On Tue, Jul 12, 2005 at 09:54:55AM -0400, Stephen Paul King wrote:
>     How familiar are you with the details of quantum mechanics? Did you 
> happen to know that the notion of an observable in QM has a complex value and 
> that a real value only obtains after the multiplication of an observable with 
> its complex conjugate? This operation of conjugation must involve the 
> selection of some basis.. This makes the problem of a pre-existing Real value 
> time to be, at least, doubly difficult. 
>     Complex numbers have no natural ordering, as opposed to the Reals, which 
> do, because in general, complex numbers do not commute with each other. Only 
> the very special subset of observables can be said to commute and thus can be 
> mapped to some notion of a "dimension" that one can have translational 
> transforms as functions. 

Tosh! I'm sorry, but you are demonstrating enormous ignorance of QM
with these statements.

1) Observables are Hermitian operators. This means that their
   eigenvalues (which are the observed outcomes) are real valued (not
   complex valued as you seem to think), and so ordering of observed
   values is _not_ the problem you think it is.

2) Complex numbers indeed do not have an ordering (being basically
   points on a plane), however they do commute. For any two complex
   numbers x and y, xy=yx.


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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
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