High School How Does Environmentally Induced Decoherence Affect Quantum State Reduction?

[rubi]

To measure an observable means to set things up so that there is a correspondence between possible values of the observable and macroscopically distinguishable states of the measuring device. An example might be an arrow that pivots in a semicircle. Then you set things up so that the angle of the pointer is affinely related to the value of a real-valued observable.

Implicit in this is the assumption that the pointer actually has a definite value. If the pointer could be in a superposition of positions, then I don't know what it would mean to say that it measures an observable. And that's the case with quantum mechanics. If the system being measured is in a superposition of different values of an observable, and you let the system interact with a measurement device, I would expect (if we analyzed the measurement device itself using quantum mechanics) the result to be that the measurement device would be put into a superposition of states. (or that a larger system, including measuring device + environment, would be put into a superposition of states).

There is a difference between the mathematical formalism and reality. The fact that QM uses the mathematics of Hilbert spaces and superpositions doesn't mean that the concept of superposition somehow applies to real objects. It can only apply to mathematical objects, like vectors in a Hilbert space. The prediction of QM isn't that something is in a superposition. The prediction is rather that we will find the pointer at $0^\circ$ 50% of the time and $180^\circ$ 50% of the time (for example). Superpositions are just an intermediate mathematical tool that allows us to obtain the numerical values for these relative frequencies, much like virtual particles are an intermediate mathematical tool. The correspondence between measurement apparata and mathematics is given by observables. Every apparatus is mathematically represented as a self-adjoint operator. That doesn't mean that the apparatus is a self-adjoint operator, which of course it isn't. We use the phrase "the particle is in a superposition" just as a metaphor. It really means "the relative frequencies that describe the particle can be adequately modeled using the mathematics of superposition".

 

[stevendaryl]

There is a difference between the mathematical formalism and reality

Okay, fine. If you want to say that QM is just a recipe for getting answers, that's the "shut up and calculate" interpretation, which is fine, as far as it goes.

 

[naima]

The book by Haroche and Raimond rebuts vanhees71's position that decoherence solves the measurement problem.

I only found this:
"
We can say, according to Einstein terminology, that the death or life of the cat has, even before being recorded by a human mind, become an element of reality (since all entanglement has been destroyed by decoherence), but this element of reality cannot be predicted, only its probability can be estimated. Some physicists find this state of affairs uncomfortable. Others are ready to accept this inherently statistical feature of quantum theory."

 

[atyy]

I only found this:
"
We can say, according to Einstein terminology, that the death or life of the cat has, even before being recorded by a human mind, become an element of reality (since all entanglement has been destroyed by decoherence), but this element of reality cannot be predicted, only its probability can be estimated. Some physicists find this state of affairs uncomfortable. Others are ready to accept this inherently statistical feature of quantum theory."

If I remember correctly, Haroche and Raimond discuss decoherence and the measurement problem extensively around p81.

 

[rubi]

The problem, which to me seems like an inconsistency in the quantum formalism, is that for a small system, such as a single electron, observables don't have definite values, in general. If an electron has spin state \left( \begin{array} \\ \alpha \\ \beta \end{array} \right), what is the z-component of its spin? The question doesn't have an answer. It's in a superposition of spin-up and spin-down. But if you take a macroscopic system such as a detector, and you measure the z-component of the spin, you don't get a superposition of answers, you get either spin-up or spin-down. The macroscopic system has a definite state.

Why do macroscopic systems have definite states, if microscopic systems don't?

If you drop the idea that mathematical terms can be directly applied to real objects ("ceci n'est pas une pipe"), this problem vanishes. A state is a mathematical representation of reality. A particle doesn't really have a position (i.e. a real number). There is no internal counter within the particle or anything like that. The real number that we ascribe to the particle is just our mathematical representation of facts about reality. You need to distinguish these concepts clearly. The idea that a list of real numbers is enough to capture all the details about the reality of a particle is flawed and the violations of Bell's inequality show that this idea can't possibly be saved (BM doesn't save it either). It's impossible for a theory to have definite values for both spin up and spin left if the theory is supposed to agree with experiments. It is a fundamental fact about our world that this can't be done (unless you want to exploit loopholes), so a theory that acknowledges this fact can't be problematic because of this. If anything, the universe is problematic.

Macroscopic systems don't have definite states (a list of real numbers that defines their physics completely) either. It's just that assuming they do is good enough for all practical purposes.

Okay, fine. If you want to say that QM is just a recipe for getting answers, that's the "shut up and calculate" interpretation, which is fine, as far as it goes.

I'm saying that QM satisfies all properties that a physical theory must have and it doesn't have inconsistencies.

 

[A. Neumaier]

Why do macroscopic systems have definite states, if microscopic systems don't?

What do you say to the answer given in the discussion in posts #83 - #109 of another thread?

 

[stevendaryl]

If you drop the idea that mathematical terms can be directly applied to real objects

As I said, that's the "shut up and calculate" interpretation, which I agree works fine.

 

[stevendaryl]

I'm saying that QM satisfies all properties that a physical theory must have and it doesn't have inconsistencies.

And I'm saying that I don't agree. You're basically doing the Copenhagen, or shut up and calculate approach, which to me is inconsistent. It requires treating macroscopic objects in a way that is inconsistent with the way that it treats microscopic objects. Since macroscopic objects are presumably made up of microscopic objects, that seems inconsistent to me.

You could say, as the Copenhagen people did, that no, macroscopic objects aren't made of microscopic objects. The microscopic world doesn't exist, it's just a mathematical fiction for doing calculations. That's fine. But then you need a different theory for macroscopic objects in order to build detectors and so forth. What theory is that? Copenhagen said that we basically treat macroscopic objects classically, which is fine as a heuristic. But to have two different theories--one for macroscopic objects and another for microscopic objects--is very distasteful to me.

 

[rubi]

As I said, that's the "shut up and calculate" interpretation, which I agree works fine.

But what more do you expect from a physical theory than a prediction of all relative frequencies?

It seems that you want the theory to assign a list of real numbers to each physical entity. This is not possible in our universe. So if the theory fails to do this, we should not blame the theory.

And I'm saying that I don't agree.

If you claim that there is an inconsistency, you should be able to derive a contradiction from QM, i.e. you should be able to derive a statement of the form $A\wedge\neg A$. Can you tell me what that statement $A$ could be?

 

[A. Neumaier]

Then you create an electron that is in a superposition α|up⟩+β|down⟩, and you send it to the detector. What happens? Well, the Copenhagen interpretation would tell us that macroscopic objects like cats are classical, not quantum. So rather than leading to a superposition of a dead cat and a live cat, what we would get is EITHER a dead cat, with probability $|α|^2$, or a live cat, with probability $|β|^2$. But that seems inconsistent to me. Why, for small systems, do we get superpositions, rather than alternatives, but for large systems, we get alternatives?

The Copenhagen interpretation says (independent of the size of the system) that the state collapses upon measurement, giving the definite outcome rather than the superposition.

 

[stevendaryl]

But what more do you expect from a physical theory than a prediction of all relative frequencies?

I do not believe that continuing to discuss this with you would be fruitful. You are obviously uninterested in my concerns. That's fine, but there is no basis for discussion.

 

[rubi]

I do not believe that continuing to discuss this with you would be fruitful. You are obviously uninterested in my concerns. That's fine, but there is no basis for discussion.

I am totally interested in your concerns, I just appear to not understand them.

 

[rubi]

And I'm saying that I don't agree. You're basically doing the Copenhagen, or shut up and calculate approach, which to me is inconsistent. It requires treating macroscopic objects in a way that is inconsistent with the way that it treats microscopic objects. Since macroscopic objects are presumably made up of microscopic objects, that seems inconsistent to me.

You could say, as the Copenhagen people did, that no, macroscopic objects aren't made of microscopic objects. The microscopic world doesn't exist, it's just a mathematical fiction for doing calculations. That's fine. But then you need a different theory for macroscopic objects in order to build detectors and so forth. What theory is that? Copenhagen said that we basically treat macroscopic objects classically, which is fine as a heuristic. But to have two different theories--one for macroscopic objects and another for microscopic objects--is very distasteful to me.

When I wrote my earlier post, your post contained only the first sentence.

I'm not doing Copenhagen. I'm probably more close to MWI or consistent histories. These interpretations don't require treating microscopic objects differently than macroscopic ones. They are treated exactly the same way. I'm basically taking MWI, but I don't accept the reality of different branches. I just take the part of MWI that predicts all the relative frequencies correctly. I claim that the relative frequencies from MWI is all we need and the idea that all the different branches really exist is non-sense or at best physically not relevant. (I think this is sometimes called post-Everett interpretation or so.)

 

[stevendaryl]

I'm not doing Copenhagen. I'm probably more close to MWI or consistent histories.

Well, my complaints about standard quantum mechanics don't apply to MWI or consistent histories. There are other concerns about those, but that's a completely different subject.

 

[rubi]

Well, my complaints about standard quantum mechanics don't apply to MWI or consistent histories. There are other concerns about those, but that's a completely different subject.

Well, nowadays, the old Copenhagen idea of a wave-function collapse is not taken seriously by the vast majority of physicists anymore. Of course, it's still used as a convenient mathematical shortcut, because even a simple calculation might become a PhD thesis in post-Everett interpretations. However, apart from the inconvenience, using QM without collapse purely as a tool to obtain relative frequencies that can be compared to experiment, I don't think there is any problem or inconsistency in the theory. Of course, there is still some weirdness left, which is forced upon us by Bell, but as I said, we can't blame the theory for that. (I would consider every non-classical theory weird, but the world just happens to require a non-classical theory.)

 

[Feeble Wonk]

If you drop the idea that mathematical terms can be directly applied to real objects ("ceci n'est pas une pipe"), this problem vanishes. A state is a mathematical representation of reality.

http://arxiv.org/pdf/1412.6213v2.pdf
But what is it representing?

 

[bhobba]

]http://arxiv.org/pdf/1412.6213v2.pdf

This is a highly technical paper - unless you unerstand those technicalities its best to ignore such papers, or start a thread of its own.

It says:
'We find that no knowledge interpretation can fully explain the indistinguishability of non-orthogonal quantum states in three and four dimensions.'

Utter rubbish - if they have done that then it would represent an overthrow of our current understanding of QM and immediately earn them a Nobel prize. It would be huge news. Almost invariably when such papers are discussed it's a misunderstanding of some sort, often of weak measurements.

Thanks
Bill

 

[rubi]

http://arxiv.org/pdf/1412.6213v2.pdf
But what is it representing?

A state is a mathematical object that contains all information that is needed to compute (by a well-defined procedure) the experimentally observable relative frequencies of events for all the observables we are interested in. We don't need to know what reality is in order to compare these frequencies to experiments. In fact, that question cannot be answered by physics and rather belongs to philosophy (which can't answer it either ).

 

[atyy]

Well, nowadays, the old Copenhagen idea of a wave-function collapse is not taken seriously by the vast majority of physicists anymore. Of course, it's still used as a convenient mathematical shortcut, because even a simple calculation might become a PhD thesis in post-Everett interpretations. However, apart from the inconvenience, using QM without collapse purely as a tool to obtain relative frequencies that can be compared to experiment, I don't think there is any problem or inconsistency in the theory. Of course, there is still some weirdness left, which is forced upon us by Bell, but as I said, we can't blame the theory for that. (I would consider every non-classical theory weird, but the world just happens to require a non-classical theory.)

This is simply not true. The only common texts that claim there is no measurement problem without hidden variables and without MWI are Ballentine and Peres.

Almost all modern texts include the collapse. I still recall your derivation of the conditional wave function - I am not sure it is right, but it looks pretty good. However, you are simply deriving the collapse. Unless you forbid the Schroedinger picture, the collapse is required as a consistency condition.

 

[rubi]

This is simply not true. The only common texts that claim there is no measurement problem without hidden variables and without MWI are Ballentine and Peres.

Almost all modern texts include the collapse. I still recall your derivation of the conditional wave function - I am not sure it is right, but it looks pretty good. However, you are simply deriving the collapse. Unless you forbid the Schroedinger picture, the collapse is required as a consistency condition.

I'm not claiming that it isn't taught anymore. It clearly is taught regularly, I even teach it myself. Not because I find it reasonable, but because it's an important tool for calculations and one must know it. However, I know no working physicist who really believes that this is what's actually going on. There certainly isn't a consensus interpretation, but the fact that collapse must be abandoned in favor of something else (whatever it is) is pretty uncontroversial in my opinion.

 

[atyy]

I'm not claiming that it isn't taught anymore. It clearly is taught regularly, I even teach it myself. Not because I find it reasonable, but because it's an important tool for calculations and one must know it. However, I know no working physicist who really believes that this is what's actually going on. There certainly isn't a consensus interpretation, but the fact that collapse must be abandoned in favor of something else (whatever it is) is pretty uncontroversial in my opinion.

But in the orthodox Copenhagen style interpretation, nobody believe this is what is really going on. There are then two flavours (1) Bohr - something else may be going on, but that is not the role of science to inquire (2) Dirac - something else is going on, and quantum mechanics will probably be replaced by a new theory some day.

So what you are saying is standard, and has been for about 70 years now, ie. if what you are saying is standard, I don't think you should give the impression that modern physicists somehow know more quantum mechanics than what is in the textbooks.

Edit: WAIT, WAIT - did you say you teach the naive wave function is real and collapse really happens? OK, you definitely should correct that!

 

[rubi]

But in the orthodox Copenhagen style interpretation, nobody believe this is what is really going on. There are then two flavours (1) Bohr - something else may be going on, but that is not the role of science to inquire (2) Dirac - something else is going on, and quantum mechanics will probably be replaced by a new theory some day.

What I mean is that nobody believes that there is a Heisenberg cut. Nature doesn't treat microscopic and macroscopic systems differently, since macroscopic systems are made from microscopic systems as well. The physics of macroscopic systems should emerge from the microscopic physics. I think that the vast majority of working physicists agrees with this point of view.

So what you are saying is standard, and has been for about 70 years now, ie. if what you are saying is standard, I don't think you should give the impression that modern physicists somehow know more quantum mechanics than what is in the textbooks.

Well, the old textbooks are still nice, but today we usually adopt a more operational point of view when teaching QM. I usually just explain the mathematical formalism and how it relates to experiments. I ignore the subject of interpretations completely.

Edit: WAIT, WAIT - did you say you teach the naive wave function is real and collapse really happens? OK, you definitely should correct that!

Words that I never mention include "real" and "reality".

 

[bhobba]

However, I know no working physicist who really believes that this is what's actually going on.

I think it would be better to say it's an idea that's gone out of favour. We have some interpretations like GRW where it definitely happens. But the formalism doesn't require it and if shut-up an calculate is your thing then of course you don't ascribe to it. I don't.

Thanks
Bill

 

[bhobba]

Words that I never mention include "real" and "reality".

They are the source of enormous problems.

Thanks
Bill

 

[rubi]

I think it would be better to say it's an idea that's gone out of favour. We have some interpretations like GRW where it definitely happens. But the formalism doesn't require it and if shut-up an calculate is your thing then of course you don't ascribe to it. I don't.

Thanks
Bill

Right, there are of course the spontaneous collapse models. But they also acknowledge the idea that the mere act of observation shouldn't influence the system unless there is a physical process going on.

 

[Feeble Wonk]

A state is a mathematical object that contains all information that is needed to compute (by a well-defined procedure) the experimentally observable relative frequencies of events for all the observables we are interested in. We don't need to know what reality is in order to compare these frequencies to experiments. In fact, that question cannot be answered by physics and rather belongs to philosophy (which can't answer it either ).

Fair enough. I can't pretend that I understand the mathematical intricacies of the paper I cited, and I obviously don't expect you to give me a definitive description of ontological "reality". Yet, my general impression was that the authors had claimed to have demonstrated that the quantum wave function is actually "something", or at least represents "something", and is not simply a mathematical tool. Perhaps I was mistaken, or perhaps the paper was rubbish, as Bill has suggested.

 

[bhobba]

Yet, my general impression was that the authors had claimed to have demonstrated that the quantum wave function is actually "something", or at least represents "something", and is not simply a mathematical tool. Perhaps I was mistaken, or perhaps the paper was rubbish, as Bill has suggested.

There is a difference between claiming something and it being true.

Their claim would overthrow our current understanding of QM so the chance of it being true is somewhere between Bucklies and zilch

We see quite a few papers like that here. Some are so bad the actual scientists that post here say it never should have got past a referee. I think this is one of those.

Thanks
Bill

 

[atyy]

What I mean is that nobody believes that there is a Heisenberg cut. Nature doesn't treat microscopic and macroscopic systems differently, since macroscopic systems are made from microscopic systems as well. The physics of macroscopic systems should emerge from the microscopic physics. I think that the vast majority of working physicists agrees with this point of view.Well, the old textbooks are still nice, but today we usually adopt a more operational point of view when teaching QM. I usually just explain the mathematical formalism and how it relates to experiments. I ignore the subject of interpretations completely.Words that I never mention include "real" and "reality".

But do you believe that the experimental results are real?

 

[bhobba]

But do you believe that the experimental results are real?

Of course he does as do I

What you don't want to do is discuss what real is which is a minefield. For example Penrose believes in the literal and very real existentance of a Platonic realm where mathematical truth lies:
https://www.quora.com/Sir-Roger-Penrose-argues-that-mathematics-literally-exists-in-the-Platonic-realm-Does-this-disprove-strong-AI

I personally say reality is what our theories describe. Circular - you bet it is - but scientific foundations is always a morass.

Thanks
Bill

 

[rkastner]

'The idea that unitary-only dynamics can lead naturally to preferred observables, such that decoherence suffices to explain emergence of classical phenomena (e.g., Zurek 2003) has been shown in the peer-reviewed literature to be problematic. However, claims continue to be made that this approach, also known as ‘Quantum Darwinism,’ is the correct way to understand classical emergence.'

Obviously it cant. An extra interpretive assumption is required. That doesn't mean however it's not the correct way to go, I don't think it is, but that means diddly squat. I read a lot on decoherence and QM interpretations but I can't recall anyone making claims it solves interpretive issue by itself. Occasionally we see posts here making that or similar claims - myself or others quickly point out its simply not possible - and pretty obviously so.

Thanks
Bill

Zurek just recently announced yet again on the arxiv that classical emergence is explained by decoherence. The points in my paper (http://arxiv.org/pdf/1603.04845v1.pdf) show that this is simply not the case: one has to put in classicality to get classicality out. So the situation is worse than just needing an extra interpretive assumption--the extra interpretive assumption is that the universe starts out classical. Decoherence is neither necessary nor sufficient for classical emergence; its relevance and utility continues to be greatly overstated. These are the points I make in my recent paper.