Re: Wave Function of the Universe?

Arnold Neumaier a =E9crit :
> [Seratend replied here in the other thread:]
>
> > This is only true, in the absolute, if the piece of metal is made of=
an
> > infinite number of particle masses (convergence in law). What we real=
ly
> > measure is the value of M=3D sum_i Mi and not <M>.
>
> No. What we measure is an approximation of
> <integral_Omega dx a^*(x)Ma(x)> over the region Omega of interest.
> This is the expression that figures in statistical mechanics
> derivations of macroscopic elasticity theory.
>
We can apply the statistics to small independent areas. This does not
change the fact that at the end what we really measure on this local
are is M_area=3D sum_{i in the area} Mi and not <M>_{area} (what you call
the approximation when the area is not well defined).
An instance (an outcome) of the object has well defined (may be unkonwn
to the observer) values of Mi in all areas (independence of Mi random
variables or commuting observables). However, at the end one sums all
over these areas (the extensive property of M) to obtain the value we
really measure (the approximation of <M>).

In my opinion, this is simply the application of the law of large
numbers and the grand or micro canonical ensembles just use this
property with additional hypotheses.=20

Seratend.

.