Octonions and relativity

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Offline FractalDave

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« on: August 10, 2018, 02:10:44 AM »
See:

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

Though personally I prefer:

a+ib+j(c+id)+k(e+if+j(g+ih))
or a+jb+k(c+jd) where a to d are complex
or a+kb where a and b are of the form x+jy where x and y are complex

4D x+jy gives the equivalent results for complex x,y as x+iy does for real x,y
8D x+ky similarly

I prefer these simply because the 4D form x+jy with x and y complex is commutative whereas quaternions aren't and the fact that standard polynomial fractals at least for the 4D form don't give the whipped-cream produced using quaternions ;)
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Offline Alef

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« Reply #1 on: November 07, 2018, 05:44:14 PM »
If someone could explain article in more everyday words. Well I downloaded all the articles ( + sci hub scientic piracy ) but it's some woodoo with occult signs.
As I understand octonions could explain standart model, particle and quantum physics way better than grant hungry superstring theories and CERN scientists praying for miracle of the new particle.

These sterile neutrons octonion math predicts could be the basic particles with no charges but the impulse and they could be misterious dark matter.


But octonion algebra is just too hard. Quaternion power 3 alredy is hudge formula. Even in the article they had mistake. It's not so suprising this aproach is not mutch used:
Quote
Correction July 22, 2018: A previous version of the “Four Special Number Systems” graphic noted that e1, e2and e3are comparable to the quaternions’ i, j and k. In the representation of the Fano plane in the graphic, e1, e2and e4are comparable to the quaternions’ i, j and k.
Throught Fano Plane looks nice.
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