Suppose
&
Start at point A.
walks A→C pointing North the whole time
walks A→B→C pointing North the whole time
When they both arrive at the North pole they will be pointing different directions.pic.twitter.com/UIO7iIDTTU
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Indeed, this is how
&could tell they are living on a curved surface.
In Physics & Mathematics, this way of moving a vector along a curved surface is known as 𝒑𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝒕𝒓𝒂𝒏𝒔𝒑𝒐𝒓𝒕.Show this thread
A nice demonstration of parallel transport.
Note
: The animation keeps the vector facing East (as opposed to North, in my previous example)
source:https://www.naturelovesmath.com/en/mathematical-physics/general-relativity-loud-and-clear/ …pic.twitter.com/ZIsGMQEUo8
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I get confused between Weyl's-"gauge" geometry, where in addition the vector's length changes on returning and conformal geometry which is I think is a space-(time) dependent Weyl group automorphism (15 dim vs 11dim)?
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