> 
> I enjoyed this post very much.  I have one question and a comment.
> Q:  I didn't know that the most general field for a vector space
> is the set of complex numbers;  why is this so?
> Comment:  You ask why QM should be linear.  In the MWI FAQ, Price
> gives a good Anthropic argument for why this should be so, based
> on the fact that if it were in the least non-linear, then it 
> would be possible to communicate between worlds.
> 
> 

A Field is a mathematical concept. It is a set of objects that satisfies a
certain set of axioms. The most general such object is the set of
complex numbers. (Actually, I just glanced at Fig 1 of Max Tegmark's
paper - maybe what I'm referring to is an "Abelian Field"). The point
is that in order to have linearity in your vector space, you need an
abelian field.

                                                Cheers

----------------------------------------------------------------------------
Dr. Russell Standish                    Director
High Performance Computing Support Unit,
University of NSW                       Phone 9385 6967
Sydney 2052                             Fax   9385 7123
Australia                               [EMAIL PROTECTED]
Room 2075, Red Centre                   http://parallel.hpc.unsw.edu.au/rks
----------------------------------------------------------------------------

Reply via email to