# Local nature of physical laws

All the laws in physics are local in nature and that's why their formulation follows differential equations. My doubt is whether the locality is a proven theorem or it is a postulate?

• Theorems are mathematics, not physics. Mathematics deals with the properties of objects that exist only in the human imagination. Sometimes, those properties map well onto real objects in the universe, as verified by experiment. Then, theorems are useful, but one must never completely trust them as proven in physics. Jun 6, 2022 at 23:14
• Quantum physics are non-local, as counterxample to your first assumption. Jun 7, 2022 at 1:52

In a thin tunnel (compared with the radius of the sphere) across a massive sphere, the acceleration of gravity in a point at a distance $$r$$ from the center is:$$\mathbf a = -\frac{4}{3}\pi G \rho \mathbf r$$ where $$\rho$$ is the density of the sphere, supposed uniform.
The divergence of $$\mathbf a$$ can be shown to be: $$\nabla \boldsymbol{ .a} = -4\pi G\rho$$.
This is a differential equation, and its solution refers not to the local density inside the tunnel (that is zero), but to $$\rho$$, the density of the sphere.