Essay Abstract

Although we often speak of fundamental particles, those in the standard model lack a formal mathematical foundation. That is, the standard model of particle theory is empirically-founded but could benefit from a formal, causal basis for consistency with cosmology. This essay will explore the notion that such a mathematical foundation exists and discuss its ability to address known problems in fundamental physics.

Author Bio

Dr Lundberg studied mathematics and graduate-level physics at CWRU thru 1980, and has continued learning about, and contributing to, theoretical physics at many conferences since. His 30-year professional career has supported his lifelong learning, based on the premise that geometry and algebraic duality extends to particle theory's quantum algebra.

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Very Interesting Wayne!

Quote

A key characteristic of a foundational theory is that it be consistent across all

physical scales. Thus a causal particle's formulation must be consistent with the No-

Boundary Wave Function, which is consistent with cosmological evolution. Takeuti

further proved3 that a self-consistent mathematical system must be finitary. This means

that fundamental particles are finite in extent (whether observable or not).

end of quote

I agree with this, and think it is a good insight.

Before leaving, are you saying that SUSY as an example fits this billet ?

You brought up the example of cyclic cosmology which is a very good point.

Can you add a bit more to it ? Thanks

BTW, you can examine my essay, and I hope you comment on it. It is in December 21st, one of the first ones

Thanks again for your lucid presentation!!

Andrew

    Dear DR Wayne R Lundberg,

    FQXI is clearly seeking to find out if there is a fundamental REALITY.

    Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

    All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

    Only the truth can set you free.

    Joe Fisher, Realist

    Thanks, Andrew.

    I didn't discuss SUSY much because I wanted to stick to the most fundamental. I recall a discussion with David Gross in which he said that the pi-0 meson requires SUSY, which is true here too. But pi-0 also has no supersymmetric partner... it has an extra internal symmetry. Same is true for Z-0 and I think Higgs. I generally don't get to that point, but did at DPF 02: talk "Architecture of a Comprehensive Theory - Understanding Beth, the Particulate Mass Functional" was posted online at http://dpf2002.velopers.net/talks_pdf/154talk.pdf .

    I also referenced my first paper on cyclic cosmology, and the DPF 09 posters include the subject. It is also an easy solution to the cosmological coincidence problem, which I talked about at the Eastern Gravity Meeting in 2015.

    I will take a look at your paper after I finish another... wish I had more time,

    Wayne

    Wayne,

    Fascinating essay and hypothesis, nicely explained, though I suspect maybe to much unexplained formulation and obscured language for the (Sci-Am) target audience, so also the judges. I certainly agree the standard model still needs a lot of work and a more consistent basis. There was much else I agreed with even though our approaches are quite different. Certainly to cyclic cosmology, (but I have a net zero cosmological constant for large t).

    I liked the geometric approach but couldn't extract a physical link between the spinning triangles and trecoil. Perhaps you may identify & elucidate. I've also always wondered why the 'triangle' is 'simplest' in 3D +t apart from degrees of freedom, also representable by the axes of a sphere, which I've always felt simpler. I do hope you can read and assess the apparent classical derivation of QM predictions that emerges.

    I'm not qualified to judge veracity (is anyone?) but that's anyway no criteria. I felt it an excellent attempt to tackle an important fundamental issue.

    Very well done. I have it right up there so far.

    Best of luck,

    Peter

      Peter,

      It was good to hear your review and point of view, as I am not a supporter of blind review processes.

      There is an important lesson in "necessary and sufficient conditions" to be made here. Perhaps I should have spun the essay in that way? To be sure, it is possible to choose a finite representation geometry which is (a) insufficient (b) necessary and sufficient or (c) super-sufficient to replicate QC/ED with gravity and energy metrics. I can list examples of each. In fact I argued that super-symmetry is super-sufficient as long ago as DPF 2000, and Amjorn's dynamical triangulation actually uses 4-tertrahedra. The key is that to replicate QCD, there is ONLY one fundamental algebra which must be used.

      So, although we think of the sphere as space-filling, it only requires one dimension, r, to describe it. The triangle requires two, plus the third which arises fundamentally due to delta-t.

      While you may have found a way to give QM a foundation (it seems there are several ways), I doubt that it has the "necessary" combinatorial algebra intrinsically tied to its geometry. so no QCD?

      The preon/Rishon combinatorial algebra says that TTT is an electron, here I gave that a representation geometry, rather than foolishly assuming it to be a point. Thus VVV is a neutrino, of whatever flavor.

      Frankly, the geometry of the neutrino evaded me for many years. Eventually it was clear that the sharp corners of a triangle induce a (a priori disallowed) mathematical singularity. More to the point, a string can be partitioned (or fractionalized), and a Band is simply a string with intrinsic stiffness. The observation that Bands have exactly THREE ground states which oscillate resolves the representation geometry issue.

      What would be interesting to study is how that stiffness causes the TTV, VTT etc quarks to seek their correctly-quantized shapes? (In some ways the inverse of your question??)

      I shall check for your cyclic variable, since some use the word without actually using Euler's fundamental equation of a circle...

      best regards,

      Wayne

      p.s. I am more concerned about 'veracity' than writing an amusing essay for this Contest. Those rules favor my approach. The FQXi venue affords a way to socialize these fundamental ideas with other (conventional _and_ unconventional) theorists, which should do more to raise awareness and interest than any conference talk. We shall see...?

      None of the contemporary physical theories, including QED, QCD, string theory and LQG features a proper foundation.

      Only the basic structure that was discovered and introduced by Garrett Birkhoff and John von Neumann in 1936 is a serious candidate for the foundation of physical reality. Some scientists followed that path but never explored it seriously. The Hilbert Book Model Project takes up the button and reaches interesting results.

      https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project

        Wayne,

        You wrote; "I doubt that it has the "necessary" combinatorial algebra intrinsically tied to its geometry. so no QCD?"

        It has. I always find it's better to read things rather than make assumptions. It's a common problem these days. I know some professors only read one paper a month! That means I've read some 10,000 more papers than many professors over the last 20 years! I haven't found conferences any substitute.

        Dirac's double stacked paired inverse orthogonal ('complementarity') states are physically implicit, and so called 'entanglement' emerges simply from maintained anti-paralell polar axes and interaction momentum exchange. The last part of the puzzle emerged only recently, deriving the Cos^2 from Cos distributions. I'm sure you'll be impressed. QCD provided a key element in the field interactions for that last part - as my last years essay identified. I suspect there's more in common but perhaps you'll advise.

        Declan's essay gives the matching computer code and plot for the ontology and experiment in mine.

        Very Best

        Peter

        Dear Wayne, Nice and entertaining work. I chose to became a relativist based on the extraordinary beauty of Einstein's geometric vision of gravity. Thus, despite I am not a particle physicist, I strongly appreciate your approach that what is "Fundamental" for particle theory should be a foundational theorem defining geometric-algebraic space-time objects. Geometrization of all physics is indeed my greatest dream. Thus, your Essay deserves my high rating. Congrats and good luck in the Contest. Cheers, Ch.

          Prof Wayne R Lundberg

          Wonderful thinking sir........That is, the standard model of particle theory is empirically-founded but could benefit from a formal, causal basis for consistency with cosmology. This essay will explore the notion that such a mathematical foundation exists and discuss its ability to address known problems in fundamental physics...........Best wishes for the new theory......

          May be you can have a look at my essay also...

          Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay and hope for reciprocity ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

          Some of the Main foundational points of Dynamic Universe Model :

          -No Isotropy

          -No Homogeneity

          -No Space-time continuum

          -Non-uniform density of matter, universe is lumpy

          -No singularities

          -No collisions between bodies

          -No blackholes

          -No warm holes

          -No Bigbang

          -No repulsion between distant Galaxies

          -Non-empty Universe

          -No imaginary or negative time axis

          -No imaginary X, Y, Z axes

          -No differential and Integral Equations mathematically

          -No General Relativity and Model does not reduce to GR on any condition

          -No Creation of matter like Bigbang or steady-state models

          -No many mini Bigbangs

          -No Missing Mass / Dark matter

          -No Dark energy

          -No Bigbang generated CMB detected

          -No Multi-verses

          Here:

          -Accelerating Expanding universe with 33% Blue shifted Galaxies

          -Newton's Gravitation law works everywhere in the same way

          -All bodies dynamically moving

          -All bodies move in dynamic Equilibrium

          -Closed universe model no light or bodies will go away from universe

          -Single Universe no baby universes

          -Time is linear as observed on earth, moving forward only

          -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

          -UGF (Universal Gravitational Force) calculated on every point-mass

          -Tensors (Linear) used for giving UNIQUE solutions for each time step

          -Uses everyday physics as achievable by engineering

          -21000 linear equations are used in an Excel sheet

          -Computerized calculations uses 16 decimal digit accuracy

          -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

          - Many predictions of Dynamic Universe Model came true....Have a look at

          http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

          I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

          Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

          In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

          I request you to please post your reply in my essay also, so that I can get an intimation that you replied

          Best

          =snp

            I would beg to differ about "only" a 1936 mathematics is a candidate. At that time, they had no QCD, only QED. It is important for a fundamental theory to account for all these quanta, and I did so in a one-to-one way with a (tripartite) string-like geometry.

            I really wish that the modern theorists who eschew ides such as yours (and mine) would attempt to put together a "whatever happened to" explaining how it is that any given theory was abandoned.

            I would suspect that the results lack a causal particle, since Seiberg's criteria seems to hard to pass. Anyway, take another look at the essay and maybe we can find a common interest?

            Wayne

            Wayne, (reply posted in my string)

            Thanks for the support. The link to QED was just what someone pointed out about field depth not anything I 'attempted' to do. However your electron model attachment looks shockingly close to my own some years ago;fqXi finalit 2013-14 Do Bob and Alice have a future? (see the figs etc towards the end). However to remove the weirdness from QM just needs those colours to 'bleed into' each other rather then just 'switch'. Is that excluded in QED?

            It seems you 'switched off' from the essay just when it opened up the ontology for a classical reproduction of QM predictions, as it headed off your own familiar path (indeed m MOST peoples paths!), so you missed the big finale! Do look again if you get a chance. It's consistent with Bell and this important paper, referred in Gordon Watson's consistent paper; Fröhner, F. H. (1998). "Missing link between probability theory and quantum mechanics: the Riesz-Fejér theorem." Z. Naturforsch. 53a, 637-654.

            Very best

            Peter

            Dear Christian,

            I studied QCD as an undergraduate, and took Relativity because I enjoyed it. I have much to learn about astrophysics and BH... in fact I found here an essay from Samir Mather https://fqxi.org/community/forum/topic/3113 which I think you will like a lot.

            Wayne

            SNP Gupta, I did so and I certainly appreciate your enthusiasm!

            There is room for insight in better understanding our universe

            Peter,

            It is good that we agree on electron representative geometry. This of course is also founded on Rishon partitions. They don't 'bleed' so much as add into and form whatever the particle charge and spin is.

            Wayne

            Hi Prof Wayne R Lundberg

            Thank you for the nice words and observations.....

            You raise an interesting topic, but like others I don't find a clear fundamental thing or principle or formulae......

            ..............My reply.......

            Here I saw many essays discussing what is fundamental etc, but in this essay, I went for the fundamental issue for energy to mass conversions and blue and redshifts and . I asked for help on observational verifications. I don't have a means for doing the observational verifications as I am an independent researcher.

            FQXi wanted this essay should not be a new essay. This original papers for this essay were published and available in the web, please refer them.

            ....................Your words.......

            This essay contest rewards well-written ideas that lead to new observations, and maybe yours ideas are that. But I can't make out how you intend to construct all of particle physics and general relativity, least of all make them into limbs of a larger consistent theory.

            ...............My reply.....

            Some people respond for such words, some will be like you of course. I am also not working for money. Some professors offered money to change into Main stream with money and Ph D etc , but I thought the Ideology of Dynamic Universe Model are better, and provide the world with more solutions and better predictions, even though nobody supports and provide any money to me. I am approaching each individual with this ideology and inviting them to to read my essay. I came to fag end of life. I don't expect much now.

            I am not intending to solve all the Physics problems, But I am working to provide solutions to cosmology portions. Thirty five experience with cosmological models taught me that there will not be any financial or otherwise support to any theory that is not supporting General theory of Relativity. I don't know why?

            ................. your words...........

            It seems to be mere philosophy, and physics requires equations. To be sure, many of the Gedanken you use could be experimentally tested, or already have been (likely also excluding this result).

            .............. My reply.............

            There were many papers available on internet with full mathematical explanation. I can not give 25 pages of mathematics in just 9 pages. I just touched it. Many the axioms are experimentally tested or having observational support, the prediction here is one of the exceptions. Hope you will help me for this....

            Thank you for your interest in Dynamic Universe Model.......

            Best Regards

            =snp

            4 days later

            No-one has the means for observational evidence, and in fact observations do more to disprove theory. So you should be looking for evidence among what is already observed that conflicts with your (not very well formulated) intuition.

            Why? Because GR works quite well. Better yet with the cosmological constant. In fact even subtle variants away from GR are very often easily disproven... I have some good amusing examples. For now the Modified Gravity camp and the Dark Energy camp are fighting it out, with a high probability of mutual exclusion. We'll have to wait and see what the Dark Energy survey concludes... unfortunately they so far have weak statistics, currently favoring CC by 3sigma or maybe more.

            I figure that data excludes your work... but don't feel alone... many well-funded theories (missing mass, i.e. gravitational collapse of the universe) have had spectacular ends (1998).

            Wayne

            Dear Wayne Lundberg,

            Thanks for reading my essay and commenting. I'm glad you enjoyed it. You suggested that I look at Seiberg, Susskind, and Toumbas on 'Space-time Non-commutation and Causality' - they discuss "the other term is an "advanced" wave which appears to leave the wall before the incoming packet arrived." They then say a conflict with Lorentz invariance is relevant. As you know I reject space-time symmetry in favor of an asymmetric energy-time interpretation of special relativity. Susskind's most recent book (my ref 19) claims to derive the Lorentz in two inertial frames "just like Einstein". That this approach is inherently geometric is reinforced by Susskind's advice:

            "When confronted with one of these paradoxes, you should draw space-time diagram".

            In other words, don't use logic (leading to 'paradox'), use geometry. Susskind is still big on strings, which many if not most physicists have moved away from. Hartl, Hawking, and Hertog in "The Classical Universes of the No Boundary Quantum State" believe that the quantum state of the universe determines whether or not it exhibits a quasi-classical realm. I have very little faith in theories based on "the quantum state of the universe."

            If I understand your essay you wish to construct fundamental quanta and properties from geometry:

            "... All fundamental particle quanta, mass and energy quantities are attributed to a geometric basis [having a dual algebra, with no geometrical properties left over]."

            While I tend to agree concerning "foundational theorem which defines geometric-algebraic space-time objects.", I perhaps misunderstand the attempts to define "finite particle representation geometry" that replicates QC/ED quantum state algebra. While I believe geometric algebra is the proper framework: (combining algebra and geometry) I do not believe that elucidating the product terms [as I understand other essays to do] and placing them in one-to-one correspondence with the elementary particles is the correct approach. The LHC has shown that a perfect fluid results from Pb-Pb and Au-Au collisions, and I believe a fluid dynamics model is required to produce the particle zoo (utilizing Yang Mills gauge). I believe the pseudo-stable states resulting actually do have geometric properties, but I see these as 'end states'. I do not see geometric properties as initial states, and thus do not believe such geometry fundamental. I hope I have understood your essay correctly.

            My best regards,

            Edwin Eugene Klingman

              Dear Edwin,

              You have an interesting belief system. It seems that you've taken a rather different approach to restoring causality to particle theory. It would necessarily be a rather more complex approach if you rely solely on Yang-Mills as fundamental and attempt to reconstruct QCD via a fluid-dynamics idea. I model them as co-fundamental, all quanta are required to have a geometrically different state as a Planck-scale basis.

              Might also note that the fluidic properties at Pb-Pb and Au-Au collisions are many orders of magnitude larger in physical scale than the Strong insteraction level(scale).

              Seiberg's causality criteria is met by my approach, in which I simply restore QC/ED algebraic basis to NBWF. In actual fact it is a convenient supporting result.

              I'd heard of the fuzzy instanton in the mid-80s but didn't like their fuzziness (which I resolve into a nonperturbative quantum geometric-state .. a quark has color due to its shape-states). Back then I focussed on the algebraic group of the state algebra (which I much later found out was a cross product of two wreath products).

              Of course there was a long era of string-theoretic dominance (cheered on by Nobel laureates, btw) in which the central question was 'how does a string model mass?'. Of course mass at the quantum scale is area-like (see the ref to book "Gravitation"), and others used that successfully. I had long objected to the assumption (GSW page 22-25) of cyclindrical symmetric closed string, with perturbations. Well they ran into a wall, got lost in the 'string theory forest 10^100' while the partitioned string is validated by the fact that, with STIFFNESS included, it is actually a BAND.

              Anyway, all of this came together at DPF '09 when HHH won the Einstein Prize for the NBWF and, there, in his prize talk, Hartle used a formula that was in the EXACT SAME form as what I use to descibe quark area-mass and energy-curvature!! WE AGREED... although Hawking and I don't yet agree on information-preserving black holes.

              Bands always coil up in a trecoil, which have three topologically distinct geometric-states. Thus Band Theory predicts massive oscillating neutrinos in a VERY FUNDAMENTAL way. Some important string-theoretic results are thus preserved (i.e. ralpha'/R ) but a Band is CORRECTLY QUANTIZED in both strong color, weak charge and spin states. Thus 1-1 and ONTO. A uniqueness proof is thus enabled...

              The consclusion I reach is that the quantum numbers of BOTH weak (thus Yang-Mills) and strong forces are co-fundamental, as they are both equally tied to geometrically quantized states. As it happens, the geometric-algebraic duality, as in Langland's Program, is thereby borne out. ALL areas of physics have a geometric basis.

              Anyway, I think I should write about quantized geometric states, starting from spinning B&W coins to the more complex geometry needed to found QCD and QED simultaneously. The green down state I illustrated does kind of presume some further insight... let me know.

              Best-

              Wayne