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.

      Dear Hans,

      Thank you very much for your comments. I appreciate quantum logic and the efforts of von Neumann and Birkhoff, and your description is most welcomed. However, I don't feel the need to include it in the discussions of foundations of quantum mechanics, not because they are wrong, they aren't, and neither because they it is not important. Quantum logic is simply a different way to formulate quantum mechanics. I don't think my arguments miss something by not including it in this limited essay about foundations :) You can take any paper or essay and say that maybe they should've cite some important work or another, so what, it has to be a reason to include it. I wish you success with your essay at this contest, I added on my to read list.

      Best regards,

      Cristi

      Dear Diogenes,

      Thank you for your comments and for your suggestions. I wish you good luck with your essay!

      Cristi

      Dear Francesco,

      > 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.

      I am not aware of any problems with the continuum in mathematics. If you mean Zeno's paradox, this was solved since antiquity, and modern mathematical analysis doesn't have such problems. I know some people claim they have them. Even Rovelli (and I would say I agree with him that the world is relational, and LQG quite a smart thing), in his book "Reality is not what it seems". He spends the entire book claiming that the continuum has problems, like Zeno's paradox, without discussing the solutions, which actually are known for long time. I mean, take the arrow paradox, it is not ok to say that space has to be divided, but avoid dividing also the time :). And that book has other arguments which simply are not true, like the one with Schrodinger's atom, which by the way, works because of continuum. It is funny because even in Loop Quantum Gravity they sum over all the discrete spin networks and take the continuum limit, but he mentions this only in a brief paragraph in the book. In fact I discussed this with Ashtekar, and he clearly endorsed both the continuum view, and a continuous spacetime on which loops or spin networks live. Also see this talk and the questions from the audience and his answers.

      Yes, in physics there are two major problems of infinities: singularities in general relativity, and the infinities you get in quantum field theory and especially quantum gravity if you do the calculations perturbatively. Singularities in general relativity are due in fact not to the theory, but to the way we wrote the equations, see Did God Divide by Zero? and the references in the essay to my papers in which I show this rigorously. The infinity in quantum theory are due to the fact that the best method currently known to physicists to do the calculations is perturbative expansion, which is not defined mathematically. So I think the universe doesn't do its calculations like this :) But if we insist to do it like this, then we should treat the particles as singularities as I explained in the papers I mention, and you get rid of infinities in the quantum case too (see this article).

      I don't claim that the world is not discrete, maybe it is. But I don't know of a discrete theory that does the job even remotely close to our continuum theories. The only reason they are researched is because they can be used to cut-of those infinities, but they are because of our methods, not because of continuum.

      > if we include the possibility of different mathematics and/or logics, why don't suppose an infinite range of them?

      I don't say that all of them describe our universe. Only one mathematical structure, in fact the equivalence class of all mathematical structures isomorphic to this one. The others may describe other universes a la Tegmark. If our universe is described by an infinite range of theories which are not isomorphic, then they are approximations that converge to the correct one.

      Best regards,

      Cristi

      Dear Cristi,

      > I am not aware of any problems with the continuum in mathematics.

      As far as I know, I agree with what you say about Rovelli and mathematic. I was talking about possibile paradoxes when the infinite is applied to physics, but I can't say if they are solvable or not, since I've no preparation in the matter. It just happens that the infinite leads to some very counter intuitive situations if applied to the physical world, like the Hilbert's hotel, or infinitesimal length of time or space (are they zeros?) - but counter intuitive doesn't mean false.

      > I don't say that all of them describe our universe. Only one mathematical structure, in fact the equivalence class of all mathematical structures isomorphic to this one. The others may describe other universes a la Tegmark. If our universe is described by an infinite range of theories which are not isomorphic, then they are approximations that converge to the correct one.

      I understand and agree :)

      Dear Cristinel Stoica

      "This essay goes beyond these, by proposing a type of fundamentalness as a mathematically consistent basis for these forms of holism, the physical laws, and the ontology of physics." Your imagination is wonderful using Indra's Net and connecting Holomorphic Fundamentalness dear Cristinel Stoica..................... very nice idea.... I highly appreciate your essay and hope for reciprocity.

      I request you 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

      Hi Christi,

      Thanks for your kind comments on mine, and informing me that my post above has gone! It was posted on the 18th but I don't have a copy. I've mailed Brendan (also noting the problem with time at the top of each essay - we've slipped back a year!)

      I have yours down for a high score but recall I had some questions. I'll check it again if needed & revert.

      You didn't seem to notice or comment on the main important new finding in my essay, but I don't know how up on QM you are. I hope you read Declan Trail's short essay with the computer code alongside it.

      Very Best

      Peter

        Hi Peter,

        > but recall I had some questions

        Not in your comment

        > You didn't seem to notice or comment on the main important new finding in my essay, but I don't know how up on QM you are.

        Don't take this personally, I gave up discussing here proposals of "fixing" quantum mechanics by making it classical years ago. Let's just say we disagree.

        Best,

        Cristi

        About revolutionizing Physics

        The FQXi contests provide some topics to discuss which I always find interesting, and I like to engage in exchanges about the main theme. Every time the contest is announced, a warning like the following is made "While this topic is broad, successful essays will not use this breadth as an excuse to shoehorn in the author's pet topic, but will rather keep as their central focus the theme of the contest." But one of the central attractions of this contest are everyone's foundational views, particularly those pet theories. And I agree that the rule is not to avoid them, but to focus on the theme, so if your pet topic is relevant to addressing the questions of the contest, then of course it should be there. I do this, in my essays I talk about my work, as long as it is relevant to the topic. Otherwise I prefer the standard platforms, which are publishing peer reviewed articles, and attending conferences.

        There are some recurrent such "pet topics" though, which usually don't find their way in good peer reviewed journals and conferences. They usually deal with disproofs of the theory of relativity, or of essential aspects of quantum mechanics. These theories are considered well-verified and solid by most physicists, so this is why they don't spend time indefinitely discussing them. It is not that they are brainwashed, it is just that they spend much more time with these theories, they know how well are tested, they did countless times the mathematics, and they know how well they explain the world from a small number of basic assumptions.

        I am a strong supporter of the idea that we should come back from time to time to question each of the basic assumptions of our theories, but at the same time we can't discuss the same arguments over and over, we also need to advance. To be more specific, I confess that as a kid, when I first read about relativity and quantum mechanics, I was very shocked, and I tried to find a more acceptable explanation for both of them. I turned them upside down in many ways, trying to figure out how I can get the same experimental results out of less shocking or less counterintuitive principles. I'm not ashamed of it, in fact I recommend it to be done by every future researcher. I consider that one should question everything. Of course, this is not feasible nowadays, because there's so much to learn, and if you want to do research, you need to progress very quickly with your understanding. But I still think it is necessary to start by questioning everything, and you should never stop.

        Now here is a trap though, because sometimes you get caught in a loop in this process. You may end out spending your entire life trying to disprove "mainstream" physics, motivated by a wrong vision. To get out of this circle, you need to question not only the standard assumptions, but also your own. But it is tempting not to do this, because what could be more gratifying than disproving Einstein or at least quantum mechanics? People endowed with brilliant minds, with great critical thinking when dealing with other areas where they didn't bet as much, can get caught in this trap. I won't say they should do something better, because I consider as fundamental ethical principle that everyone should be allowed to have their best experiences, and working at really important things is one of them.

        I had my share of such discussions of the foundations, where I was in the position to play the role of the "defender of the status-quo". Actually I didn't see myself like this, I was under the impression that we discuss honestly about some ideas, no matter how well-established they are considered. So I tried to explain why relativity works, why quantum mechanics is as it is and is not classical. Let me make a parallel: imagine you invented a mechanical device that would give you energy for free, by spinning forever. You know you can't discuss this with physicists, because they would say that the energy is conserved, period. And they are right. But I also know that by trying to explain why various perpetual motion devices didn't work, sometimes in the history we arrived at better understanding of physics. They still didn't work, but at least there was a gain. So I used to allow myself to engage in such discussions, in the idea that I can help a person escape this prison, and learn something in the process. But it was pointless, there was never a gain. And when people try to refute Bell's theorem the things are even clearer. While we can still imagine the possibility that energy is violated, considering that our theories are an approximation of the true physics, with Bell's theorem the things are different. Because Bell's theorem is a theorem. Trying to refute it is like trying to find in Euclidean geometry a right triangle which violates Pythagoras's theorem. It is simply impossible. Now, I'm not quantum police to try to show everyone's how illegal is to violate a theorem, but I just no longer want to be part of such discussions, because I have limited time. And I saw tons of disproofs of special relativity and Bell's theorem. A recurrent disproof is to take a very special setup, where Alice and Bob measure the spin along the same axis, and to assume that the two entangled particles have some definite opposite spin directions, not perpendicular to the direction along which Alice and Bob measure, and that instead of Born's rule each spin simply projects to the axis in 3D. To anyone who studied EPR and Bell's theorem is obvious that in this case you get the same result as in classical physics, because it is exactly classical. The real problem, usually not mentioned, is the general case. So limiting to this case doesn't solve the problem, no matter how fancy graphics one makes using a modification of a script I wrote in 2011.

        Bell's theorem has a hypothesis, consisting of two assumptions, and a conclusion. The conclusion is an inequality, which is satisfied in classical physics, but not in quantum mechanics. Since our universe is quantum, it means that one of the two assumptions is wrong. The two assumptions are (1) all interactions are local, and (2) the initial conditions of the systems in this game are statistically independent. It is a widespread opinion that condition (1) is violated by nature, but it is also possible that (2) or both are actually violated. So while there are still many quantum theorists who claim it makes no sense to discuss what happens with a particle between measurements, some of us want to know. And if you want to know, you have to choose what to sacrifice, (1) or (2), but it is not possible to save both. Just like it is impossible to have in Euclidean geometry a triangle which violates Pythagoras's theorem, and to maintain that the triangle has a right angle.

        The guy with the perpetual motion device may insist that it works, and when proven it doesn't, he may think that he can change this or that and still make it work. Many discussions I've had so far about relativity and quantum mechanics were just like this, as being caught in a loop. This is why I decided years ago to no longer engage in such discussions, with the risk of missing the opportunity to witness the birth of a new revolution in physics. I'd rather spend my time with my own pet theories :) In the foundations of quantum mechanics, I prefer to keep (1) as true, and sacrifice (2) (1, 2, 3, 4, 5).

        As for the contest, I see that some essays feature such ideas, and I think it is a good place to discuss them, but I prefer to focus on the part related to the current topic in my feedback, and to evaluate them solely by this.

        Success to everyone in this contest, and may we all have enlightening exchanges of ideas!

        Cristi

        Dear Cristi,

        Once again, you wrote a remarkable, original and entertaining Essay. Congrats!

        Here are some comments:

        1) I did not know the game called number scrabble. It is the clever version of a game that we call "Tris" here in Italy. I will try to play it with my son (who is developing a mathematical mind) in next future.

        2) I see that you referred to the arXiv version of your paper "The Standard Model Algebra"(which is the basis of your proposal of holomorphic unification). I downloaded it and I have seen that it is a strong work. Are you planning to publish it in some journal?

        3) Concerning the open questions of your model, in general, I do not like the idea of extra dimensions. Instead, it will be intriguing if the complex 6-dimensional vector space really arises from from the geometry of space-time. In that case, I feel that he could really be connected with a geometric unification of the Standard Model with gravity and with gravity quantization.

        4) Finally, I find the metaphor of Indra's net very elegant, as well as your whole Essay.

        Congrats again and good luck in the Contest.

        Cheers, Ch.

          Dear Christian,

          Thank you very much for your very kind comments, and for the really relevant questions. I loved very much your essay as well. About your questions:

          (2) Currently is under evaluation at AACA, which is specialized in Clifford algebras. I submitted previously at some of the top particle physics journals, but it was rejected without review, because "it is too mathematical for our profile" or simply "it doesn't fit our target audience". I've got only one review, which was positive (but the editor rejected it anyway), and the reviewer suggested that my manuscript will be better understood if I submit it to AACA, and if I can present it at a conference they had last summer. I was lucky to get accepted even though the deadline was a few weeks before. I've got positive feedback at some good conferences including the AACA one, some from experts working at GUT or with Clifford algebras.

          (3) I absolutely agree with you, and this is part of the "future plans" I mention in the last section of the paper. I don't assume extra spacetime dimensions, but indeed the Clifford algebra corresponds to a larger complex 6-dimensional space, and this algebra contains the required degrees of freedom for one generation plus gauge fields. So one of the long-term objectives is indeed to derive it from the geometry of spacetime, and I actually made some progress here, obtaining this from geometry. I didn't write a paper about this because at this point I actually found more possibilities, and I try to see which is the most natural, based on as few assumptions as possible. I will be satisfied with the one which will give the Einstein equation with the stress-energy of the SM Lagrangian. Other criteria include, of course, to have not only one generation, but three, and if possible SM parameters like the mixing matrices. And I agree with you about the quantization, for which I have some plans too. I am very motivated by "Herr Doktor"'s dream to obtain everything from geometry :) (and topology).

          (4) Thanks again!

          Best wishes,

          Cristi