I have to disagree that quaternions underlie Special Relativity. Although special relativity does use 4-vectors, those aren't quaternions.
There are equivalent formulations of SR using quaternions.
But do they generalize to GR?
The Octonion Math That Could Underpin Physics
31–40 of 192 posts
Re: The Octonion Math That Could Underpin Physics
#32A layman's quest to understand wtf this is... >In mathematics, the octonions are a normed division algebra over the real numbers . wtf is a normed division algebra?? >In mathematics, Hurwitz's theorem is a theorem [...] solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. ... right. I have the same problem when I try to understand any…
Well yeah, math books... Jokes aside, i too think we need a new framework for divulgating math that actually tells what you need to know, without just handwaving at it, BUT without the amount of technical details of a mathematics class. What do you know, i think this is Possible, too.. You can communicate a surprising amount of information if you use words properly. Of course, since this has never been done except fr…
> only do it if it made economic sense
What if writing wikipedia articles was treated like publishing on prestigious journals? (somehow)
Re: The Octonion Math That Could Underpin Physics
#33I think the following quote is the QED for academia ruining any chance at actual research: “What I had was an out-of-control intuition that these algebras were key to understanding particle physics, and I was willing to follow this intuition off a cliff if need be. Some might say I did.”
As a current PhD student, I'd say the vast majority of researchers aren't anywhere near that enthusiastic about their research.
Many marriages fail in the time it takes to complete a phd. If academia can’t find a way to fund people with actual interest then somethings wrong.
Re: The Octonion Math That Could Underpin Physics
#34Earlier quoted context omitted.
>it's just that multiplication and division lose most of their useful properties. Specifically they lose the property of not having zero divisors. There exists sedonions a,b != 0 such that ab = 0
Another (related) property that fails is that inverses stop being useful for cancellation. Inverses still exist, for every p there's a q with pq = qp = 1, but if you've got an equation ap = b you can't cancel to get a = bq, because we don't have associativity. The left hand side (ap)q doesn't equal a(pq), so you can't reduce it to a. Of course associativity doesn't hold in the octonions either, but it holds just enou…
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Re: The Octonion Math That Could Underpin Physics
#35I think that maybe if you lock a mathematical physicist in a box forever with an x-TeV collider without letting them upgrade it, they will eventually find a theory that hits all of the datapoints and depending on their philosophical weakness then declare it "final."
Surely what we're looking for is the simplest theory among the theories that hit all the datapoints. That's the theory that's most likely to be the "Theory of Everything" and therefore to continue working when we upgrade our collider.
Why would the simplest theory be the most likely to be true?
Re: The Octonion Math That Could Underpin Physics
#36Earlier quoted context omitted.
It's my understanding that most of Einstein's theory was the product of intuition, backed up after-the-fact with mathematics and experimentation. Intuition isn't a bad compass, as long as you can set it aside if reality measurably contradicts it. In fairness, Einstein never accepted quantum mechanics because they flew in the face of his intuition, but it still got him pretty far.
This is very false. Einstein's reputation was built on explaining known phenomena such as the photoelectric effect and Brownian motion. Special relativity was heavily motivated by a pile of puzzling evidence and a bunch of existing mathematics.
And he funded his studies, initially, as a hobby alongside a job. We’ve not progressed very far if ground breaking research almost requires a person to find a novel study path.
Re: The Octonion Math That Could Underpin Physics
#37I think that maybe if you lock a mathematical physicist in a box forever with an x-TeV collider without letting them upgrade it, they will eventually find a theory that hits all of the datapoints and depending on their philosophical weakness then declare it "final."
Surely what we're looking for is the simplest theory among the theories that hit all the datapoints. That's the theory that's most likely to be the "Theory of Everything" and therefore to continue working when we upgrade our collider.
Isn't it strange how the probabilistic motivation of Occam's razor loses its foundation when applied to a Theory of Everything? Simple is beautiful, that's all I've got.
Re: The Octonion Math That Could Underpin Physics
#38Earlier quoted context omitted.
Do you have an understanding of Clifford algebras? I’ve read a little about them here on hn, and they seem quite powerful. I don’t understand them enough to know if they could also be an appropriate abstraction.
Yes! Dual quaternions are a Cl(2,0,1) Clifford algebra. Good ol Cliffy invented them too. http://www.chinedufn.com/dual-quaternion-shader-explained/ Check the guy on the right getting deformed like an idiot. Compare it with the smooth criminal on the right.
> http://www.chinedufn.com/dual-quaternion-shader-explained/
Offset curve deformations blow dual quaternion's out of the water for rigging!
Re: The Octonion Math That Could Underpin Physics
#39Earlier quoted context omitted.
Surely what we're looking for is the simplest theory among the theories that hit all the datapoints. That's the theory that's most likely to be the "Theory of Everything" and therefore to continue working when we upgrade our collider.
Why would the simplest theory be the most likely to be true?
Less edge cases mean it's less likely to break if we discover a new particle or something else unexpected
Re: The Octonion Math That Could Underpin Physics
#40A layman's quest to understand wtf this is... >In mathematics, the octonions are a normed division algebra over the real numbers . wtf is a normed division algebra?? >In mathematics, Hurwitz's theorem is a theorem [...] solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. ... right. I have the same problem when I try to understand any…
For more brain melting, here's a roadmap for learning React in 2018, React and associated tech is what, 20 years old?
Here's what that looks like: https://github.com/adam-golab/react-developer-roadmap
Then consider maths, how long and how many people have been contributing to that field?