From: sorenj@rpi.edu (Jeffrey S. Sorensen)
Newsgroups: sci.nanotech
Subject: Nano-assembly and the Shannon construction theory
Date: 23 Aug 92 23:56:17 GMT
Organization: Rensselaer Polytechnic Institute, Troy NY



While I have seen many discussions regarding the operation of
nano-assembly devices, I have yet to see many discussions on the
role that quantum physics will play in such operations.  Placing
atoms into configurations that, when bonded, will result in the
desired nanostructures is not sufficient.  The atoms must be
covalently bonded, and this stage necessarily depends upon the 
quantum nature of the atom's electron shells.

Taking the example of an enzyme, the various sub-components are
held in place in a close enough proximity to make the covalent
bonding event likely.  What this means is that the jump between
the two energy states is small and the event has a high probabilty.

While this is fine for an enzyme, construction of larger structures
will require scheduling.  Unfortunately, the timing of quantum events
is predictible only in a probabilistic fashion.  Consider mechanical
nano-manipulators that bring together several molecular components.
The device cannot force them into covalent bonds, it can only hold
the components so as to make the bonding event likely.

The problem is determining when these bonding events occur.  Continuous
monitoring is impossible because of the nature of quantum physics.
While this may seem strange, attempting to monitor the event would
couple the manufacturing system to the bonding event.  None of this
makes nanotech manufacturing impossible, only more difficult.

Interestingly enough, the solution to this problem can be found in
information theory.  In order to build a macro-molecular structure, our
nano-assemblers simply hold the components in their targeted positions
for a reasonable length of time to make the event virtually certain.
A more complicated assembler would be able to operate faster by waiting
less time and taking steps to handle the mistakes that occur when the
desired bonds don't form.

What are the limits on nanotech assembly times?  They can be easily
estimated using the rate-coding theory found in any information theory
textbook.  Building assemblers that work close to the rate-coding
limits may be extremely difficult when the structures involve bonding
steps that are "highly unlikely".  However, studies of genetic mechanisms
may prove that they have evolved to work very close to the theoretical
limits.

I would welcome any comments regarding these notions and their relevance
to nanotech.  With some help on the probabilistic equations (or refs)
invovled in quantum chemistry, I could compute the theoretical limits on
speed of assembly.  (In information theory there is one limit that
represents the absolute fastest physically possible and an approximation
that gives the fastest "reasonable" speed.  Trying to squeeze out the
speed from "reasonable" to the physical limit requires system that grow
in complexity exponentially (hence unreasonable).)
Such time estimates could be useful in planing the construction of
macro-structures using nano-frabrication techniques.


-- 
____________________________________________________________________________
    Jeff Sorensen    \ "Beware of first hand  \ My monitor is sooooo small, \
sorensen@ecse.rpi.edu \ ideas!" - E.M. Forster \   when you open a file      \
Work:  (518) 276-8202  \ in "The Machine Stops" \       you break a window.   \