I Particles from a thermal source

[Demystifier]

I am still hoping for atyy or someone else to address what the Copenhagen interpretation says in the context of my post #1.
In particular, since pure states play a distinguished role in the Copenhagen interpretation, I'd like to know whether each individual particle is in a pure state after leaving the source? How is this state assigned or tested?

Is the filter a measurement in the sense of your version of the Copenhagen interpretation? If so, what does your version of the Copenhagen interpretation assert about state and properties of the single particle in the three cases (a), (b), (c)? If not, what happens to the state of a particle when passing the filter?

The only version of Copenhagen which answers "what happens" type of questions is the collapse interpretation. So here I will use this version (vanhees71, please don't read it!).

Still, we have two different versions. In one version, collapse happens only when a conscious observer observes. In another version, collapse happens whenever interaction with a macroscopic apparatus takes place. For definiteness, I will use the latter version.

So here is what happens according to this version of CI:
(a) At the moment of emission, wave function collapses into a state with a definite spin in some random direction.
(b) At the filter the wave function is either destroyed (which can also be thought of as a kind of collapse) or collapses into a state with a definite spin in the direction defined by the filter.
(c) At the measurement the wave function is destroyed (provided that it was not already destroyed at the filter) and the measuring apparatus collapses into a state of a definite outcome of spin measurement.

 

[A. Neumaier]

Wow, I've to read a lot over the weekend :-). Perhaps you can help with this effort: Is there anywhere in those papers a clear contradiction to the dynamics of quantum theory, i.e., can any of these groups, claiming to observe quantum jumps (in my opinion a clear contradiction to the basic principles of quantum theory, because there's nothing jumping at all in the dynamical equations of QT, which are all (operator valued) differential equations) or "a collapse" prove with certainty that standard quantum dynamics (including the interaction of the system with the used measurement devices!) is invalid? If so, I wonder that they didn't declare the invalidity of quantum theory, which would be a pretty certain ticket to Stockholm!

Of course the quantum jumps are due to the interaction with the measurement device, consistent with the collapse, which only happens when passing an instrument. In every interpretation, no interaction with the environment means nothing that can be measured by an observer sitting in the environment, hence unitary evolution. But if one considers the interaction with the environment and traces out its influence in a dynamical way one ends up (in the Markov approximation) with an approximate dynamics that is stochastic and dissipative and gives, under the appropriate conditions, rise to directly observable quantum jumps.

Thus there is no contradiction to shut-up-and-calculate (which leaves a lot of freedom how to relate the calculations to experiment), and everything is consistent with QM as I understand it. But since everyone has a slighly different personal understanding, and since everyone adds to the outspoken assumptions extra ad hoc twists whenever needed to interpret shut-up-and-calculate in an actual experimental settings, I do not dare to speak for everyone. You need to make up your own mind.

 

[A. Neumaier]

So here is what happens according to this version of CI:
(a) At the moment of emission, wave function collapses into a state with a definite spin in some random direction.
(b) At the filter the wave function is either destroyed (which can also be thought of as a kind of collapse) or collapses into a state with a definite spin in the direction defined by the filter.
(c) At the measurement the wave function is destroyed (provided that it was not already destroyed at the filter) and the measuring apparatus collapses into a state of a definite outcome of spin measurement.

Thanks. Can you please clarify a detail in (b)? When happens one or the other of your description? Randomly with probability $\langle P\rangle=\mbox{tr} \rho P =\phi^*\rho\phi$?

 

[Demystifier]

Thanks. Can you please clarify a detail in (b)? When happens one or the other of your description? Randomly with probability $\langle P\rangle=\mbox{tr} \rho P =\phi^*\rho\phi$?

Yes, of course.

EDIT: When I was talking about destruction, I assumed that the particles were photons. Now I have noted that you asked about electrons. Electrons are not destroyed, but absorbed without destruction. The rest is the same.

 

[A. Neumaier]

Yes, of course.

This cannot be quite correct since the particle no longer knows that it was prepared in a mixed state since it collapsed already to some pure state $\psi$. According to Born's rule, the probability should depend only on $\psi$ but the observed statistics should still be that predicted by the mixed state...

 

[A. Neumaier]

and the measuring apparatus collapses into a state of a definite outcome of spin measurement.

Hmm, I thought that in all versions of the Copenhagen interpretation, the measurement device is considered to be classical.

 

[Demystifier]

This cannot be quite correct since the particle no longer knows that it was prepared in a mixed state since it collapsed already to some pure state $\psi$. According to Born's rule, the probability should depend only on $\psi$ but the observed statistics should still be that predicted by the mixed state...

You are mixing two different kinds of probability. One is the fundamental intrinsic probability of a single particle, which depends only on $\psi$.
Another is the Bayesian emergent probability describing knowledge of the human experimentalist. Even though the system has a definite state $\psi$, the experimentalist does not know what that $\psi$ is, so his knowledge is described by $\rho$.

 

[Demystifier]

Hmm, I thought that in all versions of the Copenhagen interpretation, the measurement device is considered to be classical.

It's not the case in all versions of CI. See e.g. about the von Neumann version, which is the first version that explicitly introduced collapse.

 

[vanhees71]

Of course the quantum jumps are due to the interaction with the measurement device, consistent with the collapse, which only happens when passing an instrument. In every interpretation, no interaction with the environment means nothing that can be measured by an observer sitting in the environment, hence unitary evolution. But if one considers the interaction with the environment and traces out its influence in a dynamical way one ends up (in the Markov approximation) with an approximate dynamics that is stochastic and dissipative and gives, under the appropriate conditions, rise to directly observable quantum jumps.

But that's not Copenhagen. There you say that the dynamics is quantum but that the macroscopic measurement apparatus can be described adequately by coarsegrained dynamics, which leads to classical behavior. That's a completely different philosophy than the Copenhagen-like collapse. I disagree still about the observation of quantum jumps, because that's a contradiction to the statement just made. The equations do not lead to jumps.

Thus there is no contradiction to shut-up-and-calculate (which leaves a lot of freedom how to relate the calculations to experiment), and everything is consistent with QM as I understand it. But since everyone has a slighly different personal understanding, and since everyone adds to the outspoken assumptions extra ad hoc twists whenever needed to interpret shut-up-and-calculate in an actual experimental settings, I do not dare to speak for everyone. You need to make up your own mind.

The shut-up-and-calculate interpretation just is silent about the measurement process at all (as is almost all theoretical physics no matter whether treating classical or quantum physics). It just states that the predictions of QT are those and only those given by the Born rule, i.e., probabilistic, and you can check the corresponding predictions (only) by measuring the quantities in question very often on an ensemble of identically and independently prepared systems. I don't know of any occasion in my field of research, where anything beyond this shut-up-and-calculate interpretation is needed.

 

[A. Neumaier]

You are mixing two different kinds of probability. One is the fundamental intrinsic probability of a single particle, which depends only on $\psi$.
Another is the Bayesian emergent probability describing knowledge of the human experimentalist. Even though the system has a definite state $\psi$, the experimentalist does not know what that $\psi$ is, so his knowledge is described by $\rho$.

This has nothing to do with knowledge. The thermal source prepares particles without asking the experimentalists whether they know it. And themeasurement statistics can be automatically recorded by a dumb automatic device. Thus the probabilities involved are frquentist and not Bayesian.

The Copenhagen interpretation (collapse interpretation in what you called above the latter version, where no consciousness is involved) is surely able to explain this statistics without reference to knowledge.

It is only a matter of getting the formal details right; there is nothing in this setting that could invalidate the interpretation.

 

[A. Neumaier]

But that's not Copenhagen. There you say that the dynamics is quantum but that the macroscopic measurement apparatus can be described adequately by coarsegrained dynamics, which leads to classical behavior. That's a completely different philosophy than the Copenhagen-like collapse. I disagree still about the observation of quantum jumps, because that's a contradiction to the statement just made. The equations do not lead to jumps.

In my view (and those of at least some the authors), it is a derivation of the correctness of the Copenhagen (collapse) interpretation applied to the small system, showing (under suitable assumptions) that it gives a correct coarse-grained view of the unitary description of a far bigger system when the surrounding is ignored.

 

[A. Neumaier]

It's not the case in all versions of CI. See e.g. about the von Neumann version, which is the first version that explicitly introduced collapse.

Ok. But it should be in the version that you actually specified (collapse after passing the instrument) without conscious observr.

 

[Demystifier]

This has nothing to do with knowledge. The thermal source prepares particles without asking the experimentalists whether they know it. And themeasurement statistics can be automatically recorded by a dumb automatic device. Thus the probabilities involved are frquentist and not Bayesian.

The Copenhagen interpretation (collapse interpretation in what you called above the latter version, where no consciousness is involved) is surely able to explain this statistics without reference to knowledge.

It is only a matter of getting the formal details right; there is nothing in this setting that could invalidate the interpretation.

OK, you are right about that. Let me rephrase myself accordingly.

A single particle is in a definite state $\psi$, so its intrinsic probability is given by $\psi$. However, when you repeat the measurement many times, $\psi$ is not always the same. Therefore the measured frequencies cannot be given by a single $\psi$. Instead, the measured frequencies are given by $\rho$.

 

[A. Neumaier]

OK, you are right about that. Let me rephrase myself accordingly.

A single particle is in a definite state $\psi$, so its intrinsic probability is given by $\psi$. However, when you repeat the measurement many times, $\psi$ is not always the same. Therefore the measured frequencies cannot be given by a single $\psi$. Instead, the measured frequencies are given by $\rho$.

I think this is now correct, but the statement needs a formal supporting argument. For the Born rule gives a probability for each single particle, and it must be shown that accumulating these probabilities according to the rules of classical probability theory gives the probability as predicted by $\rho$. Such a supporting argument is needed to ensure that the collapse interpretation correctly explains the experimental record.

 

[Demystifier]

Ok. But it should be in the version that you actually specified (collapse after passing the instrument) without conscious observr.

I was not completely specific about the version I am using. In this version everything (including macroscopic objects) is described by QM.

Now you see how important it is to specify what exactly one means by "Copenhagen interpretation". There are so many versions, subversions and subsubversions.

 

[Demystifier]

I think this is now correct, but the statement needs a formal supporting argument. For the Born rule gives a probability for each single particle, and it must be shown that accumulating these probabilities according to the rules of classical probability theory gives the probability as predicted by $\rho$. Such a supporting argument is needed to ensure that the collapse interpretation correctly explains the experimental record.

I agree.

 

[A. Neumaier]

I was not completely specific about the version I am using. In this version everything (including macroscopic objects) is described by QM.

But in this version, doesn't only the total wave function of particle plus apparatus exists? I conclude this from your earlier remark about entangled particles, where the single particles have a wave function only after a complete measurement. So your claim (a) wouldn't make sense.

Now you see how important it is to specify what exactly one means by "Copenhagen interpretation". There are so many versions, subversions and subsubversions.

We should be able to find at least one (subsubsub?)version where there is collapse, no consciousness, and detectors are classical. This would give a consistent description of what happens throughout.

 

[Demystifier]

But in this version, doesn't only the total wave function of particle plus apparatus exists?

No.

I conclude this from your earlier remark about entangled particles, where the single particles have a wave function only after a complete measurement.

At that point I didn't yet completely specify the version of CI I am talking about. Now I can be more specific by claiming that single particle can have a wave function whenever collapse is involved. As I already said, collapse may happen whenever there is interaction with a macroscopic object. Even more precisely, collapse happens whenever unitary evolution of many degrees of freedom creates macroscopic branches which, without collapse, would correspond to many worlds.

So your claim (a) wouldn't make sense.

I hope it does now.

 

[Demystifier]

We should be able to find at least one (subsubsub?)version where there is collapse, no consciousness, and detecors are classical. This would give a consistent description of what happens throughout.

Versions of CI in which detectors are classical - do not involve collapse. Such versions of CI do not give any description of what happens at the microscopic level.

Niels Bohr, who was probably the strongest advocate of the view that detectors are classical, said: “Physics is not about how the world is, it is about what we can say about the world.”
He also said “Everything we call real is made of things that cannot be regarded as real.”, and “Never express yourself more clearly than you are able to think.”.

 

[vanhees71]

In my view (and those of at least some the authors), it is a derivation of the correctness of the Copenhagen (collapse) interpretation applied to the small system, showing (under suitable assumptions) that it gives a correct coarse-grained view of the unitary description of a far bigger system when the surrounding is ignored.

But the derivation contradicts the statement by the Copenhagen doctrine that there are two realms in dynamics, the quantum and the classical. The mentioned derivation proves the opposite: Classical behavior can be explained from quantum dynamics by an appropriate course-graining procedure!

 

[vanhees71]

Versions of CI in which detectors are classical - do not involve collapse. Such versions of CI do not give any description of what happens at the microscopic level.

Niels Bohr, who was probably the strongest advocate of the view that detectors are classical, said: “Physics is not about how the world is, it is about what we can say about the world”

I'd not give up hope that physics is still not only what we can say about the world but about what we can say in a logically consistent way about the world, and the assumption that the world is divided in quantum and classical dynamics is not very convincing. Classical physics should follow somehow as an approximation from quantum theory, and I think for macroscopic systems that's quite well understood in terms of coarse-graining over many microscopic details that are irrelevant for macroscopic observables which very often behave with high accuracy as described by classical physics.

 

[atyy]

Versions of CI in which detectors are classical - do not involve collapse. Such versions of CI do not give any description of what happens at the microscopic level.

Niels Bohr, who was probably the strongest advocate of the view that detectors are classical, said: “Physics is not about how the world is, it is about what we can say about the world”

What is collapse? I would usually say that Copenhagen has collapse, but collapse is not necessarily real, since the wave function itself is not necessarily real (in contrast, the detectors are classical or real).

 

[Demystifier]

What is collapse? I would usually say that Copenhagen has collapse, but collapse is not necessarily real, since the wave function itself is not necessarily real (in contrast, the detectors are classical or real).

In the version I am currently talking about (which is certainly not the Bohr's version), collapse is taken as real. Not because I particularly like that version, but because A. Neumaier wanted a version which answers "what happens" type of questions.

 

[atyy]

But the derivation contradicts the statement by the Copenhagen doctrine that there are two realms in dynamics, the quantum and the classical. The mentioned derivation proves the opposite: Classical behavior can be explained from quantum dynamics by an appropriate course-graining procedure!

I'd not give up hope that physics is still not only what we can say about the world but about what we can say in a logically consistent way about the world, and the assumption that the world is divided in quantum and classical dynamics is not very convincing. Classical physics should follow somehow as an approximation from quantum theory, and I think for macroscopic systems that's quite well understood in terms of coarse-graining over many microscopic details that are irrelevant for macroscopic observables which very often behave with high accuracy as described by classical physics.

You are wrong. Landau and Lifshitz are perfectly aware that classical mechanics can be obtained as a limit of quantum mechanics. However, that does not prevent the need for the classical world being postulated in order for quantum mechanics to make sense. There is as yet no consensus on how to have only the wave function with deterministic unitary evolution describing the whole universe.

 

[atyy]

In the version I am currently talking about (which is certainly not the Bohr's version), collapse is taken as real. Not because I particularly like that version, but because A. Neumaier wanted a version which answers "what happens" type of questions.

Yes, that clarifies it. I wasn't sure what Neumaier meant. The beauty of Copenhagen is that one can be agnostic about the reality of the wave function and collapse, yet treat them as "real" for all practical purposes. So "real" is not necessarily real.

 

[Demystifier]

Landau and Lifshitz are perfectly aware that classical mechanics can be obtained as a limit of quantum mechanics. However, that does not prevent the need for the classical world being postulated in order for quantum mechanics to make sense.

Let me make sure that I understand that. One first postulates classical mechanics as a part of QM, and then derives that in a certain limit classical mechanics is the only part of the theory that remains. Is it what you are saying?

 

[vanhees71]

You are wrong. Landau and Lifshitz are perfectly aware that classical mechanics can be obtained as a limit of quantum mechanics. However, that does not prevent the need for the classical world being postulated in order for quantum mechanics to make sense. There is as yet no consensus on how to have only the wave function with deterministic unitary evolution describing the whole universe.

The whole universe cannot be described by quantum theory, because it's a single system. So you can say a lot about the quantum state of the universe without ever being able to test this assumption, because you cannot observe an ensemble of universes. The minimal interpretation is thus admitting right away that quantum theory is not a complete description of nature.

Landau and Lifshitz, as far as their vol. III of the famous theory-book series is concerned, are pretty silent about interpretational issues and very careful concerning the collapse. That makes it one of the best QM textbooks ever written.

Of course the heuristics to get to the postulates of QT is using classical arguments, but that's not saying that QT can be derived from classical mechanics. What's for sure classical is indeed the space-time model, which is either Galileian or Minkowski space-time. We still lack a full quantum description of all of physics, particularly that of spacetime, which is necessarily closely related to the open issue with quantum gravity.

 

[atyy]

Let me make sure that I understand that. One first postulates classical mechanics as a part of QM, and then derives that in a certain limit classical mechanics is the only part of the theory that remains. Is it what you are saying?

(A) Landau and Lifshitz first postulate the classical/quantum cut. This cut is subjective and the line can be moved. However, to use quantum mechanics we need to have a cut somewhere. So classical mechanics or something like the classical world or macroscopic reality is a prerequisite for using quantum mechanics. This is really just a version of Bohr's insistence that the detectors are classical.

(B) Having made the cut, when we do quantum mechanics, in general we will get deviations from classical mechanics. If we use the path integral picture, we can take c;assical mechanics to be the saddle point approximation, and quantum mechanics as the full path integral. In situations where the saddle point approximation is very good, or when we let Planck's constant go to zero, we recover classical mechanics as a limit of quantum mechanics.

So Landau and Lifshitz say that (B) is not enough, and (A) is required for us to use quantum mechanics to make predictions.

 

[atyy]

The whole universe cannot be described by quantum theory, because it's a single system. So you can say a lot about the quantum state of the universe without ever being able to test this assumption, because you cannot observe an ensemble of universes. The minimal interpretation is thus admitting right away that quantum theory is not a complete description of nature.

Landau and Lifshitz, as far as their vol. III of the famous theory-book series is concerned, are pretty silent about interpretational issues and very careful concerning the collapse. That makes it one of the best QM textbooks ever written.

Of course the heuristics to get to the postulates of QT is using classical arguments, but that's not saying that QT can be derived from classical mechanics. What's for sure classical is indeed the space-time model, which is either Galileian or Minkowski space-time. We still lack a full quantum description of all of physics, particularly that of spacetime, which is necessarily closely related to the open issue with quantum gravity.

Yes, I am happy if you subscribe to quantum mechanics as given in Landau and Lifshitz. It is wrong but not misleading, ie. it is correct FAPP :)

 

[Demystifier]

(A) Landau and Lifshitz first postulate the classical/quantum cut. This cut is subjective and the line can be moved. However, to use quantum mechanics we need to have a cut somewhere. So classical mechanics or something like the classical world or macroscopic reality is a prerequisite for using quantum mechanics. This is really just a version of Bohr's insistence that the detectors are classical.

(B) Having made the cut, when we do quantum mechanics, in general we will get deviations from classical mechanics. If we use the path integral picture, we can take c;assical mechanics to be the saddle point approximation, and quantum mechanics as the full path integral. In situations where the saddle point approximation is very good, or when we let Planck's constant go to zero, we recover classical mechanics as a limit of quantum mechanics.

So Landau and Lifshitz say that (B) is not enough, and (A) is required for us to use quantum mechanics to make predictions.

Let me try to make an analogy from biology.

(A) To make sense of animals, one also needs plants. (Otherwise animals would have nothing to eat.)

(B) But in a certain limit animals themselves behave like plants, e.g. in a vegetative state.