Galilean spacetime as a fiber bundle

In summary, the book discusses the notion of spacetime affine structure and how it captures Newton's first law. It discusses the idea of identifying free motions (inertial motions) in this structure by a linear equation.
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Galilean spacetime has been defined as fiber bundle (over absolute time projection).
How to single out physically inertial paths through spacetime
Hi,

reading the book "The Road to Reality" by Roger Penrose I was a bit confused about the notion of Galilean spacetime as fiber bundle (section 17.2).

As explained there, each fiber over absolute time ##t## is a copy of ##\mathbf E^3## (an instance of it over each ##t##), there exist no identification between fibers nevertheless the whole bundle (the spacetime) is actually one "thing".

Now, from a physical point of view, I believe the direction of 'inertial motions' can be singled out by zero reading of accelerometers (inertial paths in spacetime are actually those having zero reading of accelerometers following them).

I'm puzzled about how identify them in each fiber (copy of ##\mathbf E^3##) without reference to a given inertial reference frame IRF
 
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cianfa72 said:
I'm puzzled about how identify them in each fiber (copy of ##\mathbf E^3##) without reference to a given inertial reference frame IRF
Does really make sense defining them in a frame invariant way ?
 
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