One problem in most theories of quantum gravity is getting a quantum scale of spacetime at very small sizes, especially the Planck scale (of about 10-33 meters), to expand into a smooth spacetime fabric at large scales (as predicted by general relativity). Benedetti's study of spacetime in two different configurations shows that applying quantum groups to spacetime results in differences in how spacetime behaves, based on the scale that it's being examined.
Specifically, Benedetti's work shows a possible link between quantum groups (which have noncommutative geometries, where xy does not equal yx) with some approaches to quantum gravity such as causal dynamical triangulations and exact renormalization group. These sort of connections between different approaches may mean that insights gained in one approach can help propel new insights in another approach, so they are significant to the development of quantum gravity theories and will hopefully bring scientists closer to a more complete understanding of how gravity will behave at quantum levels.
Related Articles:
- PhysOrg.com - Spacetime May Have Fractal Properties on a Quantum Scale
- Cornell ArXiv - Fractal Properties of Quantum Paper (abstract and click on PDF link to view the paper)
Comments
Oh why not! – Two almost impossible to visualise models now linked…
When you talk about fractal spacetime and gravity it is very difficult not to mention the work of Laurent Nottale. Laurent Nottale’s work was based on his English colleague’s work Garnet Ord who is presently in Canada. Nottale and Ord’s work was further developed using Cantor transfinite set theory by Mohamed El Naschie in England and his school. Particularly the Italian Gerrardo Iovane, The Arabian Shokri Nada and the Slovanian L. Marek-Crnjac made important contributions to the subject. There is also a large body of literature on fractal spacetime and E-infinity theory by the Chinese chapter led by Ji-Huan He in Shanghai.
These El naschie and Huan are frauds.
You can consult
Integrity Under Attack:
The State of Scholarly Publishing
By Douglas N. Arnold
http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf
Rumors of editor and journal misconduct have dominated the highly publicized case of the applied math journal Chaos, Solitons and Fractals (CSF), published by Elsevier. As reported in a 2008 article in Nature,[2] “Five of the 36 papers in the December issue of Chaos, Solitons and Fractals alone were written by its editor-in-chief, Mohamed El Naschie. And the year to date has seen nearly 60 papers written by him appear in the journal.” In fact, of the 400 papers by El Naschie indexed in Web of Science, 307 were published in CSF while he was editor-in-chief. This extremely high rate of selfpublication by the editor-in-chief led to charges that normal standards of peer-review were not upheld at CSF; it has also had a large effect on the journal’s impact factor. (Thomson Reuters calculates the impact factor of a journal in a given year as C/A, where A is the number of articles published in the journal in the preceding two years, and C is the number of citations to those articles from articles indexed in the Thomson Reuters database and published in the given year.) El Naschie’s papers in CSF make 4992 citations, about 2000 of which are to papers published in CSF, largely his own. In 2007, of the 65 journals in the Thomson Reuters category “Mathematics, Interdisciplinary Applications,” CSF was ranked number 2.
Another journal whose high impact factor raises eyebrows is the International Journal of Nonlinear Science and Numerical Simulation (IJNSNS), founded in 2000 and published by Freund Publishing House. For the past three years, IJNSNS has had the highest impact factor in the category “Mathematics, Applied.” There are a variety of connections between IJNSNS and CSF. For example, Ji-Huan He, the founder and editor-in-chief of IJNSNS, is an editor of CSF, and El Naschie is one of the two co-editors of CSF; both publish copiously, not only in their own journals but also in each other’s, and they cite each other frequently.
Let me describe another element that contributes to IJNSNS’s high impact factor. The Institute of Physics (IOP) publishes Journal of Physics: Conference Series (JPCS). Conference organizers pay to have proceedings of their conferences published in JPCS, and, in the words of IOP, “JPCS asks Conference Organisers to handle the peer review of all papers.” Neither the brochure nor the website for JPCS lists an editorial board, nor does either describe any process for judging the quality of the conferences. Nonetheless, Thomson Reuters counts citations from JPCS in calculating impact factors. One of the 49 volumes of JPCS in 2008 was the proceedings of a conference organized by IJNSNS editor-in-chief He at his home campus, Shanghai Donghua University. This one volume contained 221 papers, with 366 references to papers in IJNSNS and 353 references to He. To give you an idea of the effect of this, had IJNSNS not received a single citation in 2008 beyond the ones in this conference proceedings, it would still have been assigned a larger impact factor than any SIAM journal except for SIAM Review.
You can check yours self a typical paper for Huan using E-infinity theory
Hierarchy of wool fibers and its interpretation using E-infinity theory
Chaos, Solitons & Fractals,
Chaos,Solitons and Fractals 41 (2009)1839 –1841
Ji-Huan He, Zhong-Fu Ren, Jie Fan, Lan Xu
Abstract
Why do wool fibers show excellent advantages in warmth-retaining and many other practical properties? The paper concludes that their hierarchical structure is the key. Using E-infinity theory, its Hausdorff dimension is estimated to be about 4.2325, very close to El Naschie’s E-infinity dimension, 4.2360, revealing an optimal structure for wool fibers.
The same article again with little modifications
Hierarchy of Wool Fibers and Fractal Dimensions
International Journal of Nonlinear Sciences and Numerical Simulation,9(3),293-296, 2008
http://works.bepress.com/cgi/viewcontent.cgi?article=1037&context=ji_huan_he
You can check yours self a typical paper for Huan using E-infinity theory
Hierarchy of wool fibers and its interpretation using E-infinity theory
Chaos, Solitons & Fractals,
Chaos,Solitons and Fractals 41 (2009)1839 –1841
Ji-Huan He, Zhong-Fu Ren, Jie Fan, Lan Xu
Abstract
Why do wool fibers show excellent advantages in warmth-retaining and many other practical properties? The paper concludes that their hierarchical structure is the key. Using E-infinity theory, its Hausdorff dimension is estimated to be about 4.2325, very close to El Naschie’s E-infinity dimension, 4.2360, revealing an optimal structure for wool fibers.
The same article again with little modifications
Hierarchy of Wool Fibers and Fractal Dimensions
International Journal of Nonlinear Sciences and Numerical Simulation,9(3),293-296, 2008
http://works.bepress.com/cgi/viewcontent.cgi?article=103
7&context=ji_huan_he
Abstract
Wool fiber shows excellent advantages in warmth-retaining and many other practical properties possibly
due to its hierarchical structure. Its fractal dimension of wool fiber is calculated which is very close to the
Golden Mean, 1.618. The present study might provide a new interpretation for the reason why wool fiber
has so many excellent properties.
You can notice the confilict between the two abstracts, in the first fibre wool
has dimension 4.2325 (which is greater than the embedding space) and in the second it is 1.618. I hope El naschie can explain these remarkable results.
Can the genious Larsone (== Elnaschie) tell us who paid for Douglas N. Arnold, president of SIAM.
El naschie and his suockpuppets are too stupid and
too mentally sick. I’m not Said, every one criticise El naschie should be Said according to El naschie rule. I hope the genious El naschie can invent connection between nature and Douglas N. Arnold.
What is mentioned in my previous comments are not false they are just extracted from papers of one of the great suporter of E-infinty theory.
I hope Elnaschie gets smart enough to respond reasonably on comments.
After the experimental discovery of the golden mean in quantum mechanics there is no room anymore for conventional skepticism. Those who think in conventional terms that golden mean base quantum mechanics is pseudoscience are themselves pseudo scientists. You could say pseudoscience if we are still talking about a theory. On the other hand to deny experimental result confirming the theoretical work of dozens of researchers is pseudo philosophy per se. The golden mean was discovered in relativity by Sigalotti. It is the basis of the first rational explanation of the two slit experiment by the Egyptian Mohamed El Naschie. It underpins high energy physics as discussed by Slovenian Crnjac, Chinese Ji Huan He as well as many of their associates. El Naschie presented the first complete theory of unification based on golden geometry and golden quantum field theory. Golden geometry and topology was developed in Romania by two mathematicians. A recent magnificent book by a noted Soviet scientist Alexei Stakhov bears witness for the reality and theoretical soundness of the golden mean quantum mechanics. There will be always those who confuse rigorousness with a stubborn narrow mindedness. Those who still are able to claim that anything to do with the golden mean is esoteric and pseudo science is incarnation of narrow-mindedness masquerading in the form of stubborn mathematical rigor.
Mohamed El Naschie is the first to discover the golden mean as the basis of quantum mechanics. The idea follows in a trivial way from the fact that fractal trees neither overlap nor leave gaps only for a golden mean scale. This is very close to the concept of symplectic dynamics. This is another way to say area preserving Hamiltonian dynamics. El Naschie drives his theory using a Hilbert cube. This is nothing more than a four dimensional cube inside another four dimensional cube and so on ad infinitum. In such infinite dimensional topological space, the two slit experiment with quantum particles finds a natural resolution which is logical and consistent. The quantum dynamics of Palmer is qualitative description of Mohamed El Naschie’s quantitative description. You can find all of that superbly explained in many journal articles published by Ji Huan He as well as G. Iovane and L. Crnjac.
Repeating a lie one hundred times doesn’t change anything. It remains all the same a lie albeit repeated one hundred times. Those who are attacking Mohamed El Naschie with summary non specific statement belong to this category. What can you do when you are a failed diploma mathematician like Christoph Drosser of Die Zeit in Hamburg or a convicted criminal like Dr. Said elnashaie. He just makes some non specific remarks about the science of which he understands nothing. It is vendetta, hatred and jealousy which is driving John Baez, Said elnashaie, Quirin Schermeier and Christoph Drosser. They created El Naschie watch through their malicious spider web and connections between empty drums who are dying for recognition of any sort such as Jason Hosten and the likes of him. These people are an insult to the human race and one of the reasons I never publish anything on the internet other than this comment.
It is interesting that everyone is now talking about the golden mean and the golden mean E8. Mohamed El Naschie was the first to intimate the relationship between E8 and the golden mean and subsequently introduced a fuzzy E8 based again on the golden mean. He work does not only apply to the Ising model which was tested experimentally in the Helmholtz Center in Berlin but to everything else as well. You could say he found a general theory based on the golden mean for high energy physics. Some call it quantum golden field theory. You can read much more about it in details from a very accessible short review The theory of Cantorian spacetime and high energy particle physics (an informal review) published in Chaos, Solitons & Fractals, 41, 2009, p. 2635-2646.
from http://martialculture.com/blog/2010/01/the-golden-ratio-and-
quantum-mechanics/
El naschie is a real spark in the human written history, he is startling . Al his predictions based on E-infinity theory are well verified. Among many and just to name:
1-The well experimentally verified results about fiber wool pioneered by Huan. Who showed that the Hausdorff dimension of fiber wool is to be about 4.2325, very close to El Naschie’s E-infinity dimension, 4.2360. According to Huan this reveals an optimal structure for wool fibers. This is an easy proved fact and it doesn’t need high energy.
Hierarchy of wool fibers and its interpretation using E-infinity theory
Chaos, Solitons & Fractals, Volume 41, Issue 4, 30 August 2009, Pages 1839-1841
Ji-Huan He, Zhong-Fu Ren, Jie Fan, Lan Xu
2- A remarkable achievement of El naschie is his unique extra ordinary talent in revealing a deep connection between double slit experiment and particle physics. That is really a breakthrough in the field has never been acheived.
The two-slit experiment as the foundation of E-infinity of high energy physics
Chaos, Solitons & Fractals, Volume 25, Issue 3, August 2005, Pages 509-514
M.S. El Naschie
3- El naschie is gifted in doing simple calculations and getting non-perturbative results. While ordinary people can get results by using supper computer in a one year, El naschie get the same results straight forward by counting on his fingers without using computer at all. These are due his GOLDEN FINGERS.
On quarks confinement and asymptotic freedom
Chaos, Solitons & Fractals, Volume 37, Issue 5, September 2008, Pages 1289-1291
M.S. El Naschie
Quarks confinement
Chaos, Solitons & Fractals, Volume 37, Issue 1, July 2008, Pages 6-8
M.S. El Naschie
4- With a simple rope with knots El naschie could derive the spectrum of possible Elementary particles, and realy this is the discovery of the century.
Any one can just bring a rope with knots and could easily testify El naschie’s conjecture.
Fuzzy multi-instanton knots in the fabric of space–time and Dirac’s vacuum fluctuation
Chaos, Solitons & Fractals, Volume 38, Issue 5, December 2008, Pages 1260-1268
El naschie may be the greatest thinker in the history of mankind and his theory is the most important discovery since the invention of wheel. El naschie maybe the most remarkable event after cosmic big bang. His theory can describe every thing after big bang and I’m sure El naschie will extend his theory to accommodate what has been before big bang. Please don’t wonder it is an E-infinity theory that could deal with such a long history of time.
Comment No. 11 is by a convict. His name is Said. You can see his site under The Case of Said Elnashaie http://thecaseofsaidelnashaie.blogspot.com/. His wife is Shadia Shishini. She spent one and half years in the Women’s prison for forgery. Said together with Shadia were convicted for conspiring to rob an elderly lady of her possessions. They think they were convicted because Prof. Mohamed El Naschie encouraged the authorities to persecute them and finally convict them and confine them to a hard labor sentence. A psychopath like Said could not call it a day of course. He is ghosting around masquerading under all sorts of names spreading lies and rumors against Prof. Mohamed El Naschie. It is a sad story but the fact that some blogs like that of John Baez, Die Zeit and Nature can support such activity is beyond me. I am sure this will all come to an end with Nature sees the light and realizes that they were conned into writing an article which should never have been written because it is a tabloid article devoid of any content except that of defamation.
To: Researchers working on El Naschie E-infinity Cantorian-fractal spacetime theory of quantum high energy physics.
Dear All,
Even the most gullible, unsuspecting and least inclined to a conspiracy theory must be asking themselves by now why all this viscous attack not only against E-infinity and fractal spacetime as a theory but far worse against Prof. Ji-Huan He, L. Marek-Crnjac, Prof. Mohamed El Naschie, Gerardo Iovane and in fact every single member of the E-infinity group. Who is behind all that? Who is behind El Naschie Watch and the daily hundreds of perverted viscous comments aimed at any and everybody who has anything good to say about us, particularly Prof. El Naschie and Prof. He? Is it the establishment and what kind of establishment is this which is scared to death from a couple of simple equations and the word fractal spacetime? If I did not know better I would think that a Cantor set is where the devil himself lives or it is a code name similar to D-day or Dessert Storm only directed towards theoretical physics. In what follows I would like to explain to you in some detail that we have achieved a great deal with our theory. The work of Goldfain, Mohamed El Naschie and before them Nottale and Ord and Richard Feynman were all not in vain. I would like to explain that we are on the verge of a great truth and paradigm shift in physics. Some unteachable elements of the establishment are resorting to methods far away from science which failed in the past to prevent the inevitable. Others more cunning are working hard to translate our terminology to another terminology. The famous plagiarism which took place in Scientific American is only one of the very early and visible examples of this cunningness which is in reality lack of scientific honor as aptly described by one of us in a letter to the people concerned.
Let me start by first counting the unshakable final results which we have achieved on a few points and then we will move from there to discuss the wider picture and the experimental facts which are coming in daily. In brief we found the following results which will endure any future discoveries and could be counted as the absolutely secured part of what we have done.
1. The geometry of micro spacetime is best described by a fractal. This is the result of the work of Garnet Ord and Laurent Nottale following the pioneering idea of Richard Feynman and his path integral method.
2. The building blocks of spacetime are elementary random Cantor sets. The Hausdorff dimension of these elementary random Cantor sets is the golden mean. By varying the resolution you can obtain everything you want from an infinite collection of these Cantor sets. This is the essence of the work of Mohamed El Naschie, L. Crnjac, Ji-Huan He and also G. Iovane.
3. The expectation value for the Hausdorff dimension is 4 plus the golden mean to the power of three. This is 4.23606799. The expectation value for the topological dimension is exactly 4. The formal dimensionality is however infinite. This will bring us nearer to the theory of multiverse as I will explain later.
4. The most fundamental symmetry groups are the exceptional Lie symmetry groups. These are 8 in all forming a family. The most important member of this family is E8. What is important however is that the sum over all exceptional Lie symmetry group leads to a probability measure which is consistent with the random Cantor sets and its golden mean dimension. The sum of the dimensions of all eight groups was shown by El Naschie to give a total dimension equal 4 ¬α ̅=548 where ¬α ̅ = 137.
5. You can extend summing over exceptional Lie group to compact and non-compact exceptional Lie groups and find 17 of them. The sum of all dimensions was shown by El Naschie to be 5α ̅=685. This theory led to speculation about an even larger symmetry group, namely E12 which is more important than the recently discovered E10 and E11 but I will not consider this part of secured knowledge and I will stop here, mentioning only that Ray Munroe was the first to find E12 before El Naschie.
As for the experimental verification we now have a few extremely important ones:
1. Indication of a Cantorian spacetime and a fractal spacetime coming from an analysis of the cosmic rays and microwave background radiation. The expert on the first is Goldfain and on the second Mohamed El Naschie and you can consult their publications on this. However there are many results independent of our group confirming the same and it would be great if Goldfain could write a report for us all on this for internal use on our blog.
2. The discovery of E8 in nanostructures and the golden mean in quantum mechanics which was recently made public by the Helmholtz Center in Germany is the most definite result confirming Cantorian spacetime geometry experimentally. I say this is the tip of the iceberg. From now on you will see the golden mean mushrooming everywhere in quantum mechanics and high energy physics.
Under these circumstances many people became worried and anxious that a group like ours, not considered to be specialists in mathematical physics and high energy particle physics should have made such a major step forwards and been able to predict the masses of elementary particles and the value of fundamental constants with such precision and ease. The frustration is to a certain extent understandable and the reason is the following.
1. Garnet Ord and Nottale did not use set theory per se. Mohamed El Naschie was also not the first to propose set theory in quantum mechanics and high energy physics. The first impulse came from somewhere completely different. They came from David Finkelstein and Carl Friedrich von Weizsaker. The two great scientists were not interested in details. However Stanley Gudder in the USA and his school as well as Fay Dowker in England and her collaborators felt that partially ordered sets could solve the problem of quantum mechanics. They were rather near but not quite there because they had no simple way of performing real quantitative calculations. Far better suited to quantum mechanics are random Cantor sets. When you use them you have the golden mean. And when you use the golden mean then you have at your hand an unrivalled number system which can handle any complex computation with unheard of simplicity. This was Mohamed El Naschie’s good luck or misfortune. By pure accident or providence El Naschie stumbled on a basic problem in fundamental mathematics. Basing your number system on the irrational number and the irrational golden mean system you can see the world with new eyes with unheard of simplicity. The recent book by Alexey Stakhov published in World Scientific under the title The Mathematics of Harmony is a profound meditation on this theme. Chaos, Solitons & Fractals had the honor of publishing the larger part of Prof. Stakhov’s work. I think when certain elements in the establishment realize that we surpassed everybody else, they panicked.
2. When certain elements of the establishment panicked, they published the paper in Scientific American in 2008. To overcome the problem of not having the golden mean they used the most powerful existing new generation of computers and pretended to use their expression, that they found the holy grail of theoretical physics by calculating the four dimensionalities of spacetime from first principles using a desktop computer. One of our associates joked about them by calculating the same dimension using a pocket calculator. In fact using the golden mean you can find everything by counting on your fingers, that is if you know the rules of the golden mean arithmetic. The rest is history and you can read it on the comments of this work in Scientific American.
3. An exceptional member of the mainstream who does not normally work in quantum mechanics is Prof. Tim Palmer of the University of Oxford. This professor realized the importance of fractals for quantum mechanics. His first paper did not refer to our group at all. Later on he revised his stance and he referred to Garnet Ord, Laurent Nottale and Mohamed El Naschie on the first page of his revised ArXived paper. Later on when this paper appeared in the Royal Society, the three names were relegated to the very rear of the paper. Never the less, the man at least had sufficient objectivity to acknowledge our priority. Of course he should have noticed that there is no difference between our work using Rene Thom/El Naschie VAK and his proposal. Spacetime and phase space are exchangeable at this high energy where time is spatialized. Anyway this was at least one of the establishment acknowledging that we were there first. On a personal level we have the greatest respect for Prof. Tim Palmer who is an exceptional meteorological scientist.
4. There is at least one earlier attempt to use elements out of our work and overlook mentioning our group. The first which comes to my mind is that of Dr. Garrett Lisi. He is not a mainstream scientist at all but he was supported by some people from Perimeter Inst. in Canada. Needless to say, most of what Lisi wrote about E8 was well known to us long ago and was published in Chaos, Solitons & Fractals years before Lisi’s paper. Of course the establishment in general neither likes Lisi’s nor our work and thus we and Lisi were equal although we were more equal than Lisi in being disliked by the establishment for reasons which have no scientific basis.
5. Here I must now mention the discovery of the important utility of the multiverse. The objective of this comment is really to talk about this subject. What I have written so far was just a summary of the past. I would like to show clearly that the multiverse theory is nothing but a new label for our Cantorian spacetime theory particularly when we couple it with the holographic principle of ‘tHooft.
ON THE EQUIVALENCE BETWEEN THE MULTIVERSE THEORY OF RAPHAEL BOUSSO AND E-INFINITY THEORY
A multiverse is a universe with an infinite number of pocket universes. Please note that the most important thing here is infinity. Fractal spacetime in the E-infinity version is an infinite dimensional universe. To avoid contradictions and inconsistencies, Bousso introduced causal patch measures. This measure corresponds to the relative topological probability used in E-infinity theory. However the really interesting point comes when you apply to both theories the holographic principle. You recall from E-infinity theory that the holographic manifold of E-infinity is Klein’s modular curve. This curve has 336 triangles. These 336 correspond to SL 2,7 which constitutes 336 isometries in two dimensions being the surface. They also correspond to 336 kissing points of 10 dimensional spheres. This in turn corresponds to 336 quantum curvatures in 8 dimensions. You can think of the 336 of Klein’s modular curve as cutting the 10 dimensional spaces of the kissing spheres and flattening them to a surface. You see know the equivalence between particle like states and isometries. Since the kissing points are the points of interactions, they can be regarded as messenger particles or massless gauge bosons. In fact following the holographic principle, they represent all that is going to be particle physics of the standard model later on at lower energy. To see the connection you just compare the 496 of E8 E8 of super string theory to the sum of the electromagnetism as represented by the 137 alpha bar when you add to it Einstein’s gravity in four dimensions which is 20 and the 336 of particle physics. Now you see that it does not completely add up. There are 3 missing. This 3 can be taken care of in two ways. Either you think of them as the only electromagnetic photons which are massive, namely W minus, W plus and Z zero. Thus we have 3 plus 336 equal 339. Plus 137 plus 20 which exactly matches the 496 of super strings as should be. But there is a better geometrical way to look at that which agrees exactly with the holographic multiverse interpretation of Raphael Bousso. Remember that we have to compactify Klein’s modular curve to come to a picture similar to that of Escher’s devil and angel. This is the hyperbolic structure well known from hyperbolic geometry. To reach the boundary we could walk for ever. If there is something like an outside observer he will find that we are nearing the boundary but becoming slower and slower and never ever reach the boundary which lies at infinity. Thus although we have a finite area, we have infinite distance to the boundary. If we identify this infinite distance with infinite time then our theory becomes identical to that of Bousso. The famous chaos scientist Otto Rössler compared the situation to a pseudo sphere of a certain cosmological model. In other words, Bousso’s theory, probably unknowingly, adopts words for word our theory and there is a one to one correspondence between our terminology and the new terminology. E-infinity is a multiverse theory. It always was and it will always be. You see we are at the cutting edge of everything in theoretical physics. In addition we can calculate things and not only philosophize about it. That is why some find El Naschie more than irritating and are extremely upset that we have been supporting him because quite honestly, without this help, he could not have achieved anything. In fact without our moral support he would not have survived the last operation which he had in London.
We must think about all these things and develop them further and keep each other informed. Let us, following Leo Tolstoy, try to forgive our opponents and wish them peace of their soul so that they can leave us in peace to complete our work.
Best wishes to everyone,
E-Infinity Communication
Where can I find elementary introduction to theory of El Naschie? Thank you in advance.
What are the experts thinking of the new proposal by El Naschie for the wave collapse? It is neat but I have one problem. It is too neat and too simple to be true. I do not believe that nature is that simple. OK I know all these philosophers that marvel at creation being the most simple of simple things. Whoever believes that, with the exception of Leibniz will be canonized. Here is El Naschie’s solution of the state vector reduction. The particle is a Cantor point. It has the dimension zero and the golden mean. The zero is the Menger-Urysohn topological dimension. The golden mean is the Hausdorff dimension. In other words a quantum particle is a fractal particle. Now comes the big thing. The quantum wave or the Bohm Einstein guiding wave or the probability wave and all mean the same thing, is the empty set. The empty fractal set has a dimension minus one and the golden mean squared. The minus one is the classical Menger-Urysohn topological dimension. The golden mean squared is the corresponding Hausdorff dimension. We all know that the empty set is the neighbourhood of the zero set. Said in a less sophisticated language, the empty set is the surface of the zero set. Following this logic the wave function is simply the surface of the quantum particle. They are part and parcel of each other. Now imagine you are taking measurements. At a minimum you will enter into the empty set to catch the zero set. That way the empty set becomes non-empty follow El Naschie’s logic which I must say is sound although it sounds a bit weird. Since the empty set is no longer empty and at best becomes a zero set, then the wave set is converted into a particle set. Hey presto! There is no more wave. I see it but I cannot believe it. I believe that is what Cantor said when he thought of his discovery about the cardinality of the continuum and that the number of points in a Cantor set are equal to the number of points in a continuous line or for that matter an area cube or a hyper cube. I am a mathematician of the purest kind so I can swallow this stuff but what is the feeling of the hard-nosed physicists? Awaiting eagerly your views.
It is sure that El naschie doesn’t understand elementary quantum mechanics nor elementary physics.
When the wave function collapses due to measurement, it collapses to another wave function. For example, when you measure the momentum and you get certain value for it, then the wave function of the system directly after the measurement will be eigen function of momentum with this certain value of momentum.
I hope El naschie to do some efforts to understand what he is saying and to check standard text book on quantum mechanics.
I hope that C. Chung and Simon Cheung (El naschie’s sock-puppets == El naschie) to stop these stupid monologues. It is clear that El naschie doesn’t know physics nor mathematics except at the level of popular science even with improper understanding.
what do you mean by fractal geometry?i’m a grade 10 student interested to learn about quantum mechanics.
I would like to talk, if I am allowed to, about another subject which I think is only too fair. All the three musketeers, Prof. Garnet Ord, Dr. Laurent Nottale and Prof. Mohamed El Naschie discovered something which was all along missing. Quantum mechanics does not recognize the zero and the empty set. It is hilarious that those working in the most advanced mathematics used in physics, namely quantum theory do not know the basics of mathematics which is set theory. The basis of set theory is the zero set and the empty set. The empty set is the beginning of everything. As a consequence of this peculiar state quantum mechanics does not recognize anything to do with fractals. The non-recognition of the fine structure of fractals is the basic source of all counter-intuitive results in quantum mechanics. The results themselves are of course not counter-intuitive. What is counter-intuitive is the interpretation of the results without referring to fractal geometry. The only two scientists I know of who escape this viscous circle apart of our three musketeers are Sir Roger Penrose and Field Medalist Prof. Alain Connes. Noncommutative geometry is necessarily fractal geometry. They may call it foliation. They may call it quotient space. They may call it leaf of foliation. They may call it what they like but it is fractal. That is it is zero measure and empty sets as backbone. Almost twenty years later a notable meteorologist noticed the same thing which the three musketeers discovered twenty years earlier. This notable meteorologist is Prof. T.N. Palmer from the University of Oxford. Palmer wrote last year in the Royal Society a remarkable paper where he formulates the thesis of Ord, Nottale and El Naschie in one sentence. He concludes “quantum mechanics is blind to fractals”.
For this reason and apart of anything else I suggest that in all earnestness that it is only fair to at least consider Ord, Nottale and El Naschie for a Nobel Prize in Theoretical Physics. Sir Roger Penrose as well as Alain Connes got the equivalent of a Nobel Prize. There remains only in such a case Prof. T.N. Palmer who is a Fellow of the Royal Society. I was astonished to hear that Nature twice declined the acceptance of the work which won this year’s Nobel Prize of Physics. The two Russian born scientists who work in Manchester were discouraged but ultimately sent the paper to Science which accepted their work and five years later they shared the Nobel Prize in Physics for 2010. You cannot say that the Nobel Committee is unfair. However sometimes unfair competition clouds the vision of the Nobel Committee.
Yansen, If it is really your name and if you really meant your comment seriously and not viscously, the explanation is very simple. Quantum mechanics is incomplete. There is nothing called really measurement. What you learnt so superciliously from books is wrong. You should have read John Bell (Against Measurement). The important point is to realize that the disappearance of the interference fringes which way information is obtained is not a mystery. It is because of what you interpret wrongly as a wave collapse. El Naschie correctly identifies a fractal point with a point in noncommutative geometry with a quantum particle. Similarly a wave function is the surface of a fractal point and is the surface of a point in noncommutative geometry and is the surface of a quantum particle. A quantum particle can thus be modeled by zero set and the quantum wave by an empty set. Any interference with the empty set changes it to non-empty. You should remember that von Neumann used set theory in his famous book. He started on the wrong foot however and came like you to a wrong conclusion. In the book which was published posthumously von Neumann was correct. This is the book which El Naschie studied and you did not. Stop being arrogant because arrogance always results in stupidity. Sorry to tell you that. However if your name is John Baez then I am not sorry to say that.
The golden quantum entanglement: A new paper just published by He, L. Crnjac and several people who used to work in E-infinity theory reported a remarkable discovery which is as old as 1993. It seems El Naschie was right and orthodox quantum mechanics is based on the golden mean. It went unnoticed that the probability for quantum entanglement which L. Hardy found in 1993 is exactly equal to the golden mean to the power of five. This is 0.090169943. Interestingly Sir Roger Penrose reported this result in his monumental work The Road to Reality. However no one noticed that it is the golden mean to the power of 5. Prof. Penrose wrote it in a slightly different form unusual for mathematicians or physicists to recognize, namely as a rounded percentage like the rate of inflation in the United States. He wrote it as 9.017%. Who would have thought this is the golden mean. Even more potently this result was experimentally confirmed in Los Alamos and other famous laboratories in the US. Incredible as it may sound, El Naschie’s theory predicted this result twenty years ago. Too bad that El Naschie is not the right man for some. I don’t mind one way or another. What is right is right. Science and scientists should stick to science.
Starting with the symbol of ying and yang , The outer circle enclosing one trough of a sine wave but at the same time being one hump of two other sine-waves forming a larger circle that encloses an even larger or smaller trough. Each representing three dimensions that are observable only to the inhabitants of the dimension encompassed in that frequency range. The electron doe’s not know it is being observed, the weight of the observation pushes the wave fronts together creating density in the continuum. Gravity is an illusion of pressures created by the oscillations of all these sine-waves of probability pushing,,,
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Dark energy has been deciphered by El Naschie. Einstein’s equation must be revised to account for the missing energy. All what you need according to El Naschie is to use Nottale’s scale relativity. The end result is incredibly simple. Newton’s energy is half the mass x speed square. Einstein is almost the same but without the half and the speed is that of light. El Naschie’s revision is also basically a scaling. El Naschie’s quantum relativity energy is equal to the mass x the velocity of light squared and all divided by 22. The 22 are what is left when you take the 4 dimensions of Einstein’s space time from the 26 dimensions of Vene\ziano-Nambo string theory out. Alternatively you could think of it as the effect of 11 messenger particles which were not known at the time of Einstein. Einstein’s theory is a one degree of freedom theory because he only considered photons. The standard model has 12 messenger particles at least. That is how Nottale’s scaling leads to division by 22 which is nothing but 2 x 11. The 2 is there to take care of the super symmetric partners. The accelerated expansion is shown to be the effect of the curled 22 extra dimensions of space. Amazingly the numerical result is in complete agreement with the observation of Permlutter and the other 2 which was awarded the Nobel Prize in Physics last year.
I don’t leave a comment, however after looking at through a few of the comments on Spacetime as Fractal Geometry. I do have a couple of questions for you if you tend not to mind. Is it simply me or does it seem like some of these remarks appear like they are coming from brain dead people?
And, if you are writing on other social sites, I would like to follow you. Could you list of every one of all your social networking sites like your Facebook page, twitter feed, or linkedin profile?