Gravity as a Gradient of Uncertainty: A Probabilistic Framework for Spacetime Curvature

This work proposes a novel theory of gravity grounded in quantum probability. Rather than treating gravity as a fundamental force sourced by mass, this framework interprets gravitational curvature as the global geometric consequence of local probability suppression. Matter is described as inherently uncertain; when matter becomes spatially localized, it compresses its associated probability field, generating an uncertainty gradient. The resulting field, σ(r⃗)\sigma(\vec{r})σ(r), produces a gravitational potential ϕ∼σ\phi \sim \sigmaϕ∼σ, and a gravitational field g⃗=−∇ϕ\vec{g} = -\nabla \phig=−∇ϕ that propagates causally at the speed of light. Classical spacetime curvature, light bending, time dilation, and black hole horizons are all reinterpreted as emergent effects of this probabilistic geometry. Simulations demonstrate how uncertainty fields generated from quantum sources can reproduce gravitational phenomena without invoking dark matter or spacetime metrics. The theory offers a possible unified informational perspective that bridges quantum mechanics and general relativity.