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**Sridattadev**: *on* 10/15/12 at 19:58pm UTC, wrote Dear Cristinel, The answer to your question "Did god divide by zero?"...

**Cristinel Stoica**: *on* 10/6/12 at 18:07pm UTC, wrote Dear Visitor, Thank you for checking this page even after the contest is...

**Cristinel Stoica**: *on* 10/6/12 at 17:32pm UTC, wrote Dear Janko, Thank you for explaining, and for the references you give in...

**Janko Kokosar**: *on* 10/6/12 at 15:07pm UTC, wrote Addition: In my article I have also two references with gravitational...

**Janko Kokosar**: *on* 10/6/12 at 14:56pm UTC, wrote Dear Cristi I do not understand, why do you think that singularities are...

**Cristinel Stoica**: *on* 10/5/12 at 20:39pm UTC, wrote Dear Janko, Thank you for seeing a bit useful my research on...

**Janko Kokosar**: *on* 10/5/12 at 20:02pm UTC, wrote Dear Christi, Feynman said that "probably finite space contains finite...

**Cristinel Stoica**: *on* 10/5/12 at 20:01pm UTC, wrote Dear Jin He, Thank you for this quote, it made my day. Best regards, ...

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FQXi FORUM

February 7, 2023

CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Did God Divide by Zero? by Cristinel Stoica [refresh]

TOPIC: Did God Divide by Zero? by Cristinel Stoica [refresh]

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.

Cristi Stoica is PhD student.

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

report post as inappropriate

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

report post as inappropriate

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

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

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

report post as inappropriate

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

report post as inappropriate

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

report post as inappropriate

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

report post as inappropriate

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

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 Jonathan,

Just got informed that [the revised version of] the paper you mentioned, "Beyond the Friedmann-Lemaitre-Robertson-Walker Big Bang Singularity", is accepted to appear in "Communications in Theoretical Physics".

Best regards,

Cristi Stoica

Just got informed that [the revised version of] the paper you mentioned, "Beyond the Friedmann-Lemaitre-Robertson-Walker Big Bang Singularity", is accepted to appear in "Communications in Theoretical Physics".

Best regards,

Cristi Stoica

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

report post as inappropriate

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

report post as inappropriate

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

report post as inappropriate

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

report post as inappropriate

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

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

report post as inappropriate

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

report post as inappropriate

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

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

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

report post as inappropriate

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

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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

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

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

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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

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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

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

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

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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

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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

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

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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

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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

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

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?

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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?

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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

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 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,

Newtonian gravity is,

Substituting in for M, you get,

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.

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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,

Newtonian gravity is,

Substituting in for M, you get,

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.

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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

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 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

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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

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

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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

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Hi Israel,

Thank you for reading and commenting my essay. About "Zeno's paradox", it is in fact a fallacy, as it was understood and proven at least since the times of Aristotle and Archimedes. It is easy to see that in deriving the so-called paradox, people assume implicitly that time cannot be divided forever. They consider that it is impossible for an infinite number of time intervals to pass, even though their total length is finite. Here resides their implicit assumption, and the source of the fallacy. Now, you are free to believe "the physical world space is not composed of an infinite number of points between the endpoints of a segment". But this is not proven, as it is not proven the opposite, that spacetime is continuous. I don't know of a proof, neither for discreteness, nor for continuity. I just know that most of the theories which so far explained or described efficiently the physical world at the fundamental level, are continuous, but I admit that this may change one day. In fact, I constructed few years ago a framework which works both with continuous, and with discrete theories, because I don't consider neither of them definitively ruled out.

Best regards,

Cristi

Thank you for reading and commenting my essay. About "Zeno's paradox", it is in fact a fallacy, as it was understood and proven at least since the times of Aristotle and Archimedes. It is easy to see that in deriving the so-called paradox, people assume implicitly that time cannot be divided forever. They consider that it is impossible for an infinite number of time intervals to pass, even though their total length is finite. Here resides their implicit assumption, and the source of the fallacy. Now, you are free to believe "the physical world space is not composed of an infinite number of points between the endpoints of a segment". But this is not proven, as it is not proven the opposite, that spacetime is continuous. I don't know of a proof, neither for discreteness, nor for continuity. I just know that most of the theories which so far explained or described efficiently the physical world at the fundamental level, are continuous, but I admit that this may change one day. In fact, I constructed few years ago a framework which works both with continuous, and with discrete theories, because I don't consider neither of them definitively ruled out.

Best regards,

Cristi

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...

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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...

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‘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.

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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).

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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).

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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

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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

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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

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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

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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).

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

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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

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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

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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

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

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

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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

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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

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

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.

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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.

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Dear Lawrence,

"it would be interesting to work your problem to start in those coordinates"

I agree. I developed a method to get spacelike foliations which lead to global coordinates using the Penrose-Carter diagrams and Schwarz-Christoffel mappings, in this paper. The problem with the Schwarzschild solution is that if you want global hyperbolicity, you have to avoid extending through the singularity tau=0, but if the black hole evaporates, you can do this and get a globally hyperbolic solution.

"In my coordinates (assuming they are unique to me, which is not likely) the singularity at infinity may not have to "move" from infinity."

Two years ago Florin had a nice post at FQXi blogs. In a comment on May. 26, 2010 @ 03:34 GMT to his post I attached an early paper, in which I sketched how I would approach the problem of singularities (which I did during the next 2 years). There I presented two ways to move the singularity at infinity, but I also stressed the necessity of crossing the singularity, and a way to do it. Bellow, under the comment May. 26, 2010 @ 09:27 GMT, you made some interesting observations about this.

I hope that what I presented here will be relevant to quantum physics of the black holes, but definitely only at the singularity tau=0 my coordinates can bring something new, because at tau^2=2m, the things are equivalent to the known approaches.

Thank you for the nice and interesting comments,

Cristi

"it would be interesting to work your problem to start in those coordinates"

I agree. I developed a method to get spacelike foliations which lead to global coordinates using the Penrose-Carter diagrams and Schwarz-Christoffel mappings, in this paper. The problem with the Schwarzschild solution is that if you want global hyperbolicity, you have to avoid extending through the singularity tau=0, but if the black hole evaporates, you can do this and get a globally hyperbolic solution.

"In my coordinates (assuming they are unique to me, which is not likely) the singularity at infinity may not have to "move" from infinity."

Two years ago Florin had a nice post at FQXi blogs. In a comment on May. 26, 2010 @ 03:34 GMT to his post I attached an early paper, in which I sketched how I would approach the problem of singularities (which I did during the next 2 years). There I presented two ways to move the singularity at infinity, but I also stressed the necessity of crossing the singularity, and a way to do it. Bellow, under the comment May. 26, 2010 @ 09:27 GMT, you made some interesting observations about this.

I hope that what I presented here will be relevant to quantum physics of the black holes, but definitely only at the singularity tau=0 my coordinates can bring something new, because at tau^2=2m, the things are equivalent to the known approaches.

Thank you for the nice and interesting comments,

Cristi

I did the following calculation. I start with the Eddington-Finkelstein coordinates

ds^2 = (1 – 2m/r)dt’^2 +/- (4m/r)dt’dr + (1 + 2m/r)dr^2 + r^2dΩ^2

where t’ = t +/- (r* - r) and r* = r + 2m ln|r/2m – 1| or

dr*/dr = (1 – 2m/r)^{-1}

I then use your substitution (r, t) --- > (τ, ξτ^4). I compute the metric components

g_{ττ} = 8(ξτ^2 sqrt{τ^2 – 2m} +/- 2m/sqrt{τ^2 – 2m})

g_{ξξ} = (τ^2 – 2m)τ^6

g_{ξτ} = 8τ^3(ξτ^3(τ^2 – 2m) +/- 2m)

g_{ξr} = 4mτ^2 dξdτ

g_{τr} = 16τ(ξ +/- m/(τ^2(τ^2 – 2m)).

g_{rr} = 1 – 2m/τ^2

The metric components g_{ττ} and g_{τr} blow up at τ^2 = 2m. Also the g_{rr} component blows up at τ^2 = 0.

I suspect this is still a coordinate singularity and not a real singularity. The KruskalSzekeres coordinates with metric

ds^2 = 32m^3e^{-r/2m)/r(dU^2 - dV^2) + r^2dΩ^2

for

U = sqrt{1 - r/2m}e^{r/4m} cosh(t/4m},

V = sqrt{1 - r/2m}e^{r/4m} sinh(t/4m}.

It appears we still have a blow up problem with the 1/r ~ 1/τ^2.

Cheers LC

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ds^2 = (1 – 2m/r)dt’^2 +/- (4m/r)dt’dr + (1 + 2m/r)dr^2 + r^2dΩ^2

where t’ = t +/- (r* - r) and r* = r + 2m ln|r/2m – 1| or

dr*/dr = (1 – 2m/r)^{-1}

I then use your substitution (r, t) --- > (τ, ξτ^4). I compute the metric components

g_{ττ} = 8(ξτ^2 sqrt{τ^2 – 2m} +/- 2m/sqrt{τ^2 – 2m})

g_{ξξ} = (τ^2 – 2m)τ^6

g_{ξτ} = 8τ^3(ξτ^3(τ^2 – 2m) +/- 2m)

g_{ξr} = 4mτ^2 dξdτ

g_{τr} = 16τ(ξ +/- m/(τ^2(τ^2 – 2m)).

g_{rr} = 1 – 2m/τ^2

The metric components g_{ττ} and g_{τr} blow up at τ^2 = 2m. Also the g_{rr} component blows up at τ^2 = 0.

I suspect this is still a coordinate singularity and not a real singularity. The KruskalSzekeres coordinates with metric

ds^2 = 32m^3e^{-r/2m)/r(dU^2 - dV^2) + r^2dΩ^2

for

U = sqrt{1 - r/2m}e^{r/4m} cosh(t/4m},

V = sqrt{1 - r/2m}e^{r/4m} sinh(t/4m}.

It appears we still have a blow up problem with the 1/r ~ 1/τ^2.

Cheers LC

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Dear Lawrence,

Interesting calculations. But my substitution (r, t) --- > (tau, xi tau^4) is suited for the Schwarzschild coordinates, so I don't expect them to work as well with the Eddington-Finkelstein's or to Kruskal-Szekeres coordinates, which indeed have the 1/r blow up.

As I said, in differential geometry it is known that you can't cover any surface with only one coordinate system. For example, for the sphere you need at least two coordinates, otherwise you have coordinate singularities. If it is impossible to cover the sphere with only one coordinate system, this doesn't mean the sphere is singular. It just means that it has different topology than R^2. In general relativity the things are more complicated, for two reasons: first, we deal with 4 dimensions. Second, the metric is indefinite, and it imposes constraints, in addition to those imposed by topology. But, if we can find, for a given spacetime, two or more coordinates which cover it and generate an atlas, and in which the singularity problems are resolved, the problem is solved. So, for r=2m there are the Eddington-Finkelstein, as well ass Kruskal-Szekeres, and Gullstrand-Painlevé coordinates, which preceded all. They work only for the event horizon, not for r=0. Mine just repair the metric at r=0, in the sense that they make it benign. They apply for r

Interesting calculations. But my substitution (r, t) --- > (tau, xi tau^4) is suited for the Schwarzschild coordinates, so I don't expect them to work as well with the Eddington-Finkelstein's or to Kruskal-Szekeres coordinates, which indeed have the 1/r blow up.

As I said, in differential geometry it is known that you can't cover any surface with only one coordinate system. For example, for the sphere you need at least two coordinates, otherwise you have coordinate singularities. If it is impossible to cover the sphere with only one coordinate system, this doesn't mean the sphere is singular. It just means that it has different topology than R^2. In general relativity the things are more complicated, for two reasons: first, we deal with 4 dimensions. Second, the metric is indefinite, and it imposes constraints, in addition to those imposed by topology. But, if we can find, for a given spacetime, two or more coordinates which cover it and generate an atlas, and in which the singularity problems are resolved, the problem is solved. So, for r=2m there are the Eddington-Finkelstein, as well ass Kruskal-Szekeres, and Gullstrand-Painlevé coordinates, which preceded all. They work only for the event horizon, not for r=0. Mine just repair the metric at r=0, in the sense that they make it benign. They apply for r

Dear Cristi Stoica,

Although due to my lack of education I was unable to fully understand some of your mathematical commentary about physics abstract assumptions, I still found your scrupulously argued exceptionally well written essay quite absorbing. I was considerably helped by the exquisitely constructed graphics. As best as I could tell, you meticulously adhered to the contest’s rules by clearly identifying those physics foundational assumptions you thought were erroneous, and you gave a valid explanation for why you thought the way you did. May I please make a comment? In my essay Sequence Consequence, I thoughtfully point out that all scientific studies of snowflakes have determined that of the trillions that have fallen, no snowflakes have ever been found to be identical. Physical laws are supposed to be consistent throughout the Universe, so it seems reasonable to assume that each star is different in composition and size than every other star in the Universe is, and more importantly, each star is set at a differing intervening distance than every other star is. In your graphics, you use seemingly identical circles and triangles and squares. You use identical numbers and identical symbols in your mathematical equations. As the only realist at this site, I have to reluctantly tell you that I think one real indivisible Universe can only be occurring eternally once in one dimension.

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Although due to my lack of education I was unable to fully understand some of your mathematical commentary about physics abstract assumptions, I still found your scrupulously argued exceptionally well written essay quite absorbing. I was considerably helped by the exquisitely constructed graphics. As best as I could tell, you meticulously adhered to the contest’s rules by clearly identifying those physics foundational assumptions you thought were erroneous, and you gave a valid explanation for why you thought the way you did. May I please make a comment? In my essay Sequence Consequence, I thoughtfully point out that all scientific studies of snowflakes have determined that of the trillions that have fallen, no snowflakes have ever been found to be identical. Physical laws are supposed to be consistent throughout the Universe, so it seems reasonable to assume that each star is different in composition and size than every other star in the Universe is, and more importantly, each star is set at a differing intervening distance than every other star is. In your graphics, you use seemingly identical circles and triangles and squares. You use identical numbers and identical symbols in your mathematical equations. As the only realist at this site, I have to reluctantly tell you that I think one real indivisible Universe can only be occurring eternally once in one dimension.

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Dear Joe Fisher,

Thank you very much for the attention given to my essay, and for the kind words. I also thank you for the interesting comments. Indeed, every star is unique. Maybe when they become black holes, they lose "hair" and become identical (asymptotically), modulo few parameters like mass, angular momentum and electric charge, as some theorems seem to show. But until then, they are unique. Unfortunately, I had to cut the original manuscript, containing the mathematical descriptions of every unique star, due to the regulations of the contest (there is a limitation in the number of pages and characters) :). By the way, I don't know if you have noticed, your final remark, as well as your essay, is written in "seemingly identical" words, despite the fact that "no snowflakes have ever been found to be identical" :)

Best regards,

Cristi

Thank you very much for the attention given to my essay, and for the kind words. I also thank you for the interesting comments. Indeed, every star is unique. Maybe when they become black holes, they lose "hair" and become identical (asymptotically), modulo few parameters like mass, angular momentum and electric charge, as some theorems seem to show. But until then, they are unique. Unfortunately, I had to cut the original manuscript, containing the mathematical descriptions of every unique star, due to the regulations of the contest (there is a limitation in the number of pages and characters) :). By the way, I don't know if you have noticed, your final remark, as well as your essay, is written in "seemingly identical" words, despite the fact that "no snowflakes have ever been found to be identical" :)

Best regards,

Cristi

Dear Christinel Stoica,

“By the way, I don't know if you have noticed, your final remark, as well as your essay, is written in "seemingly identical" words, despite the fact that "no snowflakes have ever been found to be identical" :)” Touché, although I did notice that all of the physical representations of all of the real characters that made up the words I used, and all of the real spaces separating the letters and punctuation marks you mentioned are unique. I have also noticed real holes and every one of them I have seen can only best be described as being black. For instance every person totes nine unique major holes around with them wherever they go. They also have innumerable real unique tiny black holes all over their skins. Now I do not know what real methodology you could use to measure any one of these real unique black holes that would scientifically establish that they originally came either just before or immediately after there was a singular state of nothing. Nor can I see how any real measurement of any of these real black holes could determine their modern uses and functions and their actual relationship to other holes. So while I do not mind in the least anyone speculating that an imaginary old time black hole behaved differently from a real one, I do wish these dreamers would take the advice my daughters often give to me and “Get real.”

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“By the way, I don't know if you have noticed, your final remark, as well as your essay, is written in "seemingly identical" words, despite the fact that "no snowflakes have ever been found to be identical" :)” Touché, although I did notice that all of the physical representations of all of the real characters that made up the words I used, and all of the real spaces separating the letters and punctuation marks you mentioned are unique. I have also noticed real holes and every one of them I have seen can only best be described as being black. For instance every person totes nine unique major holes around with them wherever they go. They also have innumerable real unique tiny black holes all over their skins. Now I do not know what real methodology you could use to measure any one of these real unique black holes that would scientifically establish that they originally came either just before or immediately after there was a singular state of nothing. Nor can I see how any real measurement of any of these real black holes could determine their modern uses and functions and their actual relationship to other holes. So while I do not mind in the least anyone speculating that an imaginary old time black hole behaved differently from a real one, I do wish these dreamers would take the advice my daughters often give to me and “Get real.”

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Dear Joe Fisher,

"I did notice that all of the physical representations of all of the real characters that made up the words I used, and all of the real spaces separating the letters and punctuation marks you mentioned are unique."

Same for images and equations. Can one say with only words more than with words and pictures and equations?

"I have also noticed real holes and every one of them I have seen can only best be described as being black. For instance every person totes nine unique major holes around with them wherever they go."

I have to agree with your daughters :)

Returning to:

"I thoughtfully point out that all scientific studies of snowflakes have determined that of the trillions that have fallen, no snowflakes have ever been found to be identical."

I don't contradict you. On the other hand, you are missing something. Among these trillions which you claim were compared, is there any snowflake which violates the known mathematics and physics of ice crystals? The moral is that scientists try to find the general laws, the universal equations. It would be unrealistic to try to write down all possible solutions of these equations. What is realistic is to propose the equations, and then check that the new instance found in Nature respects the equations or violates them. So I have to say that you have the wrong picture of what science is, and it is that wrong picture you are fighting against.

Best regards,

Cristi

"I did notice that all of the physical representations of all of the real characters that made up the words I used, and all of the real spaces separating the letters and punctuation marks you mentioned are unique."

Same for images and equations. Can one say with only words more than with words and pictures and equations?

"I have also noticed real holes and every one of them I have seen can only best be described as being black. For instance every person totes nine unique major holes around with them wherever they go."

I have to agree with your daughters :)

Returning to:

"I thoughtfully point out that all scientific studies of snowflakes have determined that of the trillions that have fallen, no snowflakes have ever been found to be identical."

I don't contradict you. On the other hand, you are missing something. Among these trillions which you claim were compared, is there any snowflake which violates the known mathematics and physics of ice crystals? The moral is that scientists try to find the general laws, the universal equations. It would be unrealistic to try to write down all possible solutions of these equations. What is realistic is to propose the equations, and then check that the new instance found in Nature respects the equations or violates them. So I have to say that you have the wrong picture of what science is, and it is that wrong picture you are fighting against.

Best regards,

Cristi

Dear Cristi:

Enjoyed reading your essay and agree with the conclusions of the paper that God did not divide by zero.

The singularities can be shown to arise from the missing physics in GR as described in my paper - -“ From Absurd to Elegant Universe” that integrates the missing physics of spontaneous decay into a simplified form of general relativity that includes specific relativity and gravitational potential. The results of the model show that the relativistic gravitational effects at quantum scale can be successfully predicted without any singularities experienced by GR. This also eliminates the need or relevance of the so far unsuccessful efforts of unifying the gravity and other fundamental forces of the standard model. The model also resolves many other paradoxes and inconsistencies of modern physics and explains relativistic understanding of the inner workings of QM.

I would greatly welcome your thoughts on the above and comments on my paper.

Best Regards

Avtar Singh

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Enjoyed reading your essay and agree with the conclusions of the paper that God did not divide by zero.

The singularities can be shown to arise from the missing physics in GR as described in my paper - -“ From Absurd to Elegant Universe” that integrates the missing physics of spontaneous decay into a simplified form of general relativity that includes specific relativity and gravitational potential. The results of the model show that the relativistic gravitational effects at quantum scale can be successfully predicted without any singularities experienced by GR. This also eliminates the need or relevance of the so far unsuccessful efforts of unifying the gravity and other fundamental forces of the standard model. The model also resolves many other paradoxes and inconsistencies of modern physics and explains relativistic understanding of the inner workings of QM.

I would greatly welcome your thoughts on the above and comments on my paper.

Best Regards

Avtar Singh

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Cristi,

Congrats on a thought-provoking and splendidly illustrated essay. I need to read some of your other papers to fully understand your program, but it seems evident to me that the ideas are good whether or not they ultimately describe physics.

My background is algebraic geometry, and your ideas brought to mind a couple of concepts from that field that might be interesting to compare to what you are doing. The first is resolution of singularities (Hironaka); particularly blowups. When you blow up at a singularity, every point in the singular locus corresponds to an entire subspace in the exceptional fiber, so in some sense you could consider points in the blowup "zero distance apart" if they coincide in the original singular variety. The second is the fact that algebraic tangent spaces change dimension at singularities. Perhaps some analogue of these concepts in the analytic category is relevant?

My own point of view is much different; I tend to regard manifolds as too good to be true, and prefer to regard them as emerging from a more primitive structure, as I briefly describe in my essay:

On the Foundational Assumptions of Modern Physics

In any case, I enjoyed your essay and hope to learn more about your approach. Take care,

Ben Dribus

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Congrats on a thought-provoking and splendidly illustrated essay. I need to read some of your other papers to fully understand your program, but it seems evident to me that the ideas are good whether or not they ultimately describe physics.

My background is algebraic geometry, and your ideas brought to mind a couple of concepts from that field that might be interesting to compare to what you are doing. The first is resolution of singularities (Hironaka); particularly blowups. When you blow up at a singularity, every point in the singular locus corresponds to an entire subspace in the exceptional fiber, so in some sense you could consider points in the blowup "zero distance apart" if they coincide in the original singular variety. The second is the fact that algebraic tangent spaces change dimension at singularities. Perhaps some analogue of these concepts in the analytic category is relevant?

My own point of view is much different; I tend to regard manifolds as too good to be true, and prefer to regard them as emerging from a more primitive structure, as I briefly describe in my essay:

On the Foundational Assumptions of Modern Physics

In any case, I enjoyed your essay and hope to learn more about your approach. Take care,

Ben Dribus

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Dear Ben,

Thank you for the interest in my essay and for the comments. I am answering you with a delay because I was on a short vacation. Indeed, we can relate what I did with Hironaka's resolutions of singularities in Algebraic Geometry, and I did mention this connection in this paper. I've made this parallel only to show a situation in which a singularity due to the way a space (the variety) sits in a higher dimensional space is singular, but the singularity can be "blown-up". In Singular General Relativity, my point is that the blow-up is not needed in reality, but only to repair some solutions obtained under the assumption that one should identify points which are topologically distinct, but the distance between them (as measured by the metric tensor) is zero.

I look forward to reading your essay.

Good luck with the contest!

Cristi

Thank you for the interest in my essay and for the comments. I am answering you with a delay because I was on a short vacation. Indeed, we can relate what I did with Hironaka's resolutions of singularities in Algebraic Geometry, and I did mention this connection in this paper. I've made this parallel only to show a situation in which a singularity due to the way a space (the variety) sits in a higher dimensional space is singular, but the singularity can be "blown-up". In Singular General Relativity, my point is that the blow-up is not needed in reality, but only to repair some solutions obtained under the assumption that one should identify points which are topologically distinct, but the distance between them (as measured by the metric tensor) is zero.

I look forward to reading your essay.

Good luck with the contest!

Cristi

Dear Cristi,

Very interesting essay. In particular, it resolves a conundrum of myself. I was suspect about the problem why no one used different coordinate patches to solve problems in GR. Every problem I studied uses a global coordinate system but (as you also mentioned) for most manifolds there is no one. I always thought that I'm to stupid and there is an easy argument which I miss.

But as you showed, this kind of thinking is correct: singularities can be resolved by using a covering with more than one coordinate patch.

I will never forget this lesson.

Best

Tosrten

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Very interesting essay. In particular, it resolves a conundrum of myself. I was suspect about the problem why no one used different coordinate patches to solve problems in GR. Every problem I studied uses a global coordinate system but (as you also mentioned) for most manifolds there is no one. I always thought that I'm to stupid and there is an easy argument which I miss.

But as you showed, this kind of thinking is correct: singularities can be resolved by using a covering with more than one coordinate patch.

I will never forget this lesson.

Best

Tosrten

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Dear Torsten,

Thank you for the nice comments. About the little usage of different coordinate patches in GR, one possible explanation is that geometers and physicists think differently. Geometers insist so much on using a manifestly invariant language, and tend to consider physicists who work in coordinates careless. But Einstein's summation convention is a powerful tool, which reveals the common grounds of the metric as a scalar product, contraction, the lowering and raising isomorphisms, the relation between various apparently distinct tensors, which turn out to be the same by the musical isomorphisms. I was always wondering why geometers avoid working with indices (but I suspected that they use them in private, and in the papers rewrite everything in the coordinate-free notation :) ). Especially since there is a manifestly invariant version, Penrose's abstract index notation. Another possible explanation for working in one coordinate, as if it is global, may be due to the fact that in general we tend to see time as flowing. There are several hints which support the idea of a global time: quantum mechanics and QFT, the condition of global hyperbolicity, the necessity to have a global spin structure. The existence of a global time may suggest that the coordinates should be global too, although this is not necessarily true.

Best regards,

Cristi

Thank you for the nice comments. About the little usage of different coordinate patches in GR, one possible explanation is that geometers and physicists think differently. Geometers insist so much on using a manifestly invariant language, and tend to consider physicists who work in coordinates careless. But Einstein's summation convention is a powerful tool, which reveals the common grounds of the metric as a scalar product, contraction, the lowering and raising isomorphisms, the relation between various apparently distinct tensors, which turn out to be the same by the musical isomorphisms. I was always wondering why geometers avoid working with indices (but I suspected that they use them in private, and in the papers rewrite everything in the coordinate-free notation :) ). Especially since there is a manifestly invariant version, Penrose's abstract index notation. Another possible explanation for working in one coordinate, as if it is global, may be due to the fact that in general we tend to see time as flowing. There are several hints which support the idea of a global time: quantum mechanics and QFT, the condition of global hyperbolicity, the necessity to have a global spin structure. The existence of a global time may suggest that the coordinates should be global too, although this is not necessarily true.

Best regards,

Cristi

I gave your paper a high score which popped it up a bit. I am a bit dismayed at some of the higher ranked papers, some of which look like pure fluff and nonsense. Papers submitted a month ago seem to be collectively sinking like a stone.

Cheers LC

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Cheers LC

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Thank you. I'd like to see your essay and other good essays receiving more attention.

Best regards,

Cristi

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Best regards,

Cristi

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Are you bargaining, Lawrence Crowell and Cristinel Stoica? Is that fair?

Pentcho Valev

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Pentcho Valev

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Hello again Cristi,

I have come here with questions on occasion, but find a wealth of information about related topics in the comments of other readers, in your responses, and in the papers you cite which elaborate your work. In addition to 1203.1819; I have also downloaded 1112.4508 and 1108.5099 from arXiv, but I I'd still like to ask you to summarize once I get my thoughts together.

Regarding the Craig Hogan experiment; if you read his paper, it is not solely about quantum geometry being real or not, although that's in the title. His experimental apparatus is actually a bit more subtle, and his working conceptual model is closer to a purely wave-like view of reality - so there is absolutely no assumption about atoms of space or any specific type of graininess.

Therefore it should reveal any type of Planck scale variation whatsoever - if it exists. Which means that; indeed it should shed light on your work, once Hogan has a large enough data set to make meaningful statements about his results. But even a 'positive' result may not invalidate your work, but it should serve to clarify matters of Planck scale dynamics further.

Regards,

Jonathan

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I have come here with questions on occasion, but find a wealth of information about related topics in the comments of other readers, in your responses, and in the papers you cite which elaborate your work. In addition to 1203.1819; I have also downloaded 1112.4508 and 1108.5099 from arXiv, but I I'd still like to ask you to summarize once I get my thoughts together.

Regarding the Craig Hogan experiment; if you read his paper, it is not solely about quantum geometry being real or not, although that's in the title. His experimental apparatus is actually a bit more subtle, and his working conceptual model is closer to a purely wave-like view of reality - so there is absolutely no assumption about atoms of space or any specific type of graininess.

Therefore it should reveal any type of Planck scale variation whatsoever - if it exists. Which means that; indeed it should shed light on your work, once Hogan has a large enough data set to make meaningful statements about his results. But even a 'positive' result may not invalidate your work, but it should serve to clarify matters of Planck scale dynamics further.

Regards,

Jonathan

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Christi, I wanted to add;

I have only read through your essay. Once I get a handle on your approach, I'll then be reading your essay a second time for evaluation. But I think this is relatively meaningful work that you have presented well.

regards,

Jonathan

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I have only read through your essay. Once I get a handle on your approach, I'll then be reading your essay a second time for evaluation. But I think this is relatively meaningful work that you have presented well.

regards,

Jonathan

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Dear Jonathan,

Something happens at very small scale, probably at the Plank scale. Hopefully we will know what, someday. At that time, we will have more data to see what's the best description of the physical laws, and which of our theories will survive as part of the new theory. Until then, we are free to explore various theoretical possibilities, and see what experimental consequences they may have for the Plank scale. My singularities allow information to be preserved, being therefore compatible with unitary evolution, hence they don't make QFT on curved spacetime inconsistent, as it is thought in general about the singularities. This is the main purpose of the papers to which you refer. Another consequence is the dimensional reduction, which may allow QG to be perturbatively renormalizable. So, there are two links between GR and QM/QFT. In my essays for the latest two FQXi contests I approached the general relativistic part. In the first two, I worked at the other end of the bridge, the quantum one. I proposed there a description of QM which aims to explain the strange quantum properties in a way which is more compatible with GR, by being local (the price is that it has to be contextual). This approach can lead to a rebuilt of QFT (I sketched a long term program for this in the second essay), which combines naturally with GR. These are three connections between the two ends of the bridge: (1) compatibility between the singularities and unitary evolution, (2) possibility of renormalization of gravity, (3) local formulations of quantum mechanics. But the most important part will have to explain clearly why the action is quantized like this (I think that this may be accomplished perhaps by some topological structures, or maybe exotic smooth structure, as two essays from this contest propose). Hopefully, we will see someday what the ultimate explanation is, by a qualitative, nonperturbative answer. I personally am not satisfied to merely prove that they are consistent, I believe there's a deeper, more natural, and simpler explanation.

Best regards,

Cristi

Something happens at very small scale, probably at the Plank scale. Hopefully we will know what, someday. At that time, we will have more data to see what's the best description of the physical laws, and which of our theories will survive as part of the new theory. Until then, we are free to explore various theoretical possibilities, and see what experimental consequences they may have for the Plank scale. My singularities allow information to be preserved, being therefore compatible with unitary evolution, hence they don't make QFT on curved spacetime inconsistent, as it is thought in general about the singularities. This is the main purpose of the papers to which you refer. Another consequence is the dimensional reduction, which may allow QG to be perturbatively renormalizable. So, there are two links between GR and QM/QFT. In my essays for the latest two FQXi contests I approached the general relativistic part. In the first two, I worked at the other end of the bridge, the quantum one. I proposed there a description of QM which aims to explain the strange quantum properties in a way which is more compatible with GR, by being local (the price is that it has to be contextual). This approach can lead to a rebuilt of QFT (I sketched a long term program for this in the second essay), which combines naturally with GR. These are three connections between the two ends of the bridge: (1) compatibility between the singularities and unitary evolution, (2) possibility of renormalization of gravity, (3) local formulations of quantum mechanics. But the most important part will have to explain clearly why the action is quantized like this (I think that this may be accomplished perhaps by some topological structures, or maybe exotic smooth structure, as two essays from this contest propose). Hopefully, we will see someday what the ultimate explanation is, by a qualitative, nonperturbative answer. I personally am not satisfied to merely prove that they are consistent, I believe there's a deeper, more natural, and simpler explanation.

Best regards,

Cristi

Thanks Cristi,

That is a satisfying reply to my comment. There is a lot of fun stuff going on somewhere near the effective lower limits in scale, and I am also taking several strategies forward to examine this more closely. I'll be testing candidates for that deeper, more natural, and simpler solution we both believe must be there.

Your attempts to cast light are helpful.

More later,

Jonathan

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That is a satisfying reply to my comment. There is a lot of fun stuff going on somewhere near the effective lower limits in scale, and I am also taking several strategies forward to examine this more closely. I'll be testing candidates for that deeper, more natural, and simpler solution we both believe must be there.

Your attempts to cast light are helpful.

More later,

Jonathan

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Heaven Breasts and Heaven Calculus

http://vixra.org/abs/1209.0072

Since the birth of mankind, human beings have been looking for the origin of life. The fact that human history is the history of warfare and cannibalism proves that humans have not identified their origin. Humanity is still in the dark phase of lower animals. Humans can see the phenomenon of life only on Earth, and humans' vision does not exceed the one of lower animals. However, it is a fact that human beings have inherited the most advanced gene of life. Humans should be able to answer the following questions: Is the Universe hierarchical? What is Heaven? Is Heaven the origin of life? Is Heaven a higher order of life? For more than a decade, I have done an in-depth study on barred galaxy structure. Today (September 17, 2012) I suddenly discovered that the characteristic structure of barred spiral galaxies resembles the breasts of human female essentially. If the rational structure conjecture presented in the article is proved then Sun must be a mirror of the universe, and mankind is exactly the image on earth of the Heaven.

http://galaxyanatomy.com

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http://vixra.org/abs/1209.0072

Since the birth of mankind, human beings have been looking for the origin of life. The fact that human history is the history of warfare and cannibalism proves that humans have not identified their origin. Humanity is still in the dark phase of lower animals. Humans can see the phenomenon of life only on Earth, and humans' vision does not exceed the one of lower animals. However, it is a fact that human beings have inherited the most advanced gene of life. Humans should be able to answer the following questions: Is the Universe hierarchical? What is Heaven? Is Heaven the origin of life? Is Heaven a higher order of life? For more than a decade, I have done an in-depth study on barred galaxy structure. Today (September 17, 2012) I suddenly discovered that the characteristic structure of barred spiral galaxies resembles the breasts of human female essentially. If the rational structure conjecture presented in the article is proved then Sun must be a mirror of the universe, and mankind is exactly the image on earth of the Heaven.

http://galaxyanatomy.com

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Dear Cristinel

I enjoyed your generous comments on Kenneth Snelson's essay. You share with him clarity of ideas explained by beautiful graphics. I wish I was more of an expert in GR and QM to comment on the particulars of your essay, which sounds very convincing (but why are the distances on the sphere the same in spherical coordinates?). Instead I will try to tap your expertise to judge a totally different approach to unification of GR with QM (and everything else) which also solves the question of singularities.

I have explained it qualitatively in my heavily illustrated 2005 Beautiful Universe Theory on which I based my fqxi essay Fix Physics! . In my theory singularities are avoided because everything (space, matter, radiation etc.) is made up of a lattice of localized dimensionless 'building blocks' of angular momentum in units of (h) interacting with their neighbors. Call it a universe made up entirely of singularities!! GR becomes simply a matter of a density field affecting motion (for example) as classical curvature due to deceleration with a variable speed of light.

I would be honored if you, with your expertise, can read, advise, rate or comment about these two papers.

I wish you good luck with your studies.

Vladimir

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I enjoyed your generous comments on Kenneth Snelson's essay. You share with him clarity of ideas explained by beautiful graphics. I wish I was more of an expert in GR and QM to comment on the particulars of your essay, which sounds very convincing (but why are the distances on the sphere the same in spherical coordinates?). Instead I will try to tap your expertise to judge a totally different approach to unification of GR with QM (and everything else) which also solves the question of singularities.

I have explained it qualitatively in my heavily illustrated 2005 Beautiful Universe Theory on which I based my fqxi essay Fix Physics! . In my theory singularities are avoided because everything (space, matter, radiation etc.) is made up of a lattice of localized dimensionless 'building blocks' of angular momentum in units of (h) interacting with their neighbors. Call it a universe made up entirely of singularities!! GR becomes simply a matter of a density field affecting motion (for example) as classical curvature due to deceleration with a variable speed of light.

I would be honored if you, with your expertise, can read, advise, rate or comment about these two papers.

I wish you good luck with your studies.

Vladimir

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Dear Vladimir,

Thank you for the interest in my essay. You asked "but why are the distances on the sphere the same in spherical coordinates?". The answer is that when you change coordinates, the metric tensor changes too. The metric tensor is used to give the elementary length, which is integrated and gives the distance. It changes precisely so that the distance remains the same, no matter what coordinates you choose. What you wrote about your essay sounds interesting. I look forward to reading it.

Best regards,

Cristi

Thank you for the interest in my essay. You asked "but why are the distances on the sphere the same in spherical coordinates?". The answer is that when you change coordinates, the metric tensor changes too. The metric tensor is used to give the elementary length, which is integrated and gives the distance. It changes precisely so that the distance remains the same, no matter what coordinates you choose. What you wrote about your essay sounds interesting. I look forward to reading it.

Best regards,

Cristi

Dear Cristi,

I think there are possibly some minor logical glitches in constructing your case against some pre assumptions that you think are wrong in modern physics, in particular I think of assumptions 1 and 5. Assumption 1 says that Singularity theorems predict the breakdown of General Relativity (GR). As you know, I think one of the greatest, if perhaps not the greatest open problems in modern physics, because it could lead to a conciliation between GR and quantum mechanics (QM), is the issue of what happens inside a black hole and specially in the singularity point. I think most physicists would agree that if the equations of GR break that doesn't imply that reality breaks (this is connected also to your assumption 5).

The agreement I think is that we just don't understand and have no tools to explain what happens in such a limit situation. As you suggest, topology may be a source for better understanding, and I think that is an interesting idea discussed in good detail in your very fine essay. I am still bugged by the contradiction between your zero distance idea and the fact that QM seems to suggest there is a minimum length (and I also see your argument that there is no minimum mass, isn't it because photons are conventionally massless?).

I look forward to the development of your ideas, I have browsed your papers in the ArXiV.

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I think there are possibly some minor logical glitches in constructing your case against some pre assumptions that you think are wrong in modern physics, in particular I think of assumptions 1 and 5. Assumption 1 says that Singularity theorems predict the breakdown of General Relativity (GR). As you know, I think one of the greatest, if perhaps not the greatest open problems in modern physics, because it could lead to a conciliation between GR and quantum mechanics (QM), is the issue of what happens inside a black hole and specially in the singularity point. I think most physicists would agree that if the equations of GR break that doesn't imply that reality breaks (this is connected also to your assumption 5).

The agreement I think is that we just don't understand and have no tools to explain what happens in such a limit situation. As you suggest, topology may be a source for better understanding, and I think that is an interesting idea discussed in good detail in your very fine essay. I am still bugged by the contradiction between your zero distance idea and the fact that QM seems to suggest there is a minimum length (and I also see your argument that there is no minimum mass, isn't it because photons are conventionally massless?).

I look forward to the development of your ideas, I have browsed your papers in the ArXiV.

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Dear Hector Zenil,

Thank you for trying to warn me about possible minor glitches, and for taking time to read my essay. I am genuinely interested in any problem that there may be with my approach, because I would not want to come up with a wrong theory. If there are some glitches in it, I would vey much like to know precisely what they are, to fix them and get the correct theory. But I'm afraid I don't understand where you see them. You said:

"I think there are possibly some minor logical glitches in constructing your case against some pre assumptions that you think are wrong in modern physics, in particular I think of assumptions 1 and 5. Assumption 1 says that Singularity theorems predict the breakdown of General Relativity (GR). As you know, I think one of the greatest, if perhaps not the greatest open problems in modern physics, because it could lead to a conciliation between GR and quantum mechanics (QM), is the issue of what happens inside a black hole and specially in the singularity point. I think most physicists would agree that if the equations of GR break that doesn't imply that reality breaks (this is connected also to your assumption 5)."

People really do claim that singularity theorems prove that GR breaks down. There are dozens of papers and books which start with this claim, in general to sell other "more radical" theories. And what I said is that A. singularity theorems are correct, and they lead to singularities and B. singularity theorems don't prove that GR fails. They only prove that singularities appear in some very general conditions. I agree that in GR singularities appear, but I show that they are not a problem, because the equations can be put in a form which works there too.

"I think most physicists would agree that if the equations of GR break that doesn't imply that reality breaks"

Yes, and I agree too. I don't reject this. I only reject the assumption that from the existence of singularities follows that GR breaks down. As I explained, the standard equations are those who break down. But I put them in a form which works without infinities at singularities. Otherwise, at non-singular points, they are equivalent. If we divide by the volume element to get Einstein's equation in the standard form, at singularities we divide by zero. If we don't make this "simplification", and keep the equations in the densitized form, then they are valid even at singularities.

IMO, it is a good thing to extend GR beyond the limits usually assumed. My approach makes it work at singularities, both for big bang and for black holes. I think I am correct, and I think this is a progress, because it fixes important problems in GR without extra assumptions, and without modifications which then should be proven to lead to the same predictions as GR. Fixing GR should not be viewed as an enemy of other theories.

This doesn't mean that I am against the "conciliation between GR and quantum mechanics (QM)". I am for it. In fact, my singularities seem to provide a way to make gravity renormalizable, by leading in a natural way to a dimensional reduction (section 7).

"The agreement I think is that we just don't understand and have no tools to explain what happens in such a limit situation. As you suggest, topology may be a source for better understanding, and I think that is an interesting idea discussed in good detail in your very fine essay."

Well, I hope these tools I developed help, and thank you for the appreciative comment. Even if GR should be modified and replaced, and even if by quantization it will become different, they may help, as many other tools developed in GR may be inherited in other theories. But it is possible that in the real world my solution doesn't work. We don't know the final theory, maybe it will incorporate GR (hopefully with my "bug fix"), maybe not.

"I am still bugged by the contradiction between your zero distance idea and the fact that QM seems to suggest there is a minimum length (and I also see your argument that there is no minimum mass, isn't it because photons are conventionally massless?)."

I'll try to explain this. Let me state from the beginning that I agree that the Plank length may be special, although I don't know yet how. But I think there is no experimental evidence or mathematical proof that there is a minimum length. You say "QM seems to suggest there is a minimum length". I am not aware of such suggestion from QM. In QM, the discrete spectra are obtained from equations which assume continuous space and time. There's no need to assume minimal length to get the discrete spectra of electrons in the atom for example. In fact, I don't know of a way which explains some quantum spectra of observables from the assumption of a minimal length. There is though the argument that to probe the Plank distance you need Plank energies, which would create tiny black holes. If it's correct that this prevents us from seeing what happens under the Plank scale, this doesn't mean that this distance is minimal. There may be a minimal distance, or there may be not. This argument can't distinguish between the two. Now, I don't say there is no special length. This may be true. But it doesn't mean it is minimal. I think that the existence of a minimal length is an open problem (although at this time I consider that it has little chances to be true).

Thank you for taking your time to read properly my essay and the papers on which it is based, and for warning me about possible dangers. I appreciate your comments, and if you feel that I did not answer properly to your possible objections, I hope you will find time to detail them.

Best regards,

Cristi

Thank you for trying to warn me about possible minor glitches, and for taking time to read my essay. I am genuinely interested in any problem that there may be with my approach, because I would not want to come up with a wrong theory. If there are some glitches in it, I would vey much like to know precisely what they are, to fix them and get the correct theory. But I'm afraid I don't understand where you see them. You said:

"I think there are possibly some minor logical glitches in constructing your case against some pre assumptions that you think are wrong in modern physics, in particular I think of assumptions 1 and 5. Assumption 1 says that Singularity theorems predict the breakdown of General Relativity (GR). As you know, I think one of the greatest, if perhaps not the greatest open problems in modern physics, because it could lead to a conciliation between GR and quantum mechanics (QM), is the issue of what happens inside a black hole and specially in the singularity point. I think most physicists would agree that if the equations of GR break that doesn't imply that reality breaks (this is connected also to your assumption 5)."

People really do claim that singularity theorems prove that GR breaks down. There are dozens of papers and books which start with this claim, in general to sell other "more radical" theories. And what I said is that A. singularity theorems are correct, and they lead to singularities and B. singularity theorems don't prove that GR fails. They only prove that singularities appear in some very general conditions. I agree that in GR singularities appear, but I show that they are not a problem, because the equations can be put in a form which works there too.

"I think most physicists would agree that if the equations of GR break that doesn't imply that reality breaks"

Yes, and I agree too. I don't reject this. I only reject the assumption that from the existence of singularities follows that GR breaks down. As I explained, the standard equations are those who break down. But I put them in a form which works without infinities at singularities. Otherwise, at non-singular points, they are equivalent. If we divide by the volume element to get Einstein's equation in the standard form, at singularities we divide by zero. If we don't make this "simplification", and keep the equations in the densitized form, then they are valid even at singularities.

IMO, it is a good thing to extend GR beyond the limits usually assumed. My approach makes it work at singularities, both for big bang and for black holes. I think I am correct, and I think this is a progress, because it fixes important problems in GR without extra assumptions, and without modifications which then should be proven to lead to the same predictions as GR. Fixing GR should not be viewed as an enemy of other theories.

This doesn't mean that I am against the "conciliation between GR and quantum mechanics (QM)". I am for it. In fact, my singularities seem to provide a way to make gravity renormalizable, by leading in a natural way to a dimensional reduction (section 7).

"The agreement I think is that we just don't understand and have no tools to explain what happens in such a limit situation. As you suggest, topology may be a source for better understanding, and I think that is an interesting idea discussed in good detail in your very fine essay."

Well, I hope these tools I developed help, and thank you for the appreciative comment. Even if GR should be modified and replaced, and even if by quantization it will become different, they may help, as many other tools developed in GR may be inherited in other theories. But it is possible that in the real world my solution doesn't work. We don't know the final theory, maybe it will incorporate GR (hopefully with my "bug fix"), maybe not.

"I am still bugged by the contradiction between your zero distance idea and the fact that QM seems to suggest there is a minimum length (and I also see your argument that there is no minimum mass, isn't it because photons are conventionally massless?)."

I'll try to explain this. Let me state from the beginning that I agree that the Plank length may be special, although I don't know yet how. But I think there is no experimental evidence or mathematical proof that there is a minimum length. You say "QM seems to suggest there is a minimum length". I am not aware of such suggestion from QM. In QM, the discrete spectra are obtained from equations which assume continuous space and time. There's no need to assume minimal length to get the discrete spectra of electrons in the atom for example. In fact, I don't know of a way which explains some quantum spectra of observables from the assumption of a minimal length. There is though the argument that to probe the Plank distance you need Plank energies, which would create tiny black holes. If it's correct that this prevents us from seeing what happens under the Plank scale, this doesn't mean that this distance is minimal. There may be a minimal distance, or there may be not. This argument can't distinguish between the two. Now, I don't say there is no special length. This may be true. But it doesn't mean it is minimal. I think that the existence of a minimal length is an open problem (although at this time I consider that it has little chances to be true).

Thank you for taking your time to read properly my essay and the papers on which it is based, and for warning me about possible dangers. I appreciate your comments, and if you feel that I did not answer properly to your possible objections, I hope you will find time to detail them.

Best regards,

Cristi

Dear Cristinel Stoica

Hope you success with "Quantum Gravitation".

Are looking forward to your comments on my other measures:

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the...

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Hope you success with "Quantum Gravitation".

Are looking forward to your comments on my other measures:

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the...

view entire post

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Dear Cristi,

I hope you don't mind that I referenced your essay on several of the other threads. I assure you I mentioned it in a positive light! Take care,

Ben

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I hope you don't mind that I referenced your essay on several of the other threads. I assure you I mentioned it in a positive light! Take care,

Ben

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Dear Benjamin,

Thank you for telling me, and for mentioning my essay. I did not encounter the references, but I should not worry too much about them :). All jokes aside, I am sure about your good intentions.

Best regards,

Cristi

Thank you for telling me, and for mentioning my essay. I did not encounter the references, but I should not worry too much about them :). All jokes aside, I am sure about your good intentions.

Best regards,

Cristi

Hello Cristi

I must admit I have only just found your essay, and glanced through the paragraph headings. I have spent a bit more time reading your correspondence, particularly with Torsten Asselmeyer-Maluga and Jonathan Dickau.

Everything you say (and which I have seen so far) makes very nice sense. Thank you for it.

About quantization: you write "Hopefully, we will see someday what the ultimate explanation is, by a qualitative, nonperturbative answer". My essay is an attempt to guess the form of such an answer. It assumes an asymmetric Riemannian structure, and involves algebra directly derived from it and a variational principle. That is all. It also includes a discussion of the uncertainty principle which underlies the mystery of what happens at the Planck scale of distance. I hope it may appeal to you.

Best wishes, Alan H.

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I must admit I have only just found your essay, and glanced through the paragraph headings. I have spent a bit more time reading your correspondence, particularly with Torsten Asselmeyer-Maluga and Jonathan Dickau.

Everything you say (and which I have seen so far) makes very nice sense. Thank you for it.

About quantization: you write "Hopefully, we will see someday what the ultimate explanation is, by a qualitative, nonperturbative answer". My essay is an attempt to guess the form of such an answer. It assumes an asymmetric Riemannian structure, and involves algebra directly derived from it and a variational principle. That is all. It also includes a discussion of the uncertainty principle which underlies the mystery of what happens at the Planck scale of distance. I hope it may appeal to you.

Best wishes, Alan H.

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Dear Christie:

Benjamin Dribus made me alert on your essay, especially the part where information can be preserved by a BB like event. So I started reading...

Your approach of zero length is very interesting , however I think we are entering here a pure mathematical view.

In "THE CONSCIOUSNESS CONNECTION", my approach is that this mathematical view is a pure "in the mind" perception, just because of the fact that I position limits at the material universe (Planck length and time). And when I am looking at your illustrations with lengths of zero, indeed the illustrations are no longer visible...we enter a new dimension.

You loose me in the parts 6 and 7, as an architectional engineer my math' is forgotten, my approach is more philosophical, but if you take those two together maybe the whole becomes understandable.

You say : God divided by zero, and somewhere later you say that WE are doing so. I wholly agree with you, in my perception the non causal part of our consciousness in Total Simultanity is the origin of the "reality" as perceived by the causal part of our consciousness here in the arrow of time, some posts on my thread are inclined to perceive the GOD perception in this view, in fact the same as you say.

You made me think again over the concept singulairity, thank you for that.

I hope that can find some time to read/rate and comment "THE CONSCIOUSNESS CONNECTION".

Wilhelmus

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Benjamin Dribus made me alert on your essay, especially the part where information can be preserved by a BB like event. So I started reading...

Your approach of zero length is very interesting , however I think we are entering here a pure mathematical view.

In "THE CONSCIOUSNESS CONNECTION", my approach is that this mathematical view is a pure "in the mind" perception, just because of the fact that I position limits at the material universe (Planck length and time). And when I am looking at your illustrations with lengths of zero, indeed the illustrations are no longer visible...we enter a new dimension.

You loose me in the parts 6 and 7, as an architectional engineer my math' is forgotten, my approach is more philosophical, but if you take those two together maybe the whole becomes understandable.

You say : God divided by zero, and somewhere later you say that WE are doing so. I wholly agree with you, in my perception the non causal part of our consciousness in Total Simultanity is the origin of the "reality" as perceived by the causal part of our consciousness here in the arrow of time, some posts on my thread are inclined to perceive the GOD perception in this view, in fact the same as you say.

You made me think again over the concept singulairity, thank you for that.

I hope that can find some time to read/rate and comment "THE CONSCIOUSNESS CONNECTION".

Wilhelmus

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Dear Wilhelmus,

"Your approach of zero length is very interesting , however I think we are entering here a pure mathematical view."

The very prediction of the occurrence of singularities in General Relativity is purely mathematical too. If we trust maths enough to claim that GR has a problem because of singularities, then we should trust maths also when offering the solution.

"You say : God divided by zero, and somewhere later you say that WE are doing so."

I ask "Did God divide by zero", and then answer that we did, when we wrote the equations and divided by the volume element, which may vanish at singularities.

"my approach is more philosophical [...] I hope that can find some time to read/rate and comment "THE CONSCIOUSNESS CONNECTION"."

I hope too. I have a deep respect for theoretical philosophy, as a tool to explore open-mindedly various possibilities, and then to submit them to logic and critical thinking.

Best regards,

Cristi

"Your approach of zero length is very interesting , however I think we are entering here a pure mathematical view."

The very prediction of the occurrence of singularities in General Relativity is purely mathematical too. If we trust maths enough to claim that GR has a problem because of singularities, then we should trust maths also when offering the solution.

"You say : God divided by zero, and somewhere later you say that WE are doing so."

I ask "Did God divide by zero", and then answer that we did, when we wrote the equations and divided by the volume element, which may vanish at singularities.

"my approach is more philosophical [...] I hope that can find some time to read/rate and comment "THE CONSCIOUSNESS CONNECTION"."

I hope too. I have a deep respect for theoretical philosophy, as a tool to explore open-mindedly various possibilities, and then to submit them to logic and critical thinking.

Best regards,

Cristi

Here's a link to the slides of a talk I will give in two weeks at a conference: Global and local aspects of causality. Feedback welcomed.

Bravo Christi, beautiful and very well explained.Maybe my problem of the Data Transmission Delay between the awareness and the consciousness influence on the collapse of wave function is of the same order. I would like to know your opinion. Of course my text is not as thouroughfull scientific underlayed as yours , but I think we are touching the same object.

Wilhelmus

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Wilhelmus

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Dear Cristinel,

World is much simpler than you thinking.Please read my essay with the comments and you will understand how the World works.

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World is much simpler than you thinking.Please read my essay with the comments and you will understand how the World works.

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Hi Cristi,

I saw that you are, like us, one of the victims of the strange "rising and dropping" of the Community Rating.

In any case, I enjoyed in reading your interesting Essay, hence, I am going to give you an high score.

Cheers,

Ch.

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I saw that you are, like us, one of the victims of the strange "rising and dropping" of the Community Rating.

In any case, I enjoyed in reading your interesting Essay, hence, I am going to give you an high score.

Cheers,

Ch.

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Dear Dr. Corda,

Thank you very much for reading my essay. I also enjoyed yours, and singularities may very well be forbidden by quantum or even semi-classical effects, as you explain. I hope that my analysis of singularities is a safety net for the case when they exist, or a good idealization/approximation, if they don't.

Best wishes,

Cristi Stoica

Thank you very much for reading my essay. I also enjoyed yours, and singularities may very well be forbidden by quantum or even semi-classical effects, as you explain. I hope that my analysis of singularities is a safety net for the case when they exist, or a good idealization/approximation, if they don't.

Best wishes,

Cristi Stoica

Christian & Christi

You're not alone. Gangs of trolls seem to be dishing out 1's, or there's something else very wrong happening. I've dropped over 100 places overnight! Lawrence was also targeted. I think it needs investigation.

Luckily I hadn't scored yours yet which should help mitigate your drops.

Best Wishes

Peter

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You're not alone. Gangs of trolls seem to be dishing out 1's, or there's something else very wrong happening. I've dropped over 100 places overnight! Lawrence was also targeted. I think it needs investigation.

Luckily I hadn't scored yours yet which should help mitigate your drops.

Best Wishes

Peter

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Dear Cristinel Stoica,

just to let you know I've seen your essay. I love the way you have set it out so clearly, tied it up neatly beginning and end and of course the colourful eye catching diagrams that break up the text ( the coloured titles too!). Others are more qualified to discuss the detail but it is clearly relevant to the essay question. Good luck, kind regards Georgina

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just to let you know I've seen your essay. I love the way you have set it out so clearly, tied it up neatly beginning and end and of course the colourful eye catching diagrams that break up the text ( the coloured titles too!). Others are more qualified to discuss the detail but it is clearly relevant to the essay question. Good luck, kind regards Georgina

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Dear Georgina,

Thank you for the very kind words about my essay. I could not avoid using some heavy equations, because otherwise some very counterintuitive results would be more difficult to grasp or accept, if stated only in words. I tried to compensate by pictures, to make reader's life easier. Good luck with your very nice essay!

Cristi

Thank you for the very kind words about my essay. I could not avoid using some heavy equations, because otherwise some very counterintuitive results would be more difficult to grasp or accept, if stated only in words. I tried to compensate by pictures, to make reader's life easier. Good luck with your very nice essay!

Cristi

MAX PLANK:

An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

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An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

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Dear Christi,

Feynman said that "probably finite space contains finite information". Including this, I do not see problems with singularities. Of course, it is useful to analyse them to see something useful, but they will not give final answers of physics.

My essay

Best regards, Janko Kokosar

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Feynman said that "probably finite space contains finite information". Including this, I do not see problems with singularities. Of course, it is useful to analyse them to see something useful, but they will not give final answers of physics.

My essay

Best regards, Janko Kokosar

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Dear Cristi

I do not understand, why do you think that singularities are not in contradiction with Feynman's statement? If mass is located on very small volume, momentum is very uncertain. It is known that that BH with mass smaller than Planck's mass do not exists, because of this logic. So, if mass is larger, it seem that this radius can be smaller. But larger mass means larger radius of horizon. So you think about radius below horizon. But (a) why it is something below horizon if distances are uncertain below planck's distance. (b) In my essay I suspect that interior of black hole does not exist.

About Feynman's statement it is written also by Brukner (A reference in my essay). But I admit that I not find clear conection of his ideas with singularities. What do you think about Brukner's ideas in connection with singularites?

Best regards Janko Kokosar

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I do not understand, why do you think that singularities are not in contradiction with Feynman's statement? If mass is located on very small volume, momentum is very uncertain. It is known that that BH with mass smaller than Planck's mass do not exists, because of this logic. So, if mass is larger, it seem that this radius can be smaller. But larger mass means larger radius of horizon. So you think about radius below horizon. But (a) why it is something below horizon if distances are uncertain below planck's distance. (b) In my essay I suspect that interior of black hole does not exist.

About Feynman's statement it is written also by Brukner (A reference in my essay). But I admit that I not find clear conection of his ideas with singularities. What do you think about Brukner's ideas in connection with singularites?

Best regards Janko Kokosar

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Dear Janko,

Thank you for explaining, and for the references you give in the next comment. There are many unknowns here, and I think that neither of us can anticipate right now all of them. - We don't know yet the correct theory combining GR and QM. - If the radius of a black hole is known, its volume is undetermined, in the sense that it depends on the coordinates. - There are extremal black holes, which don't have a real event horizon. - The dimensional reduction which takes place in my approach doesn't imply with necessity the existence black holes lighter than the Plank mass. I just show how we can solve the problem of singularities, in GR. In the correct theory which unifies it with QM, things may be different. But since my approach provides a possible way to regularize quantum gravity, it may offer the answer (there is still much work to be done here). Anyway, quantum mechanics may add constraints to my theory, which are compatible with it as it is. For example, it may forbid, as you think, Schwarzschild black holes which are lighter than Plank mass. But this constraint is compatible with the theory. Now, I don't intend to give you a proof of compatibility. I consider your burden, to prove the incompatibility. Your statement seem to refer to GR in general, not just to my approach, so if you will prove this, it will be an interesting result. But my opinion is that there are more unknowns which are easily ignored.

Best regards,

Cristi

Thank you for explaining, and for the references you give in the next comment. There are many unknowns here, and I think that neither of us can anticipate right now all of them. - We don't know yet the correct theory combining GR and QM. - If the radius of a black hole is known, its volume is undetermined, in the sense that it depends on the coordinates. - There are extremal black holes, which don't have a real event horizon. - The dimensional reduction which takes place in my approach doesn't imply with necessity the existence black holes lighter than the Plank mass. I just show how we can solve the problem of singularities, in GR. In the correct theory which unifies it with QM, things may be different. But since my approach provides a possible way to regularize quantum gravity, it may offer the answer (there is still much work to be done here). Anyway, quantum mechanics may add constraints to my theory, which are compatible with it as it is. For example, it may forbid, as you think, Schwarzschild black holes which are lighter than Plank mass. But this constraint is compatible with the theory. Now, I don't intend to give you a proof of compatibility. I consider your burden, to prove the incompatibility. Your statement seem to refer to GR in general, not just to my approach, so if you will prove this, it will be an interesting result. But my opinion is that there are more unknowns which are easily ignored.

Best regards,

Cristi

Addition:

In my article I have also two references with gravitational principle of uncertainty [28] and [29]. It sa id that smaller distances than Planck's distances cannot be determined. But, maybe it is something useful also in [13].

Regards

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In my article I have also two references with gravitational principle of uncertainty [28] and [29]. It sa id that smaller distances than Planck's distances cannot be determined. But, maybe it is something useful also in [13].

Regards

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Dear Visitor,

Thank you for checking this page even after the contest is finished. You can leave messages, but I will not be available to answer in the following two weeks.

Best regards,

Cristi

Thank you for checking this page even after the contest is finished. You can leave messages, but I will not be available to answer in the following two weeks.

Best regards,

Cristi

Dear Cristinel,

The answer to your question "Did god divide by zero?" is, yes indeed.

God is the singularity and can be realized when one is divided by nothing (zero), meaning when one unites thy self to everything and does not feel the division or duality any more. Please see the essay Conscience is the cosmological constant in which, i have used the division by zero to mathematically prove the truth about the singularity, zero = i = infinity. I "is" the god in all of us.

Love,

Sridattadev.

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The answer to your question "Did god divide by zero?" is, yes indeed.

God is the singularity and can be realized when one is divided by nothing (zero), meaning when one unites thy self to everything and does not feel the division or duality any more. Please see the essay Conscience is the cosmological constant in which, i have used the division by zero to mathematically prove the truth about the singularity, zero = i = infinity. I "is" the god in all of us.

Love,

Sridattadev.

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