On 1/15/2025 4:55 PM, Alan Grayson wrote:
On Wednesday, January 15, 2025 at 5:15:35 PM UTC-7 Brent Meeker wrote:
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
Generally speaking, isn't a superposition a linear sum of pure states? AG
Right. And a linear sum of vectors is a vector.
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 -- You received this
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