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pellis
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- TL;DR Summary
- Should we read the Möbius-strip image as being embedded in spinor space, rather than in the 3D space of every-day experience?
On first coming across the Möbius-strip image of spinors, it seemed natural to interpret it as referring to the 3D space of everyday experience, especially as e.g. the Dirac belt and the Penrose book demonstrations appear to occur ‘naturally’ in the world of our phenomenal experience.
Doubts emerged on coming across material pointing out that spinors live in complex spinor-space, e.g. https://physics.stackexchange.com/questions/528826/what-kind-space-does-spinor-lives-in
From an alternative perspective: thinking about vectors in real space e.g. the magnetic moment or angular momentum vectors of an electron, I don’t see them as inverting under a 2-pi rotation of spatial coordinates, as would be expected of spinors; so the arrows in the Möbius-strip image shouldn't be taken to represent ordinary vectors.
Recent versions of https://en.wikipedia.org/wiki/Spinor , open “In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. ... Unlike vectors and tensors, a spinor transforms to its negative when the space [my bold] is continuously rotated through a complete turn from 0° to 360° (see picture [not showing here in PF]).”
The important bit there seems to be “the space”, which I now believe must be referring to “the [spinor] space”.
QUESTION: Should we take the arrows on the Möbius-strip image of spinors (as showing in the above-cited wiki article) as being more suggestive of a complex vector in spinor-space, rather than as ‘ordinary’ vectors in the space/spacetime of experience?
Doubts emerged on coming across material pointing out that spinors live in complex spinor-space, e.g. https://physics.stackexchange.com/questions/528826/what-kind-space-does-spinor-lives-in
From an alternative perspective: thinking about vectors in real space e.g. the magnetic moment or angular momentum vectors of an electron, I don’t see them as inverting under a 2-pi rotation of spatial coordinates, as would be expected of spinors; so the arrows in the Möbius-strip image shouldn't be taken to represent ordinary vectors.
Recent versions of https://en.wikipedia.org/wiki/Spinor , open “In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. ... Unlike vectors and tensors, a spinor transforms to its negative when the space [my bold] is continuously rotated through a complete turn from 0° to 360° (see picture [not showing here in PF]).”
The important bit there seems to be “the space”, which I now believe must be referring to “the [spinor] space”.
QUESTION: Should we take the arrows on the Möbius-strip image of spinors (as showing in the above-cited wiki article) as being more suggestive of a complex vector in spinor-space, rather than as ‘ordinary’ vectors in the space/spacetime of experience?
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