Newtonian metric vs Lorentz metric

[kent davidge]

Is it meaningful to introduce a Newtonian metric $ds^2 = dx^2 + dy^2 + dz^2$ in analogy with special relavity and the Lorentz metric?

 

[Nugatory]

That's the metric for Euclidean three-dimensional space, and as such it's meaningful. Tensor methods are generally a bit of overkill for this trivial manifold, but it's educational to rewrite the metric in some truly bizarre coordinate system with off-diagonal elements as a demonstration of how the formalism works before taking on the non-trivial manifolds of GR.

However, it's not a "Newtonian metric" and it doesn't have much to do with Newtonian physics.

 

[vanhees71]

Tensor methods are no overkill but the only way to express the fundamental laws of physics already in Newtonian mechanics ;-)).