In what sense is QM not understood ?

[stevendaryl]

Knowing the axiomatic framework upon which QM is based, what the limitations are of QM, along with how to apply QM is equivalent to understanding QM.

We don't know the limitations of QM. And, as I said, we don't know how to apply QM except in a "rule of thumb" way. The ambiguous part, as I said, is knowing when a measurement has been made. What's a measurement? The formalism doesn't tell you, but it does tell you that after a measurement, the system will be in a eigenstate of the operator corresponding to the observable being measured. So the rules depend crucially on knowing what a measurement is, and they don't tell us. I would say that this is very different from classical physics. For classical physics, it's also true that whether something is a measurement or not is fuzzy. But the laws of physics don't depend in any way on that distinction.

There is an inherent ambiguity in the Rules of Quantum Mechanics. Suppose we prepare a system in some state, and then later we let it interact with a detector, and then even later, we perform some other measurement on it. There are two different ways to analyze it: (1) We can consider the detector to be performing a measurement of some observable. In this case, the wave function collapses to an eigenstate after interacting with the detector, and we use this eigenstate to compute the probabilities for the final measurement. (2) We can consider the detector to be a quantum system in its own right, evolving according to Schrodinger's equation. In this case, the detector doesn't perform a measurement, and there is no collapse of the wave function to an eigenstate.

In principle, these two different ways of analyzing the situation could lead to different results, because if we treat the detector as a quantum system, there is the possibility for interference effects. In practice, interference effects involving macroscopic objects are unobservable.

 

[bhobba]

There is an inherent ambiguity in the Rules of Quantum Mechanics. Suppose we prepare a system in some state, and then later we let it interact with a detector, and then even later, we perform some other measurement on it. There are two different ways to analyze it: (1) We can consider the detector to be performing a measurement of some observable. In this case, the wave function collapses to an eigenstate after interacting with the detector, and we use this eigenstate to compute the probabilities for the final measurement. (2) We can consider the detector to be a quantum system in its own right, evolving according to Schrodinger's equation. In this case, the detector doesn't perform a measurement, and there is no collapse of the wave function to an eigenstate.

Decoherence resolves this - long before the detector registers a result the environment has decohered the system (detector and what is being measured) so it is in some actual (not a superposition) state.

Thanks
Bill

 

[Ken G]

IMHO the goal of science is to find truth - and empirical checking to see if its true is what science is all about. To me the real essence of science is the willingness to always doubt - to say - yes we are after the truth but it must always be checked and rechecked.

But it seems to me there is a fundamental contradiction there, which we have to manage somehow. I completely agree with your second sentiment (and I like Feynman's characterization of science as "distrusting experts", and love his description of it as a way to avoid fooling ourselves), but I think it challenges the first. How can we be looking for truth, if we are embracing doubt at all stages? It suggests that truth is not a destination, but a journey. I'm fine with that, as long as we recognize that we are, in effect, redefining the standard meaning of truth, to get it to fit science, rather than trying to fashion science, to get it to fit some impossible standard of truth.

 

[nucl34rgg]

I've joined physicsforums because I would like to understand QM in the sense meant in the topic header. Thus I've been discussing Bell's Theorem and related issues with the experts here; and obviously none of them thinks that watching a video or reading a Wikipedia article (which they may have written) will make one understand it, in that sense (funny lecture though, makes me think of Woody Allen). Which brings me to the next point:

OK then, like him I now also claim that no one understands QM. And you may quote me on that, pretending that I only meant to illustrate the idea that the quantum world, at first glance, seems very different qualitatively than the world we live in at the scales that we perceive things. However, I did not say that nor suggest that, and neither did Feynman. What I mean is very different from that, as a matter of fact it is closer to what you suggest next:

Well, that is generally what "why" questions and the word "understand" mean - as also already discussed in this thread and numerous other threads.

Then you may not be able to understand why Feynman and many other experts agree that QM is not understood. As you realized, he knew perfectly well how to mathematically describe and apply QM - he even excelled in it. We all know that that is not the sense in which QM is said to be "not understood". And in what sense it is meant, has been elaborated already by others in this thread.

That would be unachievable. However:

The problem that we are discussing here, is that we even lack a plausible model of how and why QM works. To quote Feynman also on that one:

"The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that."

It is in that sense that QM is "not understood" - as many people have tried to explain now (see for example posts #2, 16, 74, 78, 79).

PS: I think that in what way QM is "not understood" has been sufficiently explained by now.

But, don't you see how "why" questions make one run in circles, and ultimately are inherently unanswerable? The question of "why" is fundamentally unanswerable through empirical means. Science never ever tells us why. It only gives us a model of "how" that is convenient for prediction or calculation. We have no way of knowing if the model is ever REALLY true, and empirical theories that describe reality are only claimed to be "true" in that they are consistent with observed data. You cannot prove truth by sampling a few events and concluding for the general case. Thus, science doesn't "prove" something to be true. It is simply the best approach we have for approximating the "truth."

Every scientist knows this, but this is often misrepresented to the general public.

Even in mathematics, which takes a rational approach to answer mathematical questions, asking "why" beyond a certain point is unproductive because the answer eventually is just: "It follows from the definition" or rather "That's the way it is." The problem is that modern human language is capable of describing poorly defined absurdities. We are capable of asking "why" without even being precise about what we mean by "why". If we were more precise about what we meant by "why", the confusion would disappear.

Also, I wasn't trying to be rude or dismissive by suggesting a video. You really might learn something from the late Professor Sidney Coleman. That video is widely regarded as a great clarification of concepts from QM. I strongly recommend it.

Anyway, I am leaving this thread because I'm not particularly fond of Woody Allen! :) Also, my claim was "QM is understood" as a theory of physics. You countered with "The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that." which describes that physics is an attempt to explain a truth of nature, which I am saying is NOT the goal of science and has nothing to do with QM. Science cannot answer how the universe "actually works" or more generally it cannot tell us the underlying reality or truth (if there is even such a thing) precisely because it is fundamentally empirical. It can only suggest models that are consistent with observed phenomena to a given probability within a given measurement tolerance. I am afraid that the "understanding" you are seeking is in fact, not a physical theory, but rather a philosophical metaphysical theory that is ontological, which I am afraid everyone is ill equipped to provide because such a theory doesn't exist and cannot ever be formulated.

 

[stevendaryl]

Decoherence resolves this - long before the detector registers a result the environment has decohered the system (detector and what is being measured) so it is in some actual (not a superposition) state.
Thanks
Bill

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".

 

[harrylin]

[..] Also, my claim was "QM is understood" as a theory of physics. You countered with "The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that." which is an attempt to explain a truth of nature, [...] It can only suggest models that are consistent with observed phenomena to a given probability within a given measurement tolerance. [..]

Ehm no, nobody did an attempt to explain a truth of nature, and the issue that Feynman brought up was that no satisfying model for QM exists, for example his proposed model could not explain partial reflection* from a glass plate in a satisfying way - but I won't go again into such details as my earlier mistake was probably that I replied too much, so that my primary comment may have gone unnoticed. I'll stress it now: you made a claim which you next started to defend about how QM is understood, and what the goal of science supposedly is, and so on. Those are not the topic of this thread, and we all know in what way QM is understood. So thanks for elaborating on that, but it's really besides the point. And I'm also leaving this thread now- not because of videos or Woody Allen but because I think that already sufficient to-the-point answers have been given about the sense in which QM is said to be not understood.

*in his book on QED, he admits this somewhere around p.20. I was so disappointed that I did not read on for a year or so

 

[bhobba]

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".

Decoherence does resolve it. It decoheres in a very very short time so it does not spread.

The correct description is first there is a particle in a superposition of states, it interacts with the environment and in a very short time dechoreres into a state that is not in a superposition (it is in what is called a mixed state - but one where it is in some definite state 100% for sure - but the exact state is described by bog standard probability theory - quantum weirdness is no longer present) by leaking phase to the environment very very quickly, usually well before it even reaches the detector. In a few situations like the double slit experiment that leakage occurs at the detector - but that is not the norm. In some very very special circumstances like superconductivity no leakage occurs at all and then things are really weird - but not the measurement type problem weird.

Thanks
Bill

 

[Fiziqs]

Anyway, I am leaving this thread because I'm not particularly fond of Woody Allen! :) Also, my claim was "QM is understood" as a theory of physics. You countered with "The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that." which describes that physics is an attempt to explain a truth of nature, which I am saying is NOT the goal of science and has nothing to do with QM. Science cannot answer how the universe "actually works" or more generally it cannot tell us the underlying reality or truth (if there is even such a thing) precisely because it is fundamentally empirical. It can only suggest models that are consistent with observed phenomena to a given probability within a given measurement tolerance. I am afraid that the "understanding" you are seeking is in fact, not a physical theory, but rather a philosophical metaphysical theory that is ontological, which I am afraid everyone is ill equipped to provide because such a theory doesn't exist and cannot ever be formulated.

Let me see if I can give an analogy to demonstrate exactly why some people argue that physicists do not understand QM.

There is an ancient device known as the Antikythera mechanism. It was a coral encrusted device salvaged from an ancient shipwreck. After many years, and careful study, reseachers were able to reconstruct the device. It turned out to be a device for keeping track of the motion of the sun and moon, and perhaps some of the planets. It was quite intricate, and able to model the motion of the sun and moon quite closely considering the time in which it was made.

There are even more modern examples of such devices that are remarkable in the accuracy with which they can model the motions of celestial bodies. Accounting for even small anomalies in the motions of the moons and planets. These are also quite remarkable devices for their time.

But there is just one problem with these devices. For although they can model the motions of the sun, planets, and moons with remarkable detail, they say absolutely nothing about "why" these objects move the way they do. They are nice models, but the makers of these models had no understanding of the forces involved.

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. In the same way that those ancient model builders failed to "understand" the very thing that they were modeling, today's physicists fail to "understand" the forces at work within their own model. They can model it quite precisely, but being able to model it, doesn't equate to understanding it.

Those ancient brass models, and today's modern mathematical ones, both fall short in one regard, they make no attempt to explain "why".

 

[stevendaryl]

Decoherence does resolve it. It decoheres in a very very short time so it does not spread.

I don't understand that. I thought that the only difference between the environment (meaning, I think, the electromagnetic field, plus possibly other fields) and any other system is just the huge number of states. But I don't see how that changes things in principle. In particular, I don't see how the environment can select a single state out of a superposition. It can become correlated--is that what you mean? If originally you have

|ψ_environment>(|ψ_{device, A}> + |ψ_{device, B}>)

(that is, the device is in a superposition of two states, A and B) then it will rapidly decohere to get:

|ψ_{environment+system, A}> + |ψ_{environment+system, B}>

But it's still a superposition. Of course, the environment is actually described by quantum field theory, rather than quantum mechanics, but I think the same principles hold.

The correct description is first there is a particle in a superposition of states, it interacts with the environment and in a very short time dechoreres into a state that is not in a superposition (it is in what is called a mixed state - but one where it is in some definite state 100% for sure - but the exact state is described by bog standard probability theory - quantum weirdness is no longer present) by leaking phase to the environment very very quickly, usually well before it even reaches the detector.

I really don't see how that is true, unless you are treating the environment as a mixed to start with. Pure states evolve into pure states---however, as was explained by Everett in his thesis on the Universal Wave Function, a pure state with many degrees of freedom will look exactly like a mixed state, if you average over the degrees of freedom that you don't care about. But that's exactly what I was talking about--that for practical purposes, interference becomes impossible, and the lack of interference effects destroys the "nonclassical" character of quantum probabilities. It's still a superposition, though. There is no "collapse" to a single value in the physics.

In a few situations like the double slit experiment that leakage occurs at the detector - but that is not the norm. In some very very special circumstances like superconductivity no leakage occurs at all and then things are really weird - but not the measurement type problem weird.

Thanks
Bill

I'm not really sure if we are talking about two different ways of looking at the same thing, or whether you're actually claiming something contrary what I believe to be the case. Certainly for many-particle quantum mechanics, the system cannot evolve from a pure state to a mixed state. Once you go to quantum field theory, I'm not sure, any longer, but my feeling is that it's still impossible. But, as I said, for practical purposes, you can treat a system as being in a mixed state if it is correlated with an environment having many degrees of freedom.

 

[bhobba]

Those ancient brass models, and today's modern mathematical ones, both fall short in one regard, they make no attempt to explain "why".

But they do - simply not in the terms you judge as telling why. Why do objects fall - space time is curved - why is space time curved - it is dynamical - why is it dynamical - because nature has no prior geometry - why does nature have no prior geometry - no one knows - its just the way nature is - it's very intuitive when you understand it and incredibly beautiful and elegant mathematically, but no one right now really knows why. Some deeper theory may tell us why eventually - but it too will contain something where we say - its just the way nature is. Such is what any explanation contains. Its only those that don't understand this that say there is no attempt to explain why.

IMHO such a view is a variant of this its only math so it can't be reality type argument. They ignore once it is mapped to stuff external to us out there in reality land, such as for example the points and lines of Euclidean Geometry are, it is a description of reality and transcends mere math. 10 year olds leaning Geometry for the first time usually grasp it immediately but for some reason a few adults that frequent forums like this have trouble with it.

Thanks
Bill

 

[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?