Thanks Cristi, here's the skinny version...

Are you familiar with Steven Carlip's ideas on spontaneous dimensional reduction? He claims it is a generic feature of a broad class of theories. Seeing this same behavior; I assert that the Misiurewicz points in M teach us about dimensional reduction, with the specific point of focus in my recent work being the one location that appears to model pure gravity (and which turns out to have exact analytical solutions).

Accordingly; this point displays an analogy with Schwarzschild horizons, but also with BEC formation. At various times when studying that spot, varying the algorithm to reveal hidden details; I saw a clear resemblance to one or the other but was reluctant to make a linkage. Since discovering the recent paper by Dvali and Gomez, and follow ups; I've found a lot of work presses that BH event horizon/quantum critical point analogy. So I am now running with that.

Thanks for your curiosity, JJD

Hello again Cristi,

I hope you notice the hidden remark above answering your question 'how does this work?' in relation to the continuation of solutions through the horizon. I briefly explained the Misiurewicz point analogy. I have just learned too, from Bill McHarris, of a recent paper by Susskind treating gravity as a phenomenon of quantum chaos, which appears to have a strong analogy to the work I am presenting in my essay. This paper builds on other work by Shanker, Maldacena, and others on a quantum chaotic limit. It obviously ties in with the progression to chaos in the logistic map as I reference relating to M.

All the Best,

Jonathan

    Hi Jonathan,

    Yes, I did some research in dimensional reduction, and I know Carlip's papers. In many approaches to quantum gravity it appears to be one kind of another of dimensional reduction. Such approaches start with some assumptions which are intended to lead to something like this, to make gravity quantized by perturbative methods. I usually find these assumptions to be ad-hoc, in order to get the right result. My approach to singularities leads to dimensional reduction without other assumptions, and several of the other approaches follow from this automatically. One of the results that follow directly was previously obtained in the fractal universe by Calcagni (see refs in the linked paper). Maybe his approach, and other fractal approaches, can be of interest to you.

    Best regards,

    Cristi

    Hi Jonathan,

    Thank you for the details, this is interesting, although I don't know much about it. You previously mentioned dimensional reduction, this is something I researched, I replied to your comment above.

    Best regards,

    Cristi

    Dear Avtar,

    Thank you for the comments and for sharing your views, all these seem intriguing. Good luck with the contest!

    Best regards,

    Cristi

    Nice essay. Great to see Bohm's implicate order mentioned.

    Just a little point, on the attribution to Sontag of Time is nature's way of stopping everything happening at once. From John Wheeler's wikipedia page: "Time is nature's way to keep everything from happening all at once. Wheeler quoted this saying in Complexity, Entropy, and the Physics of Information (1990), p. 10, with a footnote attributing it to "graffiti in the men's room of the Pecan Street Cafe, Austin, Texas". Later publications, such as Paul Davies' 1995 book About Time (p. 236), credited Wheeler with variations of this saying, but the quip is actually much older. The earliest known source is Ray Cummings' 1922 science fiction novel The Girl in the Golden Atom, Ch. V: " 'Time,' he said, 'is what keeps everything from happening at once.' " It also appears in his 1929 novel The Man Who Mastered Time. The earliest known occurrence other than Cummings is from 1962 in Film Facts: Volume 5, p. 48".

      Dear Dean Rickles,

      Thank you very much for the comment! And for the information about the quotation about time, I didn't know about this, it's very interesting to see that it goes back to 1922! I'm happy to see that both Cummings' books are freely available online The Girl in the Golden Atom, The Man Who Mastered Time.

      Best regards,

      Cristi

      Hi Cristi,

      Fascinating general essay.I liked your questions about how to unify this gravitation with the geometry and Clifford algebras, like Hestnes you make a beautiful work.The indra net also corrélations are interesting, good luck.Best regards

        Hi Cristi:

        Congratulations. Excellent paper, well-written, concise, and thoughtful. Really enjoyed reading and agree with most of it. I have given you the highest grade it deserves. Below are some of my thoughts on and beyond what you have presented.

        I agree with your statement: "The relativity of fundamentalness implied by different axiomatizations and formulations is just epistemological fundamentalness. ......... Or maybe it is possible that something more fundamental than these exists?" Hence, the fundamental ontological reality must be beyond the selected frame of reference (axiomatizations and formulations) that biases the relative reality or ontology.

        What is fundamental is not a theory but the end state or physical reality it is supposed to depict or predict. A theory should be considered "fundamental" if the end state predicted by it is fundamental. Hence, we must define the most fundamental reality first, which in my view is the absolute Zero Point State (ZPS) that is invariant in space-time i.e. fully dilated with zero space-time. Since, a finite mass has a finite non-zero space-time, mass should also be zero in the ZPS. Such a fundamental state or reality would be immeasurable since it is absolute and not relative. A theory that predicts and bridges this absolute ZPS state with the relative (non-zero mass-energy-space-time) states of the comprehensible universe should be defined as the "Fundamental" theory. Remember, "Fundamental" refers to the predicted end state and not to the theory itself. You rightly state that quantum theories (QFT, EFT) predict arbitrarily large vacuum energy and hence are not fundamental.

        In my paper- "What is Fundamental - Is C the Speed of Light", I propose the missing physics of spontaneous mass-energy conversion (as observed in wave-particle behavior) that bridges the observed relative mass-energy-space-time states to the ZPS while resolving the paradox of the missing dark energy that is revealed as the relativistic kinetic energy, the paradox of the collapse of the wave function that is explained via transition to the classical space-time from the fully dilated space-time when a measurement is made, the black hole singularity of GR eliminated via mass dilation at small R, and solution to other current inconsistencies as well as weirdness of mainstream theories as described in my book.

        It is intriguing that in harmony with your described Indra's net, my model also depicts the universal reality as an ensemble of coexisting, complimentary (to the absolute, fundamental ZPS), parallel relativistic states corresponding to varying germs of mass-energy-space-time states of One Universe.

        I would greatly appreciate your time and feedback on my paper as to which of your criteria it satisfies?

        Thanking you in advance,

        Best Regards

        Avtar Singh

          Thank you Cristi...

          For your gracious attention and detailed thoughtful replies, you have my appreciation. I hope this excellent essay is among those awarded a prize. At this point; it appears certain you will be in the finals. You are more rigorous or thorough than I can be, your points make good sense, and they are well explicated. That would be three thumbs up, if I had an extra thumb.

          All the Best,

          Jonathan

          Hi Avtar,

          Thank you for the comments!

          You said "Hence, the fundamental ontological reality must be beyond the selected frame of reference (axiomatizations and formulations) that biases the relative reality or ontology.". Well said!

          Your other comments contain very interesting ideas as well, which I want to understand more, by reading your essay. Good luck with the contest!

          Best regards,

          Cristi

          Dear Cristinel Stoica, fundamental is what has Foundation. Physical space, which according to Descartes matter is the Foundation for fundamental physical theories. I'm here to urge researchers to develop theory everything of Descartes in the light of modern science. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where I showed how radically the physics can change if it follows the principle of identity of space and matter of Descartes. Evaluate and leave your comment there. Do not allow New Cartesian Physics go away into nothingness, which wants to be the theory of everything OO.

          Sincerely, Dizhechko Boris Semyonovich.

            Dear Cristi,

            Wow! (or maybe, as Neo would say in "The Matrix", Whoa!) What a densely packed, ambitious essay!

            As always, your present a lot of fascinating topics in interesting and insightful ways. I like how you state right away that it is hard to define "fundamental", and that, anyway, "reality tends to ignore our definitions"...

            Your analysis of the relevance of isomorphism to fundamentality is thought-provoking. By the way, nice illustration of isomorphism with the Sum 15/Tic-Tac-Toe example.

            I like how you frame the astounding weirdness of wavefunction "collapse": "the wavefunction spreads and interferes, but if you catch it, you catch the entire particle, not only that part of its wavefunction you thought was there."

            Nice discussion also of the relativity of fundamentalness, with the example of points vs lines.

            And now, for the main idea: the germ/seed that can unfold into an entire universe, or even a whole set of multiverses... Intriguing! In the same way that a holomorphic function car be recovered just by knowing the derivatives of all orders at a single point, the entire universe could be recovered from knowing everything there is to know at a given point... That's non-locality with a vengeance! :)

            I have to confess that, from the bottom of page 5 to the bottom of page 8, the density, complexity, and unfamiliarity (for me) of many concepts made it hard to follow your argument. I have downloaded your 2017 paper, "The Standard Model Algebra", and will certainly study it to get a better idea... I am fascinated by potential deeper-level explanations of the Standard Model, so I am looking forward to it.

            In your ambitious footnote 8 (on free will), you write:

            "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 here, and by this the state of the universe everywhere?"

            I find this intriguing, since it resonates somehow with my ideas about "co-emergence" that I presented in my essay in the last FQXi contest. You also write:

            "Or maybe each agent is free, but if their choices conflict with each other, then the germs of the two agents turn out to unfold in distinct universes, so again their choices don't conflict with each other."

            I also find this interesting, as it reminds me of the Q-Bism like idea that the Universe only makes sense one observer at a time (the theme of Amanda Gefter's fascinating book, "Tresspassing on Einstein's Lawn").

            In closing this already quite long comment(!), I have two questions concerning the last part of your article, "Indra's net" (lovely analogy, by the way!).

            1) You say that the information about the whole universe could be encoded at each point, in higher derivatives of the field at that point. By information, do you mean the laws, or the initial conditions as well? Or is it that the initial conditions are irrelevant because you are thinking of the whole universe as infinite, so every possible initial "local" condition happens infinitely often, so everything averages out to zero information overall in initial conditions?

            2) You say there is no need for a mechanism to unfold the state of the universe out of the germ, since the germ already contains everything that happens in the universe... Is it a similar claim than when someone who believes that the universe is a simulation says that there is no need for an actual computer to run the simulation, since the "consequences" of the simulation exist whether or not it is run?

            Congratulations once again for a strong entry. I am glad your essay is doing so well in the community vote, and I wish you good luck in the "finals"!

            Marc

              Hi Steve,

              Thank you very much! yes, Clifford algebras deserve more attention! Maybe next time you will join us with an essay.

              Best regards,

              Cristi

              Dear Dizhechko Boris Semyonovich,

              Thank you for the comments, this is very interesting.

              Best regards,

              Cristi

              Cristi,

              Three generations are ensured by topological combinatorics. {I was glad when the 4th-gen theorists were excluded years ago.} I tried to illustrate this with a trecoil band in three 'flavor' states. Of course it is massive (knew that back in 1992 when I first published the idea) and oscillates, too! A massive oscillating neutrino is VERY fundamental in the model constructed.

              Wayne

              Dear Marc,

              I appreciate very much your comments. Very insightful observations!

              Now your questions.

              > 1) You say that the information about the whole universe could be encoded at each point, in higher derivatives of the field at that point. By information, do you mean the laws, or the initial conditions as well? Or is it that the initial conditions are irrelevant because you are thinking of the whole universe as infinite, so every possible initial "local" condition happens infinitely often, so everything averages out to zero information overall in initial conditions?

              I expect the laws to be encoded in some generalization of the Cauchy-Riemann equations, and the particular solution (hence including the initial conditions) in the germ. This if the analogy with complex holomorphic functions will be proved to hold for the unified theory.

              > 2) You say there is no need for a mechanism to unfold the state of the universe out of the germ, since the germ already contains everything that happens in the universe... Is it a similar claim than when someone who believes that the universe is a simulation says that there is no need for an actual computer to run the simulation, since the "consequences" of the simulation exist whether or not it is run?

              I think there is a similarity between the two. Or rather with the block world view which contains the time flow in the frozen 4D universe. But I think there is also a major difference. I think that there is one thing, which we unfold when analyzing it say in terms of axioms and proofs, or initial conditions and time evolution, or program and simulation. The unfolding exists because we analyze this whole in a dichotomic way. This is what I mean by the relativity of fundamentalness, that there is something, which I could describe as the equivalence class of various isomorphic description, or more, as the mathematical structure underlying the description (you know the description is limited by the limits of provability and computability, but the mathematical structure itself, which we try to describe, is not. However, even the mathematical structure is in fact an equivalence class of more isomorphic structures). But who are "we"? We are just part of the whole too, so the whole is an implicate order, and at once it is numerous explicate orders which are perceived as such by the relative perspective encoded in each of the possible explications. So I think this goes way beyond having the output of a program encoded in the code in a file whether we run it or not, and doesn't require computability as in the case of simulations (which require computability even if we don't need to run them, that's why Tegmark asks these structures to be computable). Now the question is of course why do I claim I get rid of this requirement? Well, because I talk about automorphisms of the whole. Think for example at a vector space, and two distinct frames. Computation is involved only when we try to translate from one frame to another. Otherwise both frames simply see the same order in different perspectives, there is no need of computation if we don't compare them.

              Best regards,

              Cristi

              You are welcome,

              Yes perhaps I will do the next essay contest.At this moment I have serious problems in belgium and my mind is weak,best regards and good luck for this cntest, you merit a prize.Always relevant to read your works and ideas .Take care.

              • [deleted]

              Cristinel,

              It is a very ambitious essay, but I would like to offer a few counter arguments in defense of space.

              It is the nature of thought to distill signal from the noise, but might something be left out that is important, but not obvious? For instance, math overlooked zero for a long time, as it seemed to serve no function, so is physics possibly doing something similar with space?

              Supposedly space arises from geometry, but could it be in fact that geometry is mapping properties of space?

              For instance, the dimensionless point is the essential geometric concept, yet it is explicitly a multiple of zero, being dimensionless and consequently, mathematically doesn't exist. Would a dimensionless apple have any existence? Yet insisting on some minuscule dimensionality would make it a fuzzy concept, so it seems to be more intellectually pretty to make it a tiny bit mathematically contradictory, than to make it fuzzy.

              Yet what is being zeroed out, with no dimensionality, but space? What is a dimensionless point in the first place, if not an ideal of location? Which is spatial subjectivity.

              Consider that three dimensions are really just the xyz coordinate system, which is located by the 0,0,0 center point. As a subjective location, couldn't more than one center point exist in the same space? Much as billions of people, the originators of this system, are all the center points of their own space, but exist in the same space as all others. (Think how much political conflict is about applying different coordinate systems to the same space.)

              How about longitude, latitude and altitude? Are they really a perfect foundational framework for the surface of this planet, or just a very useful mapping device?

              Often it is assumed math exists as some platonic realm of order, but if it isn't and all order arose with the physical reality it describes and defines, would it be any different? If not, then wouldn't it be against Occam's razor to assume it does pre-exist the manifestation? Does the void need mathematical order, lacking any structure?

              So if we are looking for what's fundamental, wouldn't space be worth considering?

              Just a thought, but remember zero is between 1 and -1.

              Regards,

              John B Merryman

                John,

                Thank you for the comments!

                > "I would like to offer a few counter arguments in defense of space."

                I don't deny space, but I am interested in your arguments anyway.

                > "is physics possibly [overlooking] space?"

                I am not aware of physics overlooking space. I am aware of theories which claim that space is emergent, but for the moment I don't have any reason to endorse this position (and no definite reasons to refute it).

                > "Supposedly space arises from geometry, but could it be in fact that geometry is mapping properties of space?"

                Here I take the position of mathematicians, that geometry is space, or at least that it is about space.

                > "For instance, the dimensionless point is the essential geometric concept, yet it is explicitly a multiple of zero, being dimensionless and consequently, mathematically doesn't exist."

                I think that statements like "dimensionless point [...] is explicitly a multiple of zero" and that from this follows that it doesn't exist mathematically are uncommon among mathematicians. Mathematicians tend to believe that if something is a multiple of zero, then it is zero, and that zero (and its multiples) exist mathematically. Maybe you want to say that the measure of a point is zero, but even this is not true for all measures. And even if it is true, it doesn't follow from this that the point doesn't exist mathematically. This would mean that no region of space can exist, being collections of points. Or it would mean at most that all subsets of space are empty sets.

                > "Would a dimensionless apple have any existence?"

                You are mixing apples and oranges. First you talked about mathematical existence, then you illustrate that it doesn't make sense by giving as example dimensionless apples. In mathematics you can only talk about things you defined, or at least you defined them implicitly by axioms. Explicit definitions are of the form "genus-differentia", or by construction. Implicit definitions are based only on properties, on relations between things. For example, Modern formulations Euclidean geometry define points and lines by their relations (although Euclidus said things like "A point is that which has no part"). The question is, how do you define a "dimensionless apple"? It seems that the genus is "apple", and the differentia is "dimensionless". But the "differentia" reffers to how you distinguish an object from a particular genus, from the others from the same genus. The "differentia" has to be a property that some of the objects of the genus have. If none of them has that "differentia", the set of objects satisfying your definition is empty. So it doesn't make sense. It is as if you define "strictly positive negative numbers", there is no such thing. Then you say you proved a contradiction, but your proof is based on nonexisting (logically inconsistent) concepts.

                > "Consider that three dimensions are really just the xyz coordinate system, which is located by the 0,0,0 center point. As a subjective location, couldn't more than one center point exist in the same space? Much as billions of people, the originators of this system, are all the center points of their own space, but exist in the same space as all others. "

                Right, I agree. "Think how much political conflict is about applying different coordinate systems to the same space" this is true :)))

                > "How about longitude, latitude and altitude? Are they really a perfect foundational framework for the surface of this planet, or just a very useful mapping device?"

                They are a mapping device. Here's how mathematicians think about differentiable manifolds. They define them using charts. Charts are mappings of pieces of the manifold on some n-dimensional space R^n. These mappings are one-to-one between a region of the manifold and an open subset of R^n. The first rule is that the manifold is covered by these charts. The second rule is that on a region covered by two charts, the composition of one of them with the inverse of the other (which is therefore a mapping of an open region in R^n to another open region of R^n) are differentiable. We call such a collection of charts an atlas of our manifold. Then, we add all such charts which satisfy the rules to the atlas, and the result is called a complete atlas. Now, think at a region of the manifold, and all the charts on that region. Mathematicians say these charts are just mappings, we used them to define the manifold, but we don't take them as the region of the manifold. They consider as "real" what is invariant, so charts are just perspectives, not reality. What is real is the result. The composed charts which give a mapping between open sets of R^n are called transition functions, and they allow us to change the perspective. And they define isomorphisms between those open regions of R^n. So what is real to mathematician is the equivalence class defined by these isomorphisms. Mathematicians use charts to define the manifold, then they throw away the charts as being just some props to obtain the definition. They continue to use the charts for example to make calculations, they translate the properties of the manifold into statements about R^n, hence about numbers.

                So we see that the mathematicians agree that the charts are just mapping devices, but they disagree that the resulting manifold is a mapping device. An applied mathematician may use such a manifold to model some phenomena from another are of knowledge, and in this case the manifold is a tool too. But to geometers who don't apply geometry to something else, the manifold is not a tool, it is the ultimate object of their interest. So while even the hardcore mathematical Platonists will agree with you that charts are mapping devices, they would say that the manifold itself is real. They wouldn't say that they can prove it to you, but also you can't disprove them. So they are free to consider it real, and you are free to not consider it real.

                > "Often it is assumed math exists as some platonic realm of order, but if it isn't and all order arose with the physical reality it describes and defines, would it be any different? If not, then wouldn't it be against Occam's razor to assume it does pre-exist the manifestation? Does the void need mathematical order, lacking any structure?"

                Ockham's razor has two edges. The side you pick is that there is a physical reality, and there is a mathematical description of it. And if somebody believes both to be real, he has to explain a lot of things. Like why the behave the same, and then if they do the same things, why maintaining that the mathematical description is real and not a mere mapping device. (the same problem face Cartesian dualists with the mind-body problem) So you say let's use Ockham's razor to cut and separate the physical reality from the mathematical description, then discard the mathematical description as being something more than a mapping device. Someone who considers that the mathematical description is in fact the reality will agree with you to cut them exactly in the same place with Ockham's razor. The only difference is that she will discard the "physical reality". Your choice is motivated by your experience that physical reality is always there, while mathematics is in books. And you don't have to explain why the mathematics describing the physical world is isomorphic to the physical world, it is so by design, duh! But the "platonist" (this is not in fact what platonist means, but let's use it this way) would say that we have to objects doing the same thing, the physical reality and the mathematical structure. She knows very well what is a mathematical structure, but she doesn't know a definition of physical reality. So why not discarding physical reality and keeping the mathematical structure? Now the physical realist may say "but it is obvious that there is a physical world, here it is, I can experience it, I can taste an apple, qed". The mathematical realist may say "we only know about physical reality by our interactions, so what we know are not the physical objects as things-in-themselves, but our relations with them. So all there is experienced is relation. And a mathematical structure is nothing more than a collection of relations (see Universal algebra). We can't probe anything beyond the relations, hence the world is a mathematical structure. One may say though that we can keep as real the physical world and discard the mathematical structure as being a mere representation. But this is not a representation as the usual mathematical models. If you want to makea mathematical model of an apple, you will have to do a lot of complicate mathematics, and the result will be approximate. But a mathematical description of the physical laws makes our knowledge redundant. All phenomena are contained in the principles. Hence, the mathematical formulation of principles is not a mere model, because it is much more compact than the thing it models. This is why I choose to discard anything outside that mathematical structure." She may believe or not that the other mathematical structures exist physically too, but if we apply again Ockham's razor to keep the simplest option, which one you think is the simplest, the principle "all mathematical structures have physical existence", or "only the mathematical structure defined by [insert the mathematical formulation of the final theory of physics] has physical existence"?

                > "So if we are looking for what's fundamental, wouldn't space be worth considering?"

                Sure, and this is what I do (more precisely spacetime). If you look at my research papers you will see that they are about spacetime. Understanding singularities in general relativity, researching the possibility to make collapse consistent with the symmetries of spacetime, these were my main themes, and the other ones where I published less are also about spacetime. Yes, I know I said everything, including spacetime, is contained in the germ. So is this denying spacetime? I would say not. Holomorphic functions don't deny the domain on which they are defined. The domain is encoded in the germ at any of its points, but this doesn't mean that that domain doesn't exist. It only means that one of them is as real as the other.

                > "Just a thought, but remember zero is between 1 and -1"

                I can't. Zero is between -1 and 1.

                Best regards,

                Cristi