bushmonk said:
It doesn't mean that according to QM a cat is both dead and alive.
This is interpretation dependent; in the Many Worlds interpretation one
can say the cat is both dead and alive; the dead and alive cats are in different "worlds" (branches of the wave function).
The only interpretation independent thing we can say is that we do not
observe cats to be both dead and alive.
bushmonk said:
a microstate is the detailed, unknowable and rapidly changing specification of the microscopic constituents of a large system
This assumes that the microscopic constituents
have well defined states. But if they are entangled, which in something like a cat they certainly will be, the microscopic constituents do
not have well defined states. Only the overall system--the cat--does.
bushmonk said:
"Alive cat" is a crude macroscopic description.
Yes, agreed.
bushmonk said:
For that reason, using a ket with "alive cat" in it is misleading, IMHO.
Not in itself, no. Kets can be, and are, used to denote subspaces as well as individual states.
What
is misleading, IMO, is to talk as though a ket representing a (huge) subspace of a cat's Hilbert space is just like a ket describing a single qubit, at least in any way that matters for a discussion of a scenario like Schrodinger's Cat. (For example, see multiple papers published on "Wigner's Friend" type experiments in which "Wigner's Friend" type scenarios involving qubits are claimed to tell us something meaningful about such scenarios involving humans.)
bushmonk said:
This is a layman's description of the projection postulate in operation. I was using terminology from David Bohm's 1951 "Quantum Theory". The projection postulate is invoked to describe the observation that the quantum state abruptly changes, discards redundant possibilities in a random and discontinuous fashion and renormalizes.
First, as you note, this is a layman's description, and we are aiming for something better here.
Second, the description is interpretation dependent; it basically assumes either a "physical collapse" interpretation (in which "collapse" is a real physical process) or a Bohmian interpretation (in which there are nonlocal hidden variables, the particle positions, that determine the single outcomes of measurements, and "collapse" is something that happens to the wave function in consequence of the particle positions). In an interpretation like the MWI, the description would simply be wrong, as you note:
bushmonk said:
I understand the MWI discards the projection postulate. There is controversy about whether they they have succeeded in explaining what it actually observed. So I don't want to get into it.
Fair enough, but then this is off topic:
bushmonk said:
whether they have or they have not, surely they must give an account of why, in this particular cat, an oxygen molecule entered a particular cell, when, by Shrodinger's equation, it could have continued along the bloodstream. Their answer is, if I understand it correctly, that a number of cats were spawned in other worlds to realize the other possibilities. Fine.
In terms of just QM independent of any interpretation, QM makes no pretense whatever of explaining why some particular oxygen molecule entered a particular cell. Nor can we make measurements that would test any such explanation. So the only real discussion we can have of such things is an interpretation dependent discussion.
bushmonk said:
But that is very different from an electron going through both slits without decoherence. No new electrons in new worlds need be spawned. As long as decoherence is not involved, there is no need to spawn new worlds. A cat is filled to the brim with decoherence. An electron going through a double slit is not.
And in cases where there is no decoherence, the MWI does
not say that multiple worlds are spawned. (Note that the MWI was published a couple of decades at least before decoherence theory was developed, so the original MWI publications, and many pop science articles, do not correctly reflect our best current understanding in this regard.)
However, note that in the double slit experiment, when the electron hits the detector screen, decoherence
does occur, and according to the MWI, multiple worlds
are spawned. But the worlds are not "one world for each slit the electron could have gone through". The worlds are "one world for each point on the detector that the electron could have hit". In other words, the same overall interference pattern will be on the detector in each world, but the particular individual dots that make it up will be different in different worlds.