Essay Abstract
Some possibly interesting connections between Complex Octonion Algebra and Generations of particles, Mixing and Dark Matter, and thus Unreasonable Effectiveness.
Author Bio
Retired C programmer who spends way too much time reading physics.
Joel
Your view close to me
http://vixra.org/abs/1212.0030
Yuri
Hi Joel,
You ask a lot of good questions and make good comments. Your idea is one way to look at it, the other is my system. I think you will like it, it is all based on simulation. I hope you still like programming, the system is ridiculously simple.
Thanks and good luck
Dear Mr. Rice,
I thought that your essay was exceptionally well written and I do hope that it fares well in the competition.
Joe Fisher
Dear Joel,
Fields, expressional with Octonion algebra are finite and closed, whereas the universe is infinite. This implies that the micro-structures are in continuum with the macro-structures, in the universe. Thus I think your argument is, Micro-structures Vs Macro-structures that is QM vs Cosmology.
With best wishes, Jayakar
Dear Joel,
I read your essay, and would like to give you the following constructive feedback:
You advocate the use of octonion algebra to describe fundamental aspects of physics, but for someone who is not already familiar with it, it would be very difficult to discern just from reading your essay what octonion algebra even is, let alone judge the merits of your advocacy.
Also, it seems that the way you associate aspects of octonion algebra to possible properties of spacetime or of particles seems to presuppose very large conceptual jumps to get to the latter from the former.
I think it would have helped your contribution if you had spent some of the unused page allotments explaining the basics of octonion algebra, and given a fuller account of the connections that you see between it and fundamental physics. I know from personal experience that when one thinks about a particular subject matter a lot, one begins to subconsciously expect that others would be able to follow easily one's thought processes, but just remember, octonion algebra would probably be considered as of now a rather obscure field, so there would be very few people who'd have invested as much time into thinking about these possible connections as you have, and as a result most would not be able to follow your lines of reasoning.
A couple of sentences in your essay stood out in my mind:
"Hamilton's discovery of quaternion algebra revolutionized Newtonian physics."
Unless you can provide some evidence to support this claim, I think most mainstream physicists would probably disagree with it. At least I learned Hamilton's principle, the Hamiltonian approach and the Lagrangian approach without any mention of quaternion algebra, but I admit that I do not know to what extent quaternion algebra influenced the discovery of these reformulations (this is the sort of evidence I was talking about).
"Are we missing interesting theories because we are committed to particular
mathematical frameworks, or suitable ones have not been developed ?"
I take this to be a rhetorical questions with an implied affirmative answer. If so, I completely agree, although my view of this issue goes beyond the possible usefulness of octonion (or other) algebras, to include a reconsideration of the entire foundations of mathematics. At this point, classical logic lies at its heart, but I believe that it does not have a sufficient expressive power to express certain kinds of distinctions (e.g. between actuality and potentiality) without which it will be impossible to understand what quantum theory is really telling us about reality. My entry to this contest paints a picture of how the incorporation of some extensions of classical logic can lead to novel mathematical frameworks which in my view help make sense out of some highly counterintuitive aspects of the theory.
So, to summarize, while you contribution had in my view room for two sorts of improvement, I do agree with the basic message, and I think that your essay does not deserve to be at the very bottom of the lot.
Best wishes,
Armin
Dear Armin - thanks for the thoughtful and constructive comments. There have been some essays at FQXI on Octonions, by Dray & Manogue, but I should have worked on a nice introduction (instead of procrastinating). Basically I just rely on Coxeter's "Integral Cayley Numbers" result that there are 480 multiplication tables for Octonions - and not much more. One item mentioned in the 1966 lecture was a possible connection to Godel's theorems re ordinary arithmetic. It is awful that I never kept a notebook, and have not seen a paper based on that lecture, and don't know who it was.
About Hamilton, it was Gibbs who simplified Quaternions into the Vector Algebra that everybody learns in high school. See Michael Crowe "A History of Vector Analysis".
About 'are we missing ...' was one of the questions in the Essay rules. I should have put quotes around it. I usually suspect that Octonions are not so much 'useful' as something like a 'definition of particles' - not 'dressed' particles, or even 'bare' particles - just some hand-waving about how it looks too much like relevant spin-color distinctions to be dismissed as accidental. That might entail a reconsideration of the foundations of physics, since the SM makes no reference to octonions ! One needs physics to make sense of this algebra, as well as math to make sense of what physics is saying.
Dear Joel,
I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.
All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.
Joe Fisher
Dear Joel,
Your essay is very interesting and close to me in spirit and direction of the research.You put good questions and give ideas and direction of the search for a solution "structural problems":
"There are 'associations' all around us. Any atom is like an 'experimental situation' and one might wonder if the 'physical constants' are given, or does the algebra require neutral constructions of building block a priori, and the physical constants must be what they are in order to get the constructions ? In that case we can do away with questions about why the Constants are what they are. How would we consider Occam's Razor in this context ? "
"What is the bare minimum that Nature needs to crank out the universe ? "
"The Design of the World is not an answer, it is a mystery. Why does the physical world obey some laws and not others ? Is the issue the laws, meaning the behavior of particles ? Why are 'laws' the issue when we know that generations of fermions make no sense ? That is a structural issue. "
I agree that the main key - it is "Generation Structure ... " and "structural problem" in Foundations of Mathematics and Physics to be solved with the help of a very sharp Occam's razor and searching nature "fundamental constants". Alexander Zenkin in the article "SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS" says: "Truth should be drawn ..."
You draw and outlines original path to the truth ... Now is the Information age and we need a new paradigm of the Universum as a whole ...
I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld" (E.Husserl), as a picture of the world poets and philosophers.
Kind regards,
Vladimir
Your paper represents the tangible sources of matter of hindrances in the evolution of supernatural thoughts.
- Best Wishes
Miss. Sujatha Jagannathan
