On 8/28/2010 12:29 PM, Stephen P. King wrote:
Hi Bret,
Could you elaborate on this point and/or point me to a
good discussion of it? From what I have studied so far there is no
solution to the measurement problem so far in terms of an explanation
of the way that the choice is made in each successive event, world or
whatever. Even decoherence does not help things from what I can tell,
That's sort of true. Decoherence explains that measurements necessarily
involved interactions with the environment and hence the reduced density
matrix will necessarily become diagonal FAPP - but not exactly
diagonal. Since it's not *exactly* diagonal it can't be interpreted as
providing just probabilities on the diagonal.
but this business that "What's a superposition in one basis is still
an eigenfunction in some basis." is new to me. The one to one and
reversible aspect was the state itself, but this is a different
situation, no?
Right, that's the time evolution in the absence of measurments.
There is a subscript i in the symbolic representations of the
eigenvalues, eigenvectors and eigenfunctions, no? What does this
represent?
Those are the eigenvectors of the measurement operator. If the state
you're measuring is a pure state in say basis X and you measure in basis
X then you will get just that one state as an eigenvector. But if you
measure in a different basis Y then you will get projections of X onto
the eigenvectors of Y.
Brent
Onward!
Stephen P. King
*From:* everything-list@googlegroups.com
[mailto:everything-l...@googlegroups.com] *On Behalf Of *Brent Meeker
*Sent:* Saturday, August 28, 2010 1:42 PM
*To:* everything-list@googlegroups.com
*Subject:* Re: What's wrong with this?
snip.
A superposition in QM is just due to a choice of basis. What's a
superposition in one basis is still an eigenfunction in some basis.
The evolution of the state is one-to-one and time reversible. The
problem is the measurement or "measurement like" processes which give
us classical behavior. Everett's relative states (aka multiple
worlds) is one answer to this problem.
Brent
snip
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