[borisp]

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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

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For me, it seems very comforting when an "explanation" amounts to nothing more than formal mathematics. It occurs to me that in these instances, it is our demand for an intuitive explanation that needs revision, not the explanation itself.

Is it not true that you can detect these fields with your senses? Is it not true that the mathematical machinery provides an almost perfect framework to predict the content of your detections? What else is there to an explanation?

I mean, seriously, how well do you even know what matter is? Or is it simply the case that you stopped questioning its nature, since it is so trivially detected by your senses? Could it not be the case that something like force fields are simply easier for you to question?

Not trying to be a jerk here, I have asked myself these same questions. I guess I lean towards the "Copenhagen" interpretation of (quantum) physics. Von Neumann said it best: "Young man, in mathematics you don't understand things. You just get used to them." (Not implying that you are young [img]/images/graemlins/smile.gif[/img])