4 ms·
Another commenter linked this post by Scott Aaronson: https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021 The money quote (wh
by Twisol 6y ago
Another 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.