Hello Steve,

I did mention in the essay a theory named "fractal universe", which is based on scale-dependent measure. The reason I mention it is that my approach leads to the same kind of measure, but in my case it is dependent on the distance. And I argue that when we sum over higher-energy Feynman diagrams, the distances between particles get smaller, and we get a dependence on energy similar to that in the fractal universe. But my approach is not fractal, it only shares common features with the fractal universe, features it gets "for free". As for the importance of topological methods, I definitely agree.

Best regards,

Cristi

Dear Jonathan,

There are more different kinds of "dimension", and one should be careful not to mix them. For example, in CDT the topological and geometric dimensions are always 4 (there are only 4-simplices there), and what changes is the "spectral dimension", which is a totally different kind of food. Also, topological dimension is not the same as metric dimension. They can be confounded if one is not careful about "assumption 2". But in fact they are distinct, as distinct are topology and geometry. The singularities I studied and proved to be benign include standard FLRW and black hole singularities. If you think that quantum geometry contradicts my results, you should have a proof that quantum geometry never runs into singularities. This will make the supporters of quantum geometry happy.

Best regards,

Cristi

Hi Jason,

Thank you very much for reading my essay and for the kind comments. Also for the interesting question.

You said "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?".

I don't see how this works, maybe I am missing something. But I think that it would be great if you would use your argument to build a solution to this problem, so I would like to encourage you.

Good luck with the contest!

Cristi

Hi all.

Do singularities really exist?

I don't know. What if it will be proven that one of the many approaches to avoid singularities is true in our universe, and it will become evident that they do not exist? Well, I have to live with this "worry" :). Only unfalsifiable theories don't have worries. If the singularities will turn out to be inexistent, then the work I developed in the last 3 years will be useless. At least apparently: Given that Singular General Relativity is consistent, and appears to cure the infinities in QG, the theory may survive though, as a description of the classical solutions over which we sum to obtain the quantum ones. But I prefer not to speculate much about this, given that we don't know yet what Quantum Gravity is.

Best regards,

Cristi

    'Nothing is always Something', in that there is no 'zero' to define a quantity. Zero quantity refers non-existence that is unrealistic scenario of dimensionality. Universe exists in eternity.

    Dear Christinel,

    At last some figures in our try to figure Nature. Although your essay is too "technical" for me I have some intuitive words to say.

    From our "birth" to our "death" (no matter if we are particles or humans) we encompass our entanglement counterpart (although this counterpart exists in a different spacetime position). Singularities are doublets as well as everything in our world. Their "birth" (singularity) is entangled to their "death" (singularity). This does not contradict the "free will" because the later concerns the in between (birth-death) distance (period) and not the two (sub)events (birth or death).

    Information is conserved (and multiplied) during the real expansion era of a universe and it evaporates (or "vanishes") during its virtual inhalation era. The horizon of any universe is where all the existed information is stored (and represented) and this horizon (or information content) is live all the way the universe exists. Hence, the singularity is not just a point in spacetime but an entity that includes its birth, its death and its event history.

    Zero is another joker player in our physics' play. Sometimes it is used as emptiness (singularity) and sometimes as a physical value. These two meanings are completely different and their misuse confuse the matter. It seems that dividing by zero is like dividing by emptiness (which results to infinity, because from singularity could get anything as we do not care to declare the history of singularity (emptiness-zero)) in our mathematics.

    I wish you good luck to the contest

    Ioannis

    PS. by the way I wonder whether the formulae in ass. 5 should be: x^2=1/(1+h^2), y^2=h^2/(1+h^2).

      • [deleted]

      Dear Ioannis,

      Thank you for reading my essay and for the inspiring comments. And you are, of course, correct about the formulae in ass. 5.

      Good luck with the contest,

      Cristi

      Hi Cristinel,

      The way I learned about gravity, which is more Newtonian, is to assume a constant mass density rho. So the mass of the gravitating body is,

      [math]M = \frac{4}{3} \pi r^3 \rho[/math]

      Newtonian gravity is,

      [math]F = \frac{GMm}{r^2}[/math]

      Substituting in for M, you get,

      [math]F = \frac{4 G\pi m \rho r }{3}[/math]

      So when r goes to zero, the force of gravity goes to zero as well. In Newtonian physics it seems to work. Perhaps it's not this simple in general relativity.

      Dear Jason,

      I see your point now. I agree with you that Newtonian physics, although it doesn't have an upper bound for the mass density, doesn't have the same problems of singularities as GR does. Thanks for sharing your thoughts.

      Best regards,

      Cristi

      Hi Christinel,

      I guess if putting an upper limit on mass density was enough to save GR, someone would have already thought of that. I wish I had a better understanding of the R=0 singularity problem.

      • [deleted]

      The one thing which has bothered me about this coordinate transformation is that it appears that you have removed the singularity at r = 0 by replacing it with a singularity at τ^2 = 2m. Maybe some further coordinate change can eliminate that.

      Some time back I played around with the idea of letting 1 - 2m/r = e^u. then

      ds^2 = e^udt^2 - e^{-u)dr^2 dΩ^2.

      We now have to get dr from

      dr = -2me^u/(1 - e^u)^2du.

      Now the metric is

      ds^2 = e^udt^2 -2m[e^u/(1 - e^u)^4]du^2 dΩ^2.

      The singularity is at u = ∞, where the dt term blows up, and the horizon coordinate singularity at u = 0 is obvious in the du term. My rational was that the singularity had been removed "to infinity" in these coordinates and were then not a direct problem.

      Cheers LC

        Dear Lawrence,

        I don't remove the singularity, and I don't claim to do this. My purpose is to make it "benign", that is, to get rid of the infinities in g_{ab} and in the equations.

        About moving the singularity at infinities, this works for spacelike singularities, like in the Schwarzschild and Oppenheimer-Snyder black holes, if they don't evaporate. I played with this too, several years ago. The clearest way seems to me to start from the Kruskal-Szekeres coordinates. Of course, this is clear from the Penrose diagram, and indeed the singularity is moved at infinity. This is one central point of the cosmic censorship conjecture. However, if the black hole evaporates, then this approach will not work.

        Best regards,

        Cristi

        • [deleted]

        Singularity of the major Universe transfers only the dimensionality of the previous Universe to the new one, increasing the new dimensionality (by 1). There is no information transfer between the previous Universe and the present or the next one.

        I am afraid that with your method you are getting the virtual part of the Universe and not a pre- (or post-) Universe. In other words, you get the counter part of our (present) Universe. Imagine that the needle (or better the perpendicular plane, to the two lobes, in your fig. 2) as the pre-Universe. The problem of the transformation from a Universe to the next one have not been posed seriously by the physicists yet.

        Wishes Ioannis

        Hello Christi,,

        It is relevant considering the proportions correlated with distances.So lattices between quantum entangled spheres. I must insist on the importance to have a pure serie of Uniquenss. This serie is universal.The complexity appears inside this 3D and with all its integrations and derivations. The infinities and the finites groups can be proportional with rotations of spheres. If the serie of uniqueness is not inserted for all quantum entanglements and all serie, universal.So it becomes more difficult to encircle the pure spherical dynamic of distribution. Inside a kind of universal cooling, indeed the lattices are correlated and purelly physical when the contact is perfect. If the serie begins with a main central sphere, so we see that the lattices can dissapear.It is intriguing considering the space, the mass and the light. In fact they are the same in a BEC of our mind in this absolute 0. The distances indeed are correlated, if you insert the rotations and volumes of this serie of uniqueness, so we have different gauges.1 for space, 1 for hv,1 for m.The space in my line of reasoning does not turn or a little perhaps.The m and hv , them turn in opposite sense.So we have a pure GR and SR which can be optimized with the curvatures of our evolutive space time.

        the lattices between spheres are relevant when we extrapolate the fusion of 3 gauges. The increase of Entropy is of course axiomatized.

        The distances are not really a problem when the differences are explained with rotating 3D spheres.Implying the specificity of gauges, universals. If the pure thermodynamis are inserted in closed evolutive spacetime.So we can simulate if and only if the serie of uniqueness is seen correctly and at all scales in 3D fractalization of course and fortunally furthermore.

        A topological method must respect several foundamentals as our geometrical algebras......The serie of uniquenss is a finite group !!!

        Regards

        • [deleted]

        I am unsure why Hawking radiation is a problem. Physics is independent of the particular coordinate system we impose.

        I was a bit glib with the language, comparing the benign singularity at det(g) = 0 as "removed," when this is just a "converse" of the malign singularity with g_{ij} -- > ∞.I originally did this with the idea of working with a black hole that sent the singularity off to infinity. In that way the analytic functions across the horizon of a Rindler wedge could be compared to a meremorphic function: analytic everywhere but at infinity.

        There seems to be something odd going on here. Your equation 8 is singular at τ^2 = 2m. This appears to exchange the malign singularity at r = 0 with a singularity of some type on the horizon. As I communicated with you a few months ago this seems to have something to do with a dualism between quantum state interior to a black hole, or on the singularity, and the holographic states of a black hole as seen from the exterior.

        Cheers LC

        • [deleted]

        A quick corroboration of my worries about the worlds that singularity connects by this manipulation is the respond by L. B. Crowell :"... this seems to have something to do with a dualism between quantum state interior to a black hole, or on the singularity, and the holographic states of a black hole as seen from the exterior."

        P.S. Virtual part: interior to a black hole ; Real part: exterior view of BH. (A look to my essays may be helpful).

        Dear Lawrence,

        Thanks for the additional comment. I will explain some facts even if you know them, because I want to make sure that more possible readers understand what we are talking about.

        You say "Physics is independent of the particular coordinate system we impose." Well, not all coordinates are born equal (see assumption 4). If the coordinate is singular, it introduces singularity or it make worse already existent singularity. About the singularity at tau^2=m, this is the old event horizon singularity, and it is removed around the horizon by Eddington-Finkelstein coordinates already. My coordinates have the purpose to tame the genuine singularity at r=0, which cannot actually be removed. So it is not true that I exchange the r=0 singularity for that in tau^2=2m, since I don't need to fix the latter, being already fixed in Eddington-Finkelstein coordinates. The r=0 singularity is transformed in a tau=0 singularity, but which is benign in my coordinates.

        There are more charts, around the r=0 singularity, and around the event horizon singularity. There is no need to have a global chart, since the cover is done by local charts. But it may be possible to find a coordinate system which somehow interpolates between those around r=0 and around r=2m, and is global. In fact I did this using the Penrose-Carter diagrams and Schwarz-Christoffel mappings, here.

        If the black hole has spacelike singularity and lives forever, moving the singularity at infinity is enough and actually is the solution. If the black hole disappears at a finite time (Hawking evaporation can do this), then the singularity cannot be moved at infinity, simply because the moment when it vanishes is finite. In this case, two bad things happen: it is visible from the infinity, and it violates unitarity. Please see fig. 4 A. These things don't happen in the non-singular coordinates, please see Fig. 4B.

        Best regards,

        Cristi

        Dear Ioannis,

        Thank you for the extra comments. I am not sure I understand what you mean by "Singularity of the major Universe transfers only the dimensionality of the previous Universe to the new one, increasing the new dimensionality (by 1)" and why you say the dimension increases - you don't define "major Universe" and you don't justify your statements. Maybe you consider them to be well-known, but unfortunately I don't know them. You then said "I am afraid that with your method you are getting the virtual part of the Universe and not a pre- (or post-) Universe.". I see from the today comment that you explain that you call "virtual" the inside part in the black hole. So apparently you are afraid about something related to black holes, when we discuss about the big bang. If these will become more clear to me after I will read your essay, I may be able to answer. You also said that Lawrence's affirmation corroborates your claim. Maybe this is true, I cannot know, since I don't understand your worries. But his affirmation is due to a confusion between the tau=0 genuine singularity and the event horizon apparent singularity, as you can see from my reply to his comment.

        Best regards,

        Cristi

        Hello to both of you,

        I agree also with Christi, I prefer when the serie is finite. After all , a BH is just a sphere with an enormous mass, it is logic that we do not see the light. If a correct picture of horizons and events must be analyzed.So the foundamentals must be respected. It is like the einstein effect in fact with finite groups and with a spherical volume more important.It is just the same road with limits.So indeed why this infinity in the equation. Now if we want to see what is a BH really, the road is more comple about the add of series of uniquness. The superimposings so are under several universal laws. The number of spheres even in the galaxy is specific, perhaps that the serie of quantum uniquenss is also correlated with its own volumes ! Now it is sure that the serie possesses volumes more important more we go towards the main central sphere, so the main singularity and its codes.So the codes of comportments inside the 3D sphere and its intrinsic cosmological spheres and quantum spheres can be seen in a pure finite road.

        I must tell you that I am also intrigued by these BH , central to Galaxies. I know that they have a rule of mass for the universal rotations around the central sphere inside the universal sphere.But what are they if we see them really at the present and at a kind of locality. The volulmes of spheres become universal keys. The recycling of spheres become intriguing.When we insert the informations in this line of reasoning and the volumes of spheres of light....see that it becomes very relevan,t about our main codes inside our main central spheres.The central sphere is fascinating at all scale.The Universal singularity and the singularities in evolution.....

        All this reasoning implies that our quantum uniquenss is like a relativistic foto of our universal sphere and its cosmological spheres. So we have an interesting link between the central universal sphere and the central quantum spheres. What is the result is we make a simple /, Volume of the central universal sphere/ vol.of the quantum central sphere.Now it is intriguing about the volumes of singularities. We can make the same with the mass of these spheres and their rotations spinal and orbital.The / is relevant , you can even make a / of these results .The constants must appear.

        The BH have a pure complementary rule.The real universal secret is the optimization, so the spherization :)if they exist these spheres, they are reasons.They embark of course their stars and planets and moons and all quantum spheres. but I am persuaded that they have still a lot of unknown properties. The light is perhaps only for our stars and planets.Perhaps that we can see BH particules with new properties above the relativity and c.c is a probelm for the universal travel, more far, above the galaxies.Perhaps that after all, these BH have a lot of secrets for the travel between galaxies.But of course, we have already difficult to travel inside our milky way, so you imagine between galaxies. If we can go more quickly than c for a mass turning in the other sense than c, so we can extrapolate that it exists perhaps other angles of rotation for BH for example, implying so a possible travel at very interesting velocity above c. c is relevant for the teleportation, so we change m in c and after c in mass with codes.But for the universal travel, it is not sufficient. Probably that it exists several secrets due to rotations of spherical volumes.See thatt he serie of uniquenss is very relevant for the correlated link between the volumes of singularities.

        The equations , derivations and integrations can be superimposed in the two 3D scales.(quant. and cosmol.)

        • [deleted]

        First, I would like to apologize till I am an amateur (in your field) and not even a physicist, so my ability to express ideas by physics' (or even worse by mathematics') language is rather limited. Your essay was the motive to have a helpful Internet tour to the subject of Black Holes.

        According to my essays I suggest that our Universe is consisted by two subUniverses (the "real" and the "virtual") that are presented as two hyperspheres (for 3 plus 1 D) that are connected with a singularity at the BB (start, Big Bang at the one pole of hyperspheres). So, there is a singularity in between the real and virtual subUniverse. The Universe expands and half the way of its life the reality of its inhabitants switches from real to virtual (I call this edge:horizon; not unrelated to Black Hole's). This is the "time" that Universe starts to shrink until it concludes to new singularity(ies) (Big Bounce(s) at the other pole of the two hyperspheres). This new singularities transform the old Universe (pre-Universe) to the new one (post-Universe) which has bigger dimensionality (part because we start now from two singularities). This sequence of transformations are followed up to present.

        All this is referred to the major Universe (the Whole) which is the Universe we are living in. Into this major Universe numerous other universes (Black Holes, galaxies, stars,...) appear and disappear but their dimensionality can not exceed the dimensionality of the major Universe.

        Hence, there are two types of examining singularities: the procedure that connects the two subUniverses (real-virtual of the same dimensionality) and the procedure that transforms a Universe to its post-Universe (higher dimensionality) or pre-Universe (less dimensionality).

        I suppose: tau=0 is the BB singularity, tau^2=2m is Big Bounce (a singularity too), and tau^2=m is the event horizon that it does not seem a singularity to me.

        This discussion was very helpful for me but I am not going to bother you any more (for the time being), Ioannis