How do Force Fields Occupy Space?

[PairTheBoard]

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But the general idea is that "fields" are simply attributes of the manifold (usually some sort of configuration space) that one must take into consideration in any physical problem. Strictly speaking, they are smooth functions from M to E, where M is your manifold, and E is some sort of bundle over your manifold.


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ok. But is this mathematical machinery much different in principle than the old high school physics explanation that the Force Field is a collection of vectors defining the direction and magnitude of force that the field would apply at various locations? Where do these vectors come from? How do they get there? What are they made of? So now instead of just vectors we have the mathematical structures of manifolds, connections, bundles, submanifolds, smooth functions, etc. Yes these concepts model well and provide good calculations. But do they give us any better sense of answers to the above questions?

PairTheBoard