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Physics. Pharyngula. The Skeptical Teacher. Ask a Mathematician / Ask a Physicist. Not Even Wrong. I’ve just replaced the old version of my draft “spacetime is right-handed” paper (discussed here) with a new, hopefully improved version. If it is improved, thanks are due to a couple people who sent helpful comments on the older version, sometimes making clear that I wasn’t getting across at all the main idea. To further clarify what I’m claiming, here I’ll try and write out an informal explanation of what I see as the relevant fundamental issues about four-dimensional geometry, which appear even for $\mathbf R^4$, before one starts thinking about manifolds. Spinors, twistors and complex spacetime In complex spacetime $\mathbf C^4$ the story of spinors and twistors is quite simple and straightforward.

Spinors are more fundamental than vectors: one can write the space $\mathbf C^4$ of vectors as the tensor product of two $\mathbf C^2$ spaces of spinors. Real forms While the twistor/spinor story for complex spacetime is quite simple, the story of real spacetime is much more complicated.

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