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Sorry if this is a dumb question, but whatexactlydo we mean by the term parallel transport? Is it just the physicist's way of saying isometry?

Also, in my class we have just defined geodesics, and we're told that having a geodesic curve cis equivalent to demanding that the unit tangent vector be parallel transported along c. This confuses me. I can read the proof of this, and it's fine, but I don't feel any physical intuition developing here. Can someone explain, as physically as possible, why these two conditions are equivalent?

Thanks.

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# Physical intuition behind geodesics and parallel transport

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