Dear Cristi Stoica,

You wrote: "The universe is rich in complex phenomena and situations of infinite diversity, yet somehow we seem to be able to understand it to some degree, at least partially, in terms of a small number of laws and concepts."

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists 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.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

    Hi Wilhelmus,

    I am happy you enjoyed reading it, and I appreciate your comments. I look forward to read your essay, especially since you point out that our essays have so much in common.

    Best wishes,

    Cristi

    Dear Joe Fisher,

    Glad to see your comments here. From what you wrote, it seems that we share the idea that there is only one unified thing that is fundamental, even though maybe they don't look the same.

    Best regards,

    Cristi

    I wrote the following on mt blog area in response to your poar:

    This quantum hair would show up in BMS supertranslation symmetries. I have not worked out more detailed calculations of this. In fact there is a vast amount of work to be done here. In working on foundations I offer here the prospect for some measurement or observation of what might be deeper foundations.

    Of course in the end there may be no final foundation, or if there is such a foundation I suspect it is basic quantum mechanics. We might be faced with the prospect of finding layers of effective theories with respect to quantum gravity. The reason might be that quantum gravity is similar to the measurement problem and might involve self-referential encoding of quantum states. The issue of the quantum error correction problem I offer a solution involving complementarity between quantum and spacetime principles. However, this might just mean it ends up in the same conundrum as quantum measurement. Ultimately it involves quantum states encoding quantum states. Turing and Gödel rise to the occasion to tell us we can never completely understand this.

    Cheers LC

      Hi Lawrence,

      Thank you for the interesting details, I find this indeed difficult and needs much work. I wish you success with this research in the following!

      Best wishes,

      Cristi

      Cristi,

      Another good piece of writing taking an interesting and, so far, unique approach. I agree and share the Christian Huygens and Bill Unruh (to an extent) approaches. Certainly relative motion through and with respect to some medium (whether condensed 'matter' or not) propagates more quanta to re-quantize signals - the effects, consequences & implications of which is what my own essay explores & identifies. (You'll see non-integer spin is also physically derived!)

      We don't agree on all things but rightly agreement is NOT a scoring criteria. Yours is well considered and written, and also an interesting approach. I particularly agree the last p9 line and my work focuses on that.

      Well done. Up to your usual standard and provisionally down for a high score. I do hope you'll study and discuss the conclusions of mine.

      Very best

      Peter

        Peter,

        I appreciate your feedback, and I look forward to see your essay (especially to see how you got non-integer spin). Good luck with the contest!

        Best regards,

        Cristi

        Dear Cristi Stoica,

        a very interesting essay, thank you for sharing it! I appreciated very much your analysis of Relativity of fundamentalness ("We can regard points as more fundamental, lines being just sets of points, or we can regard lines as more fundamental, points being the meeting points of lines", it's a wonderful example). My essay has many points in common with the first part of yours.

        I've not fully understood how you consider this relativity only epistemological and how Holographic fundamentalness can escape such a relativity, but sadly I've not the mathematical tools to evaluate the final part of your essay, due my formation in philosophy.

        Thank you again, all the best,

        Francesco D'Isa

          Very profound contribution; pointing to holistics as fundamental structure makes great sense, esp. to better approach the universal laws of harmony in matter and living matter.

            Dear Cristinel Stoica,

            thank you for this thorough and insightful essay. It is clear and well written.

            I have also written an essay that have some points of similarity with yours, showing to some extent the limit of intuitive reductionism. I therefore appreciated your quantum holism. I would be grateful if you also give me your opinion on my ideas.

            A major difference that I see is that I feel that relying too much on the mathemantical structures, we could fall into conventionalism, devoid of empirical content.

            While waiting for your kind response, I have (already some days ago) I rated you the best.

            I wish you success with the contest!

            Best wishes,

            Flavio

              Dear Francesco D'Isa,

              Thank you for your comments, and for pointing me to some points that may be of interest to me in your essay. I look forward to read it.

              > I've not fully understood how you consider this relativity only epistemological and how Holographic fundamentalness can escape such a relativity, but sadly I've not the mathematical tools to evaluate the final part of your essay, due my formation in philosophy.

              I don't think this relativity of fundamentalness is only epistemological, I think it is the fundamental key. Holomorphy is not meant to escape epistemological fundamentalness, by contrary, it is the logical end where you arrive by taking seriously the ontological fundamentalness, if the final equations that we will eventually find have this property. If they don't, I think holomorphic fundamentalness is at least a way to grasp this idea that the ontology itself is relative, which is a feature of all mathematical structures, because of the isomorphism I mention. Thanks again for your comments,

              Best wishes,

              Cristi

              Dear Stephen,

              Thank you for your kind words. I look forward to arrive at your contribution, and I wish you success in the contest!

              Best wishes,

              Cristi

              Dear Flavio,

              I very much appreciate your comments. I noticed your essay, and I hope we will discuss soon more, since there are some very interesting points you two made.

              > A major difference that I see is that I feel that relying too much on the mathemantical structures, we could fall into conventionalism, devoid of empirical content.

              Well, here may be more to discuss. If there is something I trust in this world, there are two things, one being mathematics. I think that the universe is mathematical, in some sense that I discussed in a previous essay And the math will set you free. But I am fully aware of two things: that our mathematical models are not well understood and most likely they are not that mathematical structure that I say is the universe, and that there are limits of our mathematical reasoning (not of mathematics itself). I detailed these limits in my last year's essay The Tablet of the Metalaw.

              I agree with you that "relying too much on the mathemantical structures, we could fall into conventionalism, devoid of empirical content". But the problem is that we don't rely enough, in the sense that modern theoretical physics is made of patches of mathematical models. The most interesting parts are revealed when there are inconsistencies, internal, between our models, or between our models and the world, and it is there where I think we should dig most (I focused a large part of my research on such inconsistencies, such as the singularities in general relativity and the apparent need of collapse in quantum mechanics. And in finding better models for particles than the conventional ones). If we look back, we see that the novelty in physics is due to pushing our mathematical models to their consequences. This either lead to their rejection, or to novelty and unconventional. For example, the inconsistency between the symmetries of electrodynamics and Galileo transformations led to special relativity. GR was even less conventional, and is full of empirical content. QM, starting from a couple of experimental hints that showed inconsistency with the classical models, led to this rich quantum world as we know today. Both GR and QM are the highest unconventional, and they are indebted to mathematics. But I would say the way to hell is the same as the way to heaven, and this is mathematics. When people went for perfect mathematical consistency and simplicity, they found radical new ideas. When they went for patching the world with models, or for complicated Rube Goldberg machines, we ended in the current crisis. But this is inevitable, since we don't know the ultimate model, and we try what we hope it is, so there is a large pool of models to explore, but by the end we will throw most of them away and keep the one model (or a bunch of isomorphic ones) which is the accurate description of physics, without deviation from the empirical data. That's why I think we should do it, but with much care, and never trust a model which has inconsistencies, internal or wrt the experiment.

              I look forward to read your essay, and I wish you two success in the contest and your academic careers!

              Best wishes,

              Cristi

              Dear Cristi,

              you raised my curiosity more and more. How holomorphic fundamentalness can take seriously the ontological fundamentalness? Can't be itself relative?

              You write that, "If this will turn out to be the case, then the information about the whole universe is encoded at each point, in the higher order derivatives of the eld at that point. So the state of the universe, including the germs at all the other points of spacetime, is encoded in the germ at each point of spacetime. Not only the eld, but also spacetime itself emerges from each germ". Are your germs (or "points") something like Leibnitz monad's (they are quite similar to Indra's myth, after all). Is the ontological relativity you are talking about similar to Nagarjuna's?

              Excuse me for my questions, I can be very wrong since I can't evaluate your mathematical proposal.

              bests,

              Francesco

              Dear Francesco,

              Analytic functions and fields, in particular holomorphic functions, have the property that if you know all the (partial) derivatives at any point, they determine the value at any other point. Take for example a real analytic function like a polynomial P(x), where x is a real variable. The derivatives at x=0 allow you to determine the coefficients of the polynomial, and then you can determine P(x) for any other point x. And this works as well with the exponential, sin, cos, etc.

              Now complex holomorphic functions also are analytic, but they are more than this. So why I picked them and not just analytic functions, which would give me more chances to prove this? It is because equations in mathematical physics can have in general non-analytic solutions, but in the case of the Cauchy-Riemann the solutions can't be non-analytic.

              Holomorphic fundamentalness means that everything about the field is encoded at any point of spacetime you choose, but the same data is encoded, differently, at any other point. Here is where the relativity of such fundamentalness is, because there is no special point of spacetime. Now why I say this relativity of fundamentalness is not merely epistemological, but also ontological? Because no matter what is the ontology of your theory, that ontology at a single point contains everything. But since you are free to choose the point, the ontology at any other point also contains everything, encoded of course differently, because the partial derivatives of your fundamental field at the other point are different. So, if there is an ontology, and this is governed by universal laws, that is, they are the same everywhere (which is the basic assumption in physics), and if the fields describing the ontology are analytic, they will have this property of ontological holomorphic fundamentalness. In fact, I think the epistemological aspect will not work in practice, because you can't know all the derivatives at a given point.

              Note that by "ontology" I don't mean what one usually means, some stuff that is like what we think matter is from our daily experience. I see it more like a mathematically consistent stuff that is real but who's state is not defined prior to observations, and it becomes more and more defined as we add more (quantum) observations. But I also see it in the ways I described in this essay. I couldn't expand much this view in this essay, but I introduced the ideas gradually in the previous essays. This feature of reality of becoming gradually defined (but not gradually real) is in these essays Flowing with a Frozen River and The Tao of It and Bit. The latter introduces a bit to how I see the mathematical universe, which I expanded more in And the math will set you free. And in The Tablet of the Metalaw I continued a bit more with some ideas related to the hard problem of consciousness and some relative ontology which I will discuss later. What I wrote here is how I view the things for cca 25 years, but I introduced them gradually in my FQXi essays, which can be seen both as a series and as stand-alone.

              About Leibniz's monads and Nagarjuna's relativity, I guess we can make some connections, but I don't want to claim they are all the same. In fact, even the "Indra's net" idea I see it more like a metaphor, because I can't say that it meant exactly the same (and I only found out about it many years later I had the idea of holomorphic fundamentalness, when I told it to a friend and he mentioned Indra's net). Nagarjuna's relativity of existence vs nonexistence, where he states that all things exist/don't exist/both exist and don't exist/neither exist nor don't exist, can be compared to some things I said or where said in physics. While a common understanding is that he was an anti-realist, I think this is an oversimplification. So here are some possible connections. It can be applied to wave-particle duality in quantum mechanics. But I would rather apply it to the existence of a definite state of reality. I would apply it to the idea I explored in previous essays, that the universe is mathematical (in a sense which I tried to make clear how is different from Tegmark's). In The Tablet of the Metalaw, section "Why is there something rather than nothing", I propose that the only things that exist are those which can't not exist (here it can be paralleled with Leibniz's Contingency argument, but I think there are some essential differences), and that only mathematics and logic have this feature. But I can't say that subjective experience is reducible to mathematics, so I would say rather that there is some thing that is mathematical but also semantic, in the sense that it has embedded the 'sentience' at the origin of our subjective experience, for which the mathematical structure has the meaning of a universe. Also relativity of fundamentalness, which is both epistemological, and ontologic in the sense I mentioned, also can be connected with Nagarjuna's in some sense: if only what's fundamental exists, and what is derived doesn't, then his relativity is entailed by mine because I claim that the distinction between what's fundamental and what's derived is relative. But such ideas are open to interpretations, so I only want to point out some connections, not to claim that what I said confirmed what he said or the other way around.

              Best regards,

              Cristi

              Dear Cristi,

              In your approach, I miss the efforts of Garrett Birkhoff and John von Neumann to establish a fundament that emerges into a suitable modeling platform. In their 1936 paper, they introduced a relational structure that they called quantum logic and that mathematicians call an orthomodular lattice. It automatically emerges into a separable Hilbert space, which also introduces a selected set of number systems into the modeling platform. Hilbert spaces can only cope with division rings and separable Hilbert spaces can store discrete values but no continuums. Each infinite dimensional separable Hilbert space owns a unique non-separable Hilbert space that embeds its separable partner. In this way, the structure and the functionality of the platform grow in a restricted way. After a few steps, a very powerful and flexible modeling platform evolves. This model acts as a repository for dynamic geometric data that fit in quaternionic eigenvalues of dedicated operators. The non-separable part of the model can archive continuums that are defined by quaternionic functions.

              In other words, the foundation that was discovered by Birkhoff and von Neumann delivers a base model that can offer the basement of well-founded theories and that puts restrictions on the dimensions which universe can claim.

              Multiple Hilbert spaces can share the same underlying vector space and form a set of platforms that float on a background platform. On those platforms can live objects that hop around in a stochastic hopping path. This adds dynamics to the model.

              The orthomodular lattice acts like a seed from which a certain kind of plant grows. Here the seed turns into the physical reality that we perceive.

              Stochastic processes generate the hop landing locations and characteristic functions control these processes. These characteristic functions are the Fourier transform of the location density distribution of the hop landing location swarm that represents the elementary particle.

              This delivers the holographic control of these elementary modules. Also higher level modules are controlled by stochastic processes that own a characteristic function.

              See: "Stochastic control of the universe"; http://vixra.org/abs/1712.0243 Indirectly via the characteristic functions the universe is controlled in a holographic way.

              The Wikiversity Hilbert Book Model Project investigates this approach.

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

              http://vixra.org/author/j_a_j_van_leunen contains documents that treat some highlights of the project.

                Dear Cristi;

                This an elegant mathematical formalism for establishing the fundamental structure and laws of the physical world, based on the underlying assumptions of what is the nature of Space (what mathematical formulation, topology, is isomorphic with the real physical space), Time (what is the nature of time, where does it stem from, its properties, how it relates to space, etc. Avoiding all tautological ideas and explanations). It is not taking into account these underlying assumptions what limits your approach.

                I think your Mathematical Formalism will be very valuable once physics gets out of the maze in which it is trapped. You could have a glimpse of what I am pointing at by checking the summary of these problems I make in my essay. There I start by establishing the general concept of "Fundamental". Then I summarize an epistemological critique of the practice of theoretical science, where it is demonstrated the inadequacy of the ways science constructs the fundamental concepts for studying the fine grain of reality. Afterward I propose an expansion of the scope of physical science to include the aspects of reality that cannot be observed directly or indirectly. Then I discusses the concepts of SPACE, DISTANCE,TIME, INERTIA, MASS AND ELECTRIC CHARGE, and develop new concepts for each of these scientific parameters; redefining them in ways that allows the determination of whether or not they could be categorized as Fundamental

                  Dear Cristi,

                  thank you very much, you was very clear and your essay worth for sure my high vote. I read your essay "The Tablet of the Metalaw" as well, and found it very interesting.

                  You wrote that "Holomorphic fundamentalness means that everything about the field is encoded at any point of spacetime you choose, but the same data is encoded, differently, at any other point. Here is where the relativity of such fundamentalness is, because there is no special point of spacetime.". When you talk about "points" do you intend a discreet or continuous space-time?

                  Moreover,

                  (This is partially OT because referred to "The Tablet of the Metalaw", but it's really interesting for me because of the themes of my essay)

                  In the paragraph "Why is there something rather than nothing?", you write both that constituents and laws of physics could be different, while mathematical laws (i.e Euclidean geometry) are necessary because consistent.

                  I wonder if these laws could be different, like the others previously mentioned - even if it's harder for us to imagine. What if logical rules were different, for example? We can't imagine such a scenario, but why not: even logic is relative to a set of rules that WE find obvious and self-evident. After all, once we define a set of rules, everything within the rules can be consistent (or not) relatively to them.

                  Thank you again for sharing your writings and time,

                  Francesco

                  Dear Francesco,

                  Thank you for the reply. You asked

                  > When you talk about "points" do you intend a discreet or continuous space-time?

                  The notion of holomorphic functions or fields makes sense in a differentiable space, so in this case in a continuous spacetime. I guess it may be possible to make some model that contains everything in each point of a discrete spacetime, but I think it will be artificial. But who knows?

                  > I wonder if these laws could be different, like the others previously mentioned - even if it's harder for us to imagine. What if logical rules were different, for example? We can't imagine such a scenario, but why not: even logic is relative to a set of rules that WE find obvious and self-evident. After all, once we define a set of rules, everything within the rules can be consistent (or not) relatively to them.

                  Well, I just said there must be a mathematical structure, but not that we know it. When I said this I referred to new mathematics, but not new kind of mathematics which would be based on a different logic. Reading your essay I understand why you are interested in different logics, and there are many known non-classical logics. What's interesting is that these logics are mathematical structures, and the rules of deductions applied to derive theorems about such models still are the classical ones. An example is mentioned three comments below, Hans van Leunen's comment about quantum logic.

                  Best wishes,

                  Cristi

                  Dear Cristi,

                  thank you for reading my essay and for your insightful comment, I need some time to reply, since I want to read your other essays as well :)

                  You write that

                  > The notion of holomorphic functions or fields makes sense in a differentiable space, so in this case in a continuous spacetime. I guess it may be possible to make some model that contains everything in each point of a discrete spacetime, but I think it will be artificial. But who knows?

                  That's interesting and I intuitively agree, but it would pose the scary idea of the infinite in your model, with all its paradoxes - but I think that to manage with infinite is a necessary task. I suppose that you consider an infinitesimal unit different from zero.

                  > Well, I just said there must be a mathematical structure, but not that we know it. When I said this I referred to new mathematics, but not new kind of mathematics which would be based on a different logic.

                  That's more and more interesting, but if we include the possibility of different mathematics and/or logics, why don't suppose an infinite range of them? After all our capacities are limited, and if we can conceive more than one logic, there could be many more out there. Proceeding like this, the "universe" (in an ontologic sense) becomes very very crowded... a weird conclusion indeed - that sounds resonable to me.