The question is - when did the cat become aware of which way the
> electron was spinning as it left the Stern-Gerlach apparatus? I would
> say it was when it discovered the vial didn't smash, and it was still alive.
> The other question, from the DD perspective, is when did the sphere of
> differentiation propagate from the SG apparatus to include the cat.
Well suppose the "device" triggers the flask smashing part of the
detector apparatus depending on whether the electron is moving up and
spinning up or vice versa as in my analysis. Also say it does this on
recieiving a click from one of two geiger counters, one in the upper
area and one which picks up electrons in the lower area. The cat (or
a human in the cat's place even) can hear a click whichever area the
electron ends up in. Moreover if it takes a while for the hammer to
fall and hit the flask and this is all in full view of the cat (there
inevitably must be some length time for the device to work which is
why I pointed out the locally causal requirement) then the cat will
know that it will die if it sees the hammer start to fall. It must die
because as I have said all devices are assumed in the ideal system to
"work properly" so the cat is in a cul de sac from the time it sees
the hammer start to fall to the time it chokes on the gas - and it
knows it! (or a substituted human would) . If you replace the ideal
apparatus with non ideal systems then you can use something like the
alternate evolutions to model the situation
exp(-iHt/hbar)(|s1>|a0>)=|s1>(a|a0> + b|a1> + c|a2>)
exp(-iHt/hbar)(|s2>|a0>)=|s2>(a|a0> + c|a1> + b|a2>)
which I gave originally. with these forms the cat can't know whether
it will survive or not but by standard QTI it always will from 1st p.
so QTI requires imperfect devices.
As far as DD's differentiation is concerned I think the
differentiation propagate from the SG apparatus to include the cat.
during the time Msg operates.
So assuming a causally functioning "ideally working" system, then we
(Mc) (Mdev) ( Msg) |Ca> |Dn> |moves to right> |Xr>
=(Mc) |Ca> (Mdev) |Dn> ( Msg) |moves to right> (1/sqrt2)(|Zu> +|Zd>)
=(Mc) |Ca> (Mdev) |Dn>(1/sqrt2) [|moves up>|Zu>+|moves down>|Zd>]
during *this* time the differentiation into two bundles occurs but the
cat is still alive in both bundles (nervously watching the hammer).
However, the cul de sac is there!! because all devices including
killing machines will work properly.
=(Mc) |Ca> (1/sqrt2) [|Du>|moves up>|Zu>+Dd>|moves down>|Zd>] at
this stage the cat will watch the hammer fall (or )not and know the
worst (or not) but at the
moment it's still alive in both bundles and there's no further
differentiation - all of that is done with now. But the cul de sac is
there and now the cats from the original bundle will be finding out
which of the new bundles they are in.
= (1/sqrt2) [|Cd>|Du>|moves up>|Zu>+|Ca>|Dd>|moves down>|Zd>]
During Mc's effect the killing or sparing occurs depending on which
bundle you (the cat) are in - still no more differentiation just
separate types of evolution as the effects of the original
differentiation are propogated causally in each bundle.
If I'm making an error of thinking here then please let me know what
you think. To account for any time gap we could always assume the
(Mc) (Mdev) ( Msg) operate consecutively with no time gaps in
between. My understanding of DD's differentiation is more inferred
than concrete and I'm still trying to wade through BOI "on the run" .
I was also puzzled about your comments regarding the unitarity of what
was going on and am concerned I'm not thinking correctly in some way.
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