On 10/19/2013 12:42 AM, Jason Resch wrote:
On Fri, Oct 18, 2013 at 6:09 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 10/18/2013 1:45 PM, Jason Resch wrote:
On Fri, Oct 18, 2013 at 11:37 AM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 10/18/2013 12:42 AM, Jason Resch wrote:
But that's not compatible with Bruno's idea of eliminating the
physical
- at least not unless he can solve the basis problem.
Could you do me a favor and explain what the basis problem is in a way
that a
6th grader could understand? I've found all kinds of things said on
it, and
they all seem to be asking different things.
For physicists, it's part of the problem of explaining the emergence of
the
classical world from the quantum world. Decoherence can diagonalize
(approximately) a reduced density matrix IN SOME BASIS.
Is this the same basis as in "momentum basis" and "position basis", or is
it some
other usage of the term?
Forgive my ignorance, but what does it mean to "diagonalize a reduced density
matrix"?
It means to take an average over all the other variables except those of
interest
(i.e. the ones you measure). If you do this in a particular basis we think
it makes
the submatrix corresponding to those variables diagonal. Then it can be
interpreted
as the probabilities of the different values. Note that it is a
mathematical
operation that depends on choosing a basis, not a physical process.
Is this a process to recover the probabilities of some observation from some point of
view? I so will different probabilities be calculated if one takes a different basis?
There's only one basis in which the reduced matrix is diagonal - i.e. the 'classical
basis'. But saying which basis this is from a fundamentally quantum standpoint (not
relying on a classical world like Bohr) is part of "the basis problem".
The MWI view is that this is a physical process - which it could be IF the
basis
was not an arbitrary choice but was somehow dictated by the physics. But
so far
there are only hand waving arguments that "it must be that way".
Can you provide an example of how using a different basis leads to different
conclusions? I very much appreciate your helping me to understand this problem.
If you choose a basis in which the density matrix is not diagonal, then there's no clear
interpretation of it as probabilities. There are complex cross-terms that have not
probabilistic interpretation.
Being diagonal in one basis means it's superposition in some other
basis. So
for physicists the problem is saying what privileges or picks out the
particular bases we see in experiments. Why do our instruments have
needles
that are in eigen states of position, while some other things (e.g.
atoms) are
in eigen states of energy or eigen states of momentum. For physicists
there
are some suggestive, but not fully worked out answers to these
questions, e.g.
you get position eigenstates because the interaction term of the
Hamiltonian is
a function of position. But those answers assume the physics. If you
want to
reconstruct physics from experiences, you can't borrow the physical
explanation
to say why your experiences are classical.
I think the assumption that experiences are classical comes from the
classicality
of Turing machines (which are the supposed mechanism by which experiences
are
manifest).
I don't think there's anything either classical or quantum about Turing machines.
They are just mathematical abstractions. And assuming they read and write qubits
instead of bits doesn't change the range of things they can compute.
But qubits don't exist in normal definitions of information or Turing machines. Sure,
they can be modeled, but only by splitting the entire tape and Turing machine and having
one of them read a 1 and the other read a 0. When you do this, you are talking about two
different computational states, (you might as well model them as separate Turing
machines/programs at this point) and hence you are talking about two different minds,
not one mind that is conscious of a superpositional state.
I don't think that's right. A universal Turing machine can emulate a quantum Turing
machine, it's just less efficient. But that's part of the point of Seth Lloyd's paper and
of Scott Aaronson, that maybe efficiency is important. It's not in Bruno's theory,
because if your computing the Everything, then time is part of the computation and not
some outside measure against which to judge efficiency.
Brent
Jason
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