About observability


by batabek
Tags: observability
Demystifier
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#19
Mar22-12, 12:09 PM
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Quote Quote by lugita15 View Post
I thought in the absence of wave function collapse, everything is completely determined by Schrodinger evolution,
Not everything, only the unitary time evolution of the quantum state (wave function).

Quote Quote by lugita15 View Post
so the pointer state into collapse appears to have occured can be predicted in advance,
It cannot be predicted, because collapse into a one definite state is a nonunitary event, which Schrodinger equation does not describe.

Quote Quote by lugita15 View Post
so that any doubt about what the specific pointer state will be must arise from classical ignorance concerning the initial state or the Hamiltonian.
No. Or if you disagree, try to find a statement in the paper you mentioned which confirms your view.

Quote Quote by lugita15 View Post
So are you saying that the Copenhagen interpretation can be disproven by the quantitative details of quantum Zeno effect experiments? That's a rather bold claim.
A naive original version of Copenhagen interpretation can be disproven by quantum Zeno effect experiments, but it is still possible to introduce a refined version of Copenhagen interpretation which is compatible with quantum Zeno effect experiments.
See also
http://xxx.lanl.gov/abs/1009.4072
martinbn
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#20
Mar22-12, 01:05 PM
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Demystifier, I don't follow. He says clearly "in the absence of collapse", then you keep saying "no, because, collapse....".

Also, why is quantum Zeno a disproof of Copenhagen?
lugita15
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Mar22-12, 02:10 PM
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Quote Quote by Demystifier View Post
It cannot be predicted, because collapse into a one definite state is a nonunitary event, which Schrodinger equation does not describe.
Yes, but isn't the whole point that we have the appearance of collapse into a pointer state without actually having real collapse, so that everything stays unitary?
No. Or if you disagree, try to find a statement in the paper you mentioned which confirms your view.
I have to find time to reread the Zurek paper, but if I recall it just discusses how the interaction Hamiltonian selects a preferred pointer basis, so I don't think I'll find any confirmation there.
A naive original version of Copenhagen interpretation can be disproven by quantum Zeno effect experiments, but it is still possible to introduce a refined version of Copenhagen interpretation which is compatible with quantum Zeno effect experiments.
See also
http://xxx.lanl.gov/abs/1009.4072
That's really remarkable if true. I guess I'll have to look into that as well.
Demystifier
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#22
Mar23-12, 04:21 AM
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Quote Quote by martinbn View Post
Demystifier, I don't follow. He says clearly "in the absence of collapse", then you keep saying "no, because, collapse....".
Please quote the whole sentences, not part of sentences out of context!

Quote Quote by martinbn View Post
Also, why is quantum Zeno a disproof of Copenhagen?
Copenhagen, or at least a naive version of Copenhagen, claims that there is a strict border between classical and quantum. In this sense, it claims that measurement cannot be described by quantum mechanics, and that there can be no partial collapse.

Quantum Zeno (or more generally, decoherence) demonstrates that there is no strict border between classical and quantum. More precisely, the density matrix evolves continuously during a finite (but typically very short) time from quantum to classical.
In this sense, measurement can at least partially be described by quantum mechanics. In particular, by certain physical definition of measurement apparatus, something closely related to "partial collapse" (that is, partial diagonalization of the density matrix) is possible.
Demystifier
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#23
Mar23-12, 04:25 AM
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Quote Quote by lugita15 View Post
Yes, but isn't the whole point that we have the appearance of collapse into a pointer state without actually having real collapse, so that everything stays unitary?
That is the point of many-world interpretation of QM (which to a large extent rests on decoherence) but that is not the point of decoherence per se.

Quote Quote by lugita15 View Post
I have to find time to reread the Zurek paper, but if I recall it just discusses how the interaction Hamiltonian selects a preferred pointer basis, so I don't think I'll find any confirmation there.
I agree, but then why did you say something which was not said in the paper?
lugita15
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Mar23-12, 06:12 PM
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Quote Quote by Demystifier View Post
That is the point of many-world interpretation of QM (which to a large extent rests on decoherence) but that is not the point of decoherence per se.
So if many worlds has an explanation of which pointer state the wavefunction appears to collapse into, doesn't that mean that unitary time evolution is sufficient to tell you what the state is?
Demystifier
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Mar25-12, 08:13 AM
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Quote Quote by lugita15 View Post
So if many worlds has an explanation of which pointer state the wavefunction appears to collapse into, doesn't that mean that unitary time evolution is sufficient to tell you what the state is?
But I didn't say that many worlds explains to WHICH pointer state the wavefunction appears to collapse. It definitely does not. At best, many worlds explains why the wave function appears to collapse in only one pointer state, but it definitely does not tell WHICH one.
lugita15
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Mar25-12, 05:53 PM
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Quote Quote by Demystifier View Post
But I didn't say that many worlds explains to WHICH pointer state the wavefunction appears to collapse. It definitely does not. At best, many worlds explains why the wave function appears to collapse in only one pointer state, but it definitely does not tell WHICH one.
I'm a bit confused. In the absence of real collapse, the entire future history of the system is determined by unitary Schrodinger evolution, so if you know the initial quantum state and the Hamiltonian then the future is completely predictable, correct? So then how is it that these two pieces of information are insufficient to tell you which pointer state the wave function will appear to collapse into?
Demystifier
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#27
Mar27-12, 11:06 AM
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Quote Quote by lugita15 View Post
I'm a bit confused. In the absence of real collapse, the entire future history of the system is determined by unitary Schrodinger evolution, so if you know the initial quantum state and the Hamiltonian then the future is completely predictable, correct? So then how is it that these two pieces of information are insufficient to tell you which pointer state the wave function will appear to collapse into?
That's because in the many-world interpretation you need to distinguish two levels of reality:
(i) the multi-world, and
(ii) the single world we actually see
By knowing Hamiltonian, initial quantum state, and the Schrodinger equation, you can predict everything about the multi-world. In particular, you can predict that this multi-world will consist of MANY ordinary worlds. But it does not tell how to single out one particular single ordinary world out of this big set containing many ordinary worlds.
lugita15
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Mar28-12, 10:25 PM
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Quote Quote by Demystifier View Post
That's because in the many-world interpretation you need to distinguish two levels of reality:
(i) the multi-world, and
(ii) the single world we actually see
By knowing Hamiltonian, initial quantum state, and the Schrodinger equation, you can predict everything about the multi-world. In particular, you can predict that this multi-world will consist of MANY ordinary worlds. But it does not tell how to single out one particular single ordinary world out of this big set containing many ordinary worlds.
Are you saying that in different worlds decoherence will lead to the wave function appearing to collapse into different pointer states, so that ignorance about what world you are going to branch into translates into uncertainty about what pointer state you will see the wave function appear to collapse into?
Demystifier
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#29
Mar29-12, 02:00 AM
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Quote Quote by lugita15 View Post
Are you saying that in different worlds decoherence will lead to the wave function appearing to collapse into different pointer states, so that ignorance about what world you are going to branch into translates into uncertainty about what pointer state you will see the wave function appear to collapse into?
Yes, that's more-or-less what the many-world interpretation claims.

See also this very readable, good, short recent paper on it:
http://lanl.arxiv.org/abs/1110.0549 [to appear as a Brief Review in Modern Physics Letters]


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