Wednesday, June 8, 2016

local field equations and nonlocal components

the Poisson-equation of electrostatics (or Newtonian gravity) links the second derivatives of the potential $\Phi$ to the local charge (or matter) density $\rho$, by requiring $\Delta\Phi=4\pi(G)\rho$. this is nice, because $\Delta\Phi$ is the trace of the Hessian $\partial_i\partial_j\Phi$, making it invariant under rotations and therefore generates a spherically symmetric potential. but what fixes the off-diagonal components? would there be a possibility to measure them directly?

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