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About 10 years ago (from 20th of March 2007 to be precise) I stopped being mystified by quantum mechanics. The following is my new paper which explains why I am not mystified by quantum mechanics. In it I explain the geometrical origins of all quantum correlations, in terms of rudimentary Euclidean primitives such as points, lines, planes and volumes. It has taken me long time to crystallize my thoughts on this matter. I like to think that both Einstein and Bell would have been intrigued by my geometrical perspective. Initiated 10 years ago when I was based at Perimeter Institute in Canada, my approach may be attractive to those familiar with normed division algebras, 3- and 7-spheres, and the associated quaternionic and octonionic spinors. It is very simple and elegant. Much work still remains to be done, however.

http://philsci-archive.pitt.edu/13019/

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Here is the conclusion from the above paper:


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Let me point out here that, as some of you know, an early version of my model for the strong correlations presented in the above paper has been published already in the International Journal of Theoretical Physics: https://link.springer.com/article/10.10 ... 014-2412-2. This paper is behind the paywall, but the arXiv version of it is freely available here: https://arxiv.org/abs/1211.0784. An arXiv version of a closely related paper is also available here.

In the new paper I have presented a full generalization of the argument presented in the published paper, while also providing a rigorous mathematical and conceptual foundations to my earlier arguments. Some of the arguments of the published paper are also published in my book. The following is the link to my book at the Library of Congress Online Catalog: https://lccn.loc.gov/2013040705.

One of the reasons for writing the new paper was to remove the perception of a dependence of my argument on "extra" dimensions, which was objected to by several people with distaste for "extra" dimensions. In the new paper the “extra” dimensions are purely algebraic dimensions of the representation space. In other words, they are not really "extra" dimensions at all. The physical space is just three-dimensional, albeit compactified into S^3. Another attractive feature in the new paper is that now all of the correlations, singlet or otherwise, are derived within one and the same algebraic framework. In my earlier published work I had to perform separate calculations for the singlet case, using S^3, and the cases like the GHZ case, using S^7. Thus the new paper provides a unifying approach for all quantum correlations.

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My recent post about the above paper at LinkedIn.com: https://www.linkedin.com/in/joy-christi ... -activity/.


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551 views in two weeks! I hope at least some of the viewers on LinkedIn have downloaded the paper and actually read it.


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I have made the following post about this paper in this closed Quantum Information group:

https://www.facebook.com/groups/qinfo.s ... 730820338/

Although it is a closed group, anyone interested in their activities can apply to be a member.


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“When the facts change, I change my mind. What do you do, Sir?” --- John Maynard Keynes

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Joy, hi, very good to see you're along similar lines to the various clues i've been tracking. The clues are:

* "Pieces of E8" which contains a diagram of the root-level particles in a 30 degree phase diagram
* The picture (an older one than the current one) on wikipedia which shows that the above diagram matches exactly with "Mixing Angle"
* Castillo's 2008 paper "Spinor representation of an electromagnetic plane wave"
* Dr Randall Mill's use of Y(theta, phi) to successfully create equations to within 10dp of all major characteristics of the electron, from first principles (and many other particles).

you're on the right track sah

[edit - nearly forgot: a whole stack of other stuff which as you know i've been working on part-time].

Joy Christian wrote:***
Let me point out here that, as some of you know, an early version of my model for the strong correlations presented in the above paper has been published already in the International Journal of Theoretical Physics: https://link.springer.com/article/10.10 ... 014-2412-2. This paper is behind the paywall, but the arXiv version of it is freely available here: https://arxiv.org/abs/1211.0784. An arXiv version of a closely related paper is also available here.

joy, the reason i mentioned castillo's work is because it provides some of the mathematical conditions under which spinors may superimpose. if we assume the premise that a subatomic particle may be represented as a photon on a self-sustaining circular path, its E.M. field may be represented by a Y(theta,phi) function that has a spinor.

when we try to have more than one such subatomic particle superimposed in the same space, it is absolutely absolutely critical that the photons EM fields be stable and not undergo any kind of destabilising interference.

castillo's 2008 paper outlines ONE of those conditions: from exploration of Jones Matrices i explored the other.

further more i showed that there are only very very specific phases which may be actively involved in such superposition (on 30 degree angles).

this you will find, if you investigate, matches precisely and exactly with the line of enquiry that you have been investigating.

the piece of the puzzle that is missing from what both you and i have been independently in our own way investigating is in Dr Randall Mill's work. he successfully PROVIDES SOLUTIONS and a roadmap on how to perform the mathematical transforms necessary to derive radius and mass.

however interestingly he makes a crucial mistake in how he visualises the proton. in his work he believes that the three quarks superimpose at ONE TWENTY degree angles. most people do. this is a MISTAKE.

the superposition must take place at NINETY degree angles in order for there to not be any destabilising interference. in terms of what you are working on (and what the author of "Pieces of E8" also worked on), these "superposition" angles are highly likely to represent the "edges" connecting the geometric visualisation that you provide.

we are so close to being able to provide an answer to the "Mass Gap" problem it is very frustrating for me to be only operating on a logical deductive reasoning (i.e. non-mathematical) basis only, otherwise i would have written the paper already. ho hum.

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Thank you, lkcl, for your comments. My primary purpose in the paper linked above is to understand the origins of quantum correlations in terms of the most primitive elements of the very geometry of spacetime, with the so-called quantum entanglement (and hence quantum mechanics) resulting as a byproduct. Specific problems of particle physics is not my concern in the above paper (for that see https://arxiv.org/abs/1705.06036). Fred Diether and I did try to understand SU(3) symmetry within the framework I have presented in the above paper, but without success. Perhaps we didn't try hard enough, because I got distracted by other mundane things in life.

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Joy Christian wrote:***
Thank you, lkcl, for your comments. My primary purpose in the paper linked above is to understand the origins of quantum correlations in terms of the most primitive elements of the very geometry of spacetime, with the so-called quantum entanglement (and hence quantum mechanics) resulting as a byproduct. Specific problems of particle physics is not my concern in the above paper (for that see https://arxiv.org/abs/1705.06036). Fred Diether and I did try to understand SU(3) symmetry within the framework I have presented in the above paper, but without success. Perhaps we didn't try hard enough, because I got distracted by other mundane things in life.

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There were some intriguing partial similarities with SU(3) which might lead one to wonder if SU(3) can in fact be constructed from Euclidean primitives.
.

Joy Christian wrote:***
Thank you, lkcl, for your comments. My primary purpose in the paper linked above is to understand the origins of quantum correlations in terms of the most primitive elements of the very geometry of spacetime, with the so-called quantum entanglement (and hence quantum mechanics) resulting as a byproduct. Specific problems of particle physics is not my concern in the above paper (for that see https://arxiv.org/abs/1705.06036). Fred Diether and I did try to understand SU(3) symmetry within the framework I have presented in the above paper, but without success. Perhaps we didn't try hard enough, because I got distracted by other mundane things in life.

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hiya joy (and freddy - read your message too), good to hear from you. my feeling is: SU(3) and so on, whilst technically correct, are red herrings: avenues that, if attempted to be pursued, will not yield results. there are many reasons for this, not least is that there are simply far too many *postulated* values in the standard model which have no explanation.

dr mill's work is, staggeringly, derived from scratch on a firm theoretical basis using nothing more than Maxwell's Equations. however he has to use some rather obscure maths (that's not available in electronic form, only in books) - 2 Dimensional Fourier Transforms which he extends to 3 - in order to do it.

the thing that he missed, however, is the beautiful geometry that you've noted. i really meant it when i said that the geometric patterns are key. in the Extended Rishon Model i noted that there has been a mistake made - including by me - where everyone who has explored the Rishon Model has not noted that the Rishon Model patterns describe twelve PHASES, and that those phases exactly and precisely correlate with a looped photon's EM field in a phase-stable, phase-harmonic pattern. Y(theta,phi), spinors, Poincare Spheres, SU(2)xU(1) - all these things describe exactly the same underlying "thing", just from different perspectives... none of which have the complete picture.

the point is: it is purely a coincidence of *geometry* - sin(30) = 1/2 - that the Rishons in T (which represents the "real" part of the looped photon's phase...) and V (representing the "complex) happen to add up to a total of 1.... but it's the *phase angles* represented by Rishon Triplets that *also* have to add up, matching specifically to a N,S,E,W compass point (1, -1, i or -i in complex space)... and this is only possible to achieve with equilateral triangles, hence why we only have 12 fundamental particles.

what i did not realise until some time at the beginning of this year is that the phases of the fundamental particles (electron, quarks, neutrino) happen to match precisely and exactly with the weinberg mixing angle (12 phases, 30 degrees apart), which happens then when you combine them to obey geometric patterns which *happen* to fit precisely with the E8 Lie Group.

you have a huge piece of the puzzle here. unfortunately.... i am a computer scientist with extremely advanced reverse-engineering skills. i am not a mathematician. if i were to tackle the required mathematics to deal with the (key) mistakes that Dr Randall Mills made, it would be about.... 4 years of full-time work before i had the necessary expertise. i simply can't do that... and feed myself and my family at the same time. or complete any of the other goals that i have set.

by contrast: someone who has the prerequisite mathematical expertise - which doesn't actually involve anything more complex than differentiation and integration, FFTs and so on, where there are plenty of pre-existing formulae to start from, and even Mathematica scripts - could probably complete this in about 2-3 months flat, without really having to think very hard about it.

i'd really love for this to be tackled in a public and open fashion, as that's what i am used to dealing with. i just haven't yet found a suitable forum or environment. do you have any suggestions?

ok so i thought about this some more: joy, ignoring the actual particles themselves... if you remember the royal society christmas lectures, they did this soap-bubble trick which created the very same road-map of the main motorways between the major cities in the UK, simply by dunking two perspex sheets with pegs marking the cities into soapy water. and it had taken a *supercomputer* (of the era) to calculate that map! the point is: particles show us the actual solutions that we're searching for: we *know* the answer is there.

freddi: SU(3) won't work. however SU(2)xU(1) in the form of a poincare sphere, with additional constraints based on the extensions to castillo's 2008 paper on jones matrices mapped to spinors on a poincare sphere might just do it.

what castillo missed in his work was the fact that the superpositions have two possible solutions. his 2008 paper covered the first, but he missed the significance of the second one (one is cos theta = 0).

from the combination, the superpositions are only "successful" (stable) when the combined phase comes out to 1, -1, i or -i (0 pi/4, pi/2, 3/4 pi). but the other aspect is that the only phases that will work in the first place are those that are already on a 30 degree boundary (2pi / 12).

this gives you both the geometric patterns and the first "level" - first members - of the Lie-8 Group.

subsquent levels - subsequent members - are obtained by combining the first members with each other, *as long as* the same phase-superposition "rules" are again followed.

applied recursively.

this paper is probably relevant, although i am out of practice in reading / recognising the relevant patterns: https://arxiv.org/pdf/1603.04805

it covers how clifford algebra can turn an isocahedron (12 points... how fascinating... that would match with the 12 base particles....) into the E8 group. equation (1) page 12 reminds me of castillo's spinor-superposition equation.

lkcl wrote:freddi: SU(3) won't work. however SU(2)xU(1) in the form of a poincare sphere, with additional constraints based on the extensions to castillo's 2008 paper on jones matrices mapped to spinors on a poincare sphere might just do it.

SU(3) won't work for what?
.

FrediFizzx wrote:

lkcl wrote:freddi: SU(3) won't work. however SU(2)xU(1) in the form of a poincare sphere, with additional constraints based on the extensions to castillo's 2008 paper on jones matrices mapped to spinors on a poincare sphere might just do it.

SU(3) won't work for what?
.

sorry for not being clear, freddi. you wrote, earlier:

FrediFizzx wrote:There were some intriguing partial similarities with SU(3) which might lead one to wonder if SU(3) can in fact be constructed from Euclidean primitives.
..

lkcl wrote:sorry for not being clear, freddi. you wrote, earlier:

FrediFizzx wrote:There were some intriguing partial similarities with SU(3) which might lead one to wonder if SU(3) can in fact be constructed from Euclidean primitives.
..

??? An explanation of why you think it won't work would be nice. Otherwise I will keep assuming that SU(3) might be able to be constructed from the Euclidean primitives.

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lkcl, thanks for Pierre-Philippe Dechant's paper. I have learned from his previous paper (cited in my paper) and I am sure the one you have linked will be useful too.

Fred is right that eventually we may be able to incorporate SU(3) within my framework based on Euclidean primitives. It is just that when we worked on it last time, we ran out of steam and got distracted by other things. On the other hand, the torus SU(2) x U(1) is a natural part of the framework, so it is already working. In fact the framework is based on the torus SU(2) x SU(2), of which SU(2) x U(1) is a very special case. SU(3) gave us some difficulty, which (with hindsight) is not surprising.

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Joy Christian wrote:***
lkcl, thanks for Pierre-Philippe Dechant's paper. I have learned from his previous paper (cited in my paper) and I am sure the one you have linked will be useful too.

Fred is right that eventually we may be able to incorporate SU(3) within my framework based on Euclidean primitives. It is just that when we worked on it last time, we ran out of steam and got distracted by other things. On the other hand, the torus SU(2) x U(1) is a natural part of the framework, so it is already working. In fact the framework is based on the torus SU(2) x SU(2), of which SU(2) x U(1) is a very special case. SU(3) gave us some difficulty, which (with hindsight) is not surprising.

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that's beautiful, joy. i thought you might appreciate knowing that i took a dodecahedron, marked out the 12 base particles (by trial and error) on each face, and was then able to show that related phase-transforms (which is a shift by 5/12 of a revolution) are on the same plane (a cross-section through the centre of four faces).

i can't handle the maths but i can handle a pair of scissors, a pen and some sellotape

in about 3 hours flat i managed to easily demonstrate that there's a relationship between e(i * theta * pi), 0 <= theta < 1 in 12 increments, the equilateral triangle, the dodecahedron and the group SU(2) x U(1) - the poincare sphere. the significance of the dodecahedron: it's cross-related to E(8).

it's very hard to describe in words and even images: i'll have to do a video which i'll post on youtube later, but i'm.... this is is just so amazing.

https://youtu.be/Tv_rslYPadE

ok it's a truly dreadful and boring video, i must sincerely apologise, i have been on a split sleep-pattern, also the battery ran out but i got most things in!

the video shows how the dodecahedron faces are numbered, remember that those relate DIRECTLY to the numbers of the roots in... G2 (where G2's roots are always embedded at the centre of larger Lie Groups), as well as to a 1/2th 2pi phase map.

also it shows how increments of 4 are symmetrically geometrically spaced around the dodecahedron, how increments of 6 are likewise symmetrically geometrically spaced, there's also a pattern for 3 as well (which i apologise i didn't show), and there's a very specific and easy to follow pattern for increments of 5.

so forget the particles entirely (they just help as a guide) focus on the phase relationships,the increments of 2, 3, 4, 5 and 6 which represent phase-changes around the circle in increments of 1/12th of 2pi all have geometric patterns which help create the rules of the "group"... and they're all based simply in geometry, which is absolutely beautiful... and a lot easier for me to get my head round than the mathematics, which i can only *intuitively* grasp is involved in the work you and fred are doing. good luck and i hope this helps.

[edit] ok so a phase-shift of 4/12 is just a rotation about the z-axis of 120 degrees. a phase-shift of 6/12 (pi) is that you take the angle to the z-plane, double it, then rotate about the z-axis by 120 degrees. these two i have been able to work out as they're really easy. 1, 2, 3 and 5 are trickier, however once you have any two of those the others may be derived mathematically, because 1+2 = 3 and 2+3 = 5 so any two may be compounded to give the others.

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Nice video, Luke. I don't yet understand all the details, but I love your cardboard model of the dodecahedron. Fred is better at understanding the details of particle physics. On my part, I also like to make cardboard and paper models of the geometric objects involved in quantum and particle physics. They are a lot of fun to play with. See, for example, figure 1.5 in the appendix of this paper. It is a model of a Mobius strip. It is essential for understanding the origins of quantum correlations. I have the actual paper model made at home to understand what is going on. I might now also make a model of the dodecahedron like yours, just for the fun of it.

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