On 12/10/2012 5:41 AM, Jason Resch wrote:
On Mon, Dec 10, 2012 at 12:32 AM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 12/9/2012 5:03 PM, Jason Resch wrote:
On Sun, Dec 9, 2012 at 6:51 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 12/9/2012 4:37 PM, Jason Resch wrote:
On Sun, Dec 9, 2012 at 5:40 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 12/9/2012 12:08 PM, Jason Resch wrote:
And without a doubt the most popular interpretation of Quantum
Mechanics among working physicists is SUAC (Shut Up And
Calculate),
That's not an interpretation at all.
Well for a more philosophical statement of it see Omnes. His view
is that
once you can explain the diagonalization of the the density matrix
(either
by eigenselection, dechoherence, or just assumed per Bohr) then you
have
predicted probabilities. QM is a probabilistic theory - so
predicting
probabilities is all you can ask of it.
Is science just about its applications or about understanding the
world? I
would argue that science would not progress so far as it has if we
thought
finding the equation was the be all and end all of science. The "shut
up and
calculate" mindset can be translated as "don't ask embarrassing
questions", it
is the antithesis of scientific thinking.
Student in the 1500s: Does the earth move about the sun, or do the
planets
merely appear to move as if earth moved about the sun?
Professor in the 1500s: We have all the formulas for predicting
planetary
motion, so shut up and calculate!
Fortunately, Copernicus wasn't satisfied with that answer.
So what's your objection to Omnes? That the world just can't be
probabilistic? So instead there must be infinitely many inaccessible
worlds -
which happen to mimic a probabilistic world.
It is fine if QM is a probabilistic theory. Where I disagree with him is
in his
belief that we can never go beyond that in our understanding of it. I am
not sure
how accurate this statement is, since it is a secondary source, but
http://en.wikipedia.org/wiki/Roland_Omn%C3%A8s says: "We will never, Omnès
believes, find a common sense interpretation of quantum law itself." To
me, it
almost seems as if he says it is not worth trying to find an answer.
Suppose he'd said in 1400CE, "We will never find a common sense
interpretation of
the sphericity of the Earth." He'd have been right; we didn't, instead we
changed
'common sense'.
I don't know, I think Sagan's explanation fits most people's common sense:
http://www.youtube.com/watch?v=Jwr8CLX3NJA&t=1m19s
<http://www.youtube.com/watch?v=Jwr8CLX3NJA&t=1m19s>
I lean more towards David Deutsch who says science is about finding good
explanations.
But why isn't "It's a probabilistic world and it obeys the Born rule." a
good
explanation.
It is worse than that. From:
http://lesswrong.com/lw/q7/if_manyworlds_had_come_first/
"All right," says Nohr. He sighs. "Look, if this theory of yours were actually true—if
whole sections of the wavefunction just instantaneously vanished—it would be... let's
see. The only law in all of quantum mechanics that is non-linear, non-unitary,
non-differentiable and discontinuous. It would prevent physics from evolving locally,
with each piece only looking at its immediate neighbors. Your 'collapse' would be the
only fundamental phenomenon in all of physics with a preferred basis and a preferred
space of simultaneity. Collapse would be the only phenomenon in all of physics that
violates CPT symmetry, Liouville's Theorem, and Special Relativity. In your original
version, collapse would also have been the only phenomenon in all of physics that was
inherently mental. Have I left anything out?"
The page also asks:
But suppose that decoherence and macroscopic decoherence had been realized immediately
following the discovery of entanglement, in the 1920s. And suppose that no one had
proposed collapse theories until 1957. Would decoherence now be steadily declining in
popularity, while collapse theories were slowly gaining steam?
I'm all for finding a better explanation, i.e. a deterministic one. But
simply
postulating an ensemble of worlds to make the probabilities "deterministic"
in
arbitrary way doesn't strike me as any improvement.
MWI follows directly from a literal reading of the equations, which contain no mention
of collapse or only applying only at certain scales.
No it doesn't. It is no more than decoherence, which means that in a selected basis the
reduced density matrix becomes approximately diagonal. At that point Everett says the
different diagonal eigenvalues are the probabilities of projections onto orthogonal
subspaces, which being orthogonal can be regarded as different 'worlds'. But this suffers
the same problems as other interpretations (which is why Omnes says there isn't any
intuitive interpretation). First, there has to be a selection of a basis, which in an
experiment is made by a choice of instrument (what does your detector detect?). Whether
this is part of theory or a boundary condition depends on whether you include the
experimenter in the Hilbert space. But if you include the experimenter, you've just
backed out the boundary condition one step - you haven't eliminated it. Once the
instrument is modeled, then (in theory) you can calculate decoherence in the selected
basis and the *reduced* density matrix will become *approximately* diagonal in the
selected basis. But notice that there is nothing in the bare mathematics that tells you
the reduced density matrix gives you the probabilities. It is a choice based on the
instrument/environment division. The density matrix becomes (almost) diagonal when you
trace over the environment part (otherwise nothing has happened - or more precisely it
could unhappen). Performing this trace operation is a mathematical calculation, not part
of the physical evolution, and it philosophically equivalent to choosing a basis in which
to collapse a wave-function.
Brent
Even better, the Born rule falls out as Everett himself noticed. If anyone is
performing a stretch (postulating new things), it is those in the collapse camp who add
new conjectures to the theory in an unjustified effort to preserve the notion of a
single universe. The theory itself explains why the other universes are not observed,
so pretending we have to augment the theory by adding new postulates (observers,
collapse, born rule) to make it agree with our observations is somewhat absurd.
In the history of science efforts to keep humanity on the center stage seem to always
fail ( http://www.youtube.com/watch?v=o8GA2w-qrcg ). I think that very reason, to keep
the Earth near the "center of the universe", was and is the basis for collapse theories.
Jason
Brent
"As to the fable that there are Antipodes, that is to say,
men on the opposite side of the earth where the sun rises
when it sets to us, men who walk with their feet opposite
ours, that is on no ground credible. Even if some unknown
landmass is there, and not just ocean, "there was only one
pair of original ancestors, and it is inconceivable that
such distant regions should have been peopled by Adam's
descendants."
--- St. Augustine
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