A vanishing magnetic Weyl part is required for Newtonian theories.

Physicists want to describe gravity and geometry in worlds that follow Galilean physics, where time is absolute rather than relative. A major challenge is measuring the pure shape of spacetime using a tool called a Weyl tensorWeyl tensorA measure of space's curvature that is independent of certain observer effects. without assuming the equations of motion already hold. The authors created an off-shelloff-shellDefined without assuming specific equations of motion or constraints., scale-invariant Galilean Weyl tensor, meaning it works without those preset equations. They split it into electric and magnetic parts. They found that the magnetic part only vanishes if specific observers exist. Because standard gravity guarantees this but other theories might not, they argue a theory must allow these observers to be called Newtonian. Finally, they proved a unique boost-invariant connection can be built simply using a Coriolis fieldCoriolis fieldA field related to rotation effects in a physical system..

Why it matters

This gives theoretical physicists a clearer rule for deciding if a gravity theory is truly Newtonian. It helps standardize how we classify non-relativistic physical theories.

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