From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 17 Aug 2018, at 01:05, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
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.
Good.
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.
I do not superpose the bases. I take only into consideration that
those alternative representations describe the same singlet state. We
need to do that, because Alice has the choice of which base to use
when measuring her particle.
The alternatives do not need to actually exist in order for Alice to
make a choice. Only possibilities need exist.
That will localise her in different branches: so they all have to
exist prior to the measurement.
No, they don't have to exist as separate branches. That is to assume a
superposition, and you appear to want to deny that there is such a
superposition. You are becoming incoherent.
A singlet state describes a collection of different superposition.
You are interpreting it as a superposition of representations in
different bases. That is not part of the quantum formalism. It is just
something you have made up.
That is why both Alice and Bob are totally ignorant of the result that
can get when choosing a direction for their spin measurement.
They are ignorant of what they will get because for each of them the
probabilities of up and down are both equal to 0.5, regardless of the
direction in which they measure. You do not need to have all outcomes
pre-existing for this to be true.
You can only ever get one of two results for a spin measurement --
you can't get an infinite number of different results.
Sure, but you have a lot of choice (an infinity) for the direction
chosen for the spin measurement.
Of course, but that does not justify the idea that all branches pre-exist.
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.
Indeed. But to get a coherent MW picture, that changes nothing …
before the measurement is done.
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,
I use a bike :)
Ha, Ha!
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.
I have no problem with this. Our difference concerns the MW
interpretation of the entanglement state, like the singlet state.
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.
The position has not changed. You are still in your own fantasy world --
you use a superposition, and yet deny that you are using such a
superposition. That is incoherent.
Bruce
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