El Hombre Invisible said:
When you say the wave function continues uncollapsed 'out there', and collapse is purely a property of observation, do you mean that the wave function is completely unaltered by that observation?
No, it is not completely unaltered of course, because measurement is always associated with an interaction (of the device with the system). So you will introduce some unitary evolution associated with that interaction ; it is even exactly that interaction which will give rise to the "split" of the terms (and the obligation of choosing again "one term" to live in, according to the Born rule). "Ideal" measurements (pre-measurement interactions a la von Neumann) however, limit the interaction to entangling the state of the measurement system with the different eigenstates of the system under study, without altering first the state of the system under study.
If the system under study is in the state: a |1> + b|2> and you measure the 1/2 property (|1> and |2> are the eigenstates of the measurement operator), then you get, in an ideal pre-measurement interaction:
|m0> (a|1> + b|2>) evolves into a|m1>|1> + b|m2>|2>
A "dirty" measurement could first evolve |1> and |2> into different things, such as |A> and |B> and we'd have:
|m0> (a|1> + b|2>) evolves into a|m1> |A> + b|m2> |B>
This gives you the same measurement results, but the state after the "dirty" measurement is not the projection anymore of the state onto the "measurement eigenvector".
I mean, if you looked in the box to see that Shrodinger's cat was dead, then came back an hour later and looked again... could it be alive?
No, because the second time you look, you *remember* the result of the first measurement, so your brain is still entangled with the "dead cat" term, and you now re-measure that result. The state of your brain remembering "dead cat yesterday" is a complicated quantum state, which is essentially orthogonal to the state where you remember "live cat yesterday", and its evolution from yesterday to today will keep that essentially orthogonal under MOST possible time evolutions. This orthogonality suppresses completely the possible term in which you "remember dead cat yesterday" AND "live cat today". It is this EFFECTIVE orthogonality which makes that you cannot "switch branches" and that once in a branch (a term of the wave function), you're stuck with it for the rest of your days - so that you can just as well only work with that single term (projection).
But *in principle* one could evolve your brain states and all that goes with it (what you wrote down on paper, etc...) "dead cat yesterday" and "live cat yesterday" into two NON-orthogonal states (by un-doing the measurement interaction), and, indeed, "ressurect" the cat. However, in order to do so, you'd have to FORGET that you saw the cat dead yesterday, so you wouldn't feel any contradiction in seeing the cat live today. Such an evolution is far far far beyond our technical means, but it is, in principle, possible and that is what MWI distinguishes, as a physical theory, from any "collapse" theory.
The microscopic version, where we DO have the technology, is called "delayed quantum erasure". We don't do it with brains, but simply with photons.
cheers,
Patrick.