[extropy-chat] still no biscuit!

[scerir]

Jeff Medina wrote:
> >Heisenberg's Uncertainty Principle does not conflict with conservation
> >of momentum. It is a limit on measurement capabilities, not an
> >indicator that momentum goes "all over the ship" when position is
> >measured.

Damien wrote:
> This is simply wrong (as I understand it). It seems to imply that with
> finer or smarter measuring instruments, we could home in on both
properties
> simultaneously; this seems to be incorrect. What's more, if one knows
> position perfectly, momentum can be *anything at all*, and vice versa. It
> probably won't be, for stochastic reasons, but it could be.

Not sure to understand the points (I did not follow the
thread). 

Heisenberg's uncertainty principle, exemplified by the gamma 
ray gedanken experiment, suggests that any finite precision
measurement *disturbs* any observables non-commuting with 
the measured observable. (There is no general agreement
about the interpretation of HUP in these terms. And the HUP
has no meaning in certain cases, i.e. with bounded
observables etc. So, there are new mathematical formulations
of the HUP now, in terms of informations, entropies, etc.
And Aharonov invented a class of physical measurements which
by-pass the HUP).

Anyway he limitation on the measurement of an operator imposed 
by the presence of a conservation law was studied by Wigner,
then by Araki and Yanase. The resulting WAY theorem shows
that an operator which does not commute with a conserved 
(additive) quantity cannot be measured exactly. 

The relation between HUP and WAY is still obscure to me, 
and -to my knowledge- is still not well known in general.

Say we have a particle with position q and momentum p, 
and a measuring apparatus with position Q and momentum P. 
Let's suppose that the total momentum p + P is conserved. 
Essentially the WAY theorem says that it is impossible 
to measure particle's position q. We can only measure 
its position relative to the apparatus q - Q. 

More, by John Baez, here below:
http://math.ucr.edu/home/baez/week33.html