-particle duality, replacing statistical probability with deterministic fluid dynamics. It demonstrates that Planck's constant (h) is the physical phase-slip circulation quantum of the virtual boson BEC boundary, while Boltzmann's constant (k_B) defines the thermodynamic limit of boundary-to-plasma transitions. Furthermore, it establishes Postulate XVII, providing an electrodynamic resolution to quantum tunneling: a particle passing through a dense solid momentarily dissolves its geometric mass boundary into pure coherent field-energy (the wave state) to navigate the atomic lattice, subsequently undergoing vacuum re-nucleation (reconstructing the particle state) upon exiting the perturbing fields.
This component archives the twelfth theoretical preprint of the Redefined Mass unified field theory. This paper resolves the physical origins of fundamental quantum constants and wave-particle duality, replacing statistical probability with deterministic fluid dynamics. It demonstrates that Planck's constant (h) is the physical phase-slip circulation quantum of the virtual boson BEC boundary, while Boltzmann's constant (k_B) defines the thermodynamic limit of boundary-to-plasma transitions. Furthermore, it establishes Postulate XVII, providing an electrodynamic resolution to quantum tunneling: a particle passing through a dense solid momentarily dissolves its geometric mass boundary into pure coherent field-energy (the wave state) to navigate the atomic lattice, subsequently undergoing vacuum re-nucleation (reconstructing the particle state) upon exiting the perturbing fields.
This component archives the twelfth theoretical preprint of the Redefined Mass unified field theory. This paper resolves the physical origins of fundamental quantum constants and wave-particle duality, replacing statistical probability with deterministic fluid dynamics. It demonstrates that Planck's constant (h) is the physical phase-slip circulation quantum of the virtual boson BEC boundary, while Boltzmann's constant (k_B) defines the thermodynamic limit of boundary-to-plasma transitions. Furthermore, it establishes Postulate XVII, providing an electrodynamic resolution to quantum tunneling: a particle passing through a dense solid momentarily dissolves its geometric mass boundary into pure coherent field-energy (the wave state) to navigate the atomic lattice, subsequently undergoing vacuum re-nucleation (reconstructing the particle state) upon exiting the perturbing fields.
The probabilistic nature of quantum mechanics has long been debated as either an intrinsic property of reality or a limit of human knowledge. We propose a third option: quantum phenomena are the deterministic mechanical consequences of wave propagation through a discrete, stiffness-limited medium---the Golden-Rhombohedral Cosserat Vacuum, a five-fold symmetric quasicrystal we term the quintinuum. Building on our previous derivations of the fine-structure constant (α\alpha α) and gauge symmetries (U(1), SU(2), SU(3)) from vacuum geometry, we now derive the phenomenological behavior of quantum matter. We demonstrate that: (1) Wave-particle duality arises from the interaction between a topological defect (the particle) and its precursor strain field (the wave); (2) The uncertainty principle is a bandwidth limit imposed by the finite stiffness of the vacuum lattice; (3) Quantum non-locality results from longitudinal scalar tension relaxing through a volume-preserving medium. Crucially, by restoring the scalar component of Maxwell's original quaternionic electromagnetism, we derive the propagation speed of this longitudinal tension. We predict the ``Speed of Entanglement'' to be finite but superluminal: \begin{equation*} v_L = c \cdot \varphi^{47} \approx 2.0 \times 10^{18} \text{ m/s} \end{equation*} This framework resolves the paradoxes of the Copenhagen interpretation by replacing abstract postulates with the concrete mechanics of a golden-rhombohedral quasicrystal. The universe is not magic; it is a machine. We have found the gears.
This is Paper VI of the Planck Cube Space Theory series, providing a unified physical realist interpretation of quantum phenomena based on the axiom system of discrete spatial granularity. Key claims: The wavefunction ψψ is the slowly-varying complex envelope of the twist field (radial torsion of Planck cubes), not an abstract probability amplitude. ∣ψ∣2 is the twist density, proportional to the probability of triggering a detector (physical origin of the Born rule). The uncertainty principle arises from spatial discreteness (Δx≥ℓP0) and measurement disturbance. Wave-particle duality is unified as "particle itself (energy cluster) + accompanying twist field". Quantum entanglement originates from the topological identity of a split cubic lattice chain (no energy/information transfer, respecting special relativity). Quantum tunneling reduces to a geometric equipotential channel in the 10−14 Å interval (d=4r0), consistent with experiments. The Schrödinger equation is not a postulate, but an effective evolution equation for the twist field envelope under continuum, long-wavelength, weak-damping approximations. Statistical randomness arises from Planck-scale initial fluctuations, chaotic amplification, and detection coupling — not from intrinsic randomness. This theory does not deny the mathematical validity of quantum mechanics but provides it with a physical carrier, reducing quantum phenomena to the geometric deformations and elastic propagation of the Planck cubic lattice.
This paper provides a fully deterministic, hydrodynamic resolution of wave-particle duality within the theoretical framework of a compressible superfluid continuum (Z4DP). The study offers a causal alternative to the Copenhagen interpretation and the concept of wavefunction collapse. In the presented model, the electron is defined as a macroscopic topological defect (sink) that generates a real phase pilot wave during its motion. During the double-slit experiment, this wave passes through both slits and interferes, whereas the physical node itself (the electron) passes through only a single slit and is subsequently hydrodynamically advected by the pressure gradient of the perturbed medium. Furthermore, the paper provides an exact mechanical explanation of the "Observer Effect" (Measurement Problem): introducing a measuring device into the system does not induce a collapse of reality, but rather represents a physical input of energy that triggers hydrodynamic noise within the medium. This noise destructively modifies the fragile pilot wave, causing the electron to lose its navigational gradient and continue its trajectory purely by inertia. The modification of the system's behavior is thus a direct consequence of classical fluid mechanics, restoring determinism and objective realism to quantum phenomena without the need for probabilistic wavefunctions or many-worlds interpretations.
This monograph provides a deterministic, hydrodynamic foundation for Quantum Mechanics, replacing the probabilistic abstractions of the Copenhagen interpretation. By redefining the cosmic vacuum as a tangible, compressible Bose-Einstein Condensate (BEC), the abstract Schrödinger equation is mathematically mapped directly to the classical Euler fluid momentum equations via the Madelung Transformation. Through this hydrodynamic lens, wave-particle duality is physically resolved: a localized quantum droplet is mechanically steered by the acoustic pressure gradient of its own wake. The Heisenberg Uncertainty Principle is explicitly recontextualized as the irreducible variance of convective diffusion—a microscopic buoy subjected to the continuous turbulence of the vacuum's kinematic viscosity. Furthermore, quantum entanglement is modeled not as an abstract, non-local phenomenon, but as continuous longitudinal phononic resonance. Scaling these sub-atomic continuum mechanics to astrophysics, this framework replaces collisionless Dark Matter and stochastic planetary accretion with macroscopic acoustic nodes, viscous fluid drag, and deterministic tidal thresholds—recently validated by 2026 Chandra observations of pre-ignition EUV thermalization. Ultimately, this demonstrates that quantum mechanics is simply fluid dynamics operating at extreme limits of scale and viscosity.
A deterministic quantum mechanics theory is presented in a series of papers starting with the present one. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions, which demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns that are raised by results from the current mainstream statistical quantum theory. The meaning of particle-wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin,” the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals, and the natural collapse of the wave function as part of the solution are some of the results that emerge from the proposed deterministic quantum mechanics theory. The only postulate underlying the proposed theory is that the electron and most likely other sub-atomic particles behave like compressible fluids. The current paper also shows that quantum tunneling does not violate the energy balance because part of the electron-fluid can locally exceed the kinetic energy required to spill over the potential barrier. The phenomenon of entanglement is shown to be consistent with the proposed deterministic quantum mechanics theory. The Bohr–Schrödinger energy levels leading to the experimentally confirmed spectral lines, as well as the fine structure constant emerge directly from the solution of the equations governing the proposed deterministic quantum mechanics presented in Part II of these series of papers.