I studied physics many years ago and now 're-doing' my college degree by myself for fun.
I used to think of the path of a particle in Newtonian mechanics as a a curve in $\mathbb{R}^3$, in other words a mapping $t \in \mathbb{R} \rightarrow x(t) \in \mathbb{R}^3$.
However, while reading Schutz's book "Geometrical methods of mathematical physics", I came across an example in chapter 2 section 10 of his book where he says that the view of spacetime taken by Newtonian physics has a natural fiber bundle structure, with $\mathbb{R}$ representing the base manifold (time), and $\mathbb{R}^3$ representing the fiber (particle's position). In this interpretation, which I can see makes sense as time has an absolute meaning in Newtonian mechanics and hence can serve as base manifold since every particle in the fiber would agree on the value of $t$ through the projection onto the base, the path of a particle would be a section of the fiber $\sigma: \mathbb{R} \rightarrow \mathbb{R} \times \mathbb{R}^3$.
But I am not sure the two interpretations are equivalent, I don't think they are? So I am a bit confused now and my question is which interpretation is correct?