Layman Q: wave funtion and measurement

From: Fernando Cacciola (fernando_cacciola_at_hotmail.com)
Date: 09/03/04 

Date: Fri, 3 Sep 2004 09:23:51 -0300

Hi!

I'm reading Weinberg's "The Dream of a Final Teory" book.
It has a short and simple explanation of the meaning of a wave function for
a simple system of one particle with only two states.
I'm restating that here in my own words, but retaining some of the original
expression in the book. My questions are realted to the meaning of these
trypical expressions.

Given a particle 'P' with possible states 'X and 'Y', the wave function of
this system, when evaluated for a given time 't', gives the probability of P
to be at the states X and Y.

In the function general form, the values for X and Y are never 1 and 0 (or 0
and 1), so there is permanentely some non zero probability for X and Y,
which means that without measurement, the wave function doesn't 'define' the
state of P as absolutely X or absolutely Y.
(1) We say that during the intervals when we're not measuring it, "the
state of the system is not completely defined [as X or Y]"

However, whenever and however we measure P, we find it completely and
absolutely at either X or Y, exclusively. Therefore, upon measurement, the
wave function 'collapses' into a form where X (or Y) is 1 and Y (or X) is 0.
(2) We say that "the state of the system is completely defined only after we
measure it, definition expressed by the collapsed wave function".

Now my questions:

(a) Saying that the state of the system is or is not defined is only
expressing our knowledge of it right? I mean, it doesn't say that the system
itself, as an objective reality, doesn't have a definite state right?

(b) Saying that the wave function collapses, which is saying that
something -the wave function- changes, is telling nothing about an objective
change in the system itself right? I mean, we are only saying that we
"adpat" the tool used to describe the system as soon as we have any concrete
objective data about it.

TIA

Fernando Cacciola

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