What causes superpositions to collapse when particles are observed?

[Mukilab]

Could someone please explain why superpositions collapse when we observe particles? Surely if it is because we have interacted with the particle, then any interaction would decohere a particle, i.e. why would the magnetic fields in two electrodes (which are containing a particle) not collapsing its superposition, since it is interacting with the two electrodes?

Thank you for your timeEdit: Is there any concrete answer rather than something such as 'parallel universes'?

 

[tom.stoer]

Decoherence does not explain the collaps. Decoherence explains why a pure state interacting with an "environment" can be described by an effective diagonal density matrix of a mixed state, i.e. it explains the transition pure state → mixed state (after tracing out the environment degrees of freedom). Decoherence does not explain the "collaps" of the mixed state.

Decoherence is not an interpretation of qm, it follows from its formalism but still requires an interpretation. For Schrödinger's cat decoherence expalins why we do never observe a coherent superposition of a dead and an alive cat. But decoherence does not provide a mathematical model to calculate why in one specific experiment the cat is dead; there's still some collaps or MW interpretaion required

 

[Mukilab]

Decoherence does not explain the collaps. Decoherence explains why a pure state interacting with an "environment" can be described by an effective diagonal density matrix of a mixed state, i.e. it explains the transition pure state → mixed state (after tracing out the environment degrees of freedom). Decoherence does not explain the "collaps" of the mixed state.

Decoherence is not an interpretation of qm, it follows from its formalism but still requires an interpretation. For Schrödinger's cat decoherence expalins why we do never observe a coherent superposition of a dead and an alive cat. But decoherence does not provide a mathematical model to calculate why in one specific experiment the cat is dead; there's still some collaps or MW interpretaion required

Thank you, so what would you say was the most interpretation? Or is it all just speculation, with there being no 'true' explanation.

 

[tom.stoer]

I think the MWI became rather popular in the context of decoherence, but a collaps interpretation is possible as well.

You may call it interpretation or speculation; physically the interpretations are equivalent b/c they make the same predictions; and wouldn't call neither MWI nor colaps an "explanation".

 

[Mukilab]

One more question,

How can we 'create' superposition. Surely this is an oxymoron? Superposition is caused by a lack of interference with particles, so how, by interfering with particles, can we force them into superposition?

 

[f95toli]

You can create superposition of states by e.g. coupling two systems using a third system.
A good example would be coupling atoms/ions -each prepared in a specific state- by using a microwave cavity. In this case the coupling will be mediated by photons.

(this years Nobel prize in physics)

 

[bhobba]

Tom Stoer gave the correct answer.

Basically decoherence works like this. A pure state through interaction with the environment looses phase to it and formally looks like what is known as a mixed state. Note the word formally - by this is meant no experiment can tell it from a mixed state - but it is not a mixed state - Schlosshauer calls it an improper mixed state.

The way decohence would be used in an interpretation of QM would be to assume in the interpretation the improper mixed state is an actual mixed state. Since no experiment can tell the difference it leads to no inconsistency. If you do that much, if not all, the mystery of QM disappears. But it is an interpretative assumption which like all interpretations you may or may not accept.

The reason a mixed state solves the problem is its interpretation is an actual state the same as the measurement and the measurement reveals what is there so no collapse occurs. Decoherence does not explain how the collapse occurs - no mechanism is provided - it merely says you can interpret it that way. If it solves the measurement problem depends purely on what you are willing to accept as a solution.

My interpretation of QM is an updated version of the ensemble interpretation where you call the usual probabilities calculated from the state pre-probabilities that have the potential to represent measurement outcomes if you set up a measurement apparatus to do it but are not real until you do so. When you do so decoherence occurs in the apparatus and the measurement selects an outcome from a conceptual ensemble of possible outcomes. The difference between that and the normal ensemble interpretation is, because of decoherence, you can consider it to have that property prior to observation so no actual collapse occurs. In the normal ensemble interpretation you can't do that and you have to resort to the unnatural assumption it selects an outcome from the ensemble of measurement apparatus and system combined.

Another interpretation that uses it is decoherent histories you can read about here:
http://quantum.phys.cmu.edu/CHS/histories.html
http://www.math.rutgers.edu/~oldstein/papers/qts/node2.html

Although I like decoherent histories I don't formally hold to it because to my mind its a bit more complicated than is really necessary.

Thanks
Bill

 

[Mukilab]

Decoherence does not explain the collaps. Decoherence explains why a pure state interacting with an "environment" can be described by an effective diagonal density matrix of a mixed state, i.e. it explains the transition pure state → mixed state (after tracing out the environment degrees of freedom). Decoherence does not explain the "collaps" of the mixed state.

Decoherence is not an interpretation of qm, it follows from its formalism but still requires an interpretation. For Schrödinger's cat decoherence expalins why we do never observe a coherent superposition of a dead and an alive cat. But decoherence does not provide a mathematical model to calculate why in one specific experiment the cat is dead; there's still some collaps or MW interpretaion required

Please could you provide a link or explain how decoherence explains we will never see a superposition?

You can create superposition of states by e.g. coupling two systems using a third system.
A good example would be coupling atoms/ions -each prepared in a specific state- by using a microwave cavity. In this case the coupling will be mediated by photons.

(this years Nobel prize in physics)

Thanks, will look this up

Tom Stoer gave the correct answer.

Basically decoherence works like this. A pure state through interaction with the environment looses phase to it and formally looks like what is known as a mixed state. Note the word formally - by this is meant no experiment can tell it from a mixed state - but it is not a mixed state - Schlosshauer calls it an improper mixed state.

The way decohence would be used in an interpretation of QM would be to assume in the interpretation the improper mixed state is an actual mixed state. Since no experiment can tell the difference it leads to no inconsistency. If you do that much, if not all, the mystery of QM disappears. But it is an interpretative assumption which like all interpretations you may or may not accept.

The reason a mixed state solves the problem is its interpretation is an actual state the same as the measurement and the measurement reveals what is there so no collapse occurs. Decoherence does not explain how the collapse occurs - no mechanism is provided - it merely says you can interpret it that way. If it solves the measurement problem depends purely on what you are willing to accept as a solution.

My interpretation of QM is an updated version of the ensemble interpretation where you call the usual probabilities calculated from the state pre-probabilities that have the potential to represent measurement outcomes if you set up a measurement apparatus to do it but are not real until you do so. When you do so decoherence occurs in the apparatus and the measurement selects an outcome from a conceptual ensemble of possible outcomes. The difference between that and the normal ensemble interpretation is, because of decoherence, you can consider it to have that property prior to observation so no actual collapse occurs. In the normal ensemble interpretation you can't do that and you have to resort to the unnatural assumption it selects an outcome from the ensemble of measurement apparatus and system combined.

Another interpretation that uses it is decoherent histories you can read about here:
http://quantum.phys.cmu.edu/CHS/histories.html
http://www.math.rutgers.edu/~oldstein/papers/qts/node2.html

Although I like decoherent histories I don't formally hold to it because to my mind its a bit more complicated than is really necessary.

Thanks
Bill

Thank you for that fantastic explanation. As to your last paragraph, I'm a bit confused between the difference between your interpretation and the standard one, that is, you are saying that in your interpretation the pre-probabilities only exist once the apparatus has been set up. Surely arguing that a macroscopic measurement set up is more natural than the system itself collapsing is fallacious?

 

[mfb]

I think that is left:

why would the magnetic fields in two electrodes (which are containing a particle) not collapsing its superposition, since it is interacting with the two electrodes?

If the interaction is the same for both objects, you keep their relative phase (and the magnet does not get entangled with them), so you still can get a superposition of something*.

*without a specific experiment, it is hard to be more precise.

 

[bhobba]

Thank you for that fantastic explanation. As to your last paragraph, I'm a bit confused between the difference between your interpretation and the standard one, that is, you are saying that in your interpretation the pre-probabilities only exist once the apparatus has been set up. Surely arguing that a macroscopic measurement set up is more natural than the system itself collapsing is fallacious?

In the standard ensemble interpretation it in a rough sense went through two phases I will call pre-Kocken-Sprecker and post-Kochen-Sprecker.

Pre-Kochen-Sprecker the idea was an observation simply picked an outcome from an ensemble of possible outcomes with a certain probability. Conceptually nice and simple and was the version Einstein adhered to. Just as an aside its a fallacy to believe Einstein did not accept QM - he did - he just did not believe in Copenhagen because it postulated QM was fundamental - he believed it was incomplete as suggested by the the ensemble interpretation - it did not explain how a particular result was selected.

Post-Kochen-Sprecker according to that theorem it is not possible to ascribe a property to a system an observation reveals. Ballentine, a big champion of that interpretation, was taken back a bit by this and I read somewhere to evade the KS theorem he postulated some unknown sub-quantum process that selected it. However you don't have to do that and later versions instead simply considered the ensemble it chooses the outcome from the system and observational apparatus combined which is the version you will find in Ballentines superb book on QM - QM - A Modern Development. That way it does not have the property prior to observation - the 'reality' is the observational apparatus and system combined - it has no property prior to observation as demanded by Kochen-Sprecker.

But this is not nice and simple like the older way of looking at it - in fact it's very unnatural - you want the ensemble to be the actual outcome. This is what decoherence allows you to do. You cannot do it without an observational apparatus so any probabilities you calculate without reference to an actual observation are not really the same - so you call them a pre-probability - meaning they have to be made 'real' by decoherence and an actual observation. Decoherent Histories also views it that way.

Now this does not solve the measurement problem in the sense that would satisfy Einstein - he would have loved Decohence because it whispers in your ear - there is more going on. But whispering in your ear and being a fact are two different things. You need to make up your own mind about that - I personally don't really have any problems with it - but that's me - opinions are like bums - everyone has one - it does not make it correct.

Thanks
Bill

 

[Amok]

Guys, I was reading through the thread, and I'm curious as to what you call a mixed state or a pure state. I was taught that a mixed state is a state that can be represented by a linear combination of several states, each one associated with a value that represents the probability of a sub-system being in that state and that this is opposed to a pure state (a single quantum mechanical state). I was also taught that this is not the same as a (pure) state that is in a superposition of states (which are also associated with probabilities, but according to the CI do not reflect our ignorance on the state of the system).

 

[tom.stoer]

Pure and mixed states are both described by density operators

$$\rho = \sum_n p_n\,|n\rangle\langle n|$$

in some basis |n> with probabilities p_n

For a pure state one can always find a one-dim. ray defined via an ordinary state which is subject to the usual time-evolution defined by the Schrödinger equation. So a pure state is a projector

$$\rho(t) = |\psi,t\rangle\langle \psi,t|$$
$$\rho^2(t) = \rho(t)$$

A mixed state does not correspond to a one-dim. ray, and it is not a projector

$$\rho^2(t) \neq \rho(t)$$

 

[Amok]

Pure and mixed states are both described by density operators

$$\rho = \sum_n p_n\,|n\rangle\langle n|$$

in some basis |n> with probabilities p_n

For a pure state one can always find a one-dim. ray defined via an ordinary state which is subject to the usual time-evolution defined by the Schrödinger equation. So a pure state is a projector

$$\rho(t) = |\psi,t\rangle\langle \psi,t|$$
$$\rho^2(t) = \rho(t)$$

A mixed state does not correspond to a one-dim. ray, and it is not a projector

$$\rho^2(t) \neq \rho(t)$$

Yes, that's exactly what and how I learned. I just wanted to emphasize the probabilities p_n that appear in your first equation are ''classical'' probabilities. Some of the confusion might stem from the fact that I learned this stuff in French.

 

[tom.stoer]

yes, in a sense you could call these probabilities "classical probabilities"