On 1/15/2025 1:39 PM, Russell Standish wrote:
What you are talking about is known as the preferred basis
problem. This has been discussed on this list before.
My own take on this is that you can't ignore the observer. In any
physical situation, an observer chooses some measurement apparatus
(thereafter you can sweep the observer under the carpet, and focus on
the measurement apparatus). The measurement apparatus entangled with
the system under question has the dynamics that tensor product of
measuring apparatus state with that of the system evolves to be
diagonal in some basis, aka "einselection". And that is the origin of
the preferred basis.
In the multiverse, there will also be other observers choosing
different apparati eg ones that select a complementary basis (eg
momentum where the first chooses to measure position). These will have
a different set of preferred basis.
There is only a problem if you try to ignore the existence of
observers and measuring devices.
Cheers
On Wed, Jan 15, 2025 at 11:58:33AM -0800, Alan Grayson wrote:
It's easy to show that a Superposition does NOT imply that a system represented
by a linear sum of a pure set of basis vectors, is in all of those states
simultaneusly.This follows from the fact that the WF is an element of a vector
space, a Hilbert space, and in vector spaces there is no unique set of basis
vectors. IOW, any set of basis vectors can represent the WF of a system, and if
we claim the system is in all states of some superposition, it must also be in
all states of any other superposition.
If it's in a pure state then that is single vector in Hilbert space. So
there is a basis
that includes that vector and then the state has a single component in
that basis.
Of course there is no way to measure in that basis without already
knowing what
what it is.
Brent
And every set of basis vectors is
equivalent to, and indistinguishable from any other set of basis vectors. This
shows that Schrodinger could have denied the usual interpretation of the WF as
a superposition where the system it represented could be interpreted as being
in all pure states in its sum simultaneously, without constructing his Cat
experiment. He simply had to remind his colleagues that the set of basis
vectors in a vector space is not unique. AG
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