From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 16 Aug 2018, at 13:12, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
No, I am not OK with your notion of a 'world'. It makes no sense, and
it serves no purpose to confuse this peculiar notion with the
well-defined notion of disjoint components of the wave function.
You lost me completely. What you say is hard to relate to Everett or
any account of the wave without collapse. I think you just deny the
MW. If Alice look at the position of an electron, she will find
herself in all worlds with different position for that electron. The
worlds proportion are enacted by the density of presence of the
electron in the orbital. That follows from from elementary QM without
collapse, by the linearity of the tensor products and the linearity of
the Schroedinger wave evolution.
I think this may be the origin of your problem. If we look at a position
measurement, we have some wave function describing a wave packet as a
superposition of position eigenstates. The Schrödinger equation for a
measurement interaction with this state describes the evolution
according to the interaction with each component of the original
superposition, leading to decoherence or entanglement with the
environment, so that multiple branches emerge, each corresponding to a
different result for the position measurement.
We do not have an analogous situation with the singlet state. The only
superposition that is involved is the superposition of the two basis
vectors of the spin Hilbert space in any arbitrary direction. The
crucial point is that there is no superposition of different sets of
basis vectors. Such an idea makes no sense within the formalism of
quantum theory. So when I write the state as:
|psi> = (|u>|d> - |d>|u>)/sqrt(2)
that is the only superposition involved. I can certain write this in
terms of some other set of basis vectors, |u'> and |d'>, but these are
*alternative* representations of the state, and the alternatives are not
additive, so there is no superposition of all possible bases as there is
for all possible results of the measurement of position. You can only
ever get one of two results for a spin measurement -- you can't get an
infinite number of different results. Another way of putting this is
that you *choose* which measurement to make (i.e., the direction of your
magnets). You do not *measure* this direction.
If you want to go from your home to work there are several different
routes you can take. You can turn left at your door and go down the High
Street and catch a tram, or you can turn right at your door and go to
the station to catch a train. Or you can go into your garage and drive
your car to work. These are alternatives, and it makes no sense to add
them together. However, there is a way in which you can turn this into a
superposition: you make the choice about which way to get to work
according to the time of some radioactive decay or other random quantum
event. Then, since you are amplifying the decay time by entangling it
with a transport option, your journey routes enter in a quantum
superposition with the decay times. But this is not what you generally
do when you go to work. You usually have other reasons for choosing
between tram, train, or private car. Generally, these reasons are
complex, and you make a rational decision. You decision is not the
result of a random quantum event.
If you can grasp the distinction I am making here, you will understand
the various attempts I have made to understand your idiosyncratic
portrayal of the quantum singlet state: I tried to get a superposition
by considering the effect of random quantum fluctuations in Alice's
body; I suggested that Alice choose her measurement angle according to
the time of some radioactive decay; and no doubt I could think of other
possibilities. But you assured me that this is not what you meant. So I
can only conclude that you do not know what you are talking about.
Bruce
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