Comments on: Folding the Yoshimoto Cube, Feeding 5000

By: Mike

Mike — Sat, 09 Oct 2010 18:58:02 +0000

If you want to unify relativity with quantum mechanics, you have to start by making quantum mechanics understandable. Compared to quantum mechanics, relativity is quite classical. It is a spacetime theory and there is nothing of the totally counter intuitive result of quantum mechanics in relativity. Yes we understand time travel and twelve paradoxes and so on. None the less this is nothing compared to the paradox of the two-slit experiment and particularly wave collapse. Probability wave – what is that? However there is something new on the horizon. A major breakthrough in understanding wave collapse. This is the least we can say about this new profound discovery. The most astonishing thing about it is why it was not discovered long ago. In a nutshell the essence of the argument is as follows: A quantum particle may be modeled as a point. However it is not any point. It is a Cantor point. That means it is a fractal point taking out of Laurent Nottale’s or Garnet Ord’s fractal spacetime. Consequently it is a point but much more than a point at the same time. Every Cantor point or fractal point is by virtue of self-similarity a point representation of the entire universe, i.e. the fractal universe upon sufficient magnification. This zooming process, as explained by Nottale, has no end. This is all well known stuff from the theory of fractals. Now comes the crucial point. Since this point is nominally a point we take it to be mathematically the zero set and physically to be a quantum particle. Now the boundary of the zero set is the empty set. The empty set has no element what so ever and is given in the classical theory a dimension minus one. Never mind all these numbers. The important thing is just to keep in mind that a Cantor or a fractal point represents a quantum particle and that the boundary of this quantum particle is the empty set. It comes as no surprise that El Naschie and his E-infinity group propose that the empty set is just the mathematical name for the probability wave function of quantum mechanics. Such a wave function is devoid of energy, matter and momentum to the extent that it mystified all physicists and led Einstein as well as Bohm to call it a ghost wave. There is even a theory by both men called the guiding wave theory. The guiding wave is nothing but the empty set. So far so good. Here comes the resolution of the wave collapse problem say the group of E-infinity researchers. Any attempt to locate the quantum particle will include interference with its boundary. Since its boundary is the empty set, then any interference will make the empty set non-empty. Consequently the empty set ceases to exist. On the other hand the empty set is our quantum wave function. It follows as a trivial result that when the empty set vanishes because it becomes non-empty, then the wave function also vanishes. The group of E-infinity did not stop at this disarming explanation of the wave collapse. Using the Menger-Urysohn and the Hausdorff dimension of the zero set and the empty set, they are able to make convincing calculations and derive the topology of the spacetime manifold which allowed such physics involving the empty set wave collapse. You can read about that in preceedings of a conference in Shanghai http://www.isnd2010.com and http://www.msel-naschie.com. With a theory like that we are in a much better position to start unifying quantum mechanics with relativity and produce a real theory of quantum gravity. At least there is more hope that way.

By: E-Infinity

E-Infinity — Thu, 11 Mar 2010 16:42:53 +0000

A Slovenian scientist and mathematician following Mohamed El Naschie expand the idea of mechanical oscillators. Many papers have been published on this subject by L. Marek-Crnjac. Take a two degree of freedom oscillator. Two masses connected by two linear springs. Write the equation of motion. Set the value for the masses as well as the spring constants equal unity. The secular equation is then simply a quadratic equation. The Eigen values are golden mean related. The only positive real Eigen value is the golden mean. Imagine now that you have infinitely many such oscillators connected together. Consequently you can estimate the Eigen value using two well known theorems on Eigen values. These are the Southwell theorem and the Dunkerly theorem. They correspond to what we have studied in school about joining electrical resistance of Ome’s law. When they are successive you add the inverses and when they are parallel you add them. Eigen values are frequencies. Frequencies are energy and energy is mass. Extrapolating the whole thing to quantum mechanics as argued by El Naschie and Marek-Crnjac you have another plausibility explanation for why the golden mean will pop up in any accurate measurement in quantum mechanics phenomenon.

By: annonymous

annonymous — Sat, 20 Feb 2010 18:20:46 +0000

Dr. Ray Munroe, a theoretical physicist with some understanding of El Naschie’s theory recently said on one of his comments I think in the Fqxi blog that only time will tell if El Naschie’s theory is correct. This is a sentence which is lovely and vague. It is a political sentence, not a scientific one. I guess Munroe knows very well that El Naschie’s theory is correct. He just finds it politically risky to identify himself with a theory about which he himself has written in Chaos, Solitons & Fractals when the author of the theory is under attack from Nature’s tabloid article. When science changes to politics then it is time for scientists to take arms against politics. The difference between politics and science is that in science you do not need to wait for time to prove it. All that you need is to compute it. A simple back of an envelope calculation would immediately show that a golden mean topology and geometry is the only logical solution for the two-slit experiment. If the building blocks of the geometry and topology of quantum spacetime is governed by the Hausdorff dimension of these blocks, then no wonder that this Hausdorff dimension will manifest itself in everything physical. The Hausdorff dimension is the golden mean. Consequently the most fundamental theory, namely quantum mechanics must be based on a golden mean spacetime. Such spacetime differs completely from the classical spacetime. It differs also from spacetime of general relativity. I cannot say that it also differs from the spacetime of quantum mechanics because classical quantum mechanics is not a spacetime theory. Therefore El Naschie’s E-infinity theory elevates quantum mechanics to a spacetime theory just like relativity and classical mechanics. Interestingly depending on the resolution you can obtain all geometry of all the three fundamental theories. You can move from 0.618033989… to a rational value of 0.5 and under circumstances unity and find all the limiting behavior you wish to discover and explore. It is that complex and yet that simple. In fact cellular automata is just another form of the above based on computers. Nature consists of very simple rules. You reiterate these rules trillions of times and then you obtain the complexity which is visible in the classical world. The simple rules discovered by E-infinity are that using the golden mean Hausdorff dimension which represents an elementary random Cantor set can produce the result of a cellular automata with infinite capacity. In other words you do not even need a computer. The universe possesses an infinite computer because it possesses the golden mean. You probably recall the work of Renate Loll popularized in a Scientific American article published in 2008. What Renate Loll, Jon Ambjorn and their colleague did in this remarkable paper was reproducing some aspects of Mohamed El Naschie’s work without using golden mean Cantor sets. They replaced this powerful mathematical tool by the best computer capacity they have at present. If they want to find precisely the same result found by El Naschie, then all what they need is to find an infinitely strong computer. I am sure the reader sees that this strategy is misguided and upside down. Instead of finding an infinitely strong computer, we should find a theoretical solution. This theoretical solution happens to be the golden mean geometry and topology of E-infinity theory.

By: Manny

Manny — Sat, 06 Feb 2010 12:36:03 +0000

I am pleased that the truth has prevailed. Nature is now accused of trying to undermine Mohamed El Naschie deliberately. This accusation is not frivolous. How else can we explain the blind vicious attack by certain doubtful blogs on the golden mean work of El Naschie and how Quirin Schiermeier the journalist working for Nature utilized these vicious attacks to write a completely unacceptable article in Nature. Then came the heavenly justice when a German professor von Storch complained on his blog that the Nature article of Schiermeier deliberately misquoted him. He was gentle enough to say that the harm was not great. However in principle the harm could have been great. No one has the right to smear the reputation of anyone whether deliberately or recklessly due to irresponsible journalism. Now to the burning scientific question. How does the golden mean enter into quantum mechanics. The answer is as simple as it is ingenious. Mohamed El Naschie reformulates quantum mechanics in spacetime following the same concepts used by Richard Feynman as well the classical work of Einstein. Since the building blocks of spacetime are his elementary random Cantor sets and because these random Cantor sets possess the golden mean as a Hausdorff dimension, the golden mean slips into the fundaments of quantum mechanics. Nothing that quantum mechanics is the most fundamental theory upon which science is based, the golden mean could rightly be described as the basis of science. From this reasoning the ideas which Ed Nash expressed in his previous comment follows effortlessly.

By: Never Yet Melted » Yoshimoto Cube

Never Yet Melted » Yoshimoto Cube — Fri, 22 Jan 2010 13:34:41 +0000

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