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