On 15/06/2017 6:01 pm, Bruno Marchal wrote:
On 14 Jun 2017, at 01:06, Bruce Kellett wrote:
You seem to be taking the older view of many worlds that is favoured
by David Deutsch. This approach has serious problems with the
notorious basis problem, and there does not seem to be any principled
way from within the theory to select unambiguosly the basis in which
all of these worlds form. More recent understandings of MWI take
decoherence into account. Decoherence provides a principled dynamical
way to solve the basis problem, but it means the worlds do not
actually form until there is decoherence -- worlds cannot form until
they know what basis is relevant!
I recommend the paper I suggested to Telmo:
Michael Cuffaro, http://arxiv.org/abs/1110.2514v2
Cuffaro discusses the problems with the older form of MWI and
suggests that although many worlds might be a useful heuristic in
quantum computing, decoherence is required before worlds could be
considered to have any ontological basis. The exponential speedup
with a quantum computer is then seen in the fact that the QC
manipulates the phases inherent in the entanglement of qbits, and
doesn't have to actually calculate the function in question for all
possible inputs, as the older many worlds view requires.
Oh! I see that my explanation that the MW prevents the need of action
at a distance was neo-everettian!
Well, no! Your explanation was not anything at all because you have not
given an explanation, despite my asking many times. The best you have
managed is some general comments and a lot of hand-waving.
I am not sure I understand the paper by Currafo, as I have no
single-world interpretation of entanglement and/or quantum phase.
That must be a considerable disadvantage for you! Entanglement is
universal in quantum mechanics: every time objects interact they become
entangled. Entanglement is at the basis of the emergence of a classical
world, and since we only ever experience just one world, we must have a
single-world understanding of entanglement. I don't know what you mean
by no single-world interpretation of a quantum phase. A quantum phase is
just an angle like any other.
I think the problem you face is always going to be that of finding a
basis that is not ad hoc. If you see every superposition as a matter of
multiple worlds, then you have no interpretation of a pure quantum
state. As Brent (and everyone else) points out, a pure state is not a
superposition in the basis in which that state is one of the basis
vectors, and there are an infinite number of other bases in which it is
a superposition. So what are you going to choose? One world or an
infinity of different incompatible worlds?
At best, it would be a critics of the notion of world (be it single or
not), and this would made QM even closer to the physics extracted from
computationalism, where there is no world at all, and the
differentiation is only a relative differentiation of the
consciousness of a person. I guess mechanism is probably
neo-neo-everettian, if not neo-neo-neo-Everettian. As I said once,
despite Everett seems to disagree, it is better to talk in term of
relative state, or relative dreams, instead of world. The worlds, with
mechanism, are maximal consistent extensions, and exists only in the
mind of the numbers. The FPI are not on the worlds, but on the first
person (hopefully plural, as it seems) experience.
Probably more on this later, I have still a lot of work to do.
Meanwhile, Bruce, or anyone, you might try to explain his cluster
quantum computing in a single world, or with collapse. Cuffaro does
not provide any explanation of this, and when taken literally, his
multi-qubit entanglement requires "MW" (or many minds, many dreams,
many numbers, etc.).
I am not an expert in quantum computing, but I though Cuffaro's paper
was relatively self-explanatory. The basis problem effectively sinks the
many-worlds interpretation of quantum computing. Of course, if you have
difficulty in understanding entanglement in one world, then you might
have trouble with the multiple entangled qbits involved in cluster QC.
But the fact that there is no single basis in which this entangled
cluster can be interpreted -- the measurement bases are adaptive from
one qbit to the next -- makes any many-worlds interpretation extremely
cumbersome and artificial.
The bottom line in all of this is the need to have a definite basis in
which one's many-worlds are to be defined. QC does not appear to have
any principled way to define such a basis, whereas what Cuffaro calls
neo-Everettian approaches do -- one simply uses the basic dynamics to
define a basis that is stable against environmental decoherence. That
give a suitable basis in a way that is not ad hoc or circular.
Bruce
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