"is there a classical mechanics system that would have 3-sphere as a configuration manifold? "
The Einstein universe, the first proposed non-euclidean model of the universe was spatially just a 3-Sphere. Of the three shapes of the universe supporting isotropy and homogony (the...
I always like the balloon analogy.
The 2-D rubber represents our 3 dimensional space and as you blow the balloon up, the universe expands. That doesn't mean objects can't interact and collide with one another on the space that's expanding. It also highlights how it doesn't make sense (for the...
https://en.m.wikipedia.org/wiki/Spin_tensor
Apologies.
Thank you for your response, originally I had thought time would necessarily be explicit still as a limit of integration
I usually come across expressions for the Stress energy tensor showing them as three densities (normally over a space-like slice.
In wikipedia's article on the spin tensor, they clearly (it does not appear to be an error) both write about and express the components of the stress energy tensor as...