Quantum from Algebra

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Witness
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Quantum from Algebra

Post by Witness » Sun Jul 22, 2018 4:11 am

For the mathematically minded, an article I found interesting (a tad journalistic in some parts) about Octonions (or Cayley's Octaves as they are sometimes called):
The Peculiar Math That Could Underlie the Laws of Nature

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”
https://www.quantamagazine.org/the-octo ... s-20180720

All this sounds refreshingly Pythagorean! :mrgreen:

One of the things I grasped from quantum mechanics is that to each generator of the group(s) describing the symmetries of the theory corresponds a (material) particle. Already mind boggling.

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And the Wiki article about Octonions: https://en.wikipedia.org/wiki/Octonion

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Re: Quantum from Algebra

Post by Abdul Alhazred » Sun Jul 22, 2018 11:26 am

Hmm.

I encountered octonions in graduate school as an exercise in having a non-associative consistent system.

The interesting bit is that you get no additional properties by going to 16-ions etc. Those all can be reduced to octonions.

But (as it was at the time), useful physics stopped with quaternions (in special relativity).

As for complex numbers, electrical engineers use them all the time and you can get a real shock from an "imaginary" voltage. :coolspecs:
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Re: Quantum from Algebra

Post by sparks » Sun Jul 22, 2018 3:40 pm

Most useful in describing inductive and capacitive reactance.
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Re: Quantum from Algebra

Post by ed » Sun Jul 22, 2018 3:45 pm

this is redolent of something

ah, yes
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Re: Quantum from Algebra

Post by Abdul Alhazred » Sun Jul 22, 2018 4:01 pm

Time Cube Theory isn't wrong, it's incomprehensible.

That's how smart Gene Ray is.
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Re: Quantum from Algebra

Post by sparks » Sun Jul 22, 2018 4:11 pm

And if he wrote the script for that little hand bill above he also has a problem with the English composition.
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Re: Quantum from Algebra

Post by Witness » Mon Jul 23, 2018 4:23 am

Abdul Alhazred wrote:
Sun Jul 22, 2018 11:26 am
Hmm.

I encountered octonions in graduate school as an exercise in having a non-associative consistent system.

The interesting bit is that you get no additional properties by going to 16-ions etc. Those all can be reduced to octonions.
You have excellent memory! :figamagee:

Another part of the article I found interesting is that physicists seem to fear that nothing new will come out of the CERN accelerator – so back to hacking algebra/theory (strings also on the decline?).

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Re: Quantum from Algebra

Post by Witness » Tue Jul 24, 2018 1:56 am

P. – S.

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