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January 1928: Dirac equation unifies quantum mechanics and special relativity

(www.aps.org)
109 points thunderbong | 1 comments | 21 Nov 24 02:17 UTC | HN request time: 0.211s | source
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JPLeRouzic ◴[21 Nov 24 08:58 UTC] No.42202394[source]▶
> Quaternions

I know nothing of physics, but it seems to me that rotation fingerprints are everywhere in physics. Is this just me or is there something more tangible in this remark?

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Ono-Sendai ◴[21 Nov 24 11:11 UTC] No.42203111[source]▶
It's not just you. Dirac fields are constantly rotating. In fact the solutions are called spinors. (e.g. things that spin). There are a lot of rotations at the quantum level. It's also why complex numbers show up a lot in q.m.
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ValentinA23 ◴[21 Nov 24 14:28 UTC] No.42204619[source]▶
I've been trying to get an intuitive understanding of why multiplying by e^ix leads to a rotation in the complex plane, without going into Taylor series (too algebraic, not enough geometric). I tried to find a way to calculate the value of e in a rotational setting, maybe there is a way to reinterpret compound interests as compound rotation. Any insight ?
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1. sparky_z ◴[21 Nov 24 18:13 UTC] No.42207001[source]▶
My favorite intuitive explanation was actually written by science fiction author, Greg Egan. It takes the exact approach you're asking for, reinterpreting compound interest in a 2d rotational context on the complex plane, and doesn't use more than high school math:

https://gregegan.net/FOUNDATIONS/04/found04.html#s2

Fig. 7 is the money shot.