On 29 Dec 2013, at 23:29, meekerdb wrote:
On 12/29/2013 2:01 PM, Jason Resch wrote:
On Sun, Dec 29, 2013 at 1:47 AM, meekerdb <meeke...@verizon.net>
wrote:
On 12/28/2013 6:41 PM, Jason Resch wrote:
On Sat, Dec 28, 2013 at 8:32 PM, meekerdb <meeke...@verizon.net>
wrote:
On 12/28/2013 4:45 PM, Jason Resch wrote:
On Sat, Dec 28, 2013 at 7:12 PM, meekerdb <meeke...@verizon.net>
wrote:
On 12/27/2013 10:31 PM, Jason Resch wrote:
To that I would add the purely epistemic "non-intepretation" of
Peres and Fuchs.
"No interpretation needed" -- I can interpret this in two ways,
one way is to just take the math and equations literally (this
leads to Everett), the other is "shut up and calculate", which
leads no where really.
2. Determined by which observer? The cat is always either dead
or alive. It's just a matter of someone making a measurement to
find out.
So are you saying that before the measurement the cat is
neither alive nor dead, both alive and dead, or definitely
alive or definitely dead? If you, (and I think you are),
saying that the cat is always definitely alive
or
definitely dead, then about about the radioactive atom? Is it
ever in a state of being decayed and not decayed? If you say
no, it sounds like you are denying the reality of the
superposition, which some interpretations do, but then this
leads to difficulties explaining how quantum computers work
(which require the superposition to exist).
Superposition is just a question of basis. An eigenstate in one
basis is a superposition in another.
Can you provide a concrete example where some system can
simultaneously be considered to be both in a superposition and
not? Is this like the superposition having collapsed for
Wigner's friend while remaining for Wigner before he enters the
room?
?? Every pure state can be written as a superposition of a
complete set of basis states - that's just Hilbert space math.
So then when is the system not in a superposition?
When it's an incoherent mixture of pure states.
What makes it incoherent though?
If the density matrix is not a projection operator, i.e. rho^2 =/=
rho, it's incoherent.
But really I just meant that in theory there is a basis in which
any given pure state is just (1,0,0,...). In theory there is a
'dead&alive' basis in which Schrodinger's cat can be represented
just like a spin-up state is a superposition is a spin-left basis.
So if someone keeps alternating between measuring the spin on the y
axis, and then the spin on the x axis, are they not multiplying
themselves continuously into diverging states (under MWI)? Even
though these states only weakly interfere, are they not still
superposed (that is, the particles involved in a simultaneous
combination of possessing many different states for their
properties)?
Right, according to Everett, the world state becomes a superposition
of states of the form |x0,x1,...> where each xi is either +x, -x,
+y, or -y. And per the Bucky Ball, Young's slit experiment, the
spins don't have to observed by anyone. If the silver atom just
goes thru the Stern-Gerlach apparatus and hits the laboratory wall,
the superposition is still created. If it just goes out the window
and into space...it's not so clear.
It is very clear. IF QM is exact, the superposition does not
disappear, but get contagious to the environment (at roughly the speed
of light).
An electron in a superposition, when measured, is still in a
superposition according to MWI. It is just that the person doing
the measurement is now also caught up in that superposition.
The only thing that can destroy this superposition is to move
everything back into the same state it was originally for all the
possible diverged states, which should practically never happen
for a superposition that has leaked into the environment.
In Everett's interpretation a pure state can never evolve into a
mixture because the evolution is via a Hermitian operator, the
Hamiltonian. Decoherence makes the submatrix corresponding to the
system+instrument to approximate a mixture. That's why it can be
interpreted as giving classical probabilities.
Are there pure states in Everett's interpretation? Doesn't one have
to consider the wave function of the universe and consider it all
the way into the past?
I suppose the universe could have started in a mixed state, but most
cosmologists would invoke Ockham and assume it started in a pure
state - which, assuming only unitary evolution, means it's still in
a pure state. Of course since inflation there can be entanglements
across event horizons, so FAPP that creates mixed states.
FAPP. yes.
In any case, returning to the original point that began this
tangent, do agree that QM interpretations which are anti-realist
(or deny the reality of the superposition) are unable to describe
where the intermediate computations that produce the answer to a
quantum computation, take place?
They take place in a quantum computer.
That beg the question ...
What would Fuchs say about quantum computation?
It's a physical process whose outcome is predicted by QM.
That looks like instrumentalism and "don't ask for understanding".
Bruno
http://iridia.ulb.ac.be/~marchal/
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