- #1

- 238

- 1

## Main Question or Discussion Point

He who calls himself "Nabeshin" stated:

"It seems to me the distinction can be best seen in the following: Differential geometry is mathematics, and this will tell us what the geodesics on a given manifold are. So if we're just finding geodesics on manifolds, maybe it's the manifold corresponding to schwarzchild, we're just doing mathematics. But when I say "I'll restrict myself to Lorentzian manifolds, and I'll have that particles move on timelike geodesics" all of a sudden I'm doing physics. I've restricted myself to a subclass of mathematical theories which I have hypothesized correspond to observable reality."

What he meant to say is that when we think in terms of particles and how it moves on timelike geodesics, then it's physics. While thinking in terms of what the geodesics on a given manifold are in the differential geometry is pure mathematics."

How about the gravitational field as as tensor field. Do we use it to correspond to Newtonian gravitational field? But since gravity is pure spacetime geometry. Why do we need the idea of gravitational field as a tensor field? Why not do away with it totally and just focus on geometry?

"It seems to me the distinction can be best seen in the following: Differential geometry is mathematics, and this will tell us what the geodesics on a given manifold are. So if we're just finding geodesics on manifolds, maybe it's the manifold corresponding to schwarzchild, we're just doing mathematics. But when I say "I'll restrict myself to Lorentzian manifolds, and I'll have that particles move on timelike geodesics" all of a sudden I'm doing physics. I've restricted myself to a subclass of mathematical theories which I have hypothesized correspond to observable reality."

What he meant to say is that when we think in terms of particles and how it moves on timelike geodesics, then it's physics. While thinking in terms of what the geodesics on a given manifold are in the differential geometry is pure mathematics."

How about the gravitational field as as tensor field. Do we use it to correspond to Newtonian gravitational field? But since gravity is pure spacetime geometry. Why do we need the idea of gravitational field as a tensor field? Why not do away with it totally and just focus on geometry?