Did God Divide by Zero? by Cristinel Stoica

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.

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.

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

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

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

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).

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.)

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

It seems plausible that the τ = sqrt{2m} singularity is a pure coordinate singularity. If this is removed by going to Eddington-Finkelstein coordinates, then it would be interesting to work your problem to start in those coordinates. I might this weekend try to work with this some to see what happens.

As for Hawking radiation, you are talking about the final "POW!" when the black hole is completely evaporated. That part of the problem is not well known in any coordinates. Your objection does have a certain classical logic to it. However, by the time the black hole is down to its last 10^4 or 10^3 Planck mass units the black hole itself is probably quantum mechanical. In my coordinates (assuming they are unique to me, which is not likely) the singularity at infinity may not have to "move" from infinity. There may be some nonlocal physics which causes its disappearance without having to move at all.

I think your work might provide some machinery for looking at nonlocal quantum physics of black hole and possibly some duality between quantum fields (information) on a stretched horizon has some duality to quantum field interior to the black hole. It would be interesting if this could be demonstrated without violating the quantum Xerox principle (no-cloning). The appearance of the τ = sqrt{2m} singularity, even if it is a coordinate singularity, gives me pause to question whether information concerning the interior appears at the horizon.

Hi Cristinel

Congratulations for your nice and well written essay. It is clear and easy-to-read. I would like to leave my opinion about your question. I think that one has to differentiate the physical world and the mathematical representation of the world. Many physicists think that for every element of reality there most be an element in a mathematical structure. This could be the case, but sometimes the abstraction of reality becomes paradoxical. Recall that one of the fallacies of Zeno's paradoxes is to assume that space and time are continuous. This implies that between two real numbers we will find an infinite set of real numbers. If we follow this line of reasoning then the persistent Achilles will never catch up with the tortoise. This experiment immediately tell us that in the physical world space is not composed of an infinite number of points between the endpoints of a segment. If we accept this, we also have to accept that singularities only exist in mathematics but not in the physical world. The function 1/x is said to have a singularity at x=0, this is because at that point the function is not defined. But in the physical world a distance cannot be equal to zero, if a distance were equal to zero it would not be a distance.

I'd like to invite to read my essay, I would be happy if you could leave some comments on my essay entitled THE PREFERRED SYSTEM OF REFERENCE RELOADED.

Best wishes

Israel

HI Cristi

I do believe this "the physical world space is not composed of an infinite number of points between the endpoints of a segment" because if we assume that the physical space can be infinitely divided we will arrive at the dichotomy paradox, experience tells us however that we can always reach the opposite endpoint which evidently suggests the assumption that a physical distance is not composed of infinitely many points but only of segments greater than zero. I agree with you that there is so far, to the best of my knowledge, no unambiguous mathematical proof and that the notion of the continuum and discreteness are not well understood yet. I also agree that theories based on the continuum have been quite successful. But I think that when a line of reasoning leads to a paradox implies that some of our ideal assumptions (which were aimed at representing experience) is wrong.

On the other hand, one should keep in mind that a singularity usually leads to an infinity, but so far, no one understands the physical meaning of infinity. When we say "let us consider a physical object at an infinite distance", what do we physically mean by that? Mathematically "makes sense", physically not. I will give another physical example to make clear that there is some sort of a disparity between the physical world and the abstract one. With this I hope I could persuade you that singularities might not exist in the physical world. Suppose you have an apple and two people. Then you want to share the apple between the number of people that you have. So, we ask the question: How much apple each person will obtain? The answer is clear, 1/2. Now, if we have only one person and we ask the same question, the answer will be 1. Imagine now that there is nobody to share the apple and we ask the same question. In such case we can reply with two equivalent arguments: (1) The question no longer applies or (2) simply, the information (i.e. 1 apple and 0 persons) that I have is not the appropriate one to answer the question. It is clear that the question is demanding physical quantities different from 0 to be answered. This example teaches us that when we face a singularity is because we insist in asking the same question when the physical elements of a particular situation no longer comply with the situation when there is no singularity. As long as we have 1 apple, 0 persons and we keep asking the same question where the question is no longer legitimate, we will never get an answer. This is the case with singularities and infinities. The expression "1/x=" is a question and when we arrive at x=0 it is said that the expression is singular because it is not defined at that point, i.e., at that point the question no longer applies. We should recall that in mathematics the zero was introduced by mathematical convenience though the symbol 0 per se was not considered as a number like 1 or 2 since its meaning represents nothingness, vacuum, void, etc.. As time went by people realized its usefulness and included it in the list of numbers like any other, though we all know that the zero have some privileges in mathematics. This is one reason why one should be well aware of the distinction between the physical reality and its abstract representation.

Israel