Search FQXi


If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Contests Home


Previous Contests

What Is “Fundamental”
October 28, 2017 to January 22, 2018
Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation
read/discusswinners

Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
read/discusswinners

Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American

read/discusswinners

How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
read/discusswinners

It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
read/discusswinners

Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discusswinners

Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discusswinners

What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discusswinners

The Nature of Time
August - December 2008
read/discusswinners

Forum Home
Introduction
Terms of Use

Order posts by:
 chronological order
 most recent first

Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.

By using the FQXi Forum, you acknowledge reading and agree to abide by the Terms of Use

 RSS feed | RSS help
RECENT POSTS IN THIS TOPIC

Alexander Soiguine: on 4/22/15 at 20:27pm UTC, wrote Thank you so much David. Maybe you remember the story began more than 20...

David Hestenes: on 4/22/15 at 19:35pm UTC, wrote Nice paper, Alex. The Hopf fibration may be a key to elementary particle...

Peter Jackson: on 4/18/15 at 14:04pm UTC, wrote Alex, It's now clear what you've had to do. It's a shame you couldn't give...

Vladimir Rogozhin: on 4/8/15 at 19:39pm UTC, wrote Thank you very much, Alexander, for your concrete and rapid response. I...

Alexander Soiguine: on 4/8/15 at 15:35pm UTC, wrote Dear Vladimir, Thank you for the comment. Actually, I am just trying to...

Vladimir Rogozhin: on 4/8/15 at 10:27am UTC, wrote Dear Alexander, The idea of «Geometric evolution» is very deep and...

Alexander Soiguine: on 4/2/15 at 19:47pm UTC, wrote Dear Peter, Thank you for the your comments. The main reason of...

Peter Jackson: on 4/2/15 at 19:26pm UTC, wrote Alex, I think the importance and validity of your essay may be...


RECENT FORUM POSTS

Eckard Blumschein: "Steve, Darwin contradicted to the view of Parmenides, ..., and Einstein..." in First Things First: The...

Steve Dufourny: "Joe,do you understand that the universe is finite like our series of..." in First Things First: The...

Steve Dufourny: "this second law is so important,my theory of spherisation and these quantum..." in Mass–Energy Equivalence...

Robert McEachern: "In the case of a polarized coin, the "matched filter" detector simply adds..." in Schrödinger’s Zombie:...

Steve Dufourny: "I must explain what is the real meaning of Spherisation in my theory.It is..." in Mass–Energy Equivalence...

Georgina Woodward: "Hi Robert, thank you. I now understand the difference between decisions and..." in Schrödinger’s Zombie:...

Steve Dufourny: "lol no indeed it is not a lot,like I said I liked your general ideas.I have..." in The Demon in the Machine...

Steve Agnew: "There are three assumptions...is that a lot? The aether particle mass, the..." in The Demon in the Machine...


RECENT ARTICLES
click titles to read articles

First Things First: The Physics of Causality
Why do we remember the past and not the future? Untangling the connections between cause and effect, choice, and entropy.

Can Time Be Saved From Physics?
Philosophers, physicists and neuroscientists discuss how our sense of time’s flow might arise through our interactions with external stimuli—despite suggestions from Einstein's relativity that our perception of the passage of time is an illusion.

Thermo-Demonics
A devilish new framework of thermodynamics that focuses on how we observe information could help illuminate our understanding of probability and rewrite quantum theory.

Gravity's Residue
An unusual approach to unifying the laws of physics could solve Hawking's black-hole information paradox—and its predicted gravitational "memory effect" could be picked up by LIGO.

Could Mind Forge the Universe?
Objective reality, and the laws of physics themselves, emerge from our observations, according to a new framework that turns what we think of as fundamental on its head.


FQXi FORUM
October 15, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Geometric algebra, qubits, geometric evolution, and all that by Alexander Soiguine [refresh]
Bookmark and Share
Login or create account to post reply or comment.

Author Alexander Soiguine wrote on Feb. 13, 2015 @ 17:14 GMT
Essay Abstract

The previously initialized approach is used for description and analysis of qubits, geometric phase parameters – things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalizations of formal “complex plane” to an arbitrary variable plane in 3D, and of usual Hopf fibration to the map generated by an arbitrary unit value element are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.

Author Bio

Math/Physics Professorship, R&D in advanced simulation software. Education: St. Petersburg State University, Russia. Research work on feasibility of geometric algebra generalization of qubits for the topological quantum computing purposes, their relations to QM wave functions, unspecified variable fibration probabilities. Web-site www.soiguine.com

Download Essay PDF File

Bookmark and Share



Edwin Eugene Klingman wrote on Feb. 13, 2015 @ 22:14 GMT
Dear Alexander Soiguine,

Your most impressive essay is long on math and short on interpretation. If I were to take a stab at interpreting it, I would use your focus on 'bivector' and 'qubits' to associate the bivector representation of the spin, which is a circulation in a plane with a fixed area but undefined shape, with the orthogonal vector usually considered as the spin axis and often interpreted as a 2-D 'qubit', since the vector can point 'up' or 'down'. The well-known identification of the imaginary i with the bivector is of course Hestenes idea of the way Schrödinger unwittingly incorporated spin in his non-relativistic equation which is usually interpreted as being 'spin less'.

You appear to have discovered some unorthodox feature of Barry curvature in the form of additional bivector elements (page 8) which, as you say, appear to represent a torsion term but could use further elaboration.

I tend to agree that "With explicitly defined variable "imaginary unit" many things become not just more informative but also much simpler." You illustrate this by generalizing the Schrödinger equation.

I would appreciate any correction of my above interpretation and I would encourage you strongly to make maximum use of the comments in your thread to flesh out a very dense presentation. This is a legitimate way of presenting information that did not fit in nine pages.

I invite you to read my essay and would welcome your comments.

Best,

Edwin Eugene Klingman

Bookmark and Share
report post as inappropriate


Anonymous wrote on Feb. 15, 2015 @ 01:04 GMT
I have yet to read your paper. I just got to it now. It looks very interesting. This seems connect with modular gravity and quaternion gauge theory.

LC

Bookmark and Share
report post as inappropriate

Lawrence B Crowell replied on Feb. 15, 2015 @ 01:06 GMT
The above post was by me. I was logged out for some reason.

LC

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Feb. 15, 2015 @ 16:56 GMT
Dear Dr. Klingman,

Thank you very much for careful reading of my text.

I appreciate your comments and agree with what you said.

David Hestenes was the scientist who opened my eyes on Geometric Algebra. Though he has done huge job, but being not hundred percent consistent with the purpose to fully eliminate formal imaginary unit from traditional quantum mechanics he did not achieve new comprehensive logically perfect QM formalism.

Back to my text. What, for example, was excluded was related to Clifford translations on S^3 spheres. Moving along the translation orbit (vertical tangent space component) causes synchronic rotation in horizontal tangent space plane.

My further work will first of all be about holonomies and two point value states in the proposed geometrical algebra terms which is necessary to deal with anyons. Only practically valuable results, say demonstrating Hamiltonians that support stable anyonic states, can show that the formalism has its own value.

Sincerely,

Alex (aka Sasha) Soiguine

Bookmark and Share



Sujatha Jagannathan wrote on Feb. 16, 2015 @ 04:50 GMT
The essay is exceptionally well-written.

Simply great, Sir!

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Feb. 16, 2015 @ 23:33 GMT
Dear Dr. Fisher,

Thank you for the comment.

My text deals with something not too abstract. Imagine you are watching the rain of golden coins falling from the sky. Coins are chaotically rotating and you see them reflecting light at different random angles. This is more or less exactly what is behind the geometric algebra bivector formalism.

Sincerely,

Sasha Soiguine.

Bookmark and Share



Koorosh Shahdaei wrote on Feb. 18, 2015 @ 13:56 GMT
Dear Professor Soignine,

Thank you for the inspiring essay, in your view what is the description of the wave equation considering your arguments and the fact that classically it was based on wave particle duality and collapse of the wave function whenever the particle was observed. Do you think that the mathematical description formerly based on Hilbert space formalism is not reflecting the fact??

I have written an essay before where I used new arguments regarding the interpretation of SR and shown that length contraction doesn’t happen in a slow moving frame which is approximately inertial but uses linear transformation based on fiber bundle method.

http://fqxi.org/community/forum/topic/1769

You are also welcome to read my essay in this forum.

Kind Regards

Koorosh

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Feb. 18, 2015 @ 16:02 GMT
Dear Dr. Koorosh,

Thank you for the message. I will carefully read your essay. Do expect enjoying it. Will write more later.

Sincerely,

A. Soiguine.

Bookmark and Share



Lawrence B Crowell wrote on Feb. 20, 2015 @ 01:01 GMT
Your paper is a fascinating way to look at geometric algebra. I am thinking this is a way to represent higher or hypercomplex systems like quaternions without appealing to additional basis elements. The theory remains on the Hopf fibration between S^1 --- > S^3 --- > S^2 instead of on the next level S^3 --- > S^7 --- > S^4. It appears one is able to capture much algebraic geometry and Clifford Cl(3,1) structure this way. I have read it through a couple of times and am reading it much closer on the third reading.

Cheers LC

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Feb. 20, 2015 @ 03:11 GMT
Dear Dr. Crowell,

I am happy that you find my text interesting. You are right, the main idea was to only work with explicitly defined planes in 3D, the planes playing the role of complex planes, eliminating in this way formal algebraic using of the imaginary unit. The simplest case was considered corresponding to qubit quantum states, two-dimensional complex vectors. Generalization to higher dimensional cases should be elaborated which may correspond to multiple object quantum states. I believe you realize that we are at the very beginning of a wonderful trip.

Sincerely,

A. Soiguine.

Bookmark and Share


Lawrence B Crowell replied on Feb. 22, 2015 @ 00:51 GMT
In what I can see the B_3 and the elements β_i with the i = sqrt{-1} in effect emulate quaternions. It seems to me that you have quaternions in a different guise. In doing it this way instead of working in four dimensions you are working in 2 dimension with the B_3 group. This is an interesting way to proceed.

Cheers LC

Bookmark and Share
report post as inappropriate


Gary D. Simpson wrote on Feb. 20, 2015 @ 22:45 GMT
Alexander,



Many thanks for an excellent read. You have given me several new insights. I had not previously thought of the Clifford basis vectors as representing a plane. In retrospect, it is clear now since every vector has a plane that is normal to it. Also, I had not previously seen any advantage to Clifford over Hamilton. You have made me reconsider this. Setting i = (e2)(e3) still seems odd but at least I now understand the reason for it.

I wonder what you think of the following … Euler’s Equation is (e^i*theta) = cos(theta) + i*sin(theta). It is possible to express the dot product of two vectors by using the cosine of the angle between them. It is possible to express the cross product of two vectors by using the sine of the angle between them. Therefore, if there are two arbitrary vectors that are restricted to the j-k plane, it is possible to construct Euler’s Equation using these two vectors, and the complex i then does not appear in the right-hand side of Euler’s Equation. Is this a simplified version of your Equation 3.2?

Beginning with your Equation 6.1, I see a connection between your paper and Dr. Klingman’s paper since division by the absolute value normalizes the value to either plus or minus one. The un-numbered equation at the top of page 8 is also similar to part of Dr. Klingman’s work.

The two step rotation is a little hard for me to visualize although I generally understand your meaning. A sketch would be very nice, but with so much happening it might simply be confusing.



Best Regards and Good Luck,



Gary Simpson

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Feb. 27, 2015 @ 21:12 GMT
Dear Dr. Simpson,

Did not reply because did not have time to read the Dr. Klingman's work. Have not read yet.

Sincerely,

A. Soiguine.

Bookmark and Share



Joe Fisher wrote on Apr. 2, 2015 @ 14:49 GMT
Dear Professor Soiguine,

I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

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

Bookmark and Share
report post as inappropriate


Peter Jackson wrote on Apr. 2, 2015 @ 19:26 GMT
Alex,

I think the importance and validity of your essay may be counterpoised by appearing a bit off topic to some, and will also be a little lost on most. The preponderance of mathematics isn't encouraged in this essay format and I think it's a shame you didn't spell out the great implications.

Those may explain why it's not where I think it should be, at the head of the field. I suppose I would because, as you've seen before, the foundations of our work are entirely compatible. Indeed I hope you may look at this short video including closely related matters as well as reading my essay.

3 plane OAM gives a 'time dependent' cosmic redshift and resolves CP violations etc.

I wish you well in the contest.

Peter

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Apr. 2, 2015 @ 19:47 GMT
Dear Peter,

Thank you for the your comments. The main reason of disadvantages you are mentioning is that original text was 20 pages. I shrink it to 12 (official requirement) but soon was informed that just 9 allowed (why?). So many important explanations disappeared. I definitely need to look for a place to publish much bigger text with proposed applications, etc.

Alex.

Bookmark and Share


Peter Jackson replied on Apr. 18, 2015 @ 14:04 GMT
Alex,

It's now clear what you've had to do. It's a shame you couldn't give it more time, and many will consider it not in line with the competition guidance. I on the other hand do not, but do perceive the great value of your work, and will score it appropriately.

best of luck.

I do hope you'll make time to read and score mine as I think it may contribute to the direction you're heading, and your comments will anyway be valued.

Best of luck

Peter

Bookmark and Share
report post as inappropriate


Vladimir Rogozhin wrote on Apr. 8, 2015 @ 10:27 GMT
Dear Alexander,

The idea of «Geometric evolution» is very deep and heuristic. And if to expand this idea from "origin of geometry" in the spirit of E.Gusserl ("Origin of Geometry"), then from "beginning of the Universe" (taking into account "fundamental constants" of the Nature) to the Universe as whole in the spirit of V. Nalimov ("The self-aware Universe") ? I think that then will be revealed the deep ontological structural connection Mathematics (consciousness as an absolute vector) and Physics (direction of the evolution of Nature and states of matter).

Kind regards,

Vladimir

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Apr. 8, 2015 @ 15:35 GMT
Dear Vladimir,

Thank you for the comment. Actually, I am just trying to create quantum mechanical framework comfortable, convenient for my research purposes which are mainly about topological quantum computing. I believe your expertise in structural connections between math and physics is much deeper than mine. I am not looking so far, at least yet.

Thank you again,

Sasha

Bookmark and Share


Vladimir Rogozhin replied on Apr. 8, 2015 @ 19:39 GMT
Thank you very much, Alexander, for your concrete and rapid response. I hope that in the "topological quantum computing" concept "ontological (structural) memory" take its rightful place. My high score. I wish you success in research and contest.

Yours sincerely,

Vladimir

Bookmark and Share
report post as inappropriate


Member David Hestenes wrote on Apr. 22, 2015 @ 19:35 GMT
Nice paper, Alex.

The Hopf fibration may be a key to elementary particle topology.

.....David

Bookmark and Share
report post as inappropriate


Author Alexander Soiguine wrote on Apr. 22, 2015 @ 20:27 GMT
Thank you so much David.

Maybe you remember the story began more than 20 years ago when I was still in Russia and had read some your works on Geometric Algebra. I wrote then a small book on the subject and sent you a copy. You kindly answered confessing that Russian language was a bit problem for you.

This essay is just the beginning. I am working on some further interesting ideas. You are absolutely right about importance of Hopf fibration. All will be about even geometric subalgebras, their fibrations to complex number systems, tangent bundles, connections, etc.

Thank you again.

Alex.

Bookmark and Share



Login or create account to post reply or comment.

Please enter your e-mail address:
Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.