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Perhaps, you would appreciate a similar question. Why does the buck stop at complex numbers, and we don't need quaternions or some other "weirder" field to desc
by abdullahkhalids 6y ago
Perhaps, you would appreciate a similar question. Why does the buck stop at complex numbers, and we don't need quaternions or some other "weirder" field to describe reality?
The answer will have to grapple with both the philosophy of physics and the properties of these various fields.
- Twisol 6y agoAnother commenter linked this post by Scott Aaronson: https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021 The money quote (which leads a few more paragraphs on the details) is this: > But, while I remain less than 100% satisfied about “why the complex numbers? why not just the reals?,” there’s one conclusion that my recent circling-back to these questions has made me fully confident about. Namely: quantum mechanics over the quaternions is a flaming garbage fire, which would’ve been rejected at an extremely early stage of God and the angels’ deliberations about how to construct our universe.
- phkahler 6y agoBut elegance is irrelevant. Imaginary numbers are a subset of the quaternions, just as reals are a subset of the imaginaries. The proper question is not "do I like it" but is it necessary. The answer apparently is No for the quaternions.
- Twisol 6y agoThe referenced argument rests on superluminal communication, not elegance. The quaternions are not even sufficient, unless we believe that superluminal signaling is physical.