Talk:Orientation entanglement

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Is it correct to say (just before Formal details) "a spinor can be represented as a vector whose head is a flag lying on one side of a Möbius strip"?

This representation is a version of the "flagpole+flag+orientation-entanglement relation" image that I believe originated with Penrose, and is described in some detail in Misner, Thorne and Wheeler's "Gravitation" (MTW).

While MTW says on p. 1157 that "A spinor consists of this combination of (1) null flagpole plus (2) flag plus (3) the orientation-entanglement relation between the flag and its surroundings", nevertheless the next paragraph starts "One goes from a spinor ξ, a mathematical object with two complex components ξ1 and ξ2, to the geometric object of the "flagpole plus flag plus orientation-entanglement relation" in two steps:..." and then goes on to describe in detail how this combination is built up from 2-spinors.

In which case, might one try to diagram the 2-spinors themselves (or projections thereof), rather than the composite object described? If a spinor is an irreducible representation of a symmetry group, then shouldn't it have a geometry corresponding to its symmetry class in a similar way to that which gives the basic symmetry types of e.g. molecular structures, for which the geometries corresponding to the irreps are usually easily visualisable as the "basic" symmetries of the molecules?

If so, then the nearest I can get to a visualisation of a 2-spinor is something like a pair of co-axial helices (as complex exponential terms) that might somehow combine to form a vector, but I'm sure that's not (quite) right. 163.119.193.40 00:09, 11 November 2007 (UTC)