On 12/18/2013 4:27 PM, Stephen Paul King wrote:

Ever attempt to do a particular calculation with an actual infinite dimensionalHilbert space?

Sure.

Why not? Sure, you can mod out (using symmetries and other tricks) all of the infinitedimensions 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 Hilbertspaces 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`

No, Choosing a basis and choosing a coordinate system is NOT a convenience. You mustdo it.

`Try reading Robert Wald's "Quantum Field Theory in Curved Spacetime". He seldom chooses a`

`coordinate system.`

Especially in GR, where one cannot define the manifold unless there is a choice ofcoordinate system on the patches of local space-time used to define the manifold - whichis then run through the diffeomorphism mill...AFAIK, there is no global manifold that can be defined that does not involve therequirement of stitching together of local patches of space-time (defined per individualevents) 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.`

What must be remembered is that the "stitching operation" is very restrictive, onecannot connect patches that have events with different (other than aninfinitesimal) values of momenta and position associated with each. The math of GR isamazing once one is familiar with it...

?? Coordinate patches have momenta?? That's amazing all right. Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.