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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: 0.383s | 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. Ono-Sendai ◴[22 Nov 24 00:07 UTC] No.42209988[source]▶
The first thing to understand is that multiplying a complex number by i rotates the complex number by 90 degrees counter-clockwise around the origin. For example, 1 * i = i (e.g. 1 + 0i is mapped to 0 + 1i). And i*i = -1 (e.g. 0 + 1i is mapped to (-1 + 0i) and so on. e^ix is a continuous generalisation of this discrete rotation, as I understand it.