Development of generalized metric

[friend]

We all know how the metric of GR is a generalization of the flat Minkowski spacetime metric. But I wonder if the SR metric is generalized from the kinetic energy term of Newtonian physics. There the kinetic energy is (1/2)m*v^2=(1/2)m*dx*dx. If the mass/2 plays the role of the metric, then this looks like n_uv*dx^u*dx^v, like a differential line segment. Or what part does the kinetic term play in the SR inner product. Thanks.

 

[robphy]

The kinetic energy is associated with a Riemannian metric on "configuration space" http://books.google.com/books?id=Gc...wqohl_J&sig=dCuKErP8eu_LWZgpND-4k2WMIL4&hl=en

 

[Ich]

Wow, that's breaking a butterfly on a wheel. (I hope I got the saying right; is it symptomatic that it involves cannons in german?)
Maybe the OP wants to start with adding an appropriate numder of dt's in his equation:

(1/2)m*v^2=(1/2)m*dx*dx