Quantum Decoherence & RNR Experiment Explained

[ShayanJ]

I don't know Quantum Decoherence in detail, but I know its trying to say that wave function collapse is a result of the interaction of the system with its environment and the fact that it seems wave function collapse is incompatible with Schrodinger evolution, is only because the system alone doesn't evolve Schrodingerically but the evolution of system+environment is of course based on Schrodinger equation. It seems so nice of a theory and so compatible with observations that I thought its a very good candidate for a solution to the measurment problem.
But now comes the Renninger negative-result experiment(I assume you either read the article I gave the link to or already know about it.)
My point is, this experiment illustrates that at least a partial wave function collapse can occur without an interaction between system and environment because the space between the detectors can be a vacuum. Otherwise we are forced to include non-local interactions(or maybe interaction with a non-trivial vacuum?)
Anyway, to me, this experiment seems to be at odds with Quantum Decoherence. At least its not obvious that they're compatible!
Any ideas?

 

[PeterDonis]

I don't know Quantum Decoherence in detail, but I know its trying to say that wave function collapse is a result of the interaction of the system with its environment

That's not what decoherence says. Decoherence is present in no-collapse interpretations as well, such as the MWI. Decoherence just explains why, when a measurement is made, the various branches of the wave function that are produced quickly stop interfering with each other, so that each one acts like a classical measurement result. But that doesn't answer the further question of whether a collapse occurs: a collapse would mean that all but one of the branches of the wave function cease to exist, and decoherence doesn't tell you whether that happens.

wave function collapse is incompatible with Schrodinger evolution

This is true, but not because of decoherence. Collapse is incompatible with Schrodinger evolution because Schrodinger evolution can never make a branch of the wave function cease to exist. See above.

this experiment illustrates that at least a partial wave function collapse can occur without an interaction between system and environment

No, it doesn't, because the results of the experiment can be accounted for by no-collapse interpretations like the MWI.

Otherwise we are forced to include non-local interactions

Yes; this is really the same sort of issue raised by Bell's Theorem. It shows that some sort of non-locality is involved in decoherence.

 

[Nugatory]

I don't know Quantum Decoherence in detail, but I know its trying to say that wave function collapse is a result of the interaction of the system with its environment...

That's not what decoherence says. The point of decoherence is that we don't need to assume any form of wave function collapse associated with measurement - a coherent macroscopic superposition (and when you include the environment the system is more or less by definition macroscopic) will tend to very rapidly evolve into a state that is experimentally indistinguishable from collapse.

Consider the Renninger setup to be the entire system (nucleus, atom, and two hemispherical detectors connected to macroscopic pointers) and don't insist of invoking wave function collapse as an explanation, and the paradox largely disappears. The system states in which there is no interaction with the inner detector must evolve forward into states in which the outer detector will trigger.

It seems so nice of a theory and so compatible with observations that I thought its a very good candidate for a solution to the measurement problem.
But now comes the Renninger negative-result experiment...

Which goes to show that the measurement problem isn't going to yield that easily. Decoherence gets rid of the requirement for an ugly non-unitary collapse, but it doesn't completely resolve the overall measurement problem to everyone's satisfaction. In particular, it doesn't tell us what to do with the overall wave function of the entire system, which is happily evolving forward in a coherent superposition that is experimentally indistinguishable from a mixed state.

 

[PeterDonis]

Decoherence gets rid of the requirement for an ugly non-unitary collapse

Is that really true? Decoherence produces a wave function with branches for each possible measurement result, such that each branch is "classical", so to speak, and does so via unitary evolution. But collapse makes all but one of those branches disappear; that can't be done with a unitary transformation, decoherence or no decoherence.

 

[Nugatory]

Is that really true? Decoherence produces a wave function with branches for each possible measurement result, such that each branch is "classical", so to speak, and does so via unitary evolution. But collapse makes all but one of those branches disappear; that can't be done with a unitary transformation, decoherence or no decoherence.

Yes, but the two cases cannot be experimentally distinguished. Non-unitary collapse was introduced to explain the way that measurements always produced definite results (the cat is either alive or dead). System-wide decoherence produces the same experimental outcomes, making the assumption of collapse unnecessary.

However, that's also the reason that decoherence is not a universally satisfactory resolution to the measurement problem. Why, in the RNR experiment, should we end up in the inner-hemisphere-didn't-trigger branch instead of the did-trigger branch? Decoherence has no answer, although it does explain why once there we stay there.

 

[ShayanJ]

It seems to me that there should be only one Decoherence theory independent of which QM interpretation we're considering. Is it right? But that also somehow means introducing a new interpretation! Because, at least, there is no collapse!
But if we are to say that Decoherence isn't a new interpretation, we should accept that there should be a Decoherence theory for every interpretation, compatible only with that one. Because,for example, the Copenhagen Decoherence should explain collapse while the MWI Decoherence should explain the divergent behaviour of different branches.(Sorry if things are loose, I'm just barely familiar with MWI).

Yes; this is really the same sort of issue raised by Bell's Theorem. It shows that some sort of non-locality is involved in decoherence.

I don't think Decoherence is in any way a hidden variable theory, so Bell's theorem isn't applicable to it.
Anyway, So you're saying that the non-local interaction of wave function with detectors is accounted for in decoherence?...Well, That's not strange, QM is non-local itself!

Consider the Renninger setup to be the entire system (nucleus, atom, and two hemispherical detectors connected to macroscopic pointers) and don't insist of invoking wave function collapse as an explanation, and the paradox largely disappears. The system states in which there is no interaction with the inner detector must evolve forward into states in which the outer detector will trigger.

I can accept that decoherence has things to say about the RNR experiment but I'm prettry sure they're not like what you said. Because the event that we call a partial collapse in RNR, happens before the wave function reaches the outer detector but what you're saying requires that the process which only seems to be a collapse, should happen when the wave function reaches the outer detector which of course will be a full collapse, so what you're explaining is the eventual particle detection not something that can seem to be a partial collapse!

However, that's also the reason that decoherence is not a universally satisfactory resolution to the measurement problem. Why, in the RNR experiment, should we end up in the inner-hemisphere-didn't-trigger branch instead of the did-trigger branch? Decoherence has no answer, although it does explain why once there we stay there.

To me, what you're saying, seems to be of this sort: Having a wave function which is a linear combination of states |n>, Decoherence can't say whether state |m> is the result of measurment or state |l> or any other state. But its not supposed to answer such a question because that means determining,with certainty, the result of the experiment which is in contradiction with QM!

 

[PeterDonis]

I don't think Decoherence is in any way a hidden variable theory, so Bell's theorem isn't applicable to it.

Decoherence isn't really a "theory" at all; it's just pointing out the implications of unitary evolution when you include the degrees of freedom in the environment. In other words, it's just part of quantum mechanics--a part that wasn't really recognized until various theorists pointed it out.

So you're saying that the non-local interaction of wave function with detectors is accounted for in decoherence?...Well, That's not strange, QM is non-local itself!

Exactly: decoherence is just an implication of QM, so since QM is non-local, decoherence automatically includes non-locality.

the event that we call a partial collapse in RNR, happens before the wave function reaches the outer detector

Thinking of it as a "partial collapse" is probably not a good idea if you're trying to understand what decoherence says about this scenario. Decoherence is actually easiest to understand, IMO, if you think of it in terms of the MWI, where both branches of the wave function continue to exist. When the wave function interacts with the inner detector, it splits into two branches: one in which the inner detector triggers, and the portion of the wave function that doesn't hit the inner detector dies away; and the other in which the inner detector does not trigger, and the portion of the wave function that *does* hit the inner detector dies away. Decoherence just explains why these two branches can't interfere with each other, so that "we" can only observe the inner detector either triggering or not triggering--and whichever outcome we observe will be consistent with what we observe the outer detector doing. The question of whether the portion of the wave function corresponding to the outcome we do not observe still exists (i.e., the collapse question) is a separate question, and decoherence doesn't address it.

 

[mfb]

Exactly: decoherence is just an implication of QM, so since QM is non-local, decoherence automatically includes non-locality.

I would consider QM+decoherence as "less non-local" than collapses. Your local part of the wave function does not have to change from things done at spacelike separated events. You just don't know directly in which branch you are in, even if you know that decoherence due to the other measurement happened.

 

[PeterDonis]

Your local part of the wave function does not have to change from things done at spacelike separated events.

It does in Bell-type experiments, where spacelike separated measurements are made on entangled particles--at least in the sense that the correlations between such measurements violate the Bell inequalities.

 

[ShayanJ]

Decoherence isn't really a "theory" at all; it's just pointing out the implications of unitary evolution when you include the degrees of freedom in the environment. In other words, it's just part of quantum mechanics--a part that wasn't really recognized until various theorists pointed it out.

That was a key point, thanks.

Thinking of it as a "partial collapse" is probably not a good idea if you're trying to understand what decoherence says about this scenario. Decoherence is actually easiest to understand, IMO, if you think of it in terms of the MWI, where both branches of the wave function continue to exist. When the wave function interacts with the inner detector, it splits into two branches: one in which the inner detector triggers, and the portion of the wave function that doesn't hit the inner detector dies away; and the other in which the inner detector does not trigger, and the portion of the wave function that *does* hit the inner detector dies away. Decoherence just explains why these two branches can't interfere with each other, so that "we" can only observe the inner detector either triggering or not triggering--and whichever outcome we observe will be consistent with what we observe the outer detector doing. The question of whether the portion of the wave function corresponding to the outcome we do not observe still exists (i.e., the collapse question) is a separate question, and decoherence doesn't address it.

Your key point just made my mistake here crystal clear. So I mention it for others.
Decoherence should be employed before employing any interpretation, because its part of the formulation of the QM!

Anyway, in my first post a sudden thought came into my mind which I mentioned to. Interaction with a non-trivial vacuum. Can it also be responsible for decoherence? I know, its strange because the non-trivial vacuum itself isn't directly observable but It does interact with "real" particles like in Lamb shift. So is it considered in decoherence, or any other proposition?

 

[PeterDonis]

Interaction with a non-trivial vacuum. Can it also be responsible for decoherence?

I would say yes, but bringing in a "non-trivial vacuum" means you're not really talking about ordinary QM any more, you're talking about quantum field theory. I haven't really read any treatments of decoherence in the context of quantum field theory, and QFT raises a number of issues that aren't raised by ordinary Schrodinger equation QM.

 

[mfb]

It does in Bell-type experiments, where spacelike separated measurements are made on entangled particles--at least in the sense that the correlations between such measurements violate the Bell inequalities.

True, but the correlations are nothing you "need" locally. To describe your local part, you always get "1/sqrt(2) (|transmitted> + |absorbed>)" (where the phase between the two does not matter as this is after decoherence).
Afterwards, you can compare your result with the other result (slower than light) and see that each branch is split up in two branches, where the combined amplitude depends on the relative orientation of the measurements.

This is different from collapse interpretations, where the amplitudes after your measurement depend on the result of the measurement done far away, and spacelike separated.