In what sense is QM not understood ?

[stevendaryl]

Here's the way I understand the transition from pure state to an apparent mixed state, according to Everett: Suppose the complete wave function, system and environment, are described by the pure state |ψ> that is a product state:

|ψ> = \sum c_i,a |\phi_i> |\chi_a>

where |\phi_i> is a basis for the system you care about, and
|\chi_a> is a basis for everything else (the environment, for example).

Now, suppose we want to compute the expected value of some operator O that only involves the system, not the environment. In that case,

<\chi_b|<\phi_j| O |\phi_i> |\chi_a>
= δ_a,b <\phi_j| O |\phi_i>

So <O>
= <ψ|O|ψ>
= \sum c^*_j,a c_i,a <\phi_j| O |\phi_i>

For operator O, this result is the same as if the system were in the mixed state described by the density matrix ρ given by:

ρ = \sum c^*_j,a c_i,a |\phi_i> <\phi_j|

So, as far as operators that only depend on the system, the system acts as if it were in a mixed state.

 

[bhobba]

I don't understand that.

Hmmm. Your math below is not correct. The +'s you have should be tensor products and you need to do something called tracing over the environment - this is what causes dechorence when you work through the math.

It is not in a superposition of states after decoherence - it is in a mixed state - which is different. This is illustrated by the supposed Schroedinger Cat paradox. Without dechorence the cat is in a superposition of being alive and dead until you observe it - that is the mystery and supposed paradox. With decohrence it is not in a superposition of states - it is either alive or dead - not in a weird mixture of alive and dead. We don't know if it is alive or dead but with 100% certainty it is one or the other - not a weird quantum combination of being alive and dead at the same time - the environment has decohered that possibility out by a leaking of phase. This is the essence of quantum weirdness - this ability to be partly in two mutually exclusive possibilities such as alive and dead at the same time. Decoherence removes such weirdness at the classical level to be exactly the same as classical probability theory. When you flip a coin you know it is heads or tails - one or the other - not a combination of the two at the same time. Observing a system with decohence taken into account is like lifting your hand on a flipped coin - you see if its heads or tails - but you know its one or the other and is not in any sense a mystery or problem.

Check out:
ftp://orthodox-hub.ru/ftp2/books/_%D4%E8%E7%E8%EA%E0_%CC%E0%F2%E5%EC%E0%F2%E8%EA%E0/RevModPhys/RevModPhys%201984-2008/root/data/RevModPhys%201984-2008/pdf/RMP/v064/RMP_v064_p0339.pdf

If that article is a bit advanced then I suggest Griffiths - Consistent Quantum Theory:
https://www.amazon.com/dp/0521539293/?tag=pfamazon01-20

That text explains it at about the most elementary level possible - but even then the math is not trivial - but still understandable with effort.

Thanks
Bill

 

[stevendaryl]

QM is very much the modern equivalent, it can accurately predict the behavior of matter, but today's mathematical models are much like those ancient brass ones, they tell us absolutely nothing about "why" these particles behave the way they do.

I am disputing the claim (which some people are making) that what is weird about quantum mechanics is that it doesn't say why particles behave the way they do. I don't care about whether it says why, because at some point, "why" questions have to end with: they do it because that's the way they work.

That isn't what's weird about quantum mechanics. The fact that there is no "why" for how particles behave applies just as well to classical mechanics. What's weird about quantum is, as I have said, the fact that it doesn't say how particles behave. It says how measurements behave, and it doesn't really say what a measurement is, or which interactions count as measurements. We have rules of thumb for answering the question of what interactions count as measurements, but that's all we really have.

 

[stevendaryl]

Hmmm. Your math below is not correct. The +'s you have should be tensor products and you need to do something called tracing over the environment - this is what causes dechorence when you work through the math.

Check out:
ftp://orthodox-hub.ru/ftp2/books/_%D4%E8%E7%E8%EA%E0_%CC%E0%F2%E5%EC%E0%F2%E8%EA%E0/RevModPhys/RevModPhys%201984-2008/root/data/RevModPhys%201984-2008/pdf/RMP/v064/RMP_v064_p0339.pdf

If that article is a bit advanced then I suggest Griffiths - Consistent Quantum Theory:
https://www.amazon.com/dp/0521539293/?tag=pfamazon01-20

That text explains it at about the most elementary level possible - but even then the math is not trivial - but still understandable with effort.

Thanks
Bill

I think I understand it pretty well. I've read all those papers (long ago). And I don't think my math was mistaken. The + does NOT mean tensor product. It means a linear combination of states.

Math symbols are pretty tedious to type, so I was just using |A> |B> to mean the tensor product of |A> and |B>. I think that's pretty common, at least I've seen it many times. |A> (|B> + |C>) means the tensor product of |A> with the state |B> + |C>, which in turn is a superposition of |B> and |C>. So we have an equation:

|A> (|B> + |C>) = |A>|B> + |A>|C>

To give an example, if you have two electrons, and you ignore all degrees of freedom except the spin degrees of freedom, then a general pure state can be written as

α |up>|up> + β |up> |down> + γ |down> |up> + δ |down> |down>

where |up> |down> is the state in which the first electron has spin up and the second has spin-down, etc.

 

[bhobba]

I think I understand it pretty well. I've read all those papers (long ago). And I don't think my math was mistaken. The + does NOT mean tensor product. It means a linear combination of states.

Math symbols are pretty tedious to type, so I was just using |A> |B> to mean the tensor product of |A> and |B>. I think that's pretty common, at least I've seen it many times. |A> (|B> + |C>) means the tensor product of |A> with the state |B> + |C>, which in turn is a superposition of |B> and |C>. So we have an equation:

|A> (|B> + |C>) = |A>|B> + |A>|C>

To give an example, if you have two electrons, and you ignore all degrees of freedom except the spin degrees of freedom, then a general pure state can be written as

α |up>|up> + β |up> |down> + γ |down> |up> + δ |down> |down>

where |up> |down> is the state in which the first electron has spin up and the second has spin-down, etc.

Your claim the final outcome after decoherence is not correct. It is not:
|ψenvironment+system, A> + |ψenvironment+system, B>

There is now no plus here - it is not now in a superposition of states as indicated by a plus - it is in a mixed state which is described by a density matrix with no off diagonal elements - meaning there is no superposition of states. The physical interpretation of a mixed state is a number of pure states presented to an experimenter randomly:
http://en.wikipedia.org/wiki/Quantum_state#Mixed_states

The system after dechorence is in a specific pure state, with each pure state being classically well defined like the cat alive or dead except the exact state is random like flipping a coin.

If you have read all those texts and understood them then I am at a loss to understand your concern.

Thanks
Bill

 

[stevendaryl]

It is not in a superposition of states after decoherence - it is in a mixed state - which is different.

Check out:
ftp://orthodox-hub.ru/ftp2/books/_%D4%E8%E7%E8%EA%E0_%CC%E0%F2%E5%EC%E0%F2%E8%EA%E0/RevModPhys/RevModPhys%201984-2008/root/data/RevModPhys%201984-2008/pdf/RMP/v064/RMP_v064_p0339.pdf

I have refreshed my memory from that article, and I actually think that it confirms what I was saying---decoherence does not change the system from a pure state to a mixed state. To quote from that article:

Although nobody denies the existence and the importance
of decoherence, a criticism has been raised against
its basic significance for the interpretation of quantum
mechanics (Bell, 1975; Zurek, 1982; d'Espagnat, 1990).
Although the reduced density operator becomes diagonal,
the full density operator ρ(t) still represents a pure
state with a permanent superposition, as long as the system
remains isolated. Is it not therefore possible in principle
to perform a very refined measurement upon the environment,
revealing the existence of quantum interferences?

Omnes goes on to say why the pure state is effectively unobservable--there is no way to see interference effects involving the environment, because of the huge number (infinite, in the case of the electromagnetic field) of degrees of freedom of the environment.

 

[stevendaryl]

Your claim the final outcome after decoherence is not correct. It is not:
|ψenvironment+system, A> + |ψenvironment+system, B>

There is now no plus here - it is not now in a superposition of states as indicated by a plus - it is in a mixed state which is described by a density matrix with no off diagonal elements - meaning there is no superposition of states.

The article by Omnes explicitly says the same thing that I'm saying---after decoherence, the total system is still in a pure state, not a mixed state.

 

[bhobba]

I have refreshed my memory from that article, and I actually think that it confirms what I was saying---decoherence does not change the system from a pure state to a mixed state. To quote from that article:

That is by definition a mixed state - the off diagonal elements are zero - there is no longer any quantum superposition. What it does not do is, just like any mixed state, explain which pure state is picked out. But this is bog standard probability theory devoid of any quantum wierdness.

Thanks
Bill

 

[stevendaryl]

If you have read all those texts and understood them then I am at a loss to understand your concern.

I believe that you are misunderstanding what decoherence says. A pure state cannot evolve into a mixed state. The operation of performing a trace over environmental degrees of freedom turns a pure state density into a mixed state density matrix, but that is not a physical change in the system, that's a mathematical operation that the analyst does to reduce the state description to a description that only involves the subsystem of interest.

 

[bhobba]

The article by Omnes explicitly says the same thing that I'm saying---after decoherence, the total system is still in a pure state, not a mixed state.

I doubt that because it simply is not true.

Thanks
Bill

 

[zonde]

I would like to add my viewpoint.

First it would be reasonable to define or describe what it means "to understand".
Let's start with wikipedia article about understanding. It says number of things that I certainly agree with:
Some examples:
"1. One understands the weather if one is able to predict and to give an explanation of some of its features, etc.
2. A psychiatrist understands another person's anxieties if he/she knows that person's anxieties, their causes, and can give useful advice on how to cope with the anxiety.
3. A person understands a command if he/she knows who gave it, what is expected by the issuer, and whether the command is legitimate, and whether one understands the speaker (see 4).
4. One understands a reasoning, an argument, or a language if one can consciously reproduce the information content conveyed by the message.
5. One understands a mathematical concept if one can solve problems using it, especially problems that are not similar to what one has seen before."

There were viewpoint that are similar to examples 1. and 5. but I think that example 4. is very important too - basically you have to be able remember theory and reproduce it without errors after extended period of time.

Then wikipedia article says:
"Another significant point of view holds that knowledge is the simple awareness of bits of information. Understanding is the awareness of the connection between the individual pieces of this information. It is understanding which allows knowledge to be put to use."

I would say that it is important to have these connections between facts but I will give different reason for that. We need connections to notice when errors have crept in and corrupted our memories. So we need closed loops of connections between bits of knowledge and the more loops we have the more error proof is our "understanding".
Besides noticing errors is important because when we know where is the error we can correct it i.e. reread particular part in some book.

Next quote from wikipedia:
"Gregory Chaitin, a noted computer scientist, propounds a view that comprehension is a kind of data compression.[2] In his essay "The Limits of Reason", he argues that understanding something means being able to figure out a simple set of rules that explains it. For example, we understand why day and night exist because we have a simple model—the rotation of the earth—that explains a tremendous amount of data—changes in brightness, temperature, and atmospheric composition of the earth. We have compressed a large amount of information by using a simple model that predicts it."

This is of course important too as if we use our memory efficiently we can remember more. But when we reuse bits of knowledge we include the same bits in different loops of connections that I mentioned earlier and make our understanding stronger.


So after I have described how I understand "understanding" I can try to answer question of the topic: In what sense is QM "not understood"?

And my answer is that as long as QM stands out of all other knowledge we have to exert very high effort to keep it around i.e. learn, teach, use.
And in order to say that our understanding of QM is good it should overlap considerably with other knowledge that we have.

 

[bhobba]

The operation of performing a trace over environmental degrees of freedom turns a pure state density into a mixed state density matrix, but that is not a physical change in the system, that's a mathematical operation that the analyst does to reduce the state description to a description that only involves the subsystem of interest.

Bingo - tracing over the environment causes the off diagonal elements of the density matrix to quickly go to zero leaving only the diagonal elements. This is caused by leaking of the phase to the environment and the system is now no longer in a superposition of states but in a specific classically valid pure state - we simply do not know which one - but superposition is now gone. It is in a classically valid pure state for sure - not some weird combination of possible classical outcomes that observation needs to collapse. Quantum wierdness has now been replaced by simple classical probability theory.

The system as a whole is in a superposition of states - that remains unchanged - what has changed is the the original system is now entangled with the environment and the detector in such a way that the system and detector is in a mixed state with off diagonal elements that are effectively zero. The phase of the original superposition - ie the off diagonal elements of the density matrix of system plus detector - have been entangled and leaked out so that only classically understandable states remain. This does not explain quantum collapse but for all practical purposes gives the appearance a collapse has occurred.

Also more work needs to be done - but IMHO we now know why quantum weirdness in general does not invade the classical realm. Schroedinger's Cat is either alive or dead - not some combination of both observation needs to collapse.

Thanks
Bill

 

[stevendaryl]

That is by definition a mixed state - the off diagonal elements are zero - there is no longer any quantum superposition. What it does not do is, just like any mixed state, explain which pure state is picked out. But this is bog standard probability theory devoid of any quantum wierdness.

No, the REDUCED density matrix becomes that of a mixed state. But the reduced density matrix is NOT the state of device + environment. You start with the state of the whole shebang: environment, device, particle, etc. This state is a pure state. It's a superposition of macroscopically different situations. Then you sum over the environmental degrees of freedom to get an EFFECTIVE density matrix. This summing is an operation that you as an analyst do. It's not something that quantum mechanics is doing. Essentially, when you do that sum, you are THROWING AWAY the interference effects--the off-diagonal elements in the density matrix. You're IGNORING them.

Now, there are good reasons for doing that, and I gave you a good reason. The reduced density matrix is exactly what you need to be able to compute expectation values for operators involving the system you are interested in. So for all intents and purposes, the reduced matrix IS the right one to use for any kind of practical calculation. So our dispute is not about what people actually do, or what they SHOULD do--what they should do is to throw away the environmental degrees of freedom, and use the reduced density matrix, because that's the only information that will come into play in any practical computation. The dispute is about whether this means that a pure state has evolved into a mixed state. It hasn't. Omnes SAYS right there that it hasn't--the total system is still a pure state. (And no, the off-diagonal elements are not zero; it's the reduced matrix whose off-diagonal elements are zero.)

 

[stevendaryl]

I doubt that because it simply is not true.

I just quoted where Omnes said that. Once again:

Although the reduced density operator becomes diagonal, the full density operator ρ(t) still represents a pure state with a permanent superposition.

He's saying two different things: (1) the reduced density operator becomes diagonal (mixed state) and (2) the full density operator still represents a pure state with a PERMANENT superposition.

The full density operator does NOT become a mixed state. It does NOT become diagonal. The full density operator is the complete description of the state, and it never becomes a mixed state.

I don't understand. You refer me to an article to show how I'm wrong. The article says the same thing as I have been saying: the full state remains a pure state, even after decoherence. Now you're saying you doubt that, because it's not true. Why did you point me to Omnes' article if you didn't agree with him?

 

[stevendaryl]

Bingo - tracing over the environment causes the off diagonal elements of the density matrix to quickly go to zero leaving only the diagonal elements.

But you understand that the tracing is something that PEOPLE do. Quantum mechanics doesn't do the tracing. The complete system, which is device + the environment, does not become a mixed state. It remains a pure state. WE as analysts can decide to throw away, or trace over, the environmental degrees of freedom, because they are irrelevant for our computations. But that doesn't mean that the complete system has become a mixed state.

This is caused by leaking of the phase to the environment and the system is now no longer in a superposition of states but in a specific classically valid pure state

That isn't what Omnes says. He explicitly says that the full system is still a pure state. It's still a superposition.

- we simply do not know which one - but superposition is now gone. It is in a classically valid pure state for sure - not some weird combination of possible classical outcomes that observation needs to collapse. Quantum wierdness has now been replaced by simple classical probability theory.

I think you are mixing up two different claims. To a certain extent, I guess I don't care, because for practical purposes, it doesn't matter. But they are two different claims:

(1) The complete system is in a mixed state after decoherence.

I say that is FALSE. Omnes is agreeing that it's false. It's impossible for it to be true; pure states cannot evolve into mixed states.

(2) The relevant information about the subsystem that we care about is the reduced matrix, which describes a mixed state.

That is true. The reduced matrix describes a mixed state. My point is that the reduced matrix is NOT the state of the total system. It's something derived from the state of the total system by essentially averaging out things that we don't care about.

 

[stevendaryl]

The system as a whole is in a superposition of states - that remains unchanged - what has changed is the the original system is now entangled with the environment and the detector in such a way that the system and detector is in a mixed state with off diagonal elements that are effectively zero.

I think I read your post too quickly. It sounds like maybe we are in agreement (maybe). The system as a whole (where system means particles + detector + environment) is in a superposition of states. If we want to consider just the detector + particle, then we trace out the environmental degrees of freedom. This gives us a reduced density matrix which is no longer a pure state--it's now a mixed state. Absolutely, I agree with that. The reduced matrix is not that of a pure state.

The disagreement is over what the meaning of the reduced matrix is. I claim that it is not the state of the system, it is an EFFECTIVE state; it's a convenience for calculations.

 

[bhobba]

I claim that it is not the state of the system, it is an EFFECTIVE state; it's a convenience for calculations.

Now that is interesting - I need to think about it a bit.

Thanks
Bill

 

[sheaf]

The way I've always thought about it is that the reduced density matrix describes the case where you don't care about the details of the environment state - you trace over the environmental degrees of freedom. The question is - what are the situations for which you don't care?

An example might be where you want to model the output of a sensor, where the sensor is incapable of distinguishing between/keeping track of different environmental states, you would do this tracing operation and work with the reduced density matrix in order to describe the sensor output. The evolution would no longer be governed by the Schroedinger equation (although the system + environment is still described by the Schroedinger equation).

 

[kith]

The disagreement is over what the meaning of the reduced matrix is. I claim that it is not the state of the system, it is an EFFECTIVE state; it's a convenience for calculations.

I'd like to emphasize that it is not possible to assign a "better" state to the system. So we have two possibilities: either we accept the reduced density matrix as the real state of the system or we accept that we cannot assign a real state to a system which is entangled with another part of the whole (I think this is the main discovery of Everett but I have only read about his stuff and not the original sources themselves).

And to bhobba: I'd like to stress that even if we think that the mixed state after decoherence is a real state, it doesn't explain collapse. We have to explain, why a sinlge outcome is observed. If we have a single particle in a superposition before decoherence, we have it in a mixed state afterwards and we have no mechanism to predict which outcome we observe. Decoherence tells us, why the interference goes away. But not why we observe a single outcome.

 

[kith]

Before I go more into details, I'd like to ask the people who think that we need to understand fundamental theories better than the way we understand QM a question.

In my opinion, the crucial point in "not understanding" QM is that it does not match very well with our perception of reality. So people came up with different interpretations to make QM similar to some aspects of what they think reality should be.

But why should we expect a fundamental theory to match with our perception of reality in the first place? Isn't it ok for a fundamental theory to be "weird" - a word which is again coined by our perception?

 

[stevendaryl]

Before I go more into details, I'd like to ask the people who think that we need to understand fundamental theories better than the way we understand QM a question.

In my opinion, the crucial point in "not understanding" QM is that it does not match very well with our perception of reality. So people came up with different interpretations to make QM similar to some aspects of what they think reality should be.

But why should we expect a fundamental theory to match with our perception of reality in the first place? Isn't it ok for a fundamental theory to be "weird" - a word which is again coined by our perception?

People keep saying this, but I don't think it's true. It's not just that quantum mechanics makes "weird" predictions. It's that those predictions seem to require talking about "measurements" as a special type of interaction, even though there is nothing about a measurement that isn't fully described by the lots and lots of little non-measurement interactions.

So the situation with quantum mechanics I think is very different from other kinds of "weirdness" in physics. General Relativity is weird, in that it says things that are very different from our common experience.

 

[kith]

People keep saying this, but I don't think it's true. It's not just that quantum mechanics makes "weird" predictions. It's that those predictions seem to require talking about "measurements" as a special type of interaction, even though there is nothing about a measurement that isn't fully described by the lots and lots of little non-measurement interactions.

Well, the heart of the scientific method is to gain knowledge by doing measurements. QM is the only theory so far, where the interactions between the measurement apparatus and the system can't be neglected. So in a way, QM shows the limitations of gaining knowledge by measurements. The idea that we have an object with properties which we can simply probe doesn't hold in QM. But again, this seems to be just something we are not familiar with from our daily experience.

 

[stevendaryl]

Well, the heart of the scientific method is to gain knowledge by doing measurements. QM is the only theory so far, where the interactions between the measurement apparatus and the system can't be neglected. So in a way, QM shows the limitations of gaining knowledge by measurements. The idea that we have an object with properties which we can simply probe doesn't hold in QM. But again, this seems to be just something we are not familiar with from our daily experience.

I think that you're still missing the point. It isn't just that making a measurement involves an interaction between the system being measured and the device doing the measurement. Of course that's true--the device is made up of atoms, and atoms interact with whatever it is that is being measured.

What's weird about quantum mechanics is the fact that the interaction between device and system being measured has rules that don't apply to other types of interactions. It's NOT a matter of "limitations of gaining knowledge by measurements". If that's all it was, that would not be so mysterious.

One could certainly imagine a kind of physics where every attempt to measure a property of a particle unavoidably alters the state of the particle in an unpredictable way. There is nothing weird about that. It would impose limitations on what we can know about systems, but so what?

The thing that's weird about quantum mechanics is not the UNcertainty, it's the cases where things are CERTAIN. In an EPR-type experiment, we produce a pair of correlated spin-1/2 particles. Alice measures the spin of one of the particles along direction A. It's perfectly understandable that the process of measuring the spin of that particle might affect the particle in an uncontrollable way. That's NOT weird. But if Bob happens to be measuring the spin of the other particle along the same axis A, he's guaranteed to get the same value as Alice. That correlation isn't a matter of "Alice's measurement disturbed the system being measured".

It's the things about quantum mechanics that are certain that makes it mysterious, not the things that are uncertain.

 

[kith]

What's weird about quantum mechanics is the fact that the interaction between device and system being measured has rules that don't apply to other types of interactions.

That's true in the Kopenhagen interpretation. In most other interpretations, the measurement problem is explained by decoherence only. In particular, measurements involve only ordinary interactions there.

Your second point are nonlocal correlations. Let me just rephrase my question: why should we expect correlations to be local? I can't think of another reason than because of our perception of reality, where nonlocal correlations don't occur.

 

[Ken G]

I still say that what is "weird" about quantum mechanics is that it is the place where we encounter the issues that Bohr was always talking about-- we can no longer pretend the physicist is a "fly on the wall." And it's not just that the measurement affects the system, we can treat that as little random perturbations that create normal measurement uncertainty. Instead, it is that the very process of creating language about what is happening requires the way measurement affects the system, that's what is new. We cannot simply imagine more and more precise measurements that cause smaller and smaller effects-- the effects are fundamental, not to nature herself, but to physics. We need the effects, we need collapse, because collapse is just how we do physics-- we create the collapse on purpose, it is not some kind of accidental or unfortunate side effect of a measurement. It is the effects that allow us to talk about what is happening, so we can never talk about what is actually happening as if it was absent of those effects-- as if it would have happened even if we hadn't measured it. The interaction is what allows us to say anything about physical reality, so is part of quantum mechanics. Bohr said as much in many ways.

As to whether or not a full system, including the physicist, remains in a pure state, that is not at all known (but is known to not be what the physicist perceives). It is a matter of interpretation. It's true that one can hold that all time evolution is unitary, so you only get a mixed state when you project out the things you don't care about, but this view has never been established as true (that's essentially the many worlds interpretation). The Copenhagen interpretation says that the rationalistic logic is backward-- we don't infer that all evolution is unitary because it makes sense to say that quantum systems evolve that way and everything else comprises of quantum systems, instead what we call "a quantum system" is already a construct of our interaction with it, so collapse is there even before we have a language about unitarity. So we can't actually say what is "the state" of the full system, be it mixed or pure, because we can't test it-- it ends up being whichever way we think physics works (stemming from the observer and the collapse, toward the quantum system, which is an empiricist approach, or stemming from the quantum system and culminating in the observation, which is a rationalist approach).

Fortunately, the predictions work the same either way, so we needn't declare our metaphysical bent before we start a calculation (and "shut up and calculate" also works). But we do have to make that declaration before we can talk about fundamentally ontological entities, like the state of the "whole system", that we do not as yet have any empirical evidence about. And to those who naively claim that decoherence resolves the issue, because the "whole system" can be shown to be uncollapsed, the Copenhagenist simply responds that you still don't know anything about the whole system until you observe it, which either makes it part of an even larger system, or involves the perception of a mind, whose functioning is quite unknown.

Finally, I don't agree that what is weird is what is certain or already determined. The EPR paradox is no issue if the state of both particles is determined, that's like the left and right socks in a pair, there's no problem with nonlocality unless the states are inherently indeterminate-- but indeterminate in a way that shows correlations that are impossible with local realism. Hence the weirdness of QM stems from the role of fundamental indeterminacy-- the lesson seems to be that if you structure physics to be about what a physicist can say about reality by interacting with it, then you discover you are forced to either conclude that reality is fundamentally indeterminate about certain questions in the absence of those interactions, or invoke additional unobservable elements (like pilot waves) that can seem like a magic invented for no other purpose than to relieve the mental burden of imagining inherent indeterminacy. What we must recognize is that none of the interpretations of quantum mechanics, not Bohr's, not Everett's, not Bohm's, can both give a coherent account of what happens in a measurement, and explain why the physicist perceives only one outcome, without invoking essentially magical effects that are inherently unobservable. That's what is weird.

 

[stevendaryl]

That's true in the Kopenhagen interpretation. In most other interpretations, the measurement problem is explained by decoherence only. In particular, measurements involve only ordinary interactions there.

I don't think that's correct. Decoherence explains why we don't see superpositions of macroscopic objects. It doesn't explain why Alice and Bob have the correlations they do, in an EPR-type experiment.

Your second point are nonlocal correlations. Let me just rephrase my question: why should we expect correlations to be local? I can't think of another reason than because of our perception of reality, where nonlocal correlations don't occur.

We know that CAUSAL INFLUENCES are local. If I want to send a message from point A to point B, the message has to travel between the points, and the message's speed is limited by the speed of light. We don't understand how there can be distant correlations that are neither caused by causal influences, nor by shared information.

Anyway, I think your original point was that people have trouble with quantum mechanics because it's so different what we're used to. That is completely wrong. People are able to understand things that are very different from anything they have experienced. Relativistic effects when things travel near the speed of light is an example. General relativity in very strong gravity (near a black hole) is another example. Spacetimes with more than 3 spatial dimensions is another example. Space with nontrivial topologies (a sphere, or a torus) is another example. People are perfectly able to reason about situations that they have no experience with. So your explanation for why quantum mechanics is considered weird is just wrong.

 

[stevendaryl]

I still say that what is "weird" about quantum mechanics is that it is the place where we encounter the issues that Bohr was always talking about-- we can no longer pretend the physicist is a "fly on the wall." And it's not just that the measurement affects the system, we can treat that as little random perturbations that create normal measurement uncertainty. Instead, it is that the very process of creating language about what is happening requires the way measurement affects the system, that's what is new. We cannot simply imagine more and more precise measurements that cause smaller and smaller effects-- the effects are fundamental, not to nature herself, but to physics. We need the effects, we need collapse, because collapse is just how we do physics-- we create the collapse on purpose, it is not some kind of accidental or unfortunate side effect of a measurement. It is the effects that allow us to talk about what is happening, so we can never talk about what is actually happening as if it was absent of those effects-- as if it would have happened even if we hadn't measured it. The interaction is what allows us to say anything about physical reality, so is part of quantum mechanics. Bohr said as much in many ways.

Yes, and I don't think that Bohr's words on the topic have ever helped clarify anything. The beauty of the Copenhagen interpretation, which Bohr had a major role in developing, is that it gave as a recipe for using quantum mechanics that didn't require us to understand it.

The Copenhagen interpretation says that the rationalistic logic is backward-- we don't infer that all evolution is unitary because it makes sense to say that quantum systems evolve that way and everything else comprises of quantum systems, instead what we call "a quantum system" is already a construct of our interaction with it, so collapse is there even before we have a language about unitarity.

As I said, I don't see that the Copenhagen interpretation clarifies anything at all. It's a way to skip over what we don't understand. Which is fine, but people should pretend that they understand, in that case.

Finally, I don't agree that what is weird is what is certain or already determined. The EPR paradox is no issue if the state of both particles is determined, that's like the left and right socks in a pair,

But that's exactly what Bell's theorem proved is NOT the case.

Hence the weirdness of QM stems from the role of fundamental indeterminacy-- the lesson seems to be that if you structure physics to be about what a physicist can say about reality by interacting with it, then you discover you are forced to either conclude that reality is fundamentally indeterminate about certain questions in the absence of those interactions, or invoke additional unobservable elements (like pilot waves) that can seem like a magic invented for no other purpose than to relieve the mental burden of imagining inherent indeterminacy.

I think that's barking up the wrong tree. There is no conceptual problem with fundamental indeterminacy. You flip a coin, and you get "heads" or "tails". I don't think that there is any conceptual difficulty with introducing intrinsically nondeterministic processes. That's NOT what's strange about quantum mechanics.

What we must recognize is that none of the interpretations of quantum mechanics, not Bohr's, not Everett's, not Bohm's, can both give a coherent account of what happens in a measurement, and explain why the physicist perceives only one outcome, without invoking essentially magical effects that are inherently unobservable. That's what is weird.

I guess I would agree with that. My point is that nondeterminism by itself is not weird. The observer effecting the thing that is observed is not weird. Long-distance correlations for objects that were once in contact is not weird. The various pieces are not weird. The particular combination is what's weird.

 

[Fredrik]

Does decoherence really resolve it? It seems to me that the superposition just spreads to larger and larger subsystems. First, there is a particle in a superposition of states. Then it interacts with the detector, putting the detector into a superposition of states. Then the detector interacts with the environment, putting the environment into a superposition of states. I don't see that there is a point where anything becomes "actual".

I believe that you are misunderstanding what decoherence says. A pure state cannot evolve into a mixed state. The operation of performing a trace over environmental degrees of freedom turns a pure state density into a mixed state density matrix, but that is not a physical change in the system, that's a mathematical operation that the analyst does to reduce the state description to a description that only involves the subsystem of interest.

The calculation of a subsystem's reduced density matrix from the state of the system is of course nothing more than a calculation. But the fact that the off-diagonal elements of the reduced density matrix decrease rapidly with time, is a result of the interaction. When they are small enough to be negligible (apparently this happens very fast), the state of the subsystem (the one represented by the reduced density matrix we calculated) is for all practical purposes indistinguishable from a classical superposition. So within some small fraction of a second, it would definitely be wrong to say that the measuring device is in a quantum superposition (like e.g. |just got result A> + |just got result B>).

But if you were to say that the device is actually in one of the states that we associate with a unique result, no experiment could ever prove you wrong.

 

[Ken G]

Yes, and I don't think that Bohr's words on the topic have ever helped clarify anything. The beauty of the Copenhagen interpretation, which Bohr had a major role in developing, is that it gave as a recipe for using quantum mechanics that didn't require us to understand it.

In my experience, Bohr detractors generally just don't understand him. He did clarify something-- he clarified that we must address the role of the physicist in physics, expressly because the physicist perceives nonunitary evolution, and the postulates of QM are about unitary evolution. That's just the fact of the matter, no interpretation avoids that, they merely find different ways to address it. Bohr's approach is that of the empiricist-- if the physicist observes nonunitary evolution, then that's what happens, and the postulates embed a disconnect.

As I said, I don't see that the Copenhagen interpretation clarifies anything at all. It's a way to skip over what we don't understand. Which is fine, but people should pretend that they understand, in that case.

Bohr's approach was never about pretending anything, it was about recognizing something.

But that's exactly what Bell's theorem proved is NOT the case.

I think your understanding of Bell's theorem is rather incomplete. Your description sounds more like Bertlmann's socks, a common misconception about Bell's theorem. You can read more at http://www.optics.rochester.edu/wor...OpticsLab/2010/OPT253_reports/Justin_Lab1.pdf.

There is no conceptual problem with fundamental indeterminacy. You flip a coin, and you get "heads" or "tails". I don't think that there is any conceptual difficulty with introducing intrinsically nondeterministic processes. That's NOT what's strange about quantum mechanics.

Actually, it is just exactly what is strange about it. Not anything that's certain, read about Bertlmann's socks. Indeterminacy is the beating heart of quantum mechanics, unless one adopts the Bohm approach, and indeed that's exactly what motivated Bohm. Another interesting effect is called the quantum Zeno paradox (http://en.wikipedia.org/wiki/Quantum_Zeno_effect), where you will find that in quantum mechanics, the only way anything can change is by first becoming indeterminate, which is quite strange indeed because it is not a feature of any other theory of physics in the history of the science.

My point is that nondeterminism by itself is not weird. The observer effecting the thing that is observed is not weird.

Yes, neither of those things are weird-- what is weird is indeterminacy (not the same thing as nondeterminism).

Long-distance correlations for objects that were once in contact is not weird.

The detailed nature of those correlations is what is weird, not their existence. Bell's theorem is about subtle aspects of the details of those correlations-- which are inconsistent with "local realism." That's what Einstein thought was so weird it was an unacceptable description.

 

[Ken G]

So within some small fraction of a second, it would definitely be wrong to say that the measuring device is in a quantum superposition (like e.g. |just got result A> + |just got result B>).

To be fair, stevendaryl didn't say the measuring apparatus was in a superposition, he said the total isolated system was. This is the many-worlds interpretaiton, which comes from taking the unitarity postulate as a fundamental building block of all more complex behaviors. It just builds our concept of behavior from the ground up (rationalist), rather than from the physicist down (empiricist).

 

[bhobba]

But if you were to say that the device is actually in one of the states that we associate with a unique result, no experiment could ever prove you wrong.

Exactly. Decoherence for all practical purposes resolves the collapse of a wavefunction issue. IMHO its purely philosophical waffle if you don't like it - to some people such things are important - for me I couldn't care less.

Thanks
Bill

 

[bhobba]

And to bhobba: I'd like to stress that even if we think that the mixed state after decoherence is a real state, it doesn't explain collapse. We have to explain, why a sinlge outcome is observed. If we have a single particle in a superposition before decoherence, we have it in a mixed state afterwards and we have no mechanism to predict which outcome we observe. Decoherence tells us, why the interference goes away. But not why we observe a single outcome.

First by the definition of state it is a state.

Seriously do you think when a theory predicts it will be in a definite pure state but we don't know which one - we only know the probability - we have to explain why we only get one result. Next thing you will be saying probability theory needs to explain why you only get one result when you flip a coin.

What it doesn't do is explain why a particular result occurs just like probability theory does not explain why a head or tail occurs when you flip a coin.

What I suspect your real concern is you don't like a theory based on probabilities - which is fine - I have zero problems with it - but each to their own.

That said I recall reading some research where some models of decoherence showed chaotic behavior that may yet rescue determinism but haven't seen too much along those lines.

Thanks
Bill

 

[Ken G]

Decoherence for all practical purposes resolves the collapse of a wavefunction issue. IMHO its purely philosophical waffle if you don't like it - to some people such things are important - for me I couldn't care less.

But that can't really be true, because you like to imagine that mathematical truth has a kind of Platonic flavor to it. In the case of quantum mechanics, the Platonic/mathematical truth is that time evolution is unitary. So you still have to confront the basic problem of quantum mechanics-- we don't perceive unitary evolution of our instruments, but we do infer unitary evolution of our quantum systems. Where is the Platonism there? One can certainly punt on the whole issue, and be happy that the predictions work, but one cannot paint a Platonic version of the mathematics without addressing this core problem (Bohm or many worlds allow a Platonic interpretation, but at considerable cost in demonstrability).

 

[bhobba]

But that can't really be true, because you like to imagine that mathematical truth has a kind of Platonic flavor to it. In the case of quantum mechanics, the Platonic/mathematical truth is that time evolution is unitary.

I can't really see any conflict between my Platonic views and if reality is fundamentally probabilistic. And decoherence does not imply lack of unitary evolution - the system, environment, and measurement apparatus as a whole all evolve unitarily - the phase of the off diagonal elements of the density matrix of system and measuring apparatus simply leaks into the environment leading to decoherence - its actually a form of entanglement.

Thanks
Bill

 

[Ken G]

I can't really see any conflict between my Platonic views and if reality is fundamentally probabilistic.

If the universe is fundamentally probabilistic, then it is not fundamentally unitary in its time evolution. If I can prepare two particles as spin up, and do a sideways spin measurement, I can get left or right for different particles with equal probability, which we might regard as just fundamentally how the universe works. But since the initial states were superpositions of left and right, and the final states are one or the other, that's not unitary, if it's fundamentally probabilitistic.

And decoherence does not imply lack of unitary evolution - the system, environment, and measurement apparatus as a whole all evolve unitarily - the phase of the off diagonal elements of the density matrix of system and measuring apparatus simply leaks into the environment leading to decoherence - its actually a form of entanglement.

That does imply a lack of unitary evolution when you do an observation and only get one outcome. That's a what a lot of people forget about decoherence-- it's very good at getting a diagonal density matrix, but that's not what we observe. The observation is what is non-unitary, that's why we still need interpretations. There's only two ways I know of to make the observation unitary-- we either say that all outcomes actually occur and our perceptions are deluded (somehow) into not seeing the unitarity (so many worlds), or we say that the outcomes were specified by hidden variables so only seem non-unitary because the intial states were (somehow) not the same when the outcomes are different (deBroglie-Bohm). So Platonism + unitarity requires either Bohm or many worlds, if the unitarity is interpreted as Platonic, and not just a step in a calculation.

 

[the_pulp]

That does imply a lack of unitary evolution when you do an observation and only get one outcome. That's a what a lot of people forget about decoherence-- it's very good at getting a diagonal density matrix, but that's not what we observe. The observation is what is non-unitary, that's why we still need interpretations. There's only two ways I know of to make the observation unitary-- we either say that all outcomes actually occur and our perceptions are deluded (somehow) into not seeing the unitarity (so many worlds), or we say that the outcomes were specified by hidden variables so only seem non-unitary because the intial states were (somehow) not the same when the outcomes are different (deBroglie-Bohm). So Platonism + unitarity requires either Bohm or many worlds, if the unitarity is interpreted as Platonic, and not just a step in a calculation.

When people say "hidden variables", where they are hidden? in the system being measured? couldn't they be hidden in the instrument used to measure? Is this interpretation also called Bohmian Mechanics? can any of this two ways of "hidding variables" be coherent with locality or EPR tears everything apart?

Thanks! (is like the 4th time I ask this in this forum, everytime in a different way, but I just can't see it)

 

[Fredrik]

When people say "hidden variables", where they are hidden? in the system being measured? couldn't they be hidden in the instrument used to measure? Is this interpretation also called Bohmian Mechanics? can any of this two ways of "hidding variables" be coherent with locality or EPR tears everything apart?

Thanks! (is like the 4th time I ask this in this forum, everytime in a different way, but I just can't see it)

The variables are hidden in another theory. A theory that makes the same predictions as a quantum theory, but with variables (called ontic states) that behave the way you would expect if they represent "all the properties of the system", is called an ontological model for that quantum theory. For example, if P(s) is the probability that the system has properties s, and P(k|A,s) is the probability that the result will be k, given that the observable we're measuring is A, and that the properties (i.e. the ontic state) is s, then the expected (average) result of an A measurement should be something like Ʃ_k P(k|A,s)P(s).

The term "hidden variable theory" can be defined to mean the same thing as "ontological model for a quantum theory". The term can also be defined so that a hidden variable theory is a special kind of ontological model. Either way, a hidden variable theory is essentially just a nice theory that makes the same predictions as a quantum theory.

 

[Ken G]

Right, and the key point is that if the ontological model makes no other predictions, then it requires "overhead" that is untestable-- the predictions are the same so you get no tests on the overhead. It is then a purely metaphysical extension, like Bohmian mechanics. But, if it also makes different predictions of its own, then the ontology can be tested, and itself becomes physics. Some have suggested ways to test hidden variable theories, but it always seems like what is "hidden" is pretty darn hard to test, so I don't personally know what to make of those claims. For the time being, the different interpretations, and their ontologies, seem metaphysical and subjective. You put in your favored metaphysics, and you get out your favored interpretation-- until the "next theory" comes along to adjudicate them.

If they can be adjudicated, that is-- that never happened for classical physics, all the classical ontologies (like local realism, and the existence of attributes like momentum and position) got dropped like hot potatoes except in Bohmian mechanics. Hamiltonian mechanics (which asserts the existence of a Hamiltonian, if you are of the Platonic bent) sort of survived the transition, but it got reinterpreted quite a bit. In my opinion, it is an important aspect of physics that, even as the predictive precision converges from one theory to the next, the underlying ontology really doesn't. I think that means ontology is not a destination for physics.

 

[kith]

I don't think that's correct. Decoherence explains why we don't see superpositions of macroscopic objects.

Decoherence explaines how the system goes from a pure superposition state to a mixed state. The way how these states are interpreted decides, if it is sufficient to explain collapse or not. The simplest example is the ensemble interpretation. It states that the pure superposition state doesn't descirbe a single system, but already an ensemble of systems. So each state in the mixture corresponds to a fraction of the ensemble and in a measurement we simply draw one particular outcome.

It doesn't explain why Alice and Bob have the correlations they do, in an EPR-type experiment.

Do you mean that decoherence doesn't occur for the combined state if we only measure one component, or that we need to do more than to show the transition from the initial pure superposition state to the mixed state to "explain" the correlations?

We know that CAUSAL INFLUENCES are local. [...] We don't understand how there can be distant correlations that are neither caused by causal influences, nor by shared information.

We have an old theory which predicts something (all correlations are local) and a new theory, which modifies these predictions (nonlocal correlations are possible under very special circumstances). I don't see why EPR correlations are weird beyond the general measurement problem. And if we are able to explain the measurement problem (which I think is done in various interpretations), we have a clear mechanism how these correlations occur.

Anyway, I think your original point was that people have trouble with quantum mechanics because it's so different what we're used to. That is completely wrong. People are able to understand things that are very different from anything they have experienced.

That's right, but your examples are different from QM in two important ways. First, there are unique straightforward interpretations. They may be weird, but other interpretations seem much weirder to people (see Frederik's post about flat spacetime and deformed measurement apparatuses). And second, all your examples involve only spacetime. Theories of matter are much proner to controversy, because we ourselves consist of matter. So naturally, personal philosophical preferences have a much bigger influence on the interpretation of QM.

 

[kith]

First by the definition of state it is a state.

I meant "real" in the ontological sense. I thought this would be clear from the course of the discussion between you and stevendaryl.

What it doesn't do is explain why a particular result occurs just like probability theory does not explain why a head or tail occurs when you flip a coin.

The big difference is that in the case of the coin, I don't know the initial state. In QM, even if I know the initial state, I can't predict the outcome.

Having read your post about the projection postulate in the other thread, I don't think we have much dissent. My main point is just that the question if decoherence is enough to explain collapse depends on the interpretation of mixed states. In the ensemble interpretation or in the many worlds interpretation it is, but not in the Copenhagen interpretation. So if you say decoherence is enough, you are excluding some interpretations. That's ok, but it has to be mentioned.

 

[stevendaryl]

I don't see why EPR correlations are weird beyond the general measurement problem.

Yes, I would say that the only thing weird about quantum mechanics is the measurement problem.

And if we are able to explain the measurement problem (which I think is done in various interpretations), we have a clear mechanism how these correlations occur.

I don't think that we really have solved the measurement problem. Decoherence certainly doesn't solve it. What decoherence does is to explain why, even though we may start off with the system described by a pure state, we might end up with the system described by a mixed state. But what is a mixed state? It describes an ensemble. So there isn't just one world, but an ensemble of possible worlds. But what is a "world"?

 

[kith]

I don't think that we really have solved the measurement problem. Decoherence certainly doesn't solve it. What decoherence does is to explain why, even though we may start off with the system described by a pure state, we might end up with the system described by a mixed state. But what is a mixed state? It describes an ensemble. So there isn't just one world, but an ensemble of possible worlds. But what is a "world"?

Are you familiar with the ensemble interpretation, the many worlds interpretation and the interpretation of de Broglie and Bohm? All of them answer this question.

 

[stevendaryl]

Are you familiar with the ensemble interpretation, the many worlds interpretation and the interpretation of de Broglie and Bohm? All of them answer this question.

Yes, I'm familiar with those, and I don't find any of them very satisfactory.

 

[kith]

Yes, I'm familiar with those, and I don't find any of them very satisfactory.

Whether these interpretations are satisfactory or not is a question with various aspects. Personally, I prefer the Copenhagen interpretation because it is very close to the way science works. This is more important for me than solving the measurement problem, but I am aware of the fact that it is simply not there in other interpretations. So I don't think we need a new theory to explain it and I don't expect us to understand these things better in future theories.

 

[yoda jedi]

Yes, I would say that the only thing weird about quantum mechanics is the measurement problem.
I don't think that we really have solved the measurement problem. Decoherence certainly doesn't solve it. What decoherence does is to explain why, even though we may start off with the system described by a pure state, we might end up with the system described by a mixed state. But what is a mixed state? It describes an ensemble. So there isn't just one world, but an ensemble of possible worlds. But what is a "world"?

and by the way decoherence can be Intrinsic, Extrinsic, and Environmental
intrisc from an autonomous nonlinear quantum mechanics and solves the measurement problem.
enviromental from an environment induced supeselection (zurek joos and zeh) and do not solves the measurement problem.

 

[Fredrik]

intrisc from an autonomous nonlinear quantum mechanics and solves the measurement problem.

What are you talking about here?

 

[yoda jedi]

What are you talking about here?

an inherently nonlinear quantum mechanics in an opposition to a non inheherently nonlinear theory like CSL which the nonlinnearity is induced by a stochastic field.

 

[Ken G]

But the question is, does such a theory really exist, or are you just speculating about some new theory that might be able to resolve the measurement problem by replacing the linear simplicity of quantum mechanics with some nonlinear complexity? For my own part, I'd rather have the measurement problem!

 

[stevendaryl]

In my experience, Bohr detractors generally just don't understand him. He did clarify something-- he clarified that we must address the role of the physicist in physics, expressly because the physicist perceives nonunitary evolution, and the postulates of QM are about unitary evolution.

It seems strange to say that "we must address the role of the physicist in physics", because for practical purposes, we DON'T address the role of the physicist in physics. We use various rules of thumb for interpreting quantum predictions, and a deep understanding of the relationship between the physicist and the physics is just not important. Which is good, because we don't have any such deep understanding.

I think your understanding of Bell's theorem is rather incomplete. Your description sounds more like Bertlmann's socks, a common misconception about Bell's theorem.

I don't know why you would say that. The weird thing about QM is that it DOESN'T have a "Bertlmann's socks" interpretation of nondeterminism and correlation. I don't know why you would say that I believe the opposite of what I believe.

 

[stevendaryl]

Exactly. Decoherence for all practical purposes resolves the collapse of a wavefunction issue. IMHO its purely philosophical waffle if you don't like it - to some people such things are important - for me I couldn't care less.

I don't see a big difference between that notion of "resolving the issue" and just deciding not to worry about it. You don't actually need decoherence to decide not to worry about it--you can just stick to the recipe for quantum predictions.