Decoherence and Wave Function Collapse

[LikesIntuition]

Hi,

I was wondering whether we are sure (I know, strong word) that decoherence is the mechanism that takes us from the quantum world to our classical world. Correct me if I'm wrong, but basically decoherence is a phenomenon where we have a bunch of quantum states that, when piled onto each other, look classical? If this is so, then quantum wave functions never actually collapse, right?

I have heard arguments that simple interaction of quantum systems can't cause wave function collapse, because all making two quantum "things" interact would just provide more possible states. I've seen that argument used to defend the idea that the act of observation itself is what collapses the wave function of a quantum system. Is there any merit to this, in your most objective opinion?

The thing I'm struggling with is these two arguments are tough to compare, as one deals with wave functions actually collapsing, and the other deals with the system just starting to "look" classical, with no actual collapse occurring.

Thanks in advance!

 

[StevieTNZ]

I was wondering whether we are sure (I know, strong word) that decoherence is the mechanism that takes us from the quantum world to our classical world. Correct me if I'm wrong, but basically decoherence is a phenomenon where we have a bunch of quantum states that, when piled onto each other, look classical? If this is so, then quantum wave functions never actually collapse, right?

Correct.

I have heard arguments that simple interaction of quantum systems can't cause wave function collapse, because all making two quantum "things" interact would just provide more possible states.

Correct. Check out "Quantum Enigma" by Bruce Rosenblum and Fred Kuttner, page number eludes me at the moment.

(Sadly Bruce passed away, and I've only learned this fact just now. I had regularly contact with him, and I'm saddened to read the news.)

 

[bhobba]

I have heard arguments that simple interaction of quantum systems can't cause wave function collapse, because all making two quantum "things" interact would just provide more possible states.

That's true.

But there are a few issues.

First it can't explain actual collapse but it can explain apparent collapse. The issue lies in the difference between a proper mixed state and an improper one. Decoherence converts superposition's into improper mixed states. If it was a proper one then collapse would have occurred, but since there is no way to tell the difference the argument is for all practical purposes collapse has occurred. You can find the detail here:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Secondly, although it's usually not emphasised, but the formalism of QM doesn't actually have collapse. Its really an interpretation thing, and quite a few interpretations don't have it at all. To see it you need an axiomatic treatment. You will find such in Ballentine - QM - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

And finally collapse, in those interpretations that have it, only applies to so called filtering type observations which these days is looked on as a state preparation procedure. This means you have simply prepared the system a different way and because of that it obviously has a different state. Since a state is associated with a preparation procedure all you have done is change the preparation procedure so obviously you will have another state.

The bottom line is collapse isn't quite the issue it once was.

Thanks
Bill

 

[bhobba]

Correct.

Yes and no.

The issue is apparent collapse vs actual collapse.

Apparent collapse - yes - actual collapse no.

But as I explained above actual collapse isn't quite the issue it once was.

We now understand QM a lot better.

Thanks
Bill

 

[LikesIntuition]

Thanks! So do we *know* that the world we see is due to decoherence, and not due to actual collapse? How much interaction is necessary for decoherence?

 

[bhobba]

Thanks! So do we *know* that the world we see is due to decoherence, and not due to actual collapse? How much interaction is necessary for decoherence?

Its a bit more subtle than that. We know the world we see APPEARS the way it does due to decoherence. The bridging between that 'appears' and 'actual' is a matter of interpretation. That link I gave on decoherence and the measurement problem discusses the issue.

What is required for decoherence varies with the situation. For example calculations show a few stray photons from the CMBR is enough to decohere a dust particle and give it an apparent definite position.

But we have the quantum eraser experiment:
http://en.wikipedia.org/wiki/Quantum_eraser_experiment

What this shows is decoherence, in simple cases can even be unscrambled.

Thanks
Bill

 

[LikesIntuition]

Its a bit more subtle than that. We know the world we see APPEARS the way it does due to decoherence. The bringing between that 'appears' and 'actual' is a matter of interpretation. That link I gave on decoherence and the measurement problem discusses the issue.

I will check that link out. I have a couple more questions (which you can ignore if they're explained in the link).

First, is the reason our ability to measure things appears to be so important in quantum mechanics simply due to the fact that any observation we can ever make about the world will be enough to cause decoherence?

Second, we originally viewed QM and wave functions as giving us a list of potentialities for different states, right? So now we are saying that with decoherence, the "state" isn't even really something that exists, aren't we? It just *looks* like states happen. So our list of potentials is like a list of ways in which a system could appear when it decoherent? That seems weird and almost circular in logic, doesn't it?

Thanks again, this is really helpful!

 

[bhobba]

First, is the reason our ability to measure things appears to be so important in quantum mechanics simply due to the fact that any observation we can ever make about the world will be enough to cause decoherence?

The reason its so important is simply its the key axiom of an axiomatic treatment.

For completeness I will state it:

An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

One then applies what is called Gleason's theorem to prove a formula for that probability known as the Born rule, which is there exists a positive operator P of unit trace such that the probability of Ei is Trace (PEi). By definition P is called the state of the system.

Without a background in the math of QM the above probably will not make much sense, but the key point is they are basically the only two axioms of an axiomatic treatment. But it really is just one axiom because of that very important Gleason's theorem I mentioned. It also shows exactly what a systems state is - simply something implied by the basic axiom that aids in calculating the probabilities of outcomes.

Second, we originally viewed QM and wave functions as giving us a list of potentialities for different states, right?

A wavefunction is simply a slightly different way of expressing the state. As such its simply an aid in calculating probabilities of outcomes - in particular its square gives the probability of observing a particle at a certain position. This view of the wavefunction has been known since at least 1927 when Dirac came up with his transformation theory, which is basically what we call QM today.

So now we are saying that with decoherence, the "state" isn't even really something that exists, aren't we? It just *looks* like states happen. So our list of potentials is like a list of ways in which a system could appear when it decoherent? That seems weird and almost circular in logic, doesn't it?

As I explained the state is simply a mathematical requirement following from the basic axiom of QM. According to the FORMALISM of QM it doesn't exist in a real sense - its simply an aid, required by the mathematics, to calculate probabilities. However different interpretations give it a different meaning for their own reasons.

BTW what I have been talking about is the real deal you will not usually find in popularisations, or even beginning textbooks. Gleason's theorem and its importance is normally only discussed in advanced treatments. An exception is The Structure and Interpretation of Quantum Mechanics by Hughes:
https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20

Thanks
Bill