Particles from a thermal source

[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.

 

[atyy]

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.

In Copenhagen biology, vegetarians can eat meat, since animals are not real.

 

[vanhees71]

I'm a 2nd-order vegetarian, eating only meat from animales who themselves only eat plants ;-)). SCNR.

 

[Demystifier]

I'm a 2nd-order vegetarian

That's called second quantization in cooked-matter community.

 

[A. Neumaier]

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!

Quantum mechanics in the Copenhagen interpretation, with a quantum treatment of the small system and a classical treatment of the detector, is as good an approximation as quantum mechanics of quantum chemists who treat a single molecule by considering the nuclear motion as classical and the electronic motion as quantum. In both cases it is an approximation fully justified under known conditions by a more detailed theory.

Moreover, quantum mechanics in the Copenhagen interpretation has the strong advantage that it can be applied to single systems. See the six papers mentioned in post #28, where the ensemble interpretation apparently has to pass.

 

[A. Neumaier]

Here is what happens in my version of the Copenhagen interpretation, where there is collapse, no consciousness, and detectors are modeled as classical objects. I believe this to be the standard version of the CI, as far as one can talk about a standard one. In any case, it is the one that can be deduced under certain assumptions as an approximate description of an open system that is part of a larger isolated quantum system modeling system + detector + environment.

My description of what happens for each single particle under the conditions of post #1 is a modification of Demystifier's description, where detectors are not classical.

(a) At the moment of emission, the wave function of the particle is in a random pure state $\psi$, uniformly drawn from the Bloch sphere.
(b) At the filter the wave function of the absorbed particles ceases to exist. The particle passes with probability $|\phi^*\psi|^2=\phi^*(\psi\psi^*)\phi$ given by the Born rule, and then has the pure state $\phi$ defined by the filter. Averaged over many electrons, this probability averages to the probability specified in post #1, since the average of the $\psi\psi^*$ over the Bloch sphere is easily seen to be $\rho$.
(c) At the measurement, what happens depends upon the particle type and how the particle was detected. In case of a photon, the particle disappears. For electrons, if the number of traces in a bubble chamber is counted, the particle continues to exist, and the spin state depends on details of the interaction with the ions. For electrons detected by a Geiger counter, the particle disappears as a quantum object and becomes part of the classical detector.

 

[vanhees71]

Moreover, quantum mechanics in the Copenhagen interpretation has the strong advantage that it can be applied to single systems. See the six papers mentioned in post #28, where the ensemble interpretation apparently has to pass.

I've not found the time to read these papers. Could you point me to a specific one, where the outcome of the experiment contradicts the minimal interpretation? If this is true then Copenhagen in your definition is a different theory than quantum theory in the minimal interpretation, i.e., then there must be a result that cannot be described by the standard kinematical and dynamical postulates + Born's rule. I can't find any hint to that in the papers you cited!

 

[A. Neumaier]

I've not found the time to read these papers. Could you point me to a specific one, where the outcome of the experiment contradicts the minimal interpretation? If this is true then Copenhagen in your definition is a different theory than quantum theory in the minimal interpretation, i.e., then there must be a result that cannot be described by the standard kinematical and dynamical postulates + Born's rule. I can't find any hint to that in the papers you cited!

The minimal interpretation makes no assertions about single systems. But the experimental papers (distinguished by their titles) claim that individual quantum jumps of single systems can be observed. They don't need to explain their findings, only ensure that their experiments are done with the proper care. This is why I cited very different papers over a very long time span so that you can see that it is not a fluke.

Note that I had cited these papers as a response to your claim

In my opinion, there is not the slightest evidence for the reality of any collapse-like dynamics whatsoever!

It is your claim, so it is your task to bring the experimental evidence I provided into agreement with your claims.

If you are interested in supporting theory, you may wish to look at the highly cited paper

M.B. Plenio & P.L. Knight,
The quantum-jump approach to dissipative dynamics in quantum optics. Reviews of Modern Physics, 70 (1998), 101.
http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.70.101

Martin Plenio is Director of the Institute of Theoretical Physics at Ulm University.
Peter Knight is a Past-President of the Optical Society of America.

 

[vanhees71]

Ok, if you define shot noise as "quantum jumps", then "quantum jumps" are of course measurable and observed, but in which sense proves that quantum theory in the minimal interpretation to be wrong? Can you prove, that you cannot describe the results of these measurements with standard QT? Why do you claim that standard quantum theory in the minimal interpretation cannot be applied when the measured ensemble is prepared with the same system? I don't see any reason to claim this, and of course we can do measurements on single systems as well as we can prepare single systems in a wanted state (modulo technical complications if the state is difficult to prepare). Despite of this I wonder why "quantum jumps" are even mentioned in research papers. I'm sure there's something meant that's within standard quantum theory, which has no jumps. If I find the time, I'll have a look at these papers in detail.

 

[A. Neumaier]

if you define shot noise as "quantum jumps", then "quantum jumps" are of course measurable and observed,

If I remember correctly, the quantum jumps are jumps of the state of a single atom, measured through a continuous measurement that produces shot noise in the excited stated but none in the ground state. Thus by observing the presence or absence of shot noise one can see or hear when the atom is in the ground state or in the excited state. And one finds that the atom jumps in both directions (one stimulated, the other spontaneous) and then stays some time before it jumps again, and part of it is controllable externally.

 

[Demystifier]

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 :)

Well, I find LL confusing. At page 21 they say that apparatus is classical but attribute a wave function $\Phi$ to the apparatus. Of course, they explain what they mean by "classical" in Eq. (7.3), but it may be misleading to call it classical. The transition from (7.2) to (7.3) is really a "collapse", except that they don't call it so (which is probably what @vanhees71 likes about LL).