X-Message-Number: 20648 From: Date: Wed, 18 Dec 2002 05:45:51 EST Subject: Life force and the math swamp --part1_17b.136e26f3.2b31abdf_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit I have suggested that beyond geometry and group symetries, non local clifford space could create a new kind of forces. Clifford algebras are known as the source of the spinor formalism used in relativistic form of quantum mechanics, the so called second quantification. I'll try to give here a layman level taste of that subject for comming more practical messages on that subject. Everything started 70 years ago with the basic quantum mechanics, the Schrodinger formalism using functions and the Heisenberg brew using operators. Others have been addedlater. In all cases, time is an outside parameter, something used by the theory but not defined by it; This is similar to what is seen in classical mechanics. At that time, Relativity had unified space and time, that last being seen as the fourth dimension. So, why not a four dimensional, space-time quantum mechanics? Dirac has been the first to propose an equation solving that problem. An early drawback of the solition is that it displayed with any positive solution a negative one. Some took that seriously and predicted a form of mirror mater. Shortly after, the positon or mirror electron, was discovered in a cosmic ray track. Other anti-matter particles was discovered in the following years. Unfortunately, not all of Dirac equation predictions was as succesful as that. There was a problem with rest mass for example. Neverthless it introduced a quantity, the intrinsic angular momentum of particle described by directional vectors and that was a big success. The directional vectors was rapidly generalized to the so called spinors and it was found that these spinors obey a special class of algebras, the Clifford one. The Dirac equation problems was fixed by another equation, the Klein-Gordon one. At most that was the feeling at the time. Unfortunately, there was one or two minor difficulties in the back of the basket. So, nearly forty years after Dirac a fix was worked out for the Klein Gordon equation, it was the Dual Theory, something predicting that matter particle can be turned into energy - like one and inversely. Dual theory was not water proof and it leaked so a new fix gave supersymetry, or susy for short. Unfortunately, susy don't worked for particles with intrinsic momentum larger than two planck units. The solution was to abandon the point-like particle concept and move to one dimensional objects, the quantum susy strings. Halas, susy strings leaked too and was generalized to surface objects, the branes. Then branes was extended to to any p-dimensional objects, the p-brane theory or theories as five or six have been discovered (depending how you count them. The last idea: susy p-branes theories are all different limit cases of a single theory called M for matrix. Nobody seem able today to understand M-theory so we may have reached the end of the road, not that we have the ultimate explanation of the universe, but simply the limit of man's brain, given the current formalism. M is often presented as the search for the ultimate theory of the universe. In fact, if we look back at history, it is simply the last step in the try to include time in quantum mechanics. Why is that so difficult? Things must be taken at the roots to see why. Clasical mechanics is built on the concept of vector, small oriented line segment (don't bother here with tangent spaces...). A line segment can be defined by a start and an end point. If by convention we chose a common origin point for all vector, we must be able to write mechanics problems as therm of vector defined only by their end point. Now, a geometrical point is a 0-form in differential geometry an its dual is a function. At the basis of mechanics is the notion of distance, the square of a vector gives the square of its length or distance from one end point to the other. Reducing vector to a single point, there must be too a notion of distance, that is done with the point dual, the function: The square of a function ( the product of a function by its complex conjugate when complex numbers are used) summed over all possible variable value give the distance of the end point to the origin one. That is wat is done in quantum mechanics. This is a theory built on a space made from independent points.When Dirac included time in quantum mechanics as a dimension, he got back intrinsic angular momentum described by spinors. But spinors obey Clifford algebras and that is about nonlocal properties of space. Sudenly, quantum mechanics was shaken on its most fundamental basis: The space it is built on. There was no more isolated points, only some extended domains such dishes or blobs. Anyways, each such element included an infinity of points. So we can guess that such a theory is in fact an infinite stack of steps, each one consumming one point in an infinite set. Not only the number of steps is infinite, but we can't even count them. If we want to count them: Dirac, Klein-Gordon, Duality susy, strings, branes, p-branes, M, we have not started yet! How to go out? First, forget about including time in quantum mechanics as a dimension (time must not be a dimension, only a parameter). That is not to say all theoretical works done up to now are false, they express multipoint quantum mechanics. Simply they never close the gap and never include time as a dimension without leaving some loopholes. Second, the thing to do is to break the blob in two parts: a single (or more) point on a side describing "ordinary" quantum mechanics and a blob with the preceeding point(s) removed. This is purely clifford space without quantum mechanics. Third, we must look at a translator able to say how a domain is seen from the other. Translate is not unify, each domain will remains what it is. That is why clifford spaces must introduce fundamental new force fields, These can't be reduced (unified) with quantum or geometrical (gravitation) ones. Yvan Bozzonetti. --part1_17b.136e26f3.2b31abdf_boundary Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=20648