Hi Cristi,

I enjoyed your essay very much. Excellent writing, wonderful concepts and sound conclusions. Using a game was effective to explain isomorphism and it made the reading more fun. It also made your essay more memorable for me because I showed the game to my wife, who is an avid Sudoku player, and challenged her to figure out the numbers that would sum up to 15.

Your discussion of holographic fundamentalness is spot-on. I wish I had learned geometric (Clifford) algebra in school. I tried to pick it up a few years ago after reading a paper by David Hestenes, which I recommend for your reading (if you haven't already - I noticed you referenced Hestenes and G Sobczyk.) "Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics." Am. J. Phys. 71.2 (2003): 104-121. I've forgotten too much to fully understand what you wrote in your essay, but I remember enough to say I think you are definitely onto something. Especially your suggestion that such a unification result in a single holomorphic field.

My approach to unification is much simpler than yours, and I took a sort of inside-out (or upside-down?) approach to conclude that motion serves to separate this holomorphic field in our percepption as space (S) and time (T), both of which are forms of motion:

In your words, "Our experience unfolds the germ, creating space and time, but the germ always remains enfolded, and we with our experiences, and spacetime itself, are always enfolded inside it."

In mine, "Physical form is the manifestation or perception we observe when motion separates the field into two coherent waves, S and T, one moving outward as a quantum particle wave function and the other moving inward as the collapse of the same wave function modulated with information. The surface boundary then is the holographic interference pattern forming the apparent surface of the volume in space."

I would appreciate it if you would read my essay at "A Simple Model For Integrating Quantum And Relativistic Physics with application to the evolution of consciousness by Theodore St. John" and tell me where I go wrong. I think that the concept you call the germ is what I refer to as simply an event (in the spirit of Alfred Whithead). You said in your notes "If we want to turn the picture upside-down and consider that our choices also determine the germ, then would it be possible that our local actions determine the germ..." I think that each germ is created in each moment, collapsed into events, so our actions are inherently part of the process of making the germ(s).

What little constructive criticism I can offer seems to make your point, as you say in the last sentence of Quantum holism section, about how "mathematics can offer more adequate notions of composability and reducibility than our classical intuition does". So here it is: You threw me off a little when you talked about "shapes", e.g. "If a particle can have two possible shapes, it can also have any superposition or linear combination of these shapes." I have never heard anyone refer to the shape of objects being described by the wave function, except perhaps as it relates to particle (localized) or wave (non-localized - expanded out in all directions), both of which would be spherical, or as the peaks and valleys in the solution that refer to probability amplitudes. I know you were talking about the shape of the wave because the previous sentence was "A single particle is a wave of various possible shapes." But the word "shape" formed a mental image of the object itself. I also had trouble with the "property of the particle" in the sentence "A property of a particle," you said, "like position or momentum, is well defined only for some of the shapes. For example no shape can have well defined position and momentum simultaneously." Position and momentum are not properties of the particle; they are dynamic variables and measurement of one of them changes the state of the wavefunction to the corresponding eigenvector. The state of the particle only changes in the sense that 'measurement of its position at a given instant in time' effectively means that it is stopped in that position, so the function describing it must be one that fits its current state.

Anyway, congratulations on an excellent essay!!

Ted

    Dear Cristenel, Cristi,

    I was very impressed by your essay esp in that it makes use of the algebraic group underlying QCD. I have also constructed a well-founded geometric approach to this same problem, with an emphasis on preserving causality at is most fundamental level.

    I see that your approach generates one Std Model quark/lepton generation. This would seem to present a problem? I have also seen other similar approaches which produce four generations (or more?).

    Thus I encourage you to read my essay https://fqxi.org/community/forum/topic/3092 which discusses only the most fundamental formulations, but with particle causality ensured by consistency with NBWF.

    The algebraic group used is a subgroup of a cross product of two wreath products, which explicitly passes Seiberg's causality criteria. The essential mass/energy metrics are attributed to intrinsic _spatial_ variables of the quantum-geometric basis. It also has exactly three generations of SM fundamental particles! (which I didn't mention in the essay, but its in my older publications, cited)

    I was most impressed by your expository writing skills, which would suggest that collaboration would be very productive.

    Thus I downloaded your 2017 paper to better review its rigorous details.

    best,

    Wayne Lundberg

      Hi Ted,

      Thank you for your comments, I'm glad that you liked some ideas from my essay. I'm happy you liked Hestenes, I like him very much, although for my paper I recommend some standard textbook like Chevalley or Crumeyrolle. And for the comparison with your much simpler approach. You said you "conclude that motion serves to separate this holomorphic field in our percepption as space (S) and time (T)". Do you also use holomorphic fields and germs?

      You said "You threw me off a little when you talked about 'shapes'", and "also had trouble with the 'property of the particle'".

      :)) Let me explain it differently for you. This is what I mean by shape: wavefunctions in Schrodinger's equation are fields defined on space and changing in time, and for each (x,y,z,t) they have an amplitude and a phase. So if you draw a picture of the amplitude of the wavefunction at each point, you will see a shape. What I call "properties" correspond to Hermitian operators, for example position to a Hermitian operator x with a hat, and momentum along a direction to another Hermitian operator, i times the partial derivative with respect to that direction. A wavefunction has a definite position only when it is a Dirac distribution, so its shape is concentrated in a point. It has a definite momentum only when it is a plane wave, that is the amplitude is constant, but the phase changes linearly in a certain direction. So when a particle has a definite position it can't have a definite momentum and conversely. In general, a property is represented by a Hermitian operator (or matrix, but in the infinite dimensional Hilbert space), and a particle has that property ony if it is an eigenvector (or eigenstate) of that Hermitian matrix. In this case, the value of the property is simply the eigenvalue corresponding to that eigenvector. This is the rigorous, technical, standard definition (see for example the first page of this paper). I prefered to avoid speaking about Hermitian operators and eigenvectors because the essays are supposed to not be too technical, so instead I said "properties" and "shapes" of the wavefunction. I think this captures the idea without requiring the reader to know advanced linear algebra in Hilbert spaces. And everyone who knows the technical definition understands what I mean. And I think the reader who doesn't know understands better than if I use the usual descriptions in pop-sci literature, that "the electron is sometimes a point particle, sometimes a wave", or it is both or neither. But my effort can't please everybody. Anyway, thank you for the comments!!

      Best regards,

      Cristi

      Dear Wayne Lundberg,

      Thank you for your comments. You asked "I see that your approach generates one Std Model quark/lepton generation. This would seem to present a problem?". I think it would be better to have exactly three generations, with the correct mixing matrices. To "fix" this I could just use three copies of the model, but I think it would be better to have them be there naturally.

      Thanks for mentioning me your essay, from what you wrote here seems appealing.

      > I downloaded your 2017 paper to better review its rigorous details.

      Thanks, and please let me know if you have questions!

      Best regards,

      Cristi

      Funny things happen :)) Together with the two previous seemingly favorable comments, I've got two very small rates, probably 1. Maybe this is a coincidence, maybe somebody's playing, this is not the first time when this happens in this contest. Maybe Russian hackers? :))

      Dear Cristi,

      Thank you for your interesting and insightful essay. It was a very enjoyable read, and I liked how you worked your way through various perspectives of geometry to Klein's Erlangen Program, which unifies geometries in a way. I still find it remarkable that such unifications, in description, are possible.

      The section on Towards a Holomorphic Unification came fast and furious, as happens in an essay with a page limit. I would have liked to have seen this expanded to some degree with emphasis on the connections to the spirit of the essay. Clearly, at least another read is warranted and I will have to put some more thought into this, especially with the surprise of having geometric algebra taking a central role.

      Thank you again for an excellent thoughtful essay.

      Cheers

      Kevin Knuth

        Dear Kevin,

        Thank you for reading my essay and for the comments. The central points of my essay were (1) to argue that there is a relativity of fundamentalness (even ontological), based on isomorphism/automorphisms of mathematical structures, and (2) to propose the holomorphic fundamentalness, which is illustrated by the metaphor of Indra's net - the whole is present completely in each part. The section about unification was meant to give an example which may turn out to be holomorphic, and indeed it was too short to properly explain the content of a 33 pages paper. I guess a proper explanation would be of the length of a book, just to explain how the Standard Model fits in that matrix without gaps or new predicted particles, and has the right symmetries, charges, colors etc, all this coming from a simple algebra. In the meantime I found some new directions to develop it and I am more convinced that as a bonus will be holomorphic. Making it holomorphic was not the reason I am working at it, but it seemed a nice bonus, as I thought holomorphic fundamentalness brings a fresh view on what is "fundamental".

        Best regards,

        Cristi

        Dear Cristinel Stoica

        Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

        My essay is titled

        "Darwinian Universal Fundamental Origin". It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my novel effort judged.

        Thank you & kind regards

        Steven Andresen

        My goodness, what a wonderful essay and your writing style is impressive. I love your ideas about geometrical "laws", quantum holism and how you can relate them to particles of nature.

        One major idea that is not discussed is the quantum property of monogamy (how system and subsystem relate to one another). If your model is holistic then the only way you can have "separate" subsystems is from holographic projections from the one whole system. And these holographic system can have 100% fidelity (since they are from holomorphic vectors as per your discussion page 4) and can have the appearance of "separate" yet be part of the whole.

        Yes totally agree that the major issue is how "encoding is done" and your essay addresses that head-on.

        I feel your model cannot support monogamy and monogamous behaviour at all. Since you cannot define a measure of monogamy with your "geometry" and as shown in my essay these concepts are the only ones that can have "holograms being a part and apart of the one holistic system".

        And more serious problems arise -- you cannot have a "bird's eye view" of your model hence no independent truths can be established since you need the bird's eye to see the whole all at once so as to have objectivity in the first place.

        Sometimes your beautiful writing makes seeing the ideas difficult. Can you tweet your model as to show "the whole" and "one small atom this can encode the whole" thru a holographic vector projection on a geometry.

        After all there is only one whole holistic system that has internal holographic projections from your basic geometry.

        If you have time see my essay where I took your route, and show that it is have monogamy when considered as one whole and is monogamous when considered as "many", by using the basic properties of complex numbers and the area of the imaginary unit. What is fundamental is the area of the imaginary unit" Enjoy

          • [deleted]

          Dear Jouko Harri Tiainen,

          Thank you for the comments. You said "I feel your model cannot support monogamy and monogamous behaviour at all. Since you cannot define a measure of monogamy with your "geometry"". I don't know what gave you this impression. Quantum monogamy is a consequence of quantum mechanics, is not some effect first observed in nature and unexplained by quantum mechanics, it is actually predicted by quantum mechanics, then observed. And my model doesn't leave outside quantum mechanics. In fact, Clifford algebras encode many maximally entangled qubits. You said "And more serious problems arise -- you cannot have a "bird's eye view" of your model". I don't understand why you say so or maybe what is your own view of what a bird's eye view is. I have the feeling that you don't get many of the points of my essay. You ask "can you tweet your model", this is funny, try and tweet a general holomorphic function. You seem to believe that holomorphy means that everything is contained in a short sequence of bits, but don't forget that a power series has an infinite number of coefficients, which themselves need infinite information to be specified. Holomorphic functions have encoded the complete information at each point, in the coefficients of the power series at that point, but this doesn't mean that you can encode the full universe in a tweet or even in all the books in the universe :)

          Best regards,

          Cristi

          My thoughts on your essay have gone through three stages. Five weeks ago, I thought that the mystical net was an odd idea merely tacked on to your essay but somehow making it into the title. Later, I thought the net was relevant but too static, whereas today I realised that it was an excellent idea.

          By too static I mean that I thought it as too perfect a fractal. That is fine for a perfect fractal which gives the same image wherever one zooms into the picture. But my own model at

          https://fqxi.org/community/forum/topic/2982

          has the universe starting out with perfect symmetry and then gradually losing symmetry and gaining entropy. I wondered how breakage of symmetry could be contained in the mystical net of timeless point(s).

          Today I saw the light and can imagine your timeless spaceless point or germ as the fundamental entities in my essay. These are a 4D set of strong colour red dimensions, ditto for blue and for green and ditto for spin: making 16D in all. 4D blocks are used so as to allow colours and anticolours c.f. to matter and antimatter in a 4D spacetime block. Normal spacetime is emergent from the 16D and maybe uses the 4D of spin to add a topological twist to space. As in string theory, all these dimensions are compactified to one point which is observer dependent. An observer within the 16D could maybe observe the 16D-point as not compacted, so to call it a point or a universe depends on the observer.

          So that is one point/germ but how does that one point lead to a myriad of jewels... In my model, the point/germ has four independent time dimensions in it, so a red brane can weave its way forwards in red-time but say backwards w.r.t. green-time. The time dimensions in the 16D are pretty mixed up. In this time-endless interweaving of dimension, snags of different dimensions get caught together as particles/fields. The single point or germ does not exist in spacetime but every particle lives in spacetime and every particle has its own contents of a snag of the 16D fundamental germ. So every particle contains the same jewel although contains different aspects of the jewel, eg having a red quality rather than an antired quality. In my model this can best be seen in the hexarks (which are sub-particles of preons where each hexark has a single polar attitude to each of the possible binary qualities of the germ).

          My model has universes within particles and particles within universes. Despite, or perhaps because of, all the time dimensions in my model, there seems to be no place for free will.

            quote

            The relativity of fundamentalness implied by different axiomatizations and formulations is

            just epistemological fundamentalness. But the examples from the quantum world seem to imply

            that reality is holistic and there is a relativity of the ontology itself. Should we then take the

            whole universe as ontologically fundamental? Should we consider that what is fundamental

            are not the various sets of principles from which everything can be derived, but rather an

            equivalence class of them? Or maybe it is possible that something more fundamental than

            these exists?

            end of quote

            Cristi, this reasoning as to an equivalence class of principles, is exactly why I picked John Klauder's enhanced quantization for my bound put in the cosmological constant.

            I would like it very much if you reviewed and commented on my essay, December 21, using this analogy to rate and review why I used John Klauders enhanced quantization.

            Awaiting your reply. i.e. this is a very relevant insight.

              Greetings Cristi,

              I agree with the comment some others have made that your essay is impressive. I have long been a fan of the Indra's net metaphor, but you weave it into the whole fabric of Physics in a meaningful way. This is in some ways the kind of essay I wish I could write, if I was a little smarter and more learned in order to do the subject matter justice. That is to say you do that admirably; you explain yourself extremely well. I especially like the I-Ching characters used as binary numbers for the chapter headings - a correspondence first described by Leibniz. It will take at least one more reading to absorb all you are saying, but I will be back with more to say myself. I invite you to check out my essay when you get the chance.

              I wanted to comment that I see Andy Beckwith's message/query above, and I noticed you already had high praise for John Klauder's essay. He and I both heard John Klauder's excellent talk at FFP15 and found his work inspiring. So I'm a little curious what you think of how Andy put that formalism to work, and if you feel it is relevant.

              All the Best,

              Jonathan

                Dear Austin,

                Thank you for the comments, especially for the description of the stages you experienced. As you may know, a theory is better when you don't need or eve can't change it to accommodate new data. This means it will make better and more exact predictions, without having to change something. It is difficult to obtain this "rigidity", and the main danger is, as you said, that it may be "too static". What would be the way to get the maximal rigidity? I think this is a unified holomorphic field, because holomorphic fields are indeed the most rigid ones. Among them there are others even more rigid, like the constant ones, these indeed would be too static. But are holomorphic fields too rigid? I think not, because while they can determine everything everywhere from the data at the field, there is no way to control or determine this data completely. This is because you explore it from within the field, and no measurements can give you the field as it is, because the operators don't commute. This "protects" the field from being "hacked".

                You said "Today I saw the light and can imagine your timeless spaceless point or germ as the fundamental entities in my essay."

                One of the surprising things at this contest was that although this idea of germs seems previously unused in physics, more readers told me it seems to be consistent with their own views. This is interesting, I'll have to check it in your essay. I like this "My model has universes within particles and particles within universes.". Good luck in the contest!

                Best regards,

                Cristi

                Dear Andrew,

                Thank you very much for reading and for commenting the ideas from my essay.

                You wrote "I would like it very much if you reviewed and commented on my essay, December 21, using this analogy to rate and review why I used John Klauders enhanced quantization. Awaiting your reply. i.e. this is a very relevant insight."

                You've probably seen my comment to John Klauder's essay. The standard quantization procedure works very well, and I think geometric quantization is based on a geometric structure which is not only elegant, but contains relevant insights, so I think that it (or some version of it like enhanced quantization) may be on a good track. But there are some reasons why I am not completely satisfied with it. I'll just mention one, which is that it starts from a classical system, and applies some procedure to get a Hilbert space and hermitian operators for the classical observables, while the only thing we know is the other way around, that the world is fundamentally quantum, and the problem is to obtain the classical limit at a "macroscopic" level. The major justification of this procedure is that it gives very good predictions. This may be enough for most people, because physics is about getting the right predictions. This is why I was sympathetic with Klauder's quantization, because even if it still starts from a classical world, it seems to me to enhance this relation. But I just heard about his theory, and I didn't dive deep enough into it to seriously understand its consequences. So I was interested from the beginning to read your essay as an application of Klauder's quantization (this is in addition of wanting to read it because I'm interested in what you have to say about what is "fundamental").

                Best regards,

                Cristi

                Hello Jonathan,

                Thank you for the kind comments. You said "have long been a fan of the Indra's net metaphor ...", to me it happened the opposite: I had this idea of holomorphism long time ago together with the idea of the central role of Clifford algebras (others had the idea long before me, we differ by approaches), but only last year I heard about Indra's net which seems a suited metaphor to illustrate this. I answered Andrew on his page. I have your essay in my reading list too.

                Best regards,

                Cristi

                If you do view my contest paper, it has reference#1

                http://vixra.org/pdf/1709.0438v1.pdf

                which has more wording on the relevant ideas wrt your mysical net than my highly-condensed contest paper. Figure A and pages 1 and 2 of the vixra paper show that I referred to braids (or universes) of three 4D colour dimensions and also referred to the braids as fibre optic cables. In some sense, these braids are analogous to fields whereas the jewels in the net are (to me, at least) analogous to particles.

                To come clean, my earlier draft of the document referred to balls of wool rather than optic fibres and I even have carried some strands of red, green and blue wool in my brief case for several years. But I deleted reference to wool to avoid comments about wool-gathering, woolly ideas and dropped stitches in logic. A mystical net is a much more presentable analogy than a tangled, random hotch potch of three balls of wool.

                My model is not mathematical but builds up SM particles using SM eigenvalues of fundamental properties. To do this one needs to gather the appropriate strands of coloured wool together, taking note to get the time directions of the strands correct, and tie them together using cotton to have the appropriate number and types of strands to make correct eigenvalues for whatever particle is being made. Repeat by making cotton ties for all particles in the block universe, or is that four block universes? In between particles we have strands of wool heading, as fields, forwards and backwards in time(s), to the next particle node, which demonstrates wave/particle/wave sequentiality. Likewise(?), in the mysical net the crystals reflect on each other.

                Wrt free will, it all seems gridlocked to me with puritan predestination unfortunately predominating.

                The cotton knots above imply particle decoherence to a point which to me seem like Penrose's CCC nodes, but for particles rather than universes. I wonder if the gridlock implies no free will across CCC cycles? That is, is the next CCC cycle already predetermined within the net?

                In a way, these colour universes remind me of nearby galaxies in space but the colour universes are nearby (and interwoven) compactified universes. I suggested that our spacetime [say a brown universe] is emergent and the three colour universes are more fundamental, but that could be an observer effect and really they are all equal partners. In a red spacetime their particles could appear as interwoven strands of green, blue and brown wool and they could claim the red universe was emergent.

                In a 16D block, is complex number algebra sufficient to allow analytic differentability to obtain probability amplitudes? Wrt being unhackable, distributing the mystical net data across four universes where each has its own 'spacetime' does seem a good way of protecting the data. One can only get probability densities in one's own (one of four) spacetime universe.

                Best wishes

                Austin

                In this essay I am talking about holomorphic functions, which are known for the complex case for long time and have this property of containing in each point the complete information about the whole function. I illustrate this with "Indra's net" as a metaphor, about which I learned many years after I became interested in Clifford holomorphic functions in physics. It is not like I have a mystical idea and try to implement it, it just happens that the holomorphic functions do this, so the metaphor seems appropriate. I don't need to add wires and cables to connect everything artificially. The main point here is holomorphism, and I don't think you are interested in this in your papers. As for free-will, I started to discuss it when I tried to explain my views on quantum mechanics as not requiring collapse, and some people were worried that this will rob them of free-will. I think that whether one thinks QM is deterministic or not, it is independent on having or not free-will, and this is what I explain. I tried to explain previously that randomness isn't freedom, and anyway even if quantum mechanics is deterministic (and has to be if there is no collapse), this is not against one's freedom, because the initial conditions of the system are co-determined by future measurement setups [Flowing with a Frozen River]. Maybe this looks to you like predestination, but to me is not. If you read that reference, The Tao of It and Bit, and The universe remembers no wavefunction collapse you can see that my motivation is to keep Schrodinger's equation, which works, but to explain what we think is collapse without introducing discontinuous collapse in the time evolution (which would break Schrodinger's equation, conservation laws, and relativity). Then you will see that it has nothing to do with "predestination", but maybe it will appear so to people who believe that the state of the universe is completely defined from the beginning. This is not my position. We may disagree, but I felt I have to clarify :)

                Best wishes,

                Cristi

                Just to clarify. I did say that at first I thought that your mystical net was an odd idea merely tacked on to your essay but somehow making it into the title. It took me five weeks to see how I could make it more prosaic by analogy to my own model. I personally am anti-mystic, anti-Tao-interpretation, anti-predestination, anti-theistic, anti-Bellist and anti everything which is not completely deterministic. Also I am anti the idea of having spacetime constructed of solid 'wires' just in the same way that I don't regard my path through spacetime as a continuous, solid wire. You introduced the mystic metaphor in this thread, not me.