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
On Wed, Dec 18, 2013 at 6:45 PM, meekerdb <meeke...@verizon.net> 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.
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Stephen Paul King
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