Hi Brent,

On Wed, Dec 18, 2013 at 8:01 PM, meekerdb <meeke...@verizon.net> wrote:

>  On 12/18/2013 4:27 PM, Stephen Paul King wrote:
>
>    Ever attempt to do a particular calculation with an actual infinite
> dimensional Hilbert space?
>
>
> Sure.
>
>
>  Why not? Sure, you can mod out (using symmetries and other tricks) all
> of the infinite dimensions except some finite subset,
>
>
> You can calculate all the eigenfunctions of a finite square well.
>
>
>  but that is the act that introduces the bias that I am pointing at! The
> actual Hilbert spaces used to do calculi are finite dimensional.
>
>
> Even if you only find a finite subset of eigenfunctions, the calculation
> is still done in an infinite dimensional space.  If you create a wave
> packet it consists of infinitely many momentum eigenfunctions.  I don't see
> that cutting the
>

What else did you meant to write?



>
>
>     No, Choosing a basis and choosing a coordinate system is NOT a
> convenience. You must do it.
>
>
> Try reading Robert Wald's "Quantum Field Theory in Curved Spacetime".  He
> seldom chooses a coordinate system.
>
> I have.



>
>  Especially in GR, where one cannot define the manifold unless there is a
> choice of coordinate system on the patches of local space-time used to
> define the manifold - which is then run through the diffeomorphism mill...
>    AFAIK, there is no global manifold that can be defined that does not
> involve the requirement of stitching together of local patches of
> space-time (defined per individual events) into manifolds of arbitrary
> size.
>
>
> But that doesn't require choosing a specific coordinate system, and in
> fact for most manifolds it is impossible to choose a single coordinate
> system.
>

Non sequitur



>
>
>  What must be remembered is that the "stitching operation" is very
> restrictive, one cannot connect patches that have events with
> different (other than an infinitesimal) values of momenta and position
> associated with each. The math of GR is amazing once one is familiar with
> it...
>
>
> ?? Coordinate patches have momenta??  That's amazing all right.
>

that is not what I wrote.



>
> Brent
>
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-- 

Kindest Regards,

Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

 http://www.provensecure.us/


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