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- TL;DR Summary
- 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

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

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