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RECENT POSTS IN THIS TOPIC

Cristinel Stoica: on 3/13/18 at 11:08am UTC, wrote Dear Sylvia, I appreciate that your read and commented my essay,...

Sylvia Wenmackers: on 3/12/18 at 20:32pm UTC, wrote Dear Cristi, Thank you for telling us about Indra's net: I really liked...

Steve Dufourny: on 2/28/18 at 10:29am UTC, wrote Hello John,Cristi, Hi John, Thanks , hope you are well. I say that it is...

Cristinel Stoica: on 2/26/18 at 23:34pm UTC, wrote Dear Jonathan, Thank you for your comments, and for reminding me to...

Jonathan Dickau: on 2/26/18 at 22:56pm UTC, wrote Greetings, I have not seen a comment from you yet Cristi. If you have not...

John Cox: on 2/26/18 at 17:18pm UTC, wrote Steve, I very much agree with that. A rationale that adequately describes...

Cristinel Stoica: on 2/26/18 at 14:15pm UTC, wrote Hello Steve, Well, there is no consensus and no definitive data, we don't...

Steve Dufourny: on 2/26/18 at 13:53pm UTC, wrote Hello Cristi, I have thought a lot about how we must really consider what...


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FQXi FORUM
April 26, 2018

CATEGORY: FQXi Essay Contest - Spring, 2017 [back]
TOPIC: Indra's Net - Holomorphic Fundamentalness by Cristinel Stoica [refresh]
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This essay's rating: Community = 7.1; Public = 6.9


Author Cristinel Stoica wrote on Dec. 21, 2017 @ 21:02 GMT
Essay Abstract

If "fundamental" means something that is at the root of everything, then the physical laws and the objects to which they apply seem to be fundamental. But by looking at the mathematical structure of various theories in physics, we see that "fundamentalness" is relative, revealing a holistic nature. Various types of holism also appear in quantum theory, in Bohm's idea of implicate order, and in the holographic principle. 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. The discussion is based on various examples from particle physics and its mathematical formulation, and implications to what is "fundamental" are analyzed.

Author Bio

Theoretical physicist. Research interests: foundations of physics, gauge theory, foundations of quantum mechanics, singularities in general relativity. Interested especially in the geometric aspects of the physical laws. ArXiv: http://arxiv.org/a/stoica_o_1 Blog: http://www.unitaryflow.com/

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Scott S Gordon wrote on Dec. 21, 2017 @ 23:11 GMT
Hi Christi, You are making some interesting points (no pun intended) on a very fundamental discussion of points, lines, geometric structures, etc... You then jump into standard physics, theories and equations... Is there a place in your thinking where a line (of points) comes to possess the property of distance? Is distance something you take for granted in your theory? Would this play a role in developing your model?

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Author Cristinel Stoica replied on Dec. 22, 2017 @ 06:26 GMT
Hi Scott,

Distance is always there. In Hilbert's axiomatization of the 3D space the first 12 axioms are about incidence and order, and distance is only mentioned in the 13th axiom. But this doesn't mean that the Euclidean space goes through some phases and only in the 13th phase starts having distances. All axioms work together in no preferred order. Only in our thinking we can unfold the logic and prove many theorems in geometry before discussing distances, but as I explained, we can also start by first discussing distances. This shows a relativistic perspective on what is fundamental in a mathematical structure in general. Similarly, distance is always there in physics, even though in general relativity it is dynamic, and at the big bang it may be 0. Distance is always there in the holomorphic perspective I propose too, since it is based on geometric algebra, and implicitly on distance.

Best wishes,

Cristi

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Scott S Gordon replied on Dec. 24, 2017 @ 23:55 GMT
That is my point - I do not think that distance was always there... I think that distance also had to be created especially considering the fact that there are three independent distance directions (dimensions) in our spacetime with no reason as to why...

Consider reading my essay and see if you think distance should just be a given as it has always been considered

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Author Cristinel Stoica replied on Dec. 25, 2017 @ 17:20 GMT
A possibility is that distance appeared from a kind of symmetry breaking. For example in a theory where spacetime is a manifold, but the structure group of the tangent bundle is GL(4,R), and it is broken to SO(1,3) by some mechanism. Another possibility is conformal gravity, where you have scale invariance, so angles are invariant, but not the lengths. Note that the Standard Model without masses is conformally invariant. And then the conformal symmetry in conformal gravity is broken to SO(1,3) by some geometric mechanism, which formally is identical to Higgs and endows some of the particles with masses just like in the Standard Model. So yes, it is possible.

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Gary D. Simpson wrote on Dec. 23, 2017 @ 18:54 GMT
Christinel,

This is an excellent essay. Parts of it go beyond my ability to fully understand but I do get the general idea. I am a believer in quaternions as the basis for Physics so I am able generally to follow your arguments.

The discussion of the various types of geometries was very instructive. I have never heard of some of the systems you mention. Yet they all seem to be equivalent. Once you define what is fundamental, the axioms and theorems then develop.

The notion that all the information of the universe could be encoded at each point of the universe is profound. It is more than I can wrap my mind around. Perhaps I should stick with tic-tac-toe?

Equation 1 simply looks like multiplication of a pair of vectors to me. That is the opposite of the sum of the dot product and the cross product.

Regarding Equation 2 (Dirac Operator), is the function f a vector? If so, then is d/dx in the k direction and d/dy in the j direction?

You lose me when you get to the discussion of the standard model. Allow me to ask a question though ... can that vast menagerie of particles actually be fundamental? And how can something be fundamental if it is not stable? Surely the thing to which these particles decay must be fundamental instead?

All in all, an excellent essay. Many thanks.

Best Regards,

Gary Simpson

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Author Cristinel Stoica replied on Dec. 24, 2017 @ 06:51 GMT
Gary,

Thanks for the interest in my essay, and for the questions, which give me the opportunity to give some details, for you and others who may be interested.

> I am a believer in quaternions as the basis for Physics so I am able generally to follow your arguments.

Yes, quaternions appear more than we normally see in the usual formulations of physics. The Clifford algebras...

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Author Cristinel Stoica replied on Dec. 24, 2017 @ 06:54 GMT
There is a problem with rendering an equation in my previous comment. Let me give a link.

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David Brown wrote on Dec. 25, 2017 @ 13:43 GMT
"A major question is why these particular gauge symmetries and representations?" What is a major clue to answering the preceding question? In the list of references for "Indra's Net - Holomorphic Fundamentalness" there is no mention of Milgrom, Kroupa, or McGaugh. I say that Milgrom is the Kepler of contemporary cosmology — on the basis of overwhelming empirical evidence. Google "witten milgrom", "kroupa milgrom", and "mcgaugh milgrom".

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Author Cristinel Stoica replied on Dec. 25, 2017 @ 17:11 GMT
Hi David,

My remark "A major question is why these particular gauge symmetries and representations?" refers to the pattern of fundamental particles. Milgrom's MOND is about the rotation of galaxies, so how can it be relevant to that question? Especially since MOND, as opposed to various "dark matter" proposals, doesn't claim to require new fundamental particles, being based on modifying gravity alone.

Nevertheless, MOND is important, but my essay was not about this, you will not find the words "dark matter" or "rotations of galaxies" in it, so I don't think I was being unjust to Milgrom. My essay is about what "fundamental" means.

When we talk about fundamental laws, I think the focus should be on fundamental principles, rather than on approximations and phenomenology. Newton's gravity is an approximation, and so is a modification of Newton's gravity like MOND. A fundamental theory should in particular be generally covariant. But I have good news for Milgrom: there is a generally covariant modification of Einstein's gravity - conformal gravity - which apparently gives as a limit case Milgrom's. I mention conformal gravity for its salient features regarding the Standard Model of particle physics in the endnote #6, but it is also relevant to MOND. So if the final theory will embed conformal symmetry, MOND or something close to MOND will be an approximation of it.

Best regards,

Cristi

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Steve Dufourny replied on Jan. 8, 2018 @ 13:18 GMT
Hi Cristi and Mr Brown,

I have difficulties with this MOND , like Verlinde also has made.The fact to change this gravitation seems so odd.On the other side we search this quantum weakest force and we could insert this dark matter in encircling this standard model by this gravitation governing this universe. The fact to consider only photons like primordial informations seems odd.The problem...

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Lawrence B. Crowell wrote on Dec. 26, 2017 @ 23:18 GMT
It appears that in effect you have CL(3,3) ~ SL(3,C) or U(8) in a Clifford basis. You can break this into SU(3) and SO(3,1). I have similar ideas with SU(2,2) and the occurrence of additional quarks as dark matter.

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Author Cristinel Stoica replied on Dec. 27, 2017 @ 11:29 GMT
Hi Lawrence,

More precisely, Cl(3,3) is the complex Clifford algebra of a complex 6D space V. The space V can be decomposed as the direct sum of two complex 3D isotropic spaces, which form a Witt decomposition, and we consider them fixed. The transformations of Cl(3,3) preserving this decomposition give the SU(3)xU(1), where U(1) is for electromagnetism. They act by permuting the 8 ideals of Cl(3,3) according to the correct representations of SU(3). On these ideals, the Dirac algebra acts at left in a reducible way, which give room for SU(2) to act as well at left. So the ideals are the spinor spaces for quarks and leptons, and they transform according to the Standard Model group, with the proper representations built in.

I'm also interested in SU(2,2) and how you used it.

Best regards,

Cristi

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Lawrence B. Crowell replied on Dec. 30, 2017 @ 00:41 GMT
SL(3, C) is SU(3) in a tensor product with an 8 dimensional space, or 8 real dimension = 4 complex dimensions. So we can think of this as spinorial or complex valued spacetime with SU(3) principal bundle. The 8 dimensional space is represented only by the trace of a Hermitian matrix or its metric. You then have exp(iS) for S = ∫ds and ds the Gaussian interval. There are three copies of sl(2,C) in the group sl(3,C) which corresponds to three weights or the vector space (e_1, e_2, e_3, f_1, f_2, f_3) which are the 6 dimensional space you talk about.

I thought I would mention that the conformal diagram you have of the black hole represents one possible slicing. I can slice spatial surfaces any way that I want. I can arrange it that spatial surfaces reach the singularity inside the black hole before they reach i^+ or I^∞. The slicing and how the surfaces reach r = 0 is arbitrary.

LC

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Author Cristinel Stoica replied on Dec. 30, 2017 @ 12:04 GMT
That's interesting, considering that sl(3,C) has 16 real dimensions, and the Clifford algebra Cl(3,3,C) I used has 64 complex dimensions, and its full spinors have 8 complex dimensions.

About the black hole singularity, are you referring to this one? Slicing is not unique, of course, that's true in all solutions in general relativity, but the things are not as flexible how you may think. What matters is the atlas, not the particular solution, and the atlas has no preferred slicing. My Schwarzschild solution is analytic and is continued analytically through the singularity, and it remains so even if you apply an analytic change of coordinates and get a different slicing. Moreover, in the paper I find an infinite family of different Schwarzschild solutions analytic at the singularity, and in fact an infinite family of such atlases. But among them there is a unique one which saves the fields at singularity both geometrically and physically in the way I describe here.

Best regards,

Cristi

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Anonymous wrote on Jan. 7, 2018 @ 07:13 GMT
Hi Cristinel, I enjoyed your essay when I got into it, rather than just taking a quick look. It is full of interesting ideas that you have clearly explained. I think the question you ponder, about whether fundamental is most foundational; And how foundational should be considered when seeking the fundamental, is good. It seems to me that though material things ultimately reduce to far simpler...

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Georgina Woodward wrote on Jan. 7, 2018 @ 07:15 GMT
Hi Cristinel, I enjoyed your essay when I got into it, rather than just taking a quick look. It is full of interesting ideas that you have clearly explained. I think the question you ponder, about whether fundamental is most foundational; And how foundational should be considered when seeking the fundamental, is good. It seems to me that though material things ultimately reduce to far simpler...

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Author Cristinel Stoica replied on Jan. 7, 2018 @ 08:33 GMT
Hi Georgina,

Thank you for going into my essay, and for sending me your thoughts. I hope you'll write your ideas in an essay for this edition. Also your idea to compare the classification of particles with the deities of Terry Pratchett's Discworld is nice, I think it would be fun if you write about it :) About what's truly fundamental, who knows, many descriptions seem to work partially, to be equivalent sometimes, but I think we know very little and we need fresh ideas.

Best wishes,

Cristi

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Georgina Woodward replied on Jan. 7, 2018 @ 22:42 GMT
Hi Cristinel, I have just found out about the origin of 'Indra's' net. I didn't realize 7 was a footnote but thought it was just a reference. Having read the footnote I understand what Indra's net is and why you have chosen to propose it as a model of fundamental physics, tying in with recent ideas in physics about the holographic principle. I really like Francis H Cook's description. "we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels". It sounds beautiful. I agree that it is good to explore fresh ideas. My reservation -but what problems does it solve? In what way is it an improvement over other explanations? Plus, of course, personal bias in favour of my own explanatory framework.

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Author Cristinel Stoica replied on Jan. 8, 2018 @ 08:58 GMT
Hi Georgina,

So far, physicists found mathematical descriptions for various phenomena, which cover a large domain. You have equations describing various phenomena, combined together, and it seems that we just need a few more pieces of the puzzle and we will know everything about the fundamental structure of the universe. And maybe continuing like this we will eventually have all these pieces combined together, and covering what we know about the universe, it seems we are close. But I am not satisfied with just a collection of equations combined together. You can put all sorts of things in the Lagrangian, like new unobserved particles predicted by various models. But why these fields, these equations, these terms in the Lagrangian? My dissatisfaction is not only metaphysical or aesthetical. The problem is that the current view gives too much freedom to change the theory if new facts are discovered. I don't trust something that can be adapted so easily. I want something that once found, you can't change. And if there are new phenomena, I want those to result from that model because they are there, not because you can add them by hand. A theory that can't be adjusted has much more predictive powers, so higher chances to be falsified, and if not falsified by any conditions, to be true.

I was attracted by holomorphic functions since I first learned about them as undergraduate student. On the one hand when I read that you can use them to represent the electric field in 2D. Moving to 4D spacetime and replacing the complex field with the Clifford algebra of spacetime reveals that you can include other equations of physics, but including the other forces and the particles from the Standard Model shows that even this needs to be replaced with something richer, and I think, as I explained, that this is a larger algebra, perhaps a larger Clifford algebra, like the complex Clifford algebra Cl(3,3), or maybe another one. Different things we know in physics seem to be regained from such a structure already, without having to add them manually, and without giving us too much freedom to adjust. So I believe that such a structure exist, which naturally includes what we know and what there is to be found, but in a rigid way, so that you can't and don't need to adjust it. No mobile parts, maximum rigidity. And the most rigid mathematical fields seems to me to be the holomorphic ones.

When physicists talk about simplicity, at first sight one may think that it is about using simple constituents which are similar to what our intuition can grasp easily. But to physicists, "simple" is not "easy". On the one hand simple means the smallest number of principles, equations, and free parameters. On the other hand, it means simplicity in the mathematical sense of indecomposability. So what appears to us as being different fields, to be just different components of one thing. This sort of simplicity means rigidity.

The fact that holomorphic functions have this property the full information about the field is contained in any point was something that I found cute and aesthetically appealing, but didn't think of it from the beginning as being relevant. Later, when I found out more about things like quantum holism, the holographic principle, and the holistic ideas of Bohm, I realized that these may just be consequences of this analyticity of holomorphic functions. And only last year I found out about Indra's net, which I thought it was a good metaphor for this. And I thought this idea may be interesting for the theme of this essay contest, since it introduces an interesting type of fundamentalness.

Kind regards,

Cristi

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Jack Hamilton James wrote on Jan. 8, 2018 @ 05:16 GMT
Dear Cristi,

What an excellent essay, beautifully presented. I particularly like your Isomorphic stories section, and also the notion of Indras Net. Let's assume it is a correct depiction of reality at a fundamental level, so in reality, you have found the way indivisible units operate to create everything within it, including yourself. Do you now know enough about what this reality is? What is still missing?

Best,

Jack H James

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Author Cristinel Stoica replied on Jan. 8, 2018 @ 09:16 GMT
Dear Jack,

Thank you for reading and for the comments. You ask:

> Let's assume it is a correct depiction of reality at a fundamental level, so in reality, you have found the way indivisible units operate to create everything within it, including yourself. Do you now know enough about what this reality is? What is still missing?

The point of science is to advance in understanding as much as possible. But there is no guarantee that the scientific method based on testability of hypotheses can lead to this. There's no guarantee that every truth about the universe is in our range of testability and in our range of understanding. As for the proposals I made in this essay, they are still in the phase of being mere hypotheses, supported by some arguments like those I mentioned, but far from being proven. Much is still missing, the resulting description will have, in my opinion, to be complete, without mathematical or logical inconsistencies, without parts that can be changed or replaced (see this previous comment for more details). But even so, we may never know that we found the ultimate truth and nothing is missing :)

Best regards,

Cristi

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Steve Dufourny wrote on Jan. 8, 2018 @ 13:31 GMT
Hi Cristi ,

You tell us in your essay that waves are essential, I agree.That said you tell that these waves and oscillations can give all the shapes.It is a reasoning for the strings in fact.Can we be sure about this ? if the 1D primordial field is nt photonic and that the particles are notpoints and strings , so there is a problem because the spherical volumes and their motions witha finiet serie of spherical volumes where space disappears, we have also the combinations to create all shapes.

Best Regards

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Author Cristinel Stoica replied on Jan. 8, 2018 @ 13:56 GMT
Hi Steve,

Thank you for the remarks you made here and above, under David Brown's comment. And for the questions.

In my essay I don't favor photons and exclude the other particles. All fundamental particles evolve in time like waves, they propagate and interfere and interact. The difference is that those with mass have an additional mass term, so they are if you want like waves which don't propagate at the speed of light. Even leptons and quarks are governed by a wave equation like this with an additional mass term, obtained by applying once again the Dirac operator to the Dirac equation.

Best regards,

Cristi

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Steve Dufourny replied on Jan. 8, 2018 @ 20:40 GMT
You are welcome,

It is relevant because we arrive still to what is an electron in fact.Dirac has made a wonderful equation, we could improve it in adding this gravitation and all these motions and oscillations of spherical volumes.The positron, the electron the photon in fact are more than we can imagine.If we insert this matter nt baryonic and if my equation is correct E=m(b)c²+m(nb)l² we could extrapolate to this weakest force , the quantum gravitation but with an equation of electron but nt relativistic.Because if all is gravitationally coded and that the finite series of spherical volumes are the key.We can consider that the method can be the same with the wave functions at the difference that they are nt relativistic.We just consider particles of gravitation instead of photons and we consider them nt relativistic and perhaps also we insert this cold.We can insert the reduce planck constant and we imrpove with the spherical volumes and we insert also the motions orbital and spinal.The dirac equatin can be improved and can permit to reach this gravitation.Photons are just like a fuel.It is not easy to find all this puzzle, if we could see the truth like that it could be well lol like a picture giving us the real truths but we are far.Friendly

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Gene H Barbee wrote on Jan. 9, 2018 @ 18:30 GMT
Cristi,

A couple of things about your essay caught my attention. I developed a model of the proton by reducing data and using it to understand some aspects of atomic physics and cosmology. Admittedly, I didn’t have all the theory. Your 3*3 group indicates that 1/3 charge is related to 3 dimensions. I kept coming up with logarithms that are multiples of N=0.0986, which I wanted to understand. I did not have the relationship to Schrodinger’s equation until Edwin Klingman encouraged me to look at fundamentals of E=e0*exp(N), where N is a natural logarithm. Derivation of the relationship is in: Barbee, Gene H., Schrodinger Fundamentals for Mesons and Baryons, October 2017, vixra:1710.0306v1.

I use probability 1 for P=1=exp(iet/H)*exp(-iet/H).



The logarithm associated with the electron is N=10.136 and with the known mass 0.511 MeV we can evaluate e0.

e0=0.511/exp(10.136)=2.02e-5 MeV

With your theory, N=0.0986 is associated with fractional charge 1/3 for each of three dimensions, the value 10.431-0.0986-0.0986-0.0986=10.136 (the -1 charged electron) and E=e0*exp(0.295)=27.2e-6 MeV (the electromagnetic field energy).

In high energy collisions, the electron can revert to a quark by absorbing an anti-e neutrino and kinetic energy. I associate N=10.333 with the mass of a quark. But N=10.431 is neutral and 10.431 -0.0986=10.333 is the fractional charge (-1/3) for the quark. Four units of 2.02e-5*exp(10.33)= 0.622=2.49 MeV, the standard model mass for the Up Quark (PDG) is 2.2 MeV.

Aside: In my model, the dimensions don’t split until after the neutron is formed (by Schrodinger based quads). When they do split, neutrons proliferate (probability 1 is maintained) and the gravitational coupling constant (1/exp(90)) is established. Your concept that the rules are everywhere the same is correct and fractional charge is related to dimensions.

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Author Cristinel Stoica replied on Jan. 10, 2018 @ 13:33 GMT
Hi Gene,

Thank you for the comments and for the interesting information. I guess that the masses of the particles, the mixing matrices for leptons and quarks, and the coupling constants should emerge from something deeper, but we can still try to find the rules even if we don't know the deepest explanation.

Best regards,

Cristi

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Jochen Szangolies wrote on Jan. 11, 2018 @ 22:15 GMT
Hi Cristi,

one thing I always find striking in these contests is that there seem to be certain currents of thought that find echoes in different ways in different presentations. In some sense, it seems as though there's something in the air that many different authors are trying to capture in their different ways, some more successfully than others.

That's not to say I don't think...

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Author Cristinel Stoica replied on Jan. 12, 2018 @ 13:49 GMT
Hi Jochen,

Thank you very much for the comments.

You said "there seem to be certain currents of thought that find echoes in different ways in different presentations. In some sense, it seems as though there's something in the air that many different authors are trying to capture in their different ways, some more successfully than others.".

I guess it must be floating in the...

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Jochen Szangolies replied on Jan. 12, 2018 @ 18:07 GMT
Hi Cristi,

well, there's always a question of how much leeway we allow ourselves in seeing similarities---with enough coarse-graining, everything starts to blur together, so maybe I'm just muddling things together that are, in fact, quite different.

But for instance, Sebastian de Haro's essay talks about 'relative fundamentality', you about the 'relativity of fundamentalness' (and...

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Author Cristinel Stoica replied on Jan. 12, 2018 @ 20:51 GMT
Hi Jochen,

Wow, thank you for the summary! So it seems that, as in the Indra's net, ideas from different essays reflect ideas from others :)

Maybe we'll come back to this after I'll read them too, and others which will be posted in the meantime.

I will comment more on your page, about your essay, after I finish it.

Best regards,

Cristi

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Marcel-Marie LeBel wrote on Jan. 12, 2018 @ 16:08 GMT
Cristi,

Nice essay. I stick to the prose ... You present the “germ” which is all the derivatives of a dynamic process. In my essay, I submit that only a dynamic process can come from nothingness, without failing the primitive rule of non-contradiction.

A single quantum “spark” could start the dynamic process but, after a number of iterations of the dynamic process, the excitation would return to its point of origin and the whole thing would collapse back to nothingness.

This is why, I “think/believe” that it requires two “quantum sparks” in order to produce a self-sustaining dynamic process. The first spark starts/creates a dynamic process that would normally evolve in symmetry, returning to its point of origin. But a second spark would disturb the normal evolution of the process making it non-symmetric. The dynamic process would not return to its point of origin and the last iteration would become the new “spark”.. for another germ, which contains and maintains the asymmetry imparted by the original second spark..

Such a two quantum sparks event is most likely exceedingly rare ...

All fun and games,

All the bests,

Marcel,

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Author Cristinel Stoica replied on Jan. 12, 2018 @ 20:54 GMT
Marcel,

Thank you for the comments. This sounds really interesting: "I submit that only a dynamic process can come from nothingness, without failing the primitive rule of non-contradiction." Nice word choice, "spark" :)

Best regards,

Cristi

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Anonymous wrote on Jan. 13, 2018 @ 19:54 GMT
Hello Cristinel...

I am a tenacious advocate of a minimum unified unit of fundamentality... i.e. unity "germ"... and I find your insightful exposure of scientific dogma, cognitively refreshing.



Fundamental logic of the geometry "bench model" can be obscured by the alpha and/or numeric artifice of the semantist and/or equationist, but an operative CAD/SIM supports no illusion... i.e. it is a virtual reality not a theory.

That is to say that, it makes no difference which "geometric algebra" is applied, if the graphical spatial coordinate geometry upon which the mathematical constructs are derived, does not resolve a unified minimum unit of Spatial quantization (QI), no spatial unity "germ" can be verified.

To digitally simulate/animate the concept of Indra's net "cast in all directions"... i.e. an origin emission equal in all Spatial directions from a single point... requires resolve of an Origin Spherical Singularity Geometry, which supports infinite minimum unified volume unit shell closure expansion, as a valid CAD environment/field quantization.

REF: UQS Origin Singularity Geometry http://www.uqsmatrixmechanix.com/UQST-TVNH.php

UQS as a an Equal Qauntization Quaternion CAD environment... i.e. 6 axis... Space/Energy/Time/Info model addresses deterministic concerns by the fact that all subsequent distribution of minimum units of Energy (QE) must be resolved for the entire field in a manner consistent with emerging system intelligence (AI), on each pulse of the emission, and a minimum unit of Time (QT) is inherent in a continuously pulsed emission.

Thanks Cristinel, for sharing your insights and thus making an opportunity for comment... I would read with attention your comments on my essay entry Title: Knowledge Base (KB) Access as Fundamental to Info Processor Intelligence.

Will return to rate after I read as many essays as I have time.

S. Lingo

UQS Author/Logician

www.uqsmatrixmechanix.com

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Author Cristinel Stoica replied on Jan. 14, 2018 @ 07:05 GMT
Hello Sue,

Thank you for reading and for the comment. I'd like to come back to what you said after I read your essay, to have a better understanding. Good luck with the contest,

Cristi

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Vladimir Rogozhin wrote on Jan. 14, 2018 @ 18:58 GMT
Dear Cristi,

I read with great interest your deep, comprehensive analytical essay on the problem of fundamentality. You also give very important ideas that give direction to the way out of the crisis of fundamentality, the creation of a holistic picture of the world for physicists and poets.

Good luck!

Yours faithfully,

Vladimir

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Author Cristinel Stoica replied on Jan. 14, 2018 @ 21:12 GMT
Dear Vladimir,

Thank you for comments and reading the essay. I'm looking forward to read yours, as always!

Best wishes,

Cristi

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Wilhelmus de Wilde wrote on Jan. 15, 2018 @ 17:04 GMT
Hi Christi,

I read with much pleasure your exellent essay. I am going to study further on the mathematics you indicate because your conclusion :

"So the state of the universe, including the germs at all the other points of spacetime, is encoded in the germ at ach point of spacetime. Not only the field, but also spacetime itself emerges from each germ." is the conclusion that is one of the outcomes of my own conrtibution "FOUNDATIONAL QUANTUM REALITY LOOPS" and I hope that you will find some time to read and rate it. I don't mention the holographic model but also agree with Sontag, that “Time exists in order that everything doesn’t happen all at once ...(in my Total Simultaneity) and space exists so that it doesn’t all happen to you."

Thank you for making me think again

Wilhelmus de Wilde

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Author Cristinel Stoica replied on Jan. 15, 2018 @ 19:42 GMT
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

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Joe Fisher wrote on Jan. 15, 2018 @ 17:08 GMT
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

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Author Cristinel Stoica replied on Jan. 15, 2018 @ 19:44 GMT
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

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Lawrence B. Crowell wrote on Jan. 16, 2018 @ 15:49 GMT
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

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Author Cristinel Stoica replied on Jan. 18, 2018 @ 09:44 GMT
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

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Francesco D'Isa wrote on Jan. 20, 2018 @ 09:15 GMT
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

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Author Cristinel Stoica replied on Jan. 21, 2018 @ 05:35 GMT
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

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Francesco D'Isa replied on Jan. 21, 2018 @ 23:06 GMT
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

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Author Cristinel Stoica replied on Jan. 22, 2018 @ 11:24 GMT
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...

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Stephen I. Ternyik wrote on Jan. 20, 2018 @ 20:36 GMT
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.

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Author Cristinel Stoica replied on Jan. 21, 2018 @ 05:36 GMT
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

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Flavio Del Santo wrote on Jan. 20, 2018 @ 21:40 GMT
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

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Author Cristinel Stoica replied on Jan. 21, 2018 @ 06:04 GMT
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...

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Hans van Leunen wrote on Jan. 22, 2018 @ 12:59 GMT
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...

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Author Cristinel Stoica replied on Jan. 22, 2018 @ 18:28 GMT
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

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DIOGENES AYBAR wrote on Jan. 22, 2018 @ 14:16 GMT
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

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Author Cristinel Stoica replied on Jan. 22, 2018 @ 18:36 GMT
Dear Diogenes,

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

Cristi

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Satyavarapu Naga Parameswara Gupta wrote on Jan. 22, 2018 @ 22:06 GMT
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...

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Peter Jackson wrote on Jan. 26, 2018 @ 11:03 GMT
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

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Author Cristinel Stoica replied on Jan. 26, 2018 @ 13:58 GMT
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

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Peter Jackson replied on Jan. 30, 2018 @ 13:45 GMT
Christi,

Great conversation on my string, & thanks for your good advice. To reply to your comment above.

Yes Richard Feynman said he also 'gave up' the search as it was so difficult. But I look at it not as 'making QM classical' but as falsifying John Bell's view that "the founding fathers were wrong on that point.." that it IS classical & he, and we just hadn't found the flaw which would "take a leap of imagination" - and that we "should not stop looking" for it.

The flaw emerges as the assumption of 'no assumption' about particle pair form or dynamics. They must then assume 'superposed states' which 'can't be rotation'. Testing other models; If they're simply given Maxwell's orthogonal 'curl' as well as (left hand rule thumb) linear momenta, then anti-parallel polar axes, the mist is lifted on the classical explanation (using all 3 degrees of freedom, electron field interaction momentum exchange and known non-linear momentum distributions with field angle.

I hope anyone else reading this will take a look (also at Declan Trail's code & plot) as we'd like all to rigorously test the model pending publication.

Back to yours, as my firt post (stolen by the ghosts in the machine) - original, of interest and well written despite the misplaced comment on my string. Well done.

Best of luck

Peter

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Author Cristinel Stoica wrote on Jan. 27, 2018 @ 11:32 GMT
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...

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Christian Corda wrote on Jan. 29, 2018 @ 09:39 GMT
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.

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Author Cristinel Stoica replied on Jan. 29, 2018 @ 11:25 GMT
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...

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Christian Corda replied on Jan. 29, 2018 @ 11:33 GMT
Dear Cristi,

Thanks for your kind replies.

Yes, I think that "Herr Doktor"'s dream to obtain everything from geometry is the most fascinating thing of Science. I wish you good luck also for the AACA submission.

Cheers, Ch.

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Author Cristinel Stoica replied on Jan. 29, 2018 @ 11:42 GMT
Dear Christian,

Thank you very much, I wish you success with your research too!

Cheers,

Cristi

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Joe Fisher wrote on Jan. 29, 2018 @ 16:15 GMT
Dear Fellow Essayists

This will be my final plea for fair treatment.,

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

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

Only the truth can set you free.

Joe Fisher, Realist

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Anonymous wrote on Jan. 31, 2018 @ 19:03 GMT
Dear Christi,

very interesting - quite a detailed scenario for unification with many novel ideas. I must admit though there are many things I don't fully understand yet. For example, how is the unification approach via non-Lie-algebras related to the general theme of holographic fundamentalness? I find both ideas intriguing, but so far I can't grasp the relation. Can you help me?

In any case I'm even more convinced we should get together soon again.

Best! Heinrich

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Author Cristinel Stoica replied on Jan. 31, 2018 @ 21:17 GMT
Dear Heinrich,

Thank you for reading my essay and for the kind comments. And also for the excellent question. I hope as well that we will meet again soon and discuss more, maybe at the next DICE conference.

"how is the unification approach via non-Lie-algebras related to the general theme of holographic fundamentalness?"

The Clifford algebras are generalizations of the complex number algebra, and the Cauchy-Riemann operator generalizes to the Dirac operator. The Dirac operator is present not only in the spin 1/2 particle equations, but also the Maxwell and Yang-Mills can be formulated using it. But just having all the equations written using the Dirac operator is not enough to guarantee the solution to be holomorphic. For example, the Dirac and Maxwell equations have nonholomorphic solutions. In fact, I didn't define yet what "holomorphic" means in this context, but I have an idea which involves gravity. If the resulting equation which contains the SM and gravity will be as I expect, then it will also guarantee that the solutions are holomorphic. But it's early to say that indeed this will be the case.

I wish you success with your excellent essay!

Best wishes,

Cristi

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George Kirakosyan wrote on Feb. 1, 2018 @ 05:10 GMT
Hi Dear Christi

Your article is written in very attractive style - as every time!

I have a huge respect to Bohm's approach (despite for me a little bit more valuable De Broglie-Bohm theory!)

//Holomorphic fundamentalness may be a mathematically consistent basis for holism and the holographic principle, but until we will have the unified theory of physics, it remains an exercise of imagination.// - Your idea seems to me as very reasonable. I believe it may be realized in any of time!

Meantime I am dared to say that something has gone very wrong in our physics at the far-early beginning (that hardly anybody wish to listen!)

So, I highly welcome your new work and I wish you succeeding in this contest!

Best Regards!

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Author Cristinel Stoica replied on Feb. 1, 2018 @ 08:24 GMT
Dear George,

Thank you very much for your kind comments and for your wishes. I wish you success with the essay (which I am looking forward to read) in this contest!

Best wishes,

Cristi

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Narendra Nath wrote on Feb. 1, 2018 @ 08:50 GMT
It is a pleasure for me to see your essay coming on top few. Your mind generates ideas that simplify the geometry of growth of Physics, specially at the fundamental level of Particle Physics. On the other hand we have Cosmology where measurements are difficult , errors are large. How to construct the latter from the former at the fundamental level appears a task the human mind needs to tackle. I am amazed that fundamental particles and their connection to Higg's Boson isproving to be an enigma. Can you throw some light on why we should worry about the mass of the fundamental particles to be explained using Higg's Boson as the source? Fundamental to me means ultimate reality. It can never be approached as things tend to become difficult whenever we tend to get closer to the final solution. Many a times i feel our existing knowledge of Physics retards us to to reach a final end. If it is simple the approach should have freshness , rather than on the historical develoment of the way Physics got developed. That is , Methodology of doing sciences need to be freshened! My query is free of your expertise in Maths as i am deep down with experimental Physics. Maths can assist only in giving precision to present Physics formulations but can not go beyond the experimental facts already known firmly.

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Author Cristinel Stoica replied on Feb. 1, 2018 @ 11:26 GMT
Dear Narendra,

Thank you! You said:

> "I am amazed that fundamental particles and their connection to Higg's Boson isproving to be an enigma. Can you throw some light on why we should worry about the mass of the fundamental particles to be explained using Higg's Boson as the source?"

I consider the masses of particles one of the greatest mysteries. Historically, to get rid...

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Narendra Nath wrote on Feb. 1, 2018 @ 09:09 GMT
Indra in our literature is the name of God associated with rains.How does it occur in your native language for you to use it in your essay?

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Author Cristinel Stoica replied on Feb. 1, 2018 @ 11:27 GMT
Dear Narendra,

I borrowed the metaphor "Indra's net" to illustrate how the mathematical notion of holomorphic functions have this property that the whole is present in each of its points. Indra's net was mentioned in various Buddhist texts like the Avatamsaka Sutra, and was described in Cook(1977), chapter 1, page 2, in the following way (I mention this in my endnote 7, pages 11-12):

"We may begin with an image which has always been the favorite Hua-yen method of exemplifying the manner in which things exist. Far away in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificier in such a manner that stretches out infinitely in all directions. Inaccordance with the extravagant tastes of deities, the artificier has hung a single glittering jewel in each "eye" of the net, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring. The Hua-yen school has been fond of this image, mentioned many times in its literature, because it symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos. This relationship is said to be one of simultaneous mutual identity and mutual intercausality"

Best regards,

Cristi

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Narendra Nath replied on Feb. 1, 2018 @ 13:03 GMT
What a beautiful explanation to my enquiry? Your ingenuity of detailed analysis is remarkable. Your essay has reached the top three and i wish you reach the top. Geometry and then algebra are the off shoots of Mathematics. You are using these tools efectively in your expositions!

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Author Cristinel Stoica replied on Feb. 1, 2018 @ 13:24 GMT
Thank you, Narendra! I wish you the best for your essay too!

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adel sadeq wrote on Feb. 3, 2018 @ 11:09 GMT
Hi Cristinel

Like usual you always write good essays, relevant and direct to the issue. I have pleaded with you in the past to look very closely at mine, but it seems the time is always wrong somehow.

The reason that I like to look at mine is because it implements your program however it looks unconventional. In my idea every point in space which is as emergent as all other aspects of the fundamental structure caries all information about all other points (which represents the particles and their interaction), and that comes naturally. I have not plotted the points between the particles (not to overcrowd the results) but the information can be captured just like the point in the particles. Thank you.

https://fqxi.org/community/forum/topic/3127

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Author Cristinel Stoica replied on Feb. 3, 2018 @ 21:44 GMT
Hi Adel,

Thank you very much for your kind comments. You wrote:

> I have pleaded with you in the past to look very closely at mine, but it seems the time is always wrong somehow.

But the first time we interacted was during the last contest, and I commented on your essay. I also read your current essay, and if I will think at something helpful I'll comment. Good luck with the contest!

Best regards,

Cristi

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Author Cristinel Stoica replied on Feb. 4, 2018 @ 09:08 GMT
Hi Adel,

I commented your intriguing essay, I hope my comments are useful to you. But I can't see the connection between my proposal and your essay, which you said it implements it. Good luck with the contest!

Best regards,

Cristi

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adel sadeq replied on Feb. 4, 2018 @ 10:43 GMT
Hi Cristinel,

I really appreciate you commenting on my idea, after all you are the only customer so far:) This is a general response. The implementation of your program is hard to see and depends how much you delve, so I will address that desperately with details in the future.

Quick points. The reason that I say ill defined is because the point can go to infinity and hence it becomes uncalculable (the story is just a bit more involved but I wanted to keep it simple). As a matter of fact the first "l" that you see defined in my programs is the reminiscent of the size of the "universe" and it is just there because of the historic development, it is not needed. Because if I throw the numbers to size of it, it will make the particle to particle interaction inconsistent as I change the size of the universe. Meaning, all interaction in this setup lead to FINITE results (only particle to particle interaction). Also, I have tried all kinds of random other than uniform they do not lead to the consistent easy to interpret results that I get with uniform.

Although I know it is hard for people who have more than hundred essays to read, to really delve in some detail in my system by running the programs. However, I think still some time "maybe 15 min" should be taken to appreciate the system. Of course since I have not explained everything clearly it is easy to misunderstand. BUT I was hoping that people concentrate on the big picture i.e. the RESULTS that I have obtained and concentrate on the finer details later, and a lot of them do exist. Also many other results I have not shown.

Thank you for picking up on the bolded statement in my essay because this system represents it automatically without any fudging and it became apparent only after some development which was doing just what any generalization I was allowed to do.

Thank you again, I could not have asked for more. Comments are worth a thousand points.

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Luca Valeri wrote on Feb. 3, 2018 @ 21:01 GMT
Hi Cristi,

The picture you draw with Indra's net is beautiful and a wonderful exercise for the imagination.

My essay imagines in a way the contrary. As condition for successfully define or measure a physical property, I assume the system must be separated from the environment (in order to be unitary). I would glad, if you could find the time to read and comment on my essay.

Best regards,

Luca

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Luca Valeri replied on Feb. 3, 2018 @ 21:25 GMT
Wrong link. Here is the right link to my Essay called The quantum sheep - in defence of a positivist view on physics.

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Author Cristinel Stoica replied on Feb. 3, 2018 @ 21:47 GMT
Hi Luca,

Thank you for your comments. Your essay is in my planned reading list.

Best regards,

Cristi

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Stephen James Anastasi wrote on Feb. 4, 2018 @ 03:12 GMT
Hello Indra

Dare I say, 'Wow!' I think our work is strongly connected. The following detailed comments are provided to show the connection. My apologies if these are rather long. My question is, are the nodes in my Harmony Set the centres of your pearls?

Thoughts as I read through:

You say, ‘Isomorphisms of mathematical structures will play a central role.’ I agree. I...

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Author Cristinel Stoica replied on Feb. 4, 2018 @ 09:18 GMT
Dear Stephen,

Thank you for the comments, and for the parallels you make with your own essay. This made me curious, but more after I read it, to fully understand the connections you've made here. Until then, good luck with your essay!

Best regards,

Cristi

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Theodore St. John wrote on Feb. 4, 2018 @ 17:14 GMT
Hi Cristi,

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

Your...

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Theodore St. John replied on Feb. 4, 2018 @ 17:22 GMT
My link doesn't seem to work right in the text above. Maybe it's because I left a space in the link.

Try this.

“A Simple Model For Integrating Quantum And Relativistic Physics with application to the evolution of consciousness by Theodore St. John”

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Author Cristinel Stoica replied on Feb. 4, 2018 @ 19:43 GMT
Hi Ted,

Thank you for your comments, I'm glad that you liked some ideas from my essay. I'm happy you liked Hestenes, I like him very much, although for my paper I recommend some standard textbook like Chevalley or Crumeyrolle. And for the comparison with your much simpler approach. You said you "conclude that motion serves to separate this holomorphic field in our percepption as space (S)...

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Wayne R Lundberg wrote on Feb. 4, 2018 @ 17:46 GMT
Dear Cristenel, Cristi,

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

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

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

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

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

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

best,

Wayne Lundberg

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Author Cristinel Stoica replied on Feb. 4, 2018 @ 19:57 GMT
Dear Wayne Lundberg,

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

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

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

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

Best regards,

Cristi

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Wayne R Lundberg replied on Feb. 18, 2018 @ 15:17 GMT
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

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Member Kevin H Knuth wrote on Feb. 5, 2018 @ 13:50 GMT
Dear Cristi,

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

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

Thank you again for an excellent thoughtful essay.

Cheers

Kevin Knuth

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Author Cristinel Stoica replied on Feb. 5, 2018 @ 19:09 GMT
Dear Kevin,

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

Best regards,

Cristi

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Jouko Harri Tiainen wrote on Feb. 7, 2018 @ 04:55 GMT
My goodness, what a wonderful essay and your writing style is impressive. I love your ideas about geometrical "laws", quantum holism and how you can relate them to particles of nature.

One major idea that is not discussed is the quantum property of monogamy (how system and subsystem relate to one another). If your model is holistic then the only way you can have "separate" subsystems is...

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Anonymous replied on Feb. 7, 2018 @ 09:54 GMT
Dear Jouko Harri Tiainen,

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

Best regards,

Cristi

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austin fearnley wrote on Feb. 7, 2018 @ 15:12 GMT
My thoughts on your essay have gone through three stages. Five weeks ago, I thought that the mystical net was an odd idea merely tacked on to your essay but somehow making it into the title. Later, I thought the net was relevant but too static, whereas today I realised that it was an excellent idea.

By too static I mean that I thought it as too perfect a fractal. That is fine for a...

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Author Cristinel Stoica replied on Feb. 8, 2018 @ 04:15 GMT
Dear Austin,

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

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

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

Best regards,

Cristi

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austin fearnley replied on Feb. 9, 2018 @ 07:31 GMT
If you do view my contest paper, it has reference#1

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

which has more wording on the relevant ideas wrt your mysical net than my highly-condensed contest paper. Figure A and pages 1 and 2 of the vixra paper show that I referred to braids (or universes) of three 4D colour dimensions and also referred to the braids as fibre optic cables. In some...

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Author Cristinel Stoica replied on Feb. 9, 2018 @ 09:03 GMT
In this essay I am talking about holomorphic functions, which are known for the complex case for long time and have this property of containing in each point the complete information about the whole function. I illustrate this with "Indra's net" as a metaphor, about which I learned many years after I became interested in Clifford holomorphic functions in physics. It is not like I have a mystical...

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Andrew Beckwith wrote on Feb. 7, 2018 @ 15:21 GMT
quote

The relativity of fundamentalness implied by different axiomatizations and formulations is

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

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

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

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

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

these exists?

end of quote

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

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

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

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Author Cristinel Stoica replied on Feb. 8, 2018 @ 07:19 GMT
Dear Andrew,

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

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

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

Best regards,

Cristi

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Jonathan J. Dickau wrote on Feb. 8, 2018 @ 03:18 GMT
Greetings Cristi,

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

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

All the Best,

Jonathan

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Author Cristinel Stoica replied on Feb. 8, 2018 @ 08:36 GMT
Hello Jonathan,

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

Best regards,

Cristi

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Jonathan J. Dickau replied on Feb. 9, 2018 @ 18:08 GMT
Thanks greatly Cristi...

One thing of interest pops to mind. Following another thread; I found myself reading your paper on semi-regularizability of Schwarzschild singularities, and continuing the solution through the horizon. I immediately got excited to share that my model reveals a similar picture. Approaching the Misiurewicz point; a sequence of self-similar forms gets smaller in scale, and in reverse-mirror fashion reappear on the other side in increasing scale but in opposite phase!

This makes the Schwarzschild event horizon like a reverse mirror which mimics the information that strikes it but recreates it in opposite phase - which is what gives such a BH the appearance of a perfect black-body. One can make a circuit diagram analogy as well; the inverting feedback amplifier commonly used in op-amp circuits. The virtual ground or earth created by the amplitude null that appears at the summing junction would therefore appear like the Schwarzschild EH, as shown in the diagram attached.

All the Best,

Jonathan

attachments: 2_MandelAmp2.jpg

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Author Cristinel Stoica replied on Feb. 9, 2018 @ 21:24 GMT
Dear Jonathan,

That's interesting. One minor comment, actually my solution is continued analytically through the singularity, for the continuity through the horizon it just uses standard methods like Eddington-Finkelstein or Kruskal-Szekeres (it is irrelevant which one of them, because the atlas has different but compatible maps for horizon and singularity). The only difference between my solution and the standard Schwarzschild solution is that I use an atlas which differs only at the singularity by a singular coordinate transformation. But I think there are more differences between your solution and mine, yours involves fractals. Which makes me curious, how does this work?

Best regards,

Cristi

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Narendra Nath wrote on Feb. 10, 2018 @ 14:18 GMT
As i am not competent to enquire and seek further details on your excellent essay.But may i request you to see a manuscript i have just attached on my essay title ' Inconstancy of the Physical Constants.....' May i just request you to spare sometime to look at that manuscript as i desire your response to the same to continue my thinking in such a matter further!

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Author Cristinel Stoica replied on Feb. 11, 2018 @ 06:42 GMT
Dear Narendra, I'll gladly look at it

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Rick Lockyer wrote on Feb. 10, 2018 @ 19:51 GMT
Cristi,

Every essay contest, when I see your entry, it goes towards the top of my list, for you always have something enlightening to say. I know nothing about Indra’s Net, will look into it for context here.

I wish you would have gotten into more detail on what your expectations were for holomorphic functions for Geometric Algebras over the field of complex numbers across dimensions.

My interest is Octonion Algebra, where there are seven complex subalgebras. If the Cauchy-Riemann equations were applied for all, every irrotational field component in their expected form would be identically zero, which just would not do if one wants to cover Electrodynamics and Gravitation with potential functions.

You mentioned to Geoffrey Dixon some apparent belief one would need non-associative Physics to justify use of a generally non-associative Algebra such as Octonion Algebra. I think he came back with the quip it is a feature and not a bug. This is true, and it is required to allow it to be a division algebra. Nature is not saying use Octonion Algebras only if you have non-associative physics, since really it spans multiplicative associative, non-associative, commutative and non-commutative properties intrinsically, and not only spans but precisely tells us how they play together in the greater whole of the full complement of basis products. Nature is more likely telling us Octonion analysis can go where essentially matrix based associative algebras like tensor and spinors can’t go, with little to no limitations going the other way.

If you get a chance, look at my essay, it is called “Truth”.

Rick

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Author Cristinel Stoica replied on Feb. 11, 2018 @ 06:49 GMT
Dear Rick,

Thank you for the kind comments. You said "I wish you would have gotten into more detail on what your expectations were for holomorphic functions for Geometric Algebras". Me too :-) Yes, I guess this is interesting for octonions too, but as you pointed out if you just take complex subfields this will not work. What I mean is that the Cauchy-Riemann operator is generated to the Dirac operator (which is a generalization of that in the Dirac equation as well). This is also done for quaternions. So maybe such a generalization can be done for octonions too, and in this case it will not be the same as the Cauchy-Riemann condition for complex subspaces of octonions. But I didn't study so far how to do it. Thank you for recommending me your essay, it is on my planned readings.

Best regards,

Cristi

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Thomas Howard Ray wrote on Feb. 11, 2018 @ 02:10 GMT
Hi Cristi,

"The entire state of the universe is therefore encoded in a single class of germs."

Is there a least germ? (There is, In Indra's Pearls.)

A wonderful, imaginative essay! My essay here.

All best,

Tom

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Author Cristinel Stoica replied on Feb. 11, 2018 @ 06:50 GMT
Hi Tom,

Thank you for your kind comments. I have your essay in my reading list too, and I am looking forward to read it.

Best regards,

Cristi

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Michael Alexeevich Popov wrote on Feb. 11, 2018 @ 16:21 GMT
Christi,

I think that Fundamentalness is something which we can investigate systematically as scientists but not as the poets...

My modest attempt is made in essay entitled as "Fundamentalness of Homochirality".

Thank you for essay

Michael A.Popov

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Author Cristinel Stoica replied on Feb. 11, 2018 @ 16:35 GMT
Michael,

Ouch! I bet you didn't even read my essay :))

Cristi

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Terry Bollinger wrote on Feb. 12, 2018 @ 00:08 GMT
Professor Stoica,

[First my pledge: goo.gl/KCCujt ] The positives for your essay are:

-- This is one of the best and most accurate quick summaries of both the basics and the edges of particle physics that I’ve seen. You manage to get to Clifford algebras in just a few pages, and to do so in a way that I think gives general readers a fighting chance to follow your points and...

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Author Cristinel Stoica replied on Feb. 12, 2018 @ 15:40 GMT
Dear Terry,

Thank you very much for the comments. I loved your pledge!

You mention the Plank length. I am not convinced of this, because I see no evidence for such special distance. I think the Plank units arise because there are some equations which can be solved to get them, but why would they be relevant? If Plank length is the minimum length, then why isn't the Plank mass the...

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Avtar Singh wrote on Feb. 12, 2018 @ 16:22 GMT
Dear Cristi:

I fully agree with your conclusion - "And 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, including the observer experiencing separation in space and the flow of time. .....No additional mechanism is needed to unfold the germ, unfolding itself is part of the enfolded."

The fundamental wholesome reality of the universe can be represented without an explicit notion of separated space-time. The same conclusion is unfolded in my paper - “What is Fundamental – Is C the Speed of Light”. that describes the fundamental physics of antigravity missing from the widely-accepted mainstream physics and cosmology theories resolving their current inconsistencies and paradoxes. The missing physics depicts a spontaneous relativistic mass creation/dilation photon model that explains the yet unknown dark energy, inner workings of quantum mechanics, and bridges the gaps among relativity and Maxwell’s theories. The model also provides field equations governing the spontaneous wave-particle complimentarity or mass-energy equivalence. The key significance or contribution of the proposed work is to enhance fundamental understanding of C, commonly known as the speed of light, and Cosmological Constant, commonly known as the dark energy.

The manuscript not only provides comparisons against existing empirical observations but also forwards testable predictions for future falsification of the proposed model.

I would like to invite you to read my paper and appreciate any feedback comments.

Best Regards

Avtar Singh

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Author Cristinel Stoica replied on Feb. 14, 2018 @ 07:18 GMT
Dear Avtar,

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

Best regards,

Cristi

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Jonathan J. Dickau wrote on Feb. 14, 2018 @ 04:41 GMT
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

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Author Cristinel Stoica replied on Feb. 14, 2018 @ 07:15 GMT
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

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Jonathan J. Dickau replied on Feb. 16, 2018 @ 21:14 GMT
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

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Member Dean Rickles wrote on Feb. 15, 2018 @ 02:28 GMT
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".

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Author Cristinel Stoica replied on Feb. 15, 2018 @ 12:36 GMT
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

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Steve Dufourny wrote on Feb. 16, 2018 @ 12:14 GMT
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

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Author Cristinel Stoica replied on Feb. 18, 2018 @ 06:45 GMT
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

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Steve Dufourny replied on Feb. 18, 2018 @ 19:14 GMT
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.

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Avtar Singh wrote on Feb. 16, 2018 @ 18:27 GMT
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...

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Author Cristinel Stoica replied on Feb. 17, 2018 @ 07:23 GMT
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

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Dizhechko Boris Semyonovich wrote on Feb. 17, 2018 @ 21:47 GMT
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.

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Author Cristinel Stoica replied on Feb. 18, 2018 @ 06:47 GMT
Dear Dizhechko Boris Semyonovich,

Thank you for the comments, this is very interesting.

Best regards,

Cristi

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Member Marc Séguin wrote on Feb. 17, 2018 @ 22:30 GMT
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...

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Author Cristinel Stoica replied on Feb. 18, 2018 @ 17:37 GMT
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...

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Anonymous wrote on Feb. 19, 2018 @ 04:11 GMT
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...

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Author Cristinel Stoica replied on Feb. 19, 2018 @ 07:18 GMT
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...

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John Brodix Merryman replied on Feb. 19, 2018 @ 22:47 GMT
Cristi,

"This would mean that no region of space can exist, being collections of points."

This illustrates my point, in that if all those points have no dimensionality, i.e. some modicum of space in the first place, then they are all multiples of zero.

"Ockham's razor has two edges."

If I may describe my own view of physical reality, it is a dichotomy of energy and...

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Author Cristinel Stoica replied on Feb. 20, 2018 @ 05:56 GMT
John,

Let's take them one by one. You said "the dimensionless point is the essential geometric concept, yet it is explicitly a multiple of zero, being dimensionless and consequently, mathematically doesn't exist"

Please start by proving your statement that dimensionless points are multiples of zero. Zero is a number, a multiple of zero means zero times another number, and this is zero. And you equate the number zero with a point, which doesn't seem to be a number.

Then, assuming that you will be able to prove the previous statement, prove that if something is zero, then "mathematically doesn't exist". Do you mean zero doesn't exist mathematically?

Here is what I mean by "proof".

Best regards,

Cristi

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Armin Nikkhah Shirazi wrote on Feb. 19, 2018 @ 12:49 GMT
Dear Cristi,

You have written a very attractive introduction to your research while highlighting its solid connections to the contest topic.

A few specific comments:

1. I really enjoyed the playful example at the beginning. While the importance of isomorphisms between seemingly different structures is well recognized by physicists, mathematicians, and philosophers of physics,...

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Author Cristinel Stoica replied on Feb. 20, 2018 @ 06:36 GMT
Dear Armin,

Thank you for reading the essay and for your relevant comments.

1,2. Thank you!

3. Good question. In my essay I argued both for epistemological and ontological fundamentalness. It is not easy to separate the two, because whenever we speak about ontology we do it in a certain epistemological framework, but let's try. I hope section "Quantum holism" makes it clear...

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Armin Nikkhah Shirazi replied on Feb. 21, 2018 @ 11:32 GMT
Dear Cristi,

Thank you for elaborating on your view, which I tink I can understand a bit better now. Your view reminds me a bit of that of the presocratic philosopher Parmenides, who claimed that "All is one" i.e. that the universe and everything in it is like one solid unchanging block, and that any change or smaller parts we perceive is an illusion, a deception by our senses. It seems to me that someone who applies these ideas to fundamentality would not be so far removed from considering it a purely epistemological matter, except for the one ontological truth of the fundamentality of a unified whole.

The person who in my mind is the best known modern proponent of Parmenidean ideas in physics is Julian Barbour. Perhaps you may also have an affinity for some of his ideas on general relativity.

All the best,

Armin

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peter cameron wrote on Feb. 19, 2018 @ 23:46 GMT
Hello Cristi,

Much appreciate the number scrabble. We have a 5yo great-grandson in the care of his great-grandmother, who loves games and puzzles, will be delighted with this.

Glad to see so much interest in Clifford algebras in this year's competition, and particularly the geometric interpretation. Much agree with your statement

"If there are fundamental geometric structures in physics, we expect them to bring not only a unification of the formalism, but also of principles and of

entities like particles and fields. If we expect that the holomorphic fundamentalness plays a role in physics, probably the way is by geometric algebras."

If one takes the vacuum wavefunction to be comprised of the fundamental geometric structures of 3D Pauli algebra - one scalar, three vectors, three bivectors, and one trivector - then wavefunction interactions can be modeled by the geometric product.

This yields a 4D Dirac algebra of flat Minkowski spacetime, an 8x8 matrix that is the geometric structure of the S-matrix. Time emerges from the interactions in the form of relative phases of the interacting geometric structures that comprise the wavefunctions. It is encoded in the 4D pseudoscalars. Seems like there is no need for complex numbers in this Hestenes formulation of STA. Would much appreciate your opinion on this.

It seems there is much commonality between what you are doing and the approach Michaele and I have been taking with geometric wavefunctions. What you call Indra's net can be thought analogous to the quantized electromagnetic impedance networks that couple fundamental geometric structures in our model. We are working with Cl(1,3), tho the manner in which we assign quantized EM fields to the 8 component Pauli wavefunction seems to require three or four copies. Our group theory grasp is minimal. Have more questions, would much appreciate some help if you're interested.

and your hexagrams have me reaching for the I Ching.

Best regards,

Peter

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Author Cristinel Stoica replied on Feb. 20, 2018 @ 08:33 GMT
Hello Peter,

Thank you for reading the essay and for the insightful comments. Indeed, the Clifford algebras deserve more attention in physics. You mention Hestens, he did great job in formulating parts of physics and geometry in terms of Clifford algebra. His representation of the Dirac electron in terms of the real algebra of spacetime has interesting features, but I think it is not exactly how I would view the electron, because by dropping some of the degrees of freedom it becomes impossible to represent it in a Lorentz invariant way (by this I mean it projects some internal degrees of freedom on spacetime related quantities). The Dirac algebra is complex because it mixes the U(1) symmetry with the spacetime Clifford algebra. I think that complex numbers are in fact rotations in various real spaces, and the usual way physicists use them obfuscates this. For instance, when we take the nonrelativistic limit of the Dirac equation to get the Pauli-Schrodinger equation, different operators which square to -1 all become forgotten, and represented as i, which is the Hodge * operator in 3D. In my complex Clifford 6 model I don't clarify these differences, but I am developing a model in which they become manifest. You made me curious about your approach, I look forward to see it.

Best regards,

Cristi

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Edwin Eugene Klingman wrote on Feb. 20, 2018 @ 00:38 GMT
Dear Cristi,

You get off to a great start showing the isomorphism between 'number scrabble' and 'tic-tac-toe'. You note that "in mathematics, isomorphism's are ubiquitous", mentioning that Euclidian geometry ~ axiomatics ~ symmetries ~ numbers/equations, for example.

This supports very nicely my thesis that physicists project mathematical structure onto physical reality,...

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Author Cristinel Stoica replied on Feb. 20, 2018 @ 09:52 GMT
Dear Edwin,

Thank you for the interested comments and reading my essay.

You are right that physicists, like any other humans, project their views onto reality. But I don't think we can use this as argument to simply refute some of the achievements of physics. I would say the opposite is the right way, find where they are wrong and then conclude this was because of a wrong projection....

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Edwin Eugene Klingman replied on Feb. 20, 2018 @ 22:08 GMT
Dear Cristi,

Thank you for responding to my comment. You have certainly understood my main point, that we project interviews onto reality. However you misinterpret me when you suggest "find where they are wrong and then conclude this was because of a wrong projection."

That is exactly what I am doing!

My essay discusses the arguments for one such wrong projection. It is...

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Edwin Eugene Klingman replied on Feb. 21, 2018 @ 02:08 GMT
Dear Cristi,

After responding to you I started looking through 26 Jan 2018 copy of Physical Review Letters I received in the mail today. I was interested to find article 040406 titled

"Violation of Bell's Inequality Using Continuous Variable Measurements"

That is essentially the argument I was making above about the continuous variable deflection of silver atoms instead of Bell's constraint of +1 and -1. The current article is based on quantum optics, and therefore does not translate directly into atomic tests, but I hope you can see that it is an isomorphism of the paper I linked to above. The authors [Thearle, e al.] note that for continuum variable quantum optics the Bell test is harder to realize. But, significantly, they state

"Bell argued that quantum states with positive definite Wigner function would not violate a Bell inequality with respect to continuous variable measurements."

They claim the first observation of Bell correlations in a continuous variable system. As I said, this does not translate directly into Stern-Gerlach type of atomic tests, but I believe it is isomorphic to the continuous variable deflection measurements that I describe and that I have shown to violate Bell's inequality.

Best regards,

Edwin Eugene Klingman

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Robert D. Sadykov wrote on Feb. 21, 2018 @ 07:19 GMT
Dear Cristinel Stoica,

Your essay is very well written. I can not appreciate it from an expert point of view, because it requires much additional information, but as a simple reader I appreciate it very highly.

I wish You success with the contest!

Best wishes,

Robert Sadykov

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Author Cristinel Stoica replied on Feb. 21, 2018 @ 08:37 GMT
Dear Robert Sadykov,

Thank you for your comments. I tried to say something worth reading for people with different specializations, so I am glad you liked those parts where our expertise overlaps. I wish you success too!

Best regards,

Cristi

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Heinrich Luediger wrote on Feb. 21, 2018 @ 11:35 GMT
Dear Cristinel,

the structure of your essay is quite typical of many others. So allow me a more general criticism at this point. You begin with the human perspective, e.g.: “The universe is rich in complex phenomena and situations of infinite diversity…”. From there you jump to isomorphisms, mathematical isomorphisms to be sure. Then, after long discussion and diversion you end up in...

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Author Cristinel Stoica replied on Feb. 21, 2018 @ 13:41 GMT
Dear Heinrich,

Thank you for the comments. About the "human perspective" I talked more in an older essay when the topic was more suited for this. About emergence I wrote in my previous essay. This time I wanted to write about some new ideas I have about fundamentalness, and how I didn't pull out of my hat the holomorphic fundamentalness idea, because it is endorsed by physics, in particular by a unified model of particles which I developed.

Best regards,

Cristi

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Gary Valentine Hansen wrote on Feb. 22, 2018 @ 00:40 GMT
Cristi,

Your final words: ‘Holomorphic fundamentalness may be a mathematically consistent basis for holism and the holographic principle, but until we ... have the unified theory of physics, it remains an exercise of imagination’ is the most fundamental conclusion that can be drawn concerning the FQXi question What is ‘Fundamental’. Thank you.

No one so eloquently disclosed the importance of this turn of events as Albert Einstein in a 1921 lecture Geometrie und Erfahrung: ‘As far as the mathematical theorems refer to reality, they are not sure, and as far as they are sure, they do not refer to reality.’

It is comforting to think that everything can be reduced, through mathematics, to physics; but as you imply, and I interpret, in the absence of a unified theory of physics, we are left to ‘imagine’. Most conspicuously absent from any unified theory to date is how ephemeral topics like consciousness, dreams, ideas, indeed the ‘mind’, can possibly be embraced within a unified theory of physics.

Thanks for the therapeutic solution: ‘imagination’. Upon reflection, this is what we have been relying upon for eons; a ‘comfortable substitute explanation’ for the ‘reality’ of our ignorance of the preponderance of the constituents of ‘a universe ... rich in complex phenomena.’

Like you, ‘I ... focus on a particular meaning of “fundamental” as something that is at the root of everything.’ Apparently we have both recognized that the FQXi question What is “Fundamental?” invites a singular response. Otherwise the question would be framed: What are “Fundamental?” This ‘reality’ has guided us both to ‘imagine’ a fundamentally more fundamental concept than many others have disclosed.

Best wishes,

Gary.

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Author Cristinel Stoica replied on Feb. 22, 2018 @ 16:26 GMT
Dear Gary,

I appreciate your comments. I agree with

> "Most conspicuously absent from any unified theory to date is how ephemeral topics like consciousness, dreams, ideas, indeed the ‘mind’, can possibly be embraced within a unified theory of physics."

Indeed, a unified theory is not a theory of everything, and reductionism has serious limitations which I analyzed last year in The Tablet of the Metalaw.

I look forward to read your essay, I hope soon.

Best wishes,

Cristi

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John R. Cox wrote on Feb. 22, 2018 @ 02:43 GMT
Cristinel,

May I ask, what is your thinking on inertia? What is it?

An advertisement for something a while ago, started with the old saw, "Its simple physics. A body at rest tends to stay at rest. A body in motion tends to stay in motion." It might have been for a vitamin or nutrient suppliment, but there is nothing simple about inertia. And the generalization is really only an operational definition. It says nothing of what it is about inertia, that is the same thing for any mass independent of its state of motion.

How do you see Relativity and QM treating inertia? If you would, please.

Thank-you, respectfully, jrc

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Author Cristinel Stoica replied on Feb. 22, 2018 @ 17:47 GMT
Dear John,

Yes, at the simpler, classical or mundane level, I think "A body at rest tends to stay at rest. A body in motion tends to stay in motion" is a good definition. I can't help noticing how Newton carefully distinguishes between "rest" and "motion", which reveal his conception of an absolute space.

In GR and QM, I see inertia in a different way. One attribute is momentum, but...

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John R. Cox replied on Feb. 22, 2018 @ 19:10 GMT
Cristinel,

Thank-you, that is a highly condensed quantity of information and I'll want to read up on parts. And I have to head out in a half hour for an appointment. But the element of elasticity seems required by experiment when we consider relativistic effects at high energy; a footnote in Einstein's "Mechanics and the Attempts to Base All Physics Upon It" states, 'As a consequence of (sic) SR the energy of a closed system is equal to its inertia.' So density and elasticity must operate to close the system such that inertia translates throughout the whole energy quantity as a function of velocity.

Best wishes, jrc

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Anil Shanker wrote on Feb. 22, 2018 @ 20:46 GMT
Dear Cristi,

I enjoyed reading your essay-article. You beautifully discuss the fundamentalness in the context of holism. The conclusion as you put says it all about our limitations in grasping the depth of fundamentalness/absoluteness: "Holomorphic fundamentalness may be a mathematically consistent basis for holism and the holographic principle, but until we will have the unified theory of physics, it remains an exercise of imagination." You also allude to the free-will and germ theory. Thus, the comprehension of fundamentalness will entail a deeper journey into the worlds of biological and physical evolutions that I believe co-exist and are co-dependent.

Berst regards,

Anil

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Author Cristinel Stoica replied on Feb. 23, 2018 @ 12:11 GMT
Dear Anil,

Thank you very much for your insightful comments. Yes, all these are very complicated problems and it would be unrealistic to expect a solution coming easily from the usual reductionist framework. I enjoyed your essay too, and I wish you success!

Best regards,

Cristi

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Maxim Yurievich Khlopov wrote on Feb. 23, 2018 @ 20:06 GMT
Dear Dr. Cristi Stoica,

I have enjoyed your interesting approach to the construction of unification of fundamental forces. Just to note that the problem of SU(5) unification was also related with magnetic monopole overproduction in cosmology and a theoretical problem of hierachy of GUT and electroweak scales.

Thank you very much for your burst of interesting ideas.

With the best regards

Maxim Khlopov

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Author Cristinel Stoica replied on Feb. 24, 2018 @ 08:31 GMT
Dear Dr. Maxim Khlopov,

Thank you very much for reading the essay and for the comments. I also enjoyed reading yours.

Best regards,

Cristi

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Steve Dufourny wrote on Feb. 26, 2018 @ 13:53 GMT
Hello Cristi,

I have thought a lot about how we must really consider what is a particle.And it is important.Is a wave giving all shapes due to tensors and fields with the geometrical algebras or is it a finite system giving the properties to fields and waves.It is totally different.

Because the main causes are totally different and the primordial field also.The facts to consider that a particle is a wave able to have all shapes seem having a problem.

In fact it is not a wave which give a particle but a particle which gives a wave, it is different about the main causes even for our inertial mass and also for our quantum weakest force.That said this can converge.

Regards

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Author Cristinel Stoica replied on Feb. 26, 2018 @ 14:15 GMT
Hello Steve,

Well, there is no consensus and no definitive data, we don't know exactly what a particle is. So we should be open to all possibilities which are not definitively eliminated. For me the wave or excitation in the field seems to work better, but I think it is not the full story, the wave has to satisfy certain equation and quantization too, which I think is not understood. I have some working hypotheses which are based on geometry and topology, but no definitive answer yet. So we should feel free to explore what other possibilities may be.

Best regards,

Cristi

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John R. Cox replied on Feb. 26, 2018 @ 17:18 GMT
Steve,

I very much agree with that. A rationale that adequately describes both the observed limits of EMR and the terminus of a.m.u. with the same set of parameters and corresponding equations in real terms, is a prerequisite for unambiguous interpretations of conflicts such as EPR. You seem pretty well, Steve, its good to see. best - jrc

Cristi,

Glad to see scholarly statement of that! Where the distinction lies between a latent wave action and an absolute free rest mass of energy, is both a theoretical as well as hypothetical question given the 2.76*K ambient background of thermalized radiation. Its also nice to see recognition that a long sought and essential 'unified field theory' would not in itself constitute a TOE.

The treatment of time is always such a contentious matter, but I personally think we can accept a Platonic absolute time registered to the Earth Second, only in analysis where we can already state parameter values across distances. It was Einstein himself whom objected to interpretations of SR which bestow *real* physical dimensional change in dilated results at velocity. But that leaves the question open as to how relativistic energies kinetically accumulate and transfer. Progress needs a leap of faith, and more degrees of freedom, to make a physical consequence of Lorentz practical and genuinely realistic.

Best of luck in the contest, I have been a little surprised that Relativistic papers haven't been immediately one-bombed this time around. I would like to think that indicates some growing awareness that modern classicism does not reject probability out of hand. Regards - jrc

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Steve Dufourny replied on Feb. 28, 2018 @ 10:29 GMT
Hello John,Cristi,

Hi John,

Thanks , hope you are well.

I say that it is important this difference about main codes implying propoerties and shapes.The geometry and topology seem to be due to intrinsic codes in our particles, like if they knew what they must become.

The geometrical algebras are relevant correlated with QFT and strings, and a kind of 1D primordial field implying the main cause, but I prefer to consider that main causes are intrinsic in our particles.

The luminiferous aether seems encircled by the gravitational aether.Both of these aethers are like informations of evolution due to encodings.These informations and fields are encoded and they respect in logic the main intrinsic causes of particles implying shapes and properties, gravitational and electromagnetic.

It is important like difference.I like the E8 lie algebras but that seems not sufficient for a real understanding of the generality of our universe.The important difference is there, about the external cause or the intrinsic cause.

The pre planckain era has created particles with codes and these codes encode since the begining of this physicality and the informations of evolution are encoded and continue the road implying this diversity of matters and the building.

friendly

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Jonathan J. Dickau wrote on Feb. 26, 2018 @ 22:56 GMT
Greetings,

I have not seen a comment from you yet Cristi. If you have not read or rated my essay, now would be a good time. Time runs short and I just got bombed!

All the Best, JJD

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Author Cristinel Stoica replied on Feb. 26, 2018 @ 23:34 GMT
Dear Jonathan,

Thank you for your comments, and for reminding me to comment and rate your essay. I read it a while ago and wanted to come back to you with some questions, and then it seems I forgot. I see you got bombed, I was too, especially in the last 24 hours I went from 1 to 11, now I see it's a bit better. Me, Andrew, and maybe Karen, who were 1-bombed too, wrote about this to the organizers, since it's against the rules. All ratings between 1 and 10 are legal, but when these happen massively and without comments containing the criticism, as it happened now as the deadline is coming, it raises some questions and needs to be investigated. You had comments about my essay, please check if you rated, and if not, please do it according to how you evaluate. It is important to read and rate accordingly as many essays as possible, to make the one bombs less relevant, and also to give a better overall evaluation of the essays. Good luck in the contest!

Best regards,

Cristi

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Member Sylvia Wenmackers wrote on Mar. 12, 2018 @ 20:32 GMT
Dear Cristi,

Thank you for telling us about Indra's net: I really liked that image.

My general impression was that your essay mainly deals with fundamentalness within mathematics - which is fine -, although at crucial points it becomes clear that you do intend to address physics instead.

Regarding the long endnote 8, I wanted to suggest to you Hoefer's (2001) book chapter "Freedom from the inside out"; while he addresses the block universe rather than holomorphism, I do think there are many connections to your musings here.

Best wishes,

Sylvia - Seek Fundamentality, and Distrust It

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Author Cristinel Stoica replied on Mar. 13, 2018 @ 11:08 GMT
Dear Sylvia,

I appreciate that your read and commented my essay, especially since this phase is closed. The exchange of ideas should not be limited to getting into the finals, so if we couldn't read and comment enough, nothing stops us to continue. So I read and commented your excellent essay too - I planned to do this earlier but the time was too short. You said "My general impression was that your essay mainly deals with fundamentalness within mathematics - which is fine -, although at crucial points it becomes clear that you do intend to address physics instead." Yes, I think that about the foundations of physics there's not much to be said beyond the mathematics, except of course the empirical and epistemological bridges, which connect the theory with the reality and with our understanding. More about this in a previous essay. Roughly, I had two major points, the first being that of "relativity of fundamentalness", which I think it is universal but can be better exemplified with mathematics, and also with physics, going beyond what you identified in your essay "concrete 'elements'" and "abstract principles" as usually seen, as you also went beyond these. In the second I proposed an 'extreme' possibility of the same, holomorphicity, which unlike relativity of fundamentalness is not universal, but I think it may be realized in physics. I had the idea that the world is holomorphic in the way described here (but with much less specific details) 25 years ago, and shortly after that I realized that it may have implications to the free will. Thanks for pointing me to Hoefer's chapter, Scott also told me about it in relation to my approach to QM [1, 2] and my adjacent comments of free will for those who may think that indeterminism allows it and determinism doesn't. Hoefer's proposal doesn't need holomorphicity, it is based on determinism, and at first sight it is, wrt physical consequences, a mere reinterpretation of deterministic causality to accomodate free will, based on the block world picture from relativity. But I think it is more than this, because when I tried to see what happens if in quantum mechanics we keep unitary evolution and remove the collapse (without appealing to MWI), I got that the initial conditions have to be "delayed", or that the solutions should satisfy some "global consistency conditions" which are spread at different places and times in the block world. I see this global consistency condition mathematically as being realized in sheaf theory, which arose partially from the study of complex holomorphic functions. Holomorphicity seems to me the best way to realize this as more than reinterpreting determinism, since they are the most constrained by global, topological conditions.

Best wishes,

Cristi Stoica

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