Suppose you're a little creature living on a Möbius strip.
Then after "walking in a circle" (i.e. 2π radians), you will actually be upside-down.
In order to get back to where you started, you have to go around twice!
Check out my neat gif!
pic.twitter.com/1MMvp83IWG
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The 𝐏𝐚𝐮𝐥𝐢 𝐈𝐝𝐞𝐧𝐭𝐢𝐭𝐲 tells us how to rotate a 2 component 𝒗𝒆𝒄𝒕𝒐𝒓 of complex numbers, called a "spinor", around an axis θ̂.
for spinors, a rotation by 2π yields -1
only a rotation by 4π yields identity
..sound familiar?pic.twitter.com/ECGtLshlH2
13 replies 16 retweets 61 likesShow this thread -
Replying to @InertialObservr
I don’t get what this formula is saying... it’s not returning the complex vector that you get from rotating, it’s giving some scalar whose relation to the rotation is not at all clear. Can you elaborate?
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Replying to @silvascientist
It's a 2x2 matrix that acts on a 2 component complex vector (i.e. a spinor).
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Replying to @InertialObservr
Wait wait wait, is the dot referring to an outer product and not an inner (dot) product?
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Replying to @silvascientist
IT's referring to an inner product. σ is a vector of pauli matrices.
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Replying to @InertialObservr
I need a gif for whenever a physicist does something distasteful...
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It's perfectly well defined, and not limited to physicists
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Replying to @InertialObservr
It’s just... physics notation has a tendency to be fast and loose with what the symbols mean, and it can be a little off-putting to someone (like me) with more mathematical sensibilities... Not trying to be confrontational, just some light-hearted teasing
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Replying to @silvascientist @InertialObservr
Check out "The Theory of Spinors" by Èlie Cartan to feel better about physicists and their notation :)pic.twitter.com/yVa8fwJiiX
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