 Quote by rogerl
In minkowski spacetime. Space and time is united as one and become spacetime. In Newtonian, space and time is separate, there is no spacetime manifold.. so what kind of metric it has?
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It has two separate metrics, a temporal and a spatial one. This can be argued by the fact that the Galilei group only leaves invariant two separate, degenerate metrics. The reason, ofcourse, is the appearance of absolute time.
The theory based on this construction is called Newton-Cartan. It is a geometric reformulation of Newton.