Hello yet again,
Have you seen this work by Craig Hogan? His experiment - if successful - would provide evidence to the contrary of your theory. Last I knew, the experiment was being built, and should be running soon.
Interferometers as Probes of Planckian Quantum Geometry
All the Best,
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?
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).
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.
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
