From: <agrayson2...@gmail.com <mailto:agrayson2...@gmail.com>>
On Tuesday, June 12, 2018 at 11:36:07 PM UTC, Bruce wrote:
From: <agrays...@gmail.com>
On Tuesday, June 12, 2018 at 11:03:28 PM UTC, Bruce wrote:
From: <agrays...@gmail.com>
*Doesn't the superposition of states used in the cat
problem. or indeed any quantum superposition, requires
the system being measured to be isolated? AG *
*As I see it, the total system represented by the wf (
(Alive, Undecayed) + (Dead, Decayed) ), leaving out Dirac
symbols, must be isolated if it's regarded as a
superposition. If so, this implies the cat is also isolated. AG*
That is the root of your problem in understanding
superpositions. There is absolutely no requirement for the
system to be isolated in order for there to be a
superposition. In fact, the opposite is the case -- each
branch of the superposition decoheres by interacting with,
and becoming entangled with, the environment. That is how
quantum measurement theory proceeds. Isolation from the
environment is a condition you made up, and it is not required.
Bruce
For reasons not worth explaining, I have had doubts whether a
superposition requires isolation. But what it does require, at
least in the cat paradox, is interference among the components.
Otherwise, Schroedinger couldn't have concluded that the
superposed wf implies the cat is simultaneously alive and dead.
So the issue becomes whether a macro object like a cat has a well
defined wave length, which IIUC, is the necessary condition for
interference. AG
That is another misunderstanding on your part. Interference
between components is not necessary for a superposition.
*I didn't make that claim. I claimed that interference is necessary
for a system in a superposition to be simultaneously in all components
of the superposition. AG
*
I don't know what that means!
As Brent explained, being "regarded as a superposition" is just
choosing a coordinate system. For the cat, we can have the
'alive/dead' coordinate system, or an '(alive+dead)/(alive-dead)'
coordinate system. In the first, the cat is either alive or dead;
in the second the cat is in a superposition of the two
stateswhichever basis vector you choose. There is nothing magical
about this, it is just a matter of how you look at it.
Superpositions of classical macro objects are always possible,
just by rotating the basis vectors.
*
So if one chooses a basis where the cat is simultaneously alive and
dead, is this a problem for QM? AG
*
No problem for QM -- one does it all the time. It might not be the most
useful basis, but that doesn't mean it isn't possible. In general,
however, one has a 'preferred basis'; a basis which is stable against
environmental decoherence -- the one corresponding to what one actually
sees in the laboratory.
Bruce
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