Emergent Inverse-Square Gravity from Dipole Correlations in Bohmian Mechanics: A Vacuum Phase Randomization Framework
Newtonian gravity emerges in Bohmian mechanics through quantum potential dynamics acting on collectively correlated vacuum excitations.
Abstract
We propose that Newtonian gravity emerges in Bohmian mechanics through quantum potential dynamics acting on collectively correlated vacuum excitations. The framework rests on two foundational assumptions: (1) The Configuration-Physical Correspondence (CPC) Principle, a geometric consistency requirement stating that configuration-space distance equals physical separation in the flat spacetime limit; and (2) The Disordered Vacuum Hypothesis, which models the Beyond Standard Model (BSM) vacuum as a quenched disordered potential landscape with Sinai scaling.
We derive the stretched-exponential wavefunction R(r) ∼ exp(−λ√r) as the typical amplitude exp(⟨log T⟩) from first principles using a Variational Lifshitz argument. A fundamental challenge in such models is the “Nebula Paradox,” wherein quantum pressure tends to generate repulsive forces. We demonstrate that vacuum phase randomization, which assigns stochastic signs to pairwise interactions, naturally resolves this paradox.
Newton’s constant emerges self-consistently within this framework. We propose that the vacuum roughness parameter σ_V takes a form suggested by QCD dimensional analysis:
σ_V = g√N_c · m_p c² / √λ̄_C
where g = √(4πα_s) is the QCD coupling and N_c = 3 is the number of colors. Self-consistency of the framework, which requires that the emergent Planck length equal the BSM vacuum cutoff, yields α_s = 1/3. The measured value α_s(1 GeV) ≈ 0.33 is consistent with this requirement, though the agreement is not strongly constraining given the running of the QCD coupling. Thus G emerges self-consistently from {ℏ, c, m_p, α_s, N_c}, though the identification E_0 = E_P constitutes an implicit assumption that future BSM physics must justify.
The mass-weighted formulation ensures automatic compliance with the Weak Equivalence Principle. We propose lattice QCD calculations to independently verify the disorder parameter, providing a concrete experimental test of the framework.
Link to paper.
A Layperson’s Guide to the Paper:
The Big Question
Where does gravity come from? Einstein’s General Relativity says massive objects bend spacetime itself, and things “fall” along those curves. But GR doesn’t play well with quantum mechanics. When physicists try to combine them, the math explodes into infinities. This paper proposes a completely different answer: gravity isn’t bending spacetime at all. It’s an emergent effect of quantum mechanics operating through a “lumpy” vacuum.
The Core Idea
Imagine the vacuum of space isn’t perfectly smooth and empty, but has a random, bumpy texture at incredibly small scales. Think of it like static noise on an old TV, but in 3D and frozen in place. The paper calls this the “disordered vacuum.”
Now, in a version of quantum mechanics called Bohmian mechanics, particles aren’t just probability waves. They’re real objects guided by those waves. The wave function creates a kind of “quantum pressure” that pushes particles around.
Here’s the key insight: when two massive objects sit in this lumpy vacuum, their quantum waves interact through all the random bumps between them. The paper shows mathematically that this interaction produces a force that pulls objects together (not apart), falls off as 1/distance² (Newton’s inverse-square law), and depends on total mass rather than what the objects are made of.
In other words, it recreates gravity from quantum mechanics. No curved spacetime needed.
The “Nebula Paradox” and Its Solution
Here’s the tricky part. Quantum pressure usually pushes things apart, like how electrons resist being squeezed together. If gravity came from quantum effects, you’d naively expect repulsion, not attraction. The paper calls this the “Nebula Paradox.”
The solution is elegant. Because the vacuum is randomly lumpy, each pair of particles gets assigned a random +1 or −1 sign based on the path between them. When you add up trillions upon trillions of these interactions, the repulsive “pressure” terms have random signs, so they cancel out. It’s like flipping a coin a billion times and getting roughly equal heads and tails. But the attractive “drift” terms always have the same sign, so they add up.
The randomness destroys the repulsion while preserving the attraction. For everyday objects with something like 10²⁶ particles, the cancellation is essentially perfect.
Why Masses Matter, Not Composition
There’s a famous principle in physics called the Weak Equivalence Principle. It says gravity pulls on all materials equally. A kilogram of feathers falls at the same rate as a kilogram of iron. This has been tested to extraordinary precision.
The paper achieves this automatically. The vacuum couples to energy (which equals mass via E=mc²), not to the number of protons and neutrons. So iron, with its tightly-bound nuclei, and hydrogen, with its loose protons, experience identical gravitational acceleration at equal total mass.
The Numbers Work Out
The paper derives one key parameter (λ₀) by matching to Newton’s gravitational constant G. Remarkably, this single calibration places all the other derived quantities at physically sensible scales. The “vacuum roughness” lands at the hadronic scale (around 7 GeV), exactly where protons and neutrons live. The “vacuum stiffness” sits at the Planck scale, where quantum gravity effects are expected.
This isn’t forced. It emerges naturally from the framework.
What This Isn’t
I should be clear here. This is speculative theoretical physics, not established science. It requires “Beyond Standard Model” physics that hasn’t been observed. It doesn’t yet fully reproduce General Relativity’s predictions for things like gravitational waves and black holes. And it hasn’t made novel experimental predictions that would distinguish it from GR.
But it’s mathematically self-consistent and offers a genuinely different way to think about why gravity exists. Not as bent spacetime, but as a statistical consequence of quantum mechanics in a noisy universe.
The Philosophical Shift
If this framework were correct, gravity wouldn’t be a fundamental force at all. It would be emergent, arising from deeper quantum mechanical processes the way temperature “emerges” from molecules bouncing around. Spacetime would stay flat. The “curvature” we measure would just be an effective description of underlying quantum dynamics.
That’s a profound reconceptualization of what gravity actually is.