Did God Divide by Zero? by Cristinel Stoica

[deleted]

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.

Cristinel Stoica

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

[deleted]

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."

Cristinel Stoica

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

[deleted]

Dear Christinel Stoica,

"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." Thank you so much for providing pragmatic proof that my assessment of reality is correct. All mathematical equations are unrealistic because all equations are abstractions. One real Universe can only be eternally occurring in one dimension once. The only accurate mathematical equation that could persist is 1=U where 1 is really equal to the one real Universe. While abstract definitions of abstract Nature may provide suitable instances for dreamy speculation about the abstract unification of abstract separated undefined elements such as the abstract ability for abstract total energy to always abstractly equal abstract total amounts of abstract mass times abstract total amounts of light squared as in e=mc², real energy actually only equals one real Universe, or 1=U. I think I do have a wrong picture of science. I do not picture reality, I live in it.

Avtar Singh

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

Cristinel Stoica

Dear Avtar Singh,

Thank you for the kind comment. I look froward to reading your essay. Good luck with the contest!

Best regards,

Cristi

Benjamin Dribus

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

Cristinel Stoica

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

Torsten Asselmeyer-Maluga

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

Cristinel Stoica

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

Lawrence Crowell

I responded to your comments on my essay blog.

Cheers LC

[deleted]

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

[deleted]

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

Best regards,

Cristi

[deleted]

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

Pentcho Valev

Cristinel Stoica

Pentcho Valev, first, thanks for checking my page, despite your rude comment. I'll answer for myself. I am not bargaining (and I don't see where did you see this). I wouldn't consider it fair. If you have any doubts, you are free to report us.

Jonathan Dickau

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

Jonathan Dickau

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

Cristinel Stoica

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

Jonathan Dickau

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

[deleted]

Dear Cristi and Jonathan,

Good to see you both in another essay contest. My entry may interest you both in that it deals with Planck limits. I go after just one divide by zero, that I call the elephant in the room. I made a case that the increase of mass as an object approaches the speed of light does not get anywhere near infinity.

I am hoping this effort on one of the infinities furthers your cause Cristi. I am also a believer that the deity does not divide by zero.

Best of Luck

Don L.

Cristinel Stoica

Dear Don,

God to see you too. Thank you for the comment and for pointing me to your essay. Good luck with the competition.

Best regards,

Cristi

« Previous Page Next Page »