From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>
On 22 Aug 2018, at 01:54, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
The other sort of infinity, the one which I think you disagree with,
is typical for the superposition of tensor products, like the
singlet state ud - du. Before measurement Alice has the same
probability of finding u, or d for any measurement she can do in any
direction. Both Alice and Bob are maximally ignorant of their
possible measurement results. The MW on this, or a MW way to
interpret this, to keep the rotational symmetry, is that we have an
infinity of couples Alice+Bob, with each couple being correlated.
If not, some implicit assumption is made on u and d, like it is a
preferred base.
But the problems with any such suggestion are obvious. Firstly, Alice
does not choose her measurement angle in that way, so there is no
super-superposition created. Secondly, this construction does not
restore the rotational symmetry in any case. You might have an
infinite number of Alices, measuring the singlet at all possible
angles, but that multi-multiverse is not rotationally symmetric
either! All it needs is for Alice number 7,234,826 to poke her tongue
out and the rotational symmetry is lost! Of course, you could add yet
more multiverses to cover every possible deviation of Alice from the
stationary state. But the process rapidly becomes ridiculous.
So this Rube Goldberg construction of additional multiverses of
superpositions does not actually restore stable rotational symmetry.
So why propose such a construction? William of Ockham will rise out
of his grave to haunt you for such pointless extravagance of entities!
Alice destroys the rotational symmetry in all its universe. Not of the
whole wave, where Alice does not exist as a determinate subsystem.
I can't really parse this. The point is that when Alice interacts with
the singlet with her magnet she destroys the rotational symmetry of the
state. This symmetry is not restored by considering and large system, or
the whole wave. If anything, enlarging the context in this way simply
lessens any symmetry that might remain.
I think what you have in mind is a situation such as arises if you shine
a light through a small aperture. The photon emerges as a spherical
wave, with the rotational symmetry of such a (hemi-)spherical wave. If
there is a hemispherical screen downstream, the photon will interact
with the screen at some single point. If you consider only one branch of
the SWE evolution, this interaction point breaks the rotational
symmetry. But if you consider all branches of the wave function
together, there is a branch for every single point at which the photon
can hit the screen, so that the symmetry is preserved in the wave
function as a whole -- over the ensemble of all branches. But that is a
situation in which the environment with which the photon interacts is
itself symmetrical. If the screen, rather than being a smooth
equidistant hemisphere, is just the rough walls of the laboratory, there
is no symmetry in the points at which the photon can hit the walls, and
the rotational symmetry is lost, even in the wave function as a whole,
even by considering the superposition of all possible branches.
The take away message from this is that the symmetry of the original
system can be lost by interaction with a non-symmetrical environment.
The boundary conditions of the total system may not have the symmetries
of the original state. So loss of symmetry is ubiquitous in the
universe, even for Everettian no-collapse quantum mechanics. If you
introduce a non-symmetrical interaction into the system, the symmetry is
lost. That is all that is happening with the measurement of the spin
projection of the singlet state by Alice. Your idiosyncratic
interpretation of the tensor product, and your insistence the the
symmetry be preserved regardless of the non-symmetrical environment, are
just misguided. There is no need to try to preserve symmetry given
non-symmetrical boundary conditions.
Since the symmetry is broken, the singlet state no longer exists in its
original form, and the state that Bob measured is affected by the
measurement Alice makes. There is no more to it than this. If Alice and
Bob are space-like separated, there are some interpretational issues
with this instantaneous influence at a distance. But that just means
that quantum mechanics is not fully integrated with a total quantum
theory of space-time. No need to get agitated by this -- ride with it
until we have a more complete theory. In the meantime, this is what is
meant by non-locality.
Bruce
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