Essay Abstract

It is said that General Relativity fails, because of the occurrence of singularities, and of the non-renormalizability of Quantum Gravity.
Is this failure due to General Relativity, or to our limited understanding? If singularities exist, then did God divide by zero, or we did?
Several fundamental assumptions limited our understanding. Once we get rid of them, we can understand singularities, and see that actually they don't destroy spacetime and information. I show explicitly that the Big-Bang singularity of the FLRW model, and the black hole singularities, can be understood without modifying General Relativity or adding unphysical fields.
Singularities turn out to be our friends. They smoothen and homogenize the Big-Bang. They remove the infinities of the electromagnetic field, and provide a regularization of the quantum fields. They open a door toward a Quantum Gravity, by dimensional regularization.

Author Bio

Cristi Stoica is PhD student.

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Hi Christi,

Happy to see also your essay .

Hope you are well. It is intriguing your words "God divide by zero".

I beleive also that these singularities don't destroy the information and spacetime. Of course the space time is curved by these BH in this case.Because they have a mass. These BH are intriguing. These spheres are imrpotant in volume and mass. They have a rotation also, weak in my line of reasoning. If they have a rule about the sortings of these informations, so it is very intriguing indeed. For the universal rotation , their vol. and mass permit to embark the stars and planets of their own galaxy. They produce probably also several relevances. I beleive strongly that our 3D is essential. If we fractalize this 3D, so we have several relevances when we insert rational series. Perhaps that the p-adic numbers can help like Cauchy. Rieman and De Sitter also are welcome for the metric.

Jonathan, do you know the Ktheory and the algebric topology. I study a little this topic. I beleive that it is important to consider the fractalization of this 3D. If the Ktheory do not verify the axiom de dimension.What is really this meaning for you ? if the BB is a singularity, and if now this cenetr is the central sphere of our universal sphere, so in my line of reasoning, the actual volume and mass of this central sphere is very very important.

I gree about the rules of complementarity and regularization. The synchros and sortings are essential for a global harmonious oscillation. The dimensional regularization is a pure 3D at my humble opinion. The hidden variables and causalities must respect the proportions of rotations of 3D spheres. The universal mechanic is relativistically the same at all 3D scales.(quant.or cosmol.). The p-adic numbers permit at my opinion to begin with the number 1, if we insert the correct convergent series with a completion, of pure dterminism.So we can see these singularities and their correlated volumes and mass. We can use the real numbers for the tazxonomy of complexification inside the serie of primes and p-adic numbers. R,Q and Qp can be classed inside a pure 3D Sphere and its intrinsic spheres. I beleive strongly that we cannot understand the puzzle if we do not consider the serie of uniqueness. That is why the universal fractal is essential. between 1 and x. After we play with this serie at all 3D scales.

Regards

    Hi Christi,

    I look forward to reading your essay, having just read your paper "BEYOND THE FRIEDMANN-LEMAITRE-ROBERTSON-WALKER BIG BANG SINGULARITY" as one of the major sources of a paper by Andrew Beckwith I was asked to comment on. It looks like your essay is largely based on that work.

    And hello also Steve. It is intriguing to find a comment from you here, though, before I arrived. According to Witten, K-theory will reveal differences between structures with similar attributes cohomology does not. Examples are higher-d spheres, tubes and 'hills' on a brane, which are all clearly distinguished from each other by K-theory.

    And I like the fractals too, but maybe the comment was meant for Cristi or the other Jonathan. Thanks for the space, Cristi. I'll comment further when I actually read your essay.

    Regards,

    Jonathan

      Dear Cristi Stoica,

      A very impressive essay, not to mention visually beautiful and with an exceptionally catchy and appropriate title. The topics you cover are quite important. The idea of transforming to a better behaved solution is of course not new, but the hullaballoo about singulatities has gone on for at least a century, so it would appear that your solution is new. If you'ved solved the singularity problems for GR and QFT that's a big deal. Your approach makes sense to me, and you've provided lots of references to apparently detailed examples.

      I particularly like your conjecture for figure 5, since I am not a great believer in quantum fluctuations of the vacuum.

      You note in your essay that it is a logical continuation of your previous FQXi essay, but does not depend on it. The same applies to my essays, and a number of other authors. I think this means that we can expect to see increasing quality in the essays, and I think it's already evident.

      Good luck in the contest,

      Edwin Eugene Klingman

        Dear Steve,

        Thank you for the nice comments. I'm fine, thanks, and I hope you are well too. You make interesting comments and connections between various ideas.

        Best regards,

        Cristi

        Dear Jonathan,

        Thank you for your welcome comment. Indeed, this essay builds upon previous work I done, including the paper you mentioned. I look forward to reading your essay.

        Good luck in the contest.

        Cristi

        Dear Edwin,

        Thank you very much for commenting on my essay and for your kind words. I based the conjecture on the dimensional reduction which accompanies the benign singularities. If particles are like this, then these singularities have a benefic effect on the fields, contrary to what one usually expects.

        I look forward to reading your essay and those of the others. Good luck to you too.

        Best regards,

        Cristi

        Christi

        A very well written and presented case. You do verge on axiomising that space is not directional, but Christian and Tom show that it may be so. From the astronomical viewpoint we have CMBR anisotropy and the axis of flow, which supports this. I believe you may gain from it.

        What would your opinion be of a twin version of your 'vortex' model A, joined at the (non) singularity so reverting to forming the inner 'half' of a toroid (the rest of the toroid naturally follows).

        I have been exploring these, and indeed Active Galactic Nuclei (AGN's) or SMBH's are of course toroidal. The form is also scale invariant, (see the stellar scale version at the Crab Nebula heart) so may extend from the scale of the universe(s) to particles.

        This model also explains the 'accretion disc' and jets of quasars, which are EM toroidal fields (as Earth's) with the re-ionized matter ejected from the centre in both directions (precessing).

        A 'big bounce' recycled universe process then emerges from the intrinsic rotation of space, on the lines of Dicke/Peebles and indeed Penrose.

        Is this a possible valid extension of relevant part of your model?

        There are many consistent parts in my own essay which tackles the fundamental kinetic matters and derives relativity direct from a quantum mechanism. In particular I love your 'intimate dance between matter and spacetime' which I resolve in an unusual way, and also agree with your trust in the "evolution equations", but analysing the temporal evolution of Raman scattering with non zero media co-motion.

        Very well done. I hope you will read carefully and comment on mine.

        Peter

          Dear Peter,

          I am glad you read and like my essay.

          Concerning space anisotropy, it happens often in physics. In fact, even in my essay, the singularities exhibit anisotropy. At the singularities, some directions behave differently, and also there are anisotropies between space and time.

          The twin vortices you mention may be related to the Kerr black holes, especially since you mention EM toroidal fields, and explanation of accretion disks and jets. These, and the Big Bounce due to rotation, are compatible with what I am doing, because I consider that my results just extend General Relativity to singularities.

          I look forward to reading your essay.

          Best regards,

          Cristi

          Thanks Christi,

          I am trying to evolve even with my personal problems. I learn in fact, it is, after all, my only one reason of being. I must found a good american University.

          I d like to continue to study and to improve my works.I am disgusted by my country. And I must solve also the probelms of my mother. She is very tired morally speaking in fact and me also. My works about this spherization's Theory is the only one thing that I have and my mother. I d like go at Princeton, to have my Phd.And to improve my works.i d like also test and experiment my models and inventions. But I don't know how I can do ? I have contacted Princeton. I like also Stanford or Berkeley in California.But I don't know how I can do to have a scholarship. My economical situation is weak in fact. I have not a job furthermore. I am near my mother. I must move in fact. I have always dreamt to be in an american university in fact you know.

          Regards

          Hello again, Cristi,

          I apologize, because even though I have not finished reading your essay; I already have a number of questions, comments and possible objections - arising from points made in the earlier paper I did read. Foremost; does being able to address mathematical complications in solving Einstein's equations completely address Physics concerns near the Planck scale? Here are my thoughts.

          You are describing a unique construction where everything goes to zero and the Planck scale is not conserved in any way, but the dimensionless point is rather tricky to correctly address even if you do make the event-horizon boundary go away, because going to 0-d is the ultimate dimensional reduction. Going there, even for a brief instant, establishes a condition where there is no metric as such.

          But of course, we are viewing from off the page; if it is assumed the timeline continues on the other side of the zero point, then the existence of duration in time is assumed for space - otherwise it could not exist at all. That is; spatial dimensions can only be said to have an extent if their extendedness persists in time long enough to be observed. As Fotini Markopoulou said of Wheeler-DeWitt in one paper; this assumes a kind of God's eye view - that can survey the universe from outside it.

          My Math Physics intuition of spacetime says that the spatial dimensions can only go to absolute zero if time never does. That is; maybe the minimum length is actually the Planck time, and for a brief instant all the mass/energy in the universe is concentrated in the time direction. This would not violate concerns about catastrophic flop transitions (in the fabric of spacetime) that Brian Greene raised in The Elegant Universe, as Greene may also offer a solution.

          If we assume that, rather than a geometric point, there is a 0-brane - at the point of singularity - this might provide a solution or allay such concerns. My understanding is that - by analogy to the spheres - the 0-brane is actually a pair of points bracketing a location on a line, and making that a time-like dimension treats the 0-brane as an instanton. That way, space can go to zero, but the dimension of time allowing for spatial dimensions to exist can persist while that happens.

          I guess the last point is more ontological, rather than being a Physics concern, but any thoughts on the above matters are appreciated.

          Regards,

          Jonathan

            Dear Jonathan,

            I'm happy to hear from you again.

            You asked: "Foremost; does being able to address mathematical complications in solving Einstein's equations completely address Physics concerns near the Planck scale?"

            My first efforts were directed to solving the problem of singularities in General Relativity. GR is about Einstein's equation, and not about Plank scale. The equations led to singularities, and my first concern was to see what happens there.

            You said: "You are describing a unique construction where everything goes to zero ..."

            It is not quite true that "everything goes to zero". Only some quantities go to zero, in a way which cancels what we expect to go to infinity. I tried to offer a mathematical description of what's going on there, and it appears that the things are better than it is usually claimed.

            "... and the Planck scale is not conserved in any way, but the dimensionless point is rather tricky to correctly address even if you do make the event-horizon boundary go away, because going to 0-d is the ultimate dimensional reduction. Going there, even for a brief instant, establishes a condition where there is no metric as such."

            I am not sure what you mean by conserving the Plank scale. Should General Relativity obey assumptions about a minimal length, which belong to other theories? I doubt. I can't see why the Plank length is considered minimal length, while we don't ask the Plank mass be the minimal mass. Obviously, the reason is that the elementary particles are lighter than that. Now, making the assumption that the Plank length is some kind of atom of distance belongs to some theories which consider that this will solve the problem of Quantum Gravity, and as a bonus, the problem of singularities, by forcing a bounce. But what if GR can handle its own mess? My point is that solving the singularities doesn't necessarily require modifications of GR, such as discretization of space, branes, etc.

            While most of my papers on which this essay is based are about GR, a recent one suggested that singularities behave nice for QFT too, tempering the divergences in QFT and in Quantum Gravity. If this is true, then the main raison d'être of the discrete theories will vanish. I have nothing against them, but I don't think one should ask other approaches to copy them. Anyway, the approaches to Quantum Gravity try hard to mimic the successes of GR. Any success of GR will be inherited in the successful theory of quantum gravity, no matter how radical it may be. For this reason, even if GR will turn out to be a limit of a better theory (being it a discrete one), I can hope that my work will still be helpful, for the same reason why any advance in GR will be useful.

            Best regards,

            Cristi Stoica

            Dear Jonathan,

            I think, if it will be successful, it will provide evidence for quantum geometry. I realize that you think that my approach is not compatible with quantum geometry. Could it be because you make the assumption 2 from my essay?

            Best regards,

            Cristi Stoica

            Hi Cristi, Jonathan,

            If Hogan's experiment succeeds, then perhaps there will be evidence of a Planck length. Until then, it is certainly only an assumption. I personally believe that Planck action can be meaningful in a continuum, with no fundamental length at all, which, I guess, supports Cristi's approach. By the way, Jonathan's comment above reminded me of the topic of your previous essay, which I had not yet had time to review, so I do see how you are building on earlier ideas.

            Best,

            Edwin Eugene Klingman

            Hi Edwin, Jonathan,

            An experiment proving that there is a minimal distance will contradict my results. But quantum geometry doesn't necessarily say this, and I don't see a conflict. Anyway, if an experiment which is about to be done will be able to tell something about my theory, I can only be happy :)

            Best regards,

            Cristi

            Hello again Cristi,

            Thank you for taking the time for a detailed answer. I'll be finishing your essay, and have a look at the QFT paper. This is very interesting stuff, and it could be foundational. I don't want to needlessly cast doubt, or to be a stick in the mud, but having taken up the issue of emergent dimensionality in my own paper, I cannot help but wonder what issues lurk below the surface of your theory - relating to this.

            Like it or not - a point is 0-dimensional, and there are drawbacks to having a spacetime that is actually 0-d, as it has no extent in time. You are stopped cold if there is not a timeline left to continue. So it seems there is a disconnect. But I will read more before commenting further. Maybe my lack of understanding is the issue.

            All the Best,

            Jonathan

            Hello to both of you,

            Christi sorry for the space.

            Jonathan and Christi, the K theory seems relevant, the topology in 3D appears. The geometrical algebras are interesting when the finite groups are categorificated. Furthermore a real quantization canbe made in proportion with the rotations. The completude of bodies, natural and physical, of numbers(the p and the series), when we interpret the pure physicality, is convergent only when the axiom of dimensionality respectt the axiom of proportions due to rotations. The volumes also can be fractalized. But I believe strongly and I insist on the necessity to use the serie of uniqueness, universal. An entanglement is like a relativistic foto of our Universal 3D sphere.In fact the infinities and the finite groups are on a specific spherization of optimization. The dimensions are a fractalization of our 3D, there I can agree. But the superimposings or parallelizations or convergences or iterations must be rational! If not we have false projective systems where we loose our foundamental laws due to these spheres and their volumes and their rotations more the polarization of evolution between these fermions and these bosons. The strings in a pure sphericality can be relevant about the synchros and sortings between the bosonic spheres and the fermionic spheres. If the oscillations and its periodicity is an universal sphericality.So there are several relevances considering a pure fractalization of our 3d. The axiom of dimensionality is an interesting tool when the finite groups are analyzed with an universal uniqueness.

            Regards

            Hi Cristinel,

            Very bold title; that's good!

            Wings and prison: I could not have made a better argument. It is absolutely true that you have to take some chances, make a hypothesis, even if it flies in the face of conventional wisdom. Just be able to defend or duck when people challenge what you (someone) says. Even when people disagree with a hypothesis (or an idea) readers can see the topic from a new point of view; they can consider possibilities that they've never thought of. That's the point.

            You argue that singularities do not necessarily destroy a theory. But do singularities actually exist? If you divide the mass of a black hole by R = 0, that gives you a singularity, right? However, if the radius goes to zero, then so does the mass-energy content inside of a spherical region of radius r (r goes to zero). Doesn't that save us from singularities?