Ever attempt to do a particular calculation with an actual infinite dimensional Hilbert space? Why not? Sure, you can mod out (using symmetries and other tricks) all of the infinite dimensions except some finite subset, 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. No, Choosing a basis and choosing a coordinate system is NOT a convenience. You must do it. 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. 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...
On Wed, Dec 18, 2013 at 6:45 PM, meekerdb <[email protected]> wrote: > On 12/18/2013 3:16 PM, Stephen Paul King wrote: > > My point is not about any kind of "specialness", *the same condition > follows for any frame that is consistent with the math*. There is no such > thing, mathematically, as a "view from nowhere" or, equivalently, for a > "god's eye point of view." God is dead and so is his "view". > For QM, things are even more restrictive: one has to assume that the > Hilbert space of the wave function is *finite* and a choice of the basis > of that space <http://en.wikipedia.org/wiki/Basis_%28linear_algebra%29>must > be done. That's the math... > > > ?? A Hilbert space is an infinite dimensional vector space. Choosing a > basis in only a calculational convenience, like choosing a coordinate > system. The choice has no effect on any physics, just on how hard or easy > some calculation is. > > Brent > > -- > You received this message because you are subscribed to a topic in the > Google Groups "Everything List" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/everything-list/1NWmK1IeadI/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 [email protected] http://www.provensecure.us/ “This message (including any attachments) is intended only for the use of the individual or entity to which it is addressed, and may contain information that is non-public, proprietary, privileged, confidential and exempt from disclosure under applicable law or may be constituted as attorney work product. If you are not the intended recipient, you are hereby notified that any use, dissemination, distribution, or copying of this communication is strictly prohibited. If you have received this message in error, notify sender immediately and delete this message immediately.” -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
