http://www.scirp.org/journal/PaperInformation.aspx?PaperID=5129

Hi, I took a venture into this area myself in 2011 and have referred to it again as seen in further JHEPGC articles, which have appeared in 2016 and 2017

My take, is that what is crucial is the concept of asociative geometry and when it does and does not break down, and the Octonians are a good vehicle to examine it

Although I did not state it earlier, my work on the cosmological constant was based upon themes of the contributions of Octonionic space time.;

Please feel free to examine my essay, December 21st and interpret it with this in mind

Thank you for your wonderful essay

Andrew

    http://www.scirp.org/journal/PaperInformation.aspx?PaperID=5129

    Has this in it

    Octonionic Gravity Formation, Its Connections to Micro Physics

    Full-Text HTML Download Download as PDF (Size:394KB) PP. 13-18

    DOI: 10.4236/ojm.2011.11002 4,520 Downloads 8,836 Views Citations

    Author(s) Leave a comment Andrew Beckwith

    Affiliation(s)

    .

    ABSTRACT

    We ask if Octonionic quantum gravity is a relevant consideration near the Planck scale. Furthermore, we examine whether gravitational waves would be generated during the initial phase, , of the universe when triggered by changes in spacetime geometry; i.e. what role would an increase in degrees of freedom have in setting the conditions during , so that the result of these conditions can be observed and analyzed by a gravitational detector. The micro physics interaction is due to the formation of a pre Planckian to Planckian space time transition in spatial dimensions at and near the Planck dimensional values, i.e. 10-33 centimeters in spatial dimensions. This transition would be abrupt and arising in micro physics regimes of space time.

    KEYWORDS

    High-Frequency Gravitational Waves (HFGW), Symmetry, Causal Discontinuity

    Cite this paper

    A. Beckwith, "Octonionic Gravity Formation, Its Connections to Micro Physics," Open Journal of Microphysics, Vol. 1 No. 1, 2011, pp. 13-18. doi: 10.4236/ojm.2011.11002.

    References

    [1] L. Crowell, Quantum Fluctuations of Space-time, in World Scientific Series in Contemporary Chemical Physics, Volume 25, Singapore, Republic of Singapore, 2005.

    [2] A. W. Beckwith, "Identifying a Kaluza- Klein treatment of a Graviton permitting a de-celeration parameter Q(Z) as an alternative to standard DE ",Journal of Cosmology, Volume 13, 2011, http://journalofcosmology/BeckwithGraviton.pdf

    [3] F. Li, and N. Yang, "Phase and Polarization State of High Frequency Gravitational waves", Chin Phys. Lett. Vol 236, No 5(2009), 050402, pp 1-4

    [4] F. Li,. M.,Tang, D. Shi, "Electromagnetic response of a Gaussian beam to high frequency relic gravitational waves in quintessential inflationary models", PRD 67, 104008 (2003), pp1-17

    [5] S. Chaturvedi, "Mutually Unbiased Bases", Pramana Journal of Physics, Vol. 52, No. 2, pp 345-350

    [6] John C. Baez, "Renyi Entropy and Free Energy", http://arxiv.org/abs/1102.2098

    [7] A. W. Beckwith, arXiv:0804.0196 [physics.gen-ph], AIP Conf.Proc. 969:1018-1026, 2008

    [8] D. K., Park, H. Kim, H., and S. Tamarayan, "Nonvanishing Cosmological Constant of Flat Universe in Brane world Senarios," Phys. Lett. B 535, 5-10 (2002).

    [9] A. W. Beckwith," How to Use the Cosmological Schwinger Principle for Energy Entropy, and "atoms of Space-Time" to Create a Thermodynamic Space-Time and Multiverse"; accepted for the DICE 2010 proceedings; http://vixra.org/abs/1101.0024, 2010

    [10] M. Maggiorie,. "Gravitational Wave Experiments and Early Universe Cosmology", Physics Reports 331 (2000) pp. 283-367

    [11] G. t' Hooft, Beyond the Quantum, edited by Th. M. Nieuwenhuizen et al. Singapore, World Press Scientific, 2006; http://arxiv.org/PS_cache/quant-ph/pdf/0604/0604008v2.pdf.

    http://www.scirp.org/journal/PaperInformation.aspx?PaperID=79959

    The Transition from Pre-Octonionic to Octonionic Gravity and How It May Be Pertinent to a Re-Do of the HUP for Metric Tensors

    Full-Text HTML XML Download Download as PDF (Size:572KB) PP. 727-753

    DOI: 10.4236/jhepgc.2017.34055 93 Downloads 140 Views

    Author(s) Leave a comment Andrew Walcott Beckwith Affiliation(s)

    Physics Department, College of Physics, Chongqing University Huxi Campus, Chongqing, China.

    ABSTRACT

    The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real "instants", is avoided by having initial Octonionic geometry embedded in a larger, nonlinear "pilot model" (semi classical) embedding structure. The Penrose suggestion of recycled space time avoiding a "big crunch" is picked as the embedding structure, so as to avoid the "instants" of time issue. Getting Octionic gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the complication of then afterwards "Schrodinger equation" states of the universe, and the transformation of Octonionic gravity to existing space-time is explored via its possible linkage to a new version of the HUP involving metric tensors. We conclude with how specific properties of Octonion numbers algebra influence the structure and behavior of the early-cosmology model. This last point is raised in Section 14, and is akin to a phase transition from Pre-Octonionic geometry, in pre-Planckian space-time, to Octonionic geometry in Planckian space-time. A simple phase transition is alluded to; making this clear is as simple as realizing that Pre-Octonionic is for Pre-Planckian Space-time and Octonionic is for Planckian Space-time. We state that the Standard Model of physics occurs during Planckian Space-time. We also argue that the Standard Model does not apply to Pre Planckian Space-time. This is commensurate with the Octonion number system NOT applying in pre-Planckian space-time, but applying in Plankian space-time. And the last line of Equation (54) gives a minimum time step in pre-Planckian space-time when we do NOT have the Standard Model of physics, or Octonionic Geometry.

    KEYWORDS

    Octonionic Geometry, Cyclic Conformal Cosmology (Penrose), Modified HUP

    That is the recent iteration as opposed to what I did in 2011

    Again, the methodology, was implicitly used in My December 21st essay

    Hi Rick , thank you for sharing your passion for algebra and in particular octonians.

    At the beginning you state "mathematics is a language of unambiguous truth", I used to think that the certainty of mathematical solutions do make it more reliable than other kinds of communication. Though statistics is notorious for misleading. Having read "Creating perspective on set theory" by Christophe Tournayre, in this competition, I have been re-considering my opinion. I found this paper "When is one thing equal to some other thing?" Barry Mazur (2007) www.math.harvard.edu/~mazur/preprints/when_is_one.pdf Which showed me that even something as common place as use of the equality symbol is not simple and not immune from ambiguity. Also a statement, mathematical or otherwise, can be true, as in not false; and yet not be the whole truth. A more complete truthfulness painting an entirely different picture. An algebraic description can give a singular viewpoint of a phenomenon but does not give all viewpoints, which would be the whole truth. Something Peter is approaching with different observations of the same rotating phenomenon. None of the singular values being the whole truth.

    In a universe where there is sequential passage of time, as needed by QM and fitting the arrows of time, there is non-commutivity. As new Now follows previous Now definitely and so when things happen in the representation is important. Which is something in favour of quaternions ( and maybe their big bother). Though as I see it the real number line is not an actual dimension of the universe where physics is happening, but a history time line without physical counterpart. You mention 4 dimensional space from primary sense perceptions. That has to be a separate 'map' space from the former representing where physics is happening. The sense space has a time dimension, and non simultaneity of events can happen as the time is related to signal transmissions and not the foundational sequential passage of time. The two different forms of universe can not be described by just the one form of the algebra because of the fundamental difference in what time is in each. If quaternions were used for both in one version there is the non physical history time line and in the other the geometric time dimension.

    Thank you for food for thought. I am going to think on about non associativity in nature and whether it is needed in a representation, and about representation of the different kinds of field, that you discussed. Kind regards Georgina

      I posted this on Geoffrey Dixon's essay thread, may be interesting to readers coming here:

      Geoffrey,

      Knowing you are not big on the Cayley-Dickson doubling algorithm, I did neglect to mention another reason my Quaternion triplet enumeration algorithm is cooler than yours (no offense intended). That would be for enumerating the triplets for the sedenions. For Octonion Algebra I used the binary numbers 1 through 7 and partitioned the triplets with the bit wise exclusive or logic function. This can be extended to the sedenions by going to binary 1 through 15, of course representing directly the 15 non-scalar basis elements enumerations. Doing the exclusive or logic operation on binary 1 through 15 partitions them into 35 unique closed triplet sets, and since there are (n-1)*(n-2) = 15*14 = 210 basis products not e0 * en, en * e0 or en * en fixed product rules, and each triplet does 6 rules, 35*6 = 210, covering all 210 basis products with 35 Quaternion triplets.

      For each Octonion subalgebra using this enumeration technique the seven non-scalar basis element indexes will exclusive or to a zero result, as well each Quaternion index triplet. If you take away from the seven Octonion non-scalar basis indexes any set of three which are Quaternion triplet indexes, the remaining four basis elements are called "basic quads" and their indexes will also exclusive or to zero. They are basic quads because given just them, the exclusive or of any two will be the index of one of the companion Quaternion basis triplets and all are provided 2 up with this.

      This gives a method to determine how many Octonion subalgebra candidates there would be, just go through all quads of distinct indexes 1 through 15 for combinations that exclusive or to zero. A simple computer program will show there are 105 such quads. Any Octonion definition has seven Quaternion triplets each with a unique basic quad, so we would expect to see 105/7 = 15 candidate Octonion subalgebras. Each of the 35 Quaternion triplets occurs in 3 Octonion subalgebras 3*35 = 105.

      The rub is you can't make all 15 Octonion subalgebra candidates represent valid normed composition algebras, e.g. division algebras. An algebraic proof the sedenions are not a division algebra? Maybe so.

      Thought you might find this interesting.

      Rick

      Dear Rick

      I agee and like the term Truth is most important, but I am wondering how to measure it or who can measure it?

      Here is my essay that really think there is some fundamental trurh about the nature of particle and gravity, please comment.

      Best wishes

      Bashir

        Dear Rick

        Here is my essay

        https://fqxi.org/community/forum/topic/3143

        Bashir Yusuf.

        Hello Mr Lockyer,

        It seems relevant these octonions not commutative to unify this gravitation, have you already thought about the fact to insert the spherical volumes and their motions and this DM not baryonic.Because we cannot find this weakest force wityh these lie algebras, it lacks something.I read the works of Hestenes with the spinrs and geometrical algebras, it is a good tool also,that said this quantum weakest force have difficluties to appear .....Best regards and congratulations for your essay, good luck :)

        Hello yet again Rick,

        I wanted to pass this on. The Kricker and Joshi paper is behind a pay wall at Elsevier; but a scanned copy of the manuscript was available from Kricker's web page. So here is that paper "Bifurcation Phenomena of the Non-Associative Octonion Quadratic."

        Enjoy,

        Jonathan

          Darn...

          I guess just less than 1 MB is not good enough. I'll send it your way the old fashioned way - e-mail.

          Regards, JJD

          Hello yet again Rick,

          While looking for something else; I happened upon these papers by a researcher I mentioned above, which should be of great interest to you, given the subject matter. I hope it adds something, rather than detracts, and I have not read these for detail enough to know. From Merab Gogberashvili

          Octonionic Electrodynamics and

          Octonionic Version of Dirac Equations

          Enjoy, JJD

          Jonathan,

          Added a new class to my scripting called NUMBERS, for doing Octonion math on 8D arrays of numeric values. Methods are so far add, subtract, multiply with Algebra choice and selective conjugation, return the norm, multiply and divide all by real number, output to console/text file. You should be able to create your own complex number, Quaternion number or Octonion number Mandelbrot sets with it. Tried something as a test, iteration Z_n+1 = Z_n ^2 + c, bailing on stationary norm with assigned value of 0, else iteration loop count to have the norm go past 1000000, staying in Quaternions. We all minutes to do a 1000 x 1000 grid of 2 Quaternion non-scalar starting points with increments .00001 with the starting points fixed for other 2 and c being fixed same non grid elements. Got some kind of pattern, have not plotted. What do you use to plot colored plots?

          Rick

            Wow, autocorrect sucks, need to read first. Within a few minutes, like 10 to do 1000 x 1000 grid

            Far Out!

            I've used a purpose-built program written in Pascal for years to convert arrays of integers into 24-bit color values (3 5-bit values for R,G,&B). It's pretty cumbersome, and I have it making files in an obsolete format then converting that to TIFF, but I can deconstruct and re-construct that code to modern specs in fairly short order. It breaks the number palette into ranges, separates odd and even values, and then uses an algorithm to produce color gradients within each range. Your progress gives me a good reason to get back into the programming end of things.

            All the Best,

            Jonathan

            Hi Rick,

            I just sent you an e-mail with a snippet of code which is the subroutine for color assignment using a 24-bit palette. The choices for colors and ranges created by that code looks like this image for the standard Mandelbrot Set plot.

            Good Luck!

            JonathanAttachment #1: MandelCrop.jpg

            Dear Rick

            If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

            Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

            My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

            Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

            For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

            My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

            By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

            To steal a phrase from my essay "A world product of evolved optimization".

            Best of luck for the conclusion of the contest

            Kind regards

            Steven Andresen

            Darwinian Universal Fundamental Origin

              As advertised attached is my JavaScript symbolic algebra tool, along with my verification script for my derivation of the Octonion conservation of energy and momentum equations. Also just for fun is a Mandelbrot set script that can do complex, Quaternion and Octonion iteration loops.

              It requires you to download the free Node.js runtime and has only been used on a Windows 7 machine by me. Expand the attached zip file (hopefully it will be there), read the pdf, have fun.

              RickAttachment #1: OctonionScripting.zip