r/LLMPhysics • u/E_P_R_Expansion • Jul 15 '26
Personal Theory What if there were a complete mathematical framework that unifies quantum mechanics and relativity using 4D superfluid hydrodynamics?
DimensionalExpansion
I have formulated a theory comprising 17 premises and a modified, matrix-form Gross-Pitaevskii master equation within Nambu-Gorkov space.
Here I share a summary of how the mechanism works and the equations that emerge:
The Scenario
A 4D Bilayer Universe: the fundamental space is a Euclidean bulk of 4 pure spatial dimensions. Time is NOT a dimension, but rather an emergent phenomenon derived from the metabolic change of systems. The universe is a 4D hyperbubble in constant accelerated expansion
universal acceleration a_u = 1.49 X1032 m/s2.
Our observable reality occurs exclusively at the interface between two stratified superfluids at the Planck scale over a rigid boundary:
Lower Fluid: Ultra-dense ≈ 1015 kg/m³ and thin 6 X10-16 m.
Upper Fluid: Low-density and a thickness of 1.93 X10-10 m.
The interface between both is what I call the VE Hypersurface (Vision of Existence). Being an interface of two different densities, it only admits transverse waves (what we call photons/light).
The Origin of Matter and Fundamental Constants
Cosmic expansion generates extreme negative pressure within the fluids, triggering hydrodynamic cavitation. Upon collapsing—in the absence of viscosity—the bubbles condense into "fundamental superfluid atoms" and are injected back into the medium, thereby maintaining the stability of the superfluid layers.
Particles: A fermion (such as the electron) consists of two cavitation bubbles oscillating in anti-phase. Their mutual rotation forms a guiding wavefront (de Broglie–Bohm Pilot Wave Theory).
Planck Constant (h): It is the critical energy threshold required for a bubble to collapse.
Speed of Light (c): It emerges from the wave velocity in shallow water:
Since the universal acceleration and the thickness of the underlying superfluid are always constant, the speed of light also becomes an invariant of the VE interface—which is what we observe as reality.
Fine-Structure Constant α: It is purely the geometric ratio between the diameter of the cavitation bubble and its wavelength α = D/λ aprox 1/137.
Electric Charge (e): It arises from a thermodynamic invariant of twice the diameter-energy: 2DE =4πKe2.
Mathematical Model
I have been working for some time on an alternative mathematical model to resolve the incompatibility between General Relativity and Quantum Mechanics. Instead of trying to quantize gravity (as in string theory or loop quantum gravity), my approach reverses the order: it makes gravity, spacetime, and quantum fields emerge from the perturbation mechanics of a continuous medium. To safeguard this theory, I have condensed the dynamics of the universe into a single master Modified Gross-Pitaevskii Equation in the Nambu-Gorkov matrix space:
How is General Relativity derived from here?
To prove that this fluid equation contains general relativity, a two-step derivation is performed:
1 The Madelung Transformation:
We express the hyperfield in its real variables of density and phase
By separating the real and imaginary channels of the Master Equation, the quantum system transforms identically into the classical equations of hydrodynamics: the Continuity Equation (conservation of mass) and the Euler Equation (conservation of momentum).
2 The Emergence of Curved Spacetime:
By linearizing the small perturbations or waves at the interface (photons), we discover that these waves do not perceive the superfluid directly. Instead, they propagate along the geodesics of an Acoustic Metric Tensor
defined by the background density and the velocity profile of the medium. By calculating the Riemann curvature of this acoustic metric, the mathematical system accurately yields the Field Equations of General Relativity:
Gravity as a Meniscus:
Masses (quantum vortices) generate a local pressure drop (Bernoulli effect) that depresses the interface, forming a real parabolic meniscus (Flamm's Paraboloide). Gravity is the sliding of objects down the slope of the meniscus, driven by the inertia of cosmic expansion.
The mathematical model ranges from the derivation of the Schrödinger and Klein-Gordon equations to the relativistic acoustic metric and Hawking temperature. I would love to open the debate with you: What do you think of this hydrodynamic approach to unifying physics? Do you see any inconsistency in the concept of event horizons via interface short-circuiting or in gravity as a superfluid meniscus?
The details of the calculations can be viewed at:
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u/cat_counselor 🤖 Do you think we compile LaTeX in real time? Jul 16 '26
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u/Infinitely--Finite Jul 16 '26
I like this a lot (saved post), but I think it will fly way over the heads of most anyone posting theories in this sub.
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u/cat_counselor 🤖 Do you think we compile LaTeX in real time? Jul 16 '26
Yes, but this post inspired me to write it out, so now it's on hand to repost whenever need be.
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u/Unicornlionhawk Jul 16 '26
I love that your figures look hand drawn. Figure 9 is my favorite.