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.
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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/ZIsGMQEUo8Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo
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parallel transportn
End of conversation
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Read about this just yesterday in
@seanmcarroll's From Eternity to Here!Thanks. Twitter will use this to make your timeline better. UndoUndo
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Grest now I'm tempted to write a story called Parrallel Transport...
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This is how mathematicians know math is real. One arrives at a true but unprovable from one direction, and another arrives at the same true but unprovable from another direction.
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