This page is a single-source, website-first research note for Project Curvature. The central claim is operational: two quantum preparations can share the same ⟨ρ̂⟩ yet differ in Var(ρ̂), and gravity may—under this proposal—distinguish them.
Standard semiclassical gravity sources the classical field from the expectation value ⟨T̂μν⟩. VSSG introduces a deterministic correction sourced by irreducible quantum fluctuations (variance). This yields a concrete discriminator: coherent superposition and incoherent mixture can share the same ⟨ρ̂⟩ but differ in Var(ρ̂), producing a measurable difference in gravitationally mediated phase (weak-field).
In the Newtonian (weak-field, slow-motion) regime, the gravitational potential satisfies:
Practical note: for pointlike masses, define a smeared density operator ρ̂σ over a small length σ to keep Var(ρ̂σ) finite. The platform choice controls σ (effective localization scale).
For a “two-lump” equal-weight superposition, the variance contribution scales like:
If an experiment measures gravitational phase to fractional precision ε without detecting a deviation:
That turns a foundational idea into a real experimental constraint.
Start with gravity-mediated phase / entanglement style experiments: two masses placed into spatial superpositions, where Newtonian gravity induces branch-dependent phases. The discriminator is: coherent superposition vs incoherent mixture at the same ⟨ρ̂⟩.
Implementation details (m, separation, coherence time, σ definition) will be tailored once you pick a target apparatus (e.g., levitated optomechanics, matter-wave interferometry, or hybrid resonator systems).
Imagine gravity is like a “pull” that comes from mass. Usually we say gravity only cares about where the mass is on average. But quantum things can be in two places at once.
We test it by putting tiny masses into a quantum “two-places” state and measuring whether gravity creates a slightly different phase effect than the normal average-gravity prediction.