What Are the Key Questions Surrounding Quantum Decoherence?

[greypilgrim]

Well, FAPP any discussion about interpretations is moot.

As I said, in the first case a throw of dice would not lead to separate worlds, in the second it would, even if the off-diagonal terms are way below detectability. Why is this no big interpretational difference?

 

[cube137]

I have zero idea why you are arguing something so obvious. For example if GRW was true collapse prepares proper mixed states all the time - and that's just one possibility.

Also look around you - there are many many ways proper mixed states can be prepared eg using a dice. That the universe is in a pure state - assuming such is possible which is controversial - changes nothing of that.

Thanks
Bill

Bill. You said a cat can never be in pure state.. and pure state only applied to electrons, buckeyball and few others. Why did you say above that "That the universe is in a pure state - assuming such is possible which is controversial..." Why didn't you just say categorically the universe is never a pure state because even a cat can't be pure state? What do you mention controversial.. how can the universe even be conjectured as being a pure state. Maybe you meant because the universe was a close system.. meaning likewise if the cat had oxygen tank and could breath inside a totally shielded box.. it is possible to be in pure state? But what part would have interferences in the particles of the cat (or the universe if you think the possibility the universe can be in pure state because you use the words (assuming such is possible which is controversial )? Sorry for quoting from this old thread. but just want to directly question something you mentioned here and the thread title is appropriate for it too anyway.

 

[bhobba]

"That the universe is in a pure state - assuming such is possible which is controversial..."

That contradicts nothing I have said.

I mentioned previously 'Modelling a system as pure is done not because its actually like that - its done to have a tractable model'

Then I asked you to think about it. I suggest you do the same here.

Nugatory wrote:

If you're going to dig as deeply into the formalism as you want to, you're going to have to learn the math - there is no other way to get to where you want to be. Atyy's link is very good, but it is written for people who have already been through a no-kidding college-level introduction to quantum mechanics, where the basic notion of states as vectors in a Hilbert space is taught. Only after you've been through that will you be ready to take on the density matrix formalism.ten in the left/right basis but not when written in the up/down basis; #2 is the other way around. All four of these states will have off-diagonal elements in one basis or the other.

Once you have done that then we can chat about if the universe is in a pure state or not. There is an issue if the concept of state is itself applicable to the entire universe - it turns out to be very interpretation dependant. But delving into that requires knowing what a state is in a technical sense.

Thanks
Bill

 

[cube137]

That contradicts nothing I have said.

I mentioned previously 'Modelling a system as pure is done not because its actually like that - its done to have a tractable model'

What is meant by tractable model?

Then I asked you to think about it. I suggest you do the same here.

Nugatory wrote:Once you have done that then we can chat about if the universe is in a pure state or not. There is an issue if the concept of state is itself applicable to the entire universe - it turns out to be very interpretation dependant. But delving into that requires knowing what a state is in a technical sense.

Thanks
Bill

Just a clue.. I'm reading the paper and I understood Nugatory stuff. What interpretation (is it Many worlds) in which the universe is in pure state? But how can all the particles in the universe form interference? maybe pure state is not really about interferences but more of trace 1 where the vector in Hilbert space is not in any axis (any component)?

 

[bhobba]

What is meant by tractable model?

Its obvious - they have the meaning as per a dictionary. In mathematical modelling, and physics is a mathematical model, you often make simplifying assumptions to actually solve problems. Its done all the time - so frequently, and so obviously, its seldom explicitly mentioned.

Just a clue.. I'm reading the paper and I understood Nugatory stuff. What interpretation (is it Many worlds) in which the universe is in pure state? But how can all the particles in the universe form interference? maybe pure state is not really about interferences but more of trace 1 where the vector in Hilbert space is not in any axis (any component)?

Google is your friend:
https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

To discuss it you need to know what a state preparation procedure is, and what a filtering type observation is. When you can explain that, in your own words, not with a link, then we can discuss it. And please start a new thread - this is departing from the threads topic.

Thanks
Bill

 

[A. Neumaier]

what an improper mixed density operator is. Its 100% quantum.

No. Mixing (unlike superposition) is both a classical and a quantum phenomenon.

Classical mechanics is (in terms of its kinematics) just the special case of quantum mechanics where all operators define superselection sectors. Thus the only pure states considered are those from an orthonormal basis, and the only operators considered are diagonal and hence have fixed (eigen)values in each allowed pure state.

A mixed state composed of orthogonal pure states (which is what one has in classical mechanics) is just a positive semidefinite diagonal density matrix with trace 1 - i.e., a traditional probability distribution.

 

[A. Neumaier]

Assuming our world is indeed governed by quantum laws and the wavefunction of the universe is pure (and the universe doesn't interact with anything, so that its time evolution is unitary), can proper mixed states even exist?

Yes, since we usually only consider small localized subsystems, and the mixing occurs through restriction to the subsystem (typically by trace formation). The mixed state is the usual situation - it requires extreme care to create a pure state, and can be done only if the subsystem considered only has very few and discrete degrees of freedom.

Whether the universe is in a pure or a mixed state we cannot tell since we observe only little pieces of it.

 

[bhobba]

No. Mixing (unlike superposition) is both a classical and a quantum phenomenon.

True.

Thanks
Bill