Quantum uncertainty is not a result of random chance but is actually built into the rigid geometric architecture of the universe.
Most people think the fuzziness of the quantum world comes from statistical probability. This study argues that indeterminacy is a structural property of phase space governed by symplectic topology. The limits on what we can know are essentially hard-coded into the shape of the vacuum. This shifts the focus from messy statistics to clean, convex geometry. It suggests that the laws of physics are far more structured and less random than previously imagined.
On Quantum Indeterminacy
arXiv · 2605.01103
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic topology, and does not rely on statistical descriptors such as variances or covariances. Instead, we associate to empirical position and momentum data with convex bodies whose mutual relations encode the fundamental constraints of quantum mechanics. The central tools