What is the accepted interpretation of the quantum nature of matter?

[DrChinese]

Say that you are outside of a system, is that system in a superposition of states, even if particles in that system are colliding?

All quantum systems are in a superposition of states at all times. But not all properties of that system are necessarily in a superposition. It is possible that the basis of the superposition can change from one property to another. However, that can normally only occur upon some kind of interaction with the outside environment.

As has been mentioned in posts by several mentors, collisions may or may not cause various types of collapse. Don't forget that a closed system can have virtual interactions, effectively meaning that you can't make a strong statement about what is going on inside it.

 

[Feeble Wonk]

I'd like to make sure that I clearly understand what the debate is here. Could you please define in layman's terms what is meant by a "mixed" state/ensemble versus a "proper" state/ensemble?

I suppose I should also ask if the "mixed/pure" designation is equivalent to the "proper/improper" ensemble designation.

 

[stevendaryl]

I suppose I should also ask if the "mixed/pure" designation is equivalent to the "proper/improper" ensemble designation.

An "improper" mixed state is the result of what's called "tracing out" unobservable degrees of freedom. Basically, it's a way of converting a pure state into an effective mixed state. The system is not really in a mixed state, but can be treated as if it were.

A "proper" mixed state is one that arises from ignorance about the true pure state. For example, you flip a coin. If it's heads, you put the system in state A. If it's tails, you put the system in state B. If I don't get to see the result of the coin toss, then I would describe the state as a 50/50 mixture of the two states. It's really in one state or the other, I just don't know which.

Something that adds another level of complexity in thinking about these things is that in general, a system will be in a mixed state of superpositions. So both kinds of "mixing" are involved. There is no way by testing to uniquely sort out which aspects of the probabilities are due to mixing and what aspects are due to superpositions.

 

[bhobba]

I'd like to make sure that I clearly understand what the debate is here. Could you please define in layman's terms what is meant by a "mixed" state/ensemble versus a "proper" state/ensemble?

It has been bought up in many threads where those terms have been used. Unfortunately, unless you know enough of the technicalities to understand the link I gave, then its impossible to explain. At a certain point in discussing these things in lay terms the jig is up - and unfortunately it is here.

However the following book does explain it:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

If you really want to understand QM - not just hand-wavey lay stuff - then the above is a must.

Thanks
Bill

 

[hellsteiger]

Seems to me there is some sort of relativity here, that to someone outside of a system, it is seen as being in a pure state, regardless of whether decoherence is occurring within that system for whatever reasons.

If this outside observer where to then interact with the system it could be put into a mixed state.

Or should I interpret it more this way: a state is pure unless collisions occur within the system that cause it to decohere regardless of whether the system is closed or not.

 

[bhobba]

Seems to me there is some sort of relativity here, that to someone outside of a system, it is seen as being in a pure state, regardless of whether decoherence is occurring within that system for whatever reasons.If this outside observer where to then interact with the system it could be put into a mixed state. Or should I interpret it more this way: a state is pure unless collisions occur within the system that cause it to decohere regardless of whether the system is closed or not.

Its none of those things.

Here is a paper that explains it:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

If you don't know the technical details of QM then the above paper is likely gibberish - but unfortunately the jig is up with this one in explaining it in lay terms.

I will do my best - but it is almost certainly very unsatisfactory.

After decoherence a superposition is converted to a mixed state. Observationally its exactly the same as if collapse occurred - there is no way to tell the difference. It explains what's called apparent collapse. Now there are two types of mixed states - the ones from decoherence - and those called proper. The difference is if it was proper then collapse would have actually occurred rather than simply apparently occurred. There is an interpretation called the ignorance interpretation that I hold to that is very simple - all you do is say - somehow - the mixed state is a proper mixed state. How does that happen - blank out - that's why its called the ignorance interpretation.

Thanks
Bill

 

[Derek Potter]

There is an interpretation called the ignorance interpretation that I hold to that is very simple - all you do is say - somehow - the mixed state is a proper mixed state. How does that happen - blank out - that's why its called the ignorance interpretation.

But what is the motivation for the ignorance interpretation? As proper and improper mixtures are observationally the same why not just let them be? The only benefit I can think of is that by saying that the improper mixture is proper you can conveniently ignore what happens to the environment. Wouldn't it be better to explicitly say you can do this - and either prove it as a theorem or postulate it directly?

 

[bhobba]

But what is the motivation for the ignorance interpretation?

Simplicity. Unless you assume its a proper mixed state then you can't explain how an objective classical world emerges independent of observation ie you will require an actual observation to collapse it. There are other ways of resolving it - but this is the simplest and most direct.

Choosing an interpretation is simply what appeals to you - there is no right or wrong.

Thanks
Bill

 

[Derek Potter]

Simplicity. Unless you assume its a proper mixed state then you can't explain how an objective classical world emerges independent of observation ie you will require an actual observation to collapse it. There are other ways of resolving it - but this is the simplest and most direct.
Choosing an interpretation is simply what appeals to you - there is no right or wrong.

OK, but why would you want an objective classical world to emerge if the appearence of an objective classical world emerges perfectly well even without the additional supposition? I realize that MWI, for instance, assumes that the loose ends of measurement theory are resolvable. However, assuming that they can be tidied up isn't anywhere near as pernicious as assuming that two things which are defined to be different are "somehow" the same. The first bridges over our current lack of complete understanding, the second dismisses an actual contradiction. Interpretation may be a matter of personal taste but surely inconsistency is not acceptable? So how do you make your assumption self-consistent? - the word "somehow" doesn't seem to resolve the inconsistency.

 

[bhobba]

OK, but why would you want an objective classical world to emerge if the appearence of an objective classical world emerges perfectly well even without the additional supposition?

Because it doesn't.

Consider the following mixed state 1/2 |a><a| + 1/2 |b><b|.

If its an improper mixed state what pure state is it in.? If it is a proper mixed state what pure state is it in?

Thanks
Bill

 

[Derek Potter]

Because it doesn't.
Consider the following mixed state 1/2 |a><a| + 1/2 |b><b|.
If its an improper mixed state what pure state is it in? If it is a proper mixed state what pure state is it in?

I don't understand your question. Mixed states are not pure states, that's why they're called mixed. You just have to be careful what you mean by "it". If you mean the system under observation then "it" is in a mixed state. If you mean the system under observation plus the observer plus the environment than "it" is in a pure state. Your state 1/2 |a><a| + 1/2 |b><b| does not mention the entanglement with the environment etc. which is crucial. I do understand that measurement theory only yields an apparent mixed state to a very close approximation, but if the approximation is so close that an improper mixed state is indistinguishable from a proper one, then we have accounted for the appearence of a classical world. Why demand anything more? Perhaps I'm missing something?

 

[bhobba]

I don't understand your question. Mixed states are not pure states, that's why they're called mixed.

Its simple. For the improper mixed state its not a pure state in any way or form. For the proper mixed state its in either pure state |a><a| or pure state |b><b| with 50-50 probability. That's the key difference.

Now let's apply that to, for example, the situation where a dust particle is decohered to be in a mixed state of position by some stray photons. Because its an improper mixed state you can't say it has an actual position which would require it to be in a pure state which is an eigenstate of position. So you have solved nothing. However if you interpret it as a proper mixed state then it is in an actual eigenstate of position - it objectively has an actual position. This in no way depends on if its observed or not. Objectively objects posses properties - its common-sense classical.

Thanks
Bill

 

[Derek Potter]

Objectively objects posses properties - its common-sense classical.

Oh, I see. You just want "actual common-sense classicality" rather than "appearence of common-sense classicality" and you add it axiomatically. The fact remains you are interpreting a pig as a cow which is hardly a matter of personal taste.

 

[bhobba]

Oh, I see. You just want "actual common-sense classicality" rather than "appearence of common-sense classicality" and you add it axiomatically. The fact remains you are interpreting a pig as a cow which is hardly a matter of personal taste.

That's almost axiomatically what personal taste is. If you find looking at a pig as a cow is what you like - that's entirely up to you.

Thanks
Bill

 

[Derek Potter]

That's almost axiomatically what personal taste is. If you find looking at a pig as a cow is what you like - that's entirely up to you.

You don't run my local take-away by any chance do you? :)

 

[Feeble Wonk]

Its none of those things.

Here is a paper that explains it:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

If you don't know the technical details of QM then the above paper is likely gibberish - but unfortunately the jig is up with this one in explaining it in lay terms.

I will do my best - but it is almost certainly very unsatisfactory.

After decoherence a superposition is converted to a mixed state. Observationally its exactly the same as if collapse occurred - there is no way to tell the difference. It explains what's called apparent collapse. Now there are two types of mixed states - the ones from decoherence - and those called proper. The difference is if it was proper then collapse would have actually occurred rather than simply apparently occurred. There is an interpretation called the ignorance interpretation that I hold to that is very simple - all you do is say - somehow - the mixed state is a proper mixed state. How does that happen - blank out - that's why its called the ignorance interpretation.

Thanks
Bill

This is getting closer to what I was asking for. I've looked at the Susskind book before (from your suggestion, thank you). Unfortunately, I put it back down when it appeared that my my nonexistent calc skills would prevent me from being able to fully understand what he was saying. I accept, begrudgingly, that my understanding of these concepts will always have that limitation, and the "jig is up" in terms of me ever being able to DO quantum mechanics. What I'm desperately searching for is a knowledgeable authority articulately skilled enough to explain to me "what" the math is saying about "what" is reaaaallly going on. My (perhaps unrealistic) presumption is that the math is describing a physical process that is actually occurring "out there" in reality.

Your description of what a "proper" mixed state means is helpful. But, it leaves open serious questions about what decoherence is "really" doing. It sounds as if you are saying that environmental decoherence simply places limits on what quantum states "can" occur, but plays no role in determining what "does" occur. This is particularly evident when you take the "ignorance" approach. Mr Potter's argument seems (to me anyway) to be asking if there is more to QT than it's statistical predictive ability. Your approach might work "mathematically", but it seems logically inconsistent IF the math is representing a physical "reality" that is actually "out there"

 

[Feeble Wonk]

I don't mean for that to sound argumentative. And I realize that what I'm asking for is beyond current levels of knowledge within the physics community. But there seem to be basic logical implications from what you are saying that question physical "reality".

 

[Feeble Wonk]

Sorry... In retrospect, I withdraw my question. It's going to lead down the track to philosophy, and I don't want to blow up this thread.