On 30 Dec 2013, at 00:52, meekerdb wrote:
On 12/29/2013 3:31 PM, Jason Resch wrote:
On Sun, Dec 29, 2013 at 5:29 PM, meekerdb <[email protected]>
wrote:
On 12/29/2013 2:01 PM, Jason Resch wrote:
On Sun, Dec 29, 2013 at 1:47 AM, meekerdb <[email protected]>
wrote:
On 12/28/2013 6:41 PM, Jason Resch wrote:
On Sat, Dec 28, 2013 at 8:32 PM, meekerdb <[email protected]>
wrote:
On 12/28/2013 4:45 PM, Jason Resch wrote:
On Sat, Dec 28, 2013 at 7:12 PM, meekerdb <[email protected]>
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.
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.
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.
And the quantum computer is a coherent, long-lived superposition
with a number of real states exponential with the number of its
qubits.
I'm not sure what you mean by "a number of real states"? It has
only one state (which is in a complex Hilbert space), which can be
written as a superposition of some set of basis states - but that's
true of my refrigerator too.
But your fridge cannot exploit the superposition like a quantum
computer do. I agree with Deutsch and Jason that a quantum computation
is quasi-not explainable without being realist on quantum
superposition. In fact I agree with Deutsch that the two slits
experiment, with the particles sent one at a time, provides already a
strong evidence for "real physical" (but not necessarily primitive)
superposition.
If superpositions are real and long-lived, and involve an arbitrary
number of particles, it seems there is no reason that people could
not also be in superpositions.
What would Fuchs say about quantum computation?
It's a physical process whose outcome is predicted by QM.
We limit the power and effectiveness our own theories and stifle
progress, when we don't put forward theories that make bold
statements about reality.
And we divert progress when we adopt intuitively appealing theories
with no operational content and try to reify them.
Bohr's (and seemingly Fuch's) positions are so conservative as to
never be falsified,
Nevertheless they both published more papers than Everett (whose
interpretation doesn't seem testable either - if it were, it would
be a theory instead of an intepretation).
Everett abandonned physics.
"the number of publication" cannot be invoked to judge the validity of
a logical point or a theory. It measure your willingness to publish or
perish, only.
but they also inhibit progress and new understandings. For example,
general purpose quantum computers may not have been invented had
Deutsch not been operating under Everett's paradigm.
Feynman wrote about quantum computation well before Deutsch.
He was a many-worlder, even if, like François Englert, he was not so
much "proud" of that aspect of nature, and never insisted on that
aspect of the quantum reality.
"You are the only contemporary physicist, besides Laue, who sees
that one cannot get around the assumption of reality, if only one
is honest. Most of them simply do not see what sort of risky game
they are playing with reality—reality as something independent of
what is experimentally established." --- Einstein in a letter to
Schrodinger
Everybody believes in reality. Nobody agrees on what it is. :-)
Which makes it an interesting subject for long conversation and fun
among good willing people ...
Bruno
http://iridia.ulb.ac.be/~marchal/
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