I Particles from a thermal source

[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).

 

[vanhees71]

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.

It "jumps" on a macroscopic scale. Shot noise is of course only measurable on an ensemble. Here you use a single atom and excite it with lasers, i.e., you prepare it with a time-dependent external em. field. The shot noise comes from very many excitation-relaxation processes. So it's no contradiction to the ensemble interpretation at all. I still don't know, how to make sense of the probabilistic content of QT according to Born's rule if not by measuring an ensemble, be it the preparation of many identical atoms or, as in this case, a single atom in a trap, a quantum dot and other fascinating ways the AMO physicists can handle nowadays!

 

[A. Neumaier]

It "jumps" on a macroscopic scale. Shot noise is of course only measurable on an ensemble. Here you use a single atom and excite it with lasers, i.e., you prepare it with a time-dependent external em. field. The shot noise comes from very many excitation-relaxation processes. So it's no contradiction to the ensemble interpretation at all. I still don't know, how to make sense of the probabilistic content of QT according to Born's rule if not by measuring an ensemble, be it the preparation of many identical atoms or, as in this case, a single atom in a trap, a quantum dot and other fascinating ways the AMO physicists can handle nowadays!

Whatever the origin of the shot noise, its presence indicates an excited state of the single atom, and its absence indicates the ground state. Thus by observing the statistics of the shot noise you can observe how the atom changes states. And the observed fact is that the atom remains in the ground state until excited by an external stimulus. Then it jumps at a random time (predictable in the mean) into the excited state and stays there again until at another random time (predictable in the mean) it jumps back to the ground state. Thus one can predict only the fraction of time the atom is in one eigenstate of H or the other, consistent with the ensemble interpretation. However, in addition, one can see from the experiment the temporal behavior of the single atom, and it jumps! There is only one atom, so there is no question that it is the single system that jumps. This is an observable fact as much as anything that can be observed in the quantum domain.

 

[vanhees71]

I only object against "jump". It sounds like a discontinuous process of some quantity, but there's no such thing in quantum theory. The transition from one to the other state is a continuous process. It takes time to get from one state of definite energy to another. This is the content of the time-energy uncertainty relation.

 

[A. Neumaier]

The transition from one to the other state is a continuous process. It takes time to get from one state of definite energy to another. This is the content of the time-energy uncertainty relation.

Just as a measurement (or a jump of a swimmer into the water) takes time. The Copenhagen interpretation idealizes the measurement to be instantaneous, and hence works with an instantaneous jump. As these experiments show, this is a quite reasonable approximation, unless you highly resolve the time. It was certainly fully adequate for the measurements done at the time the Copenhagen interpretation was formed.

It is the same kind of idealization physicists use when they say (in derivations of linear response theory, say) that they switch on the interaction at time $t=0$. Switching also takes time but is treated as instantaneous, since the difference doesn't matter for the purpose at hand.

 

[stevendaryl]

Bohmian mechanics always takes a view that the full closed system is in a pure state, even if an open subsystem is in a mixed state.

That isn't clear to me. Surely you can use Bohmian mechanics to reason about mixed states? A mixed state for the full system can be interpreted as ignorance about the true wave function. You could do the same thing in Bohmian mechanics, right?

 

[Demystifier]

That isn't clear to me. Surely you can use Bohmian mechanics to reason about mixed states? A mixed state for the full system can be interpreted as ignorance about the true wave function. You could do the same thing in Bohmian mechanics, right?

Right! What I meant to say is that you cannot calculate deterministic Bohmian trajectories if you only know the mixed state.

 

[Dilatino]

Just as a measurement (or a jump of a swimmer into the water) takes time. The Copenhagen interpretation idealizes the measurement to be instantaneous, and hence works with an instantaneous jump. As these experiments show, this is a quite reasonable approximation, unless you highly resolve the time. It was certainly fully adequate for the measurements done at the time the Copenhagen interpretation was formed.

It is the same kind of idealization physicists use when they say (in derivations of linear response theory, say) that they switch on the interaction at time $t=0$. Switching also takes time but is treated as instantaneous, since the difference doesn't matter for the purpose at hand.

But is there not, due to the time/energy uncertainty, an upper limit to how much you could increase the time resolution to observe a quantum process without distroying the system?
Also, how can one observe the measurement process itself, as observing something means measuring it ...?

 

[A. Neumaier]

But is there not, due to the time/energy uncertainty, an upper limit to how much you could increase the time resolution to observe a quantum process without destroying the system?

Yes, there is, as in any idealized description. Modeling the jump of the swimmer with a camera resolution (24 pictures per second) one clearly sees a continuous movement. In the quantum case, it is similar but slifghtly different: One cannot say between two shot noise events whether the atom observed is now undergoing a jump, but one can say it in retrospect after sufficient time has passed. And one can deduce estimates for the time needed to complete a jump (as in the case of a swimmer).

Also, how can one observe the measurement process itself, as observing something means measuring it ...?

As always in quantum mechanics, from the outside. Thus if you model the detector for measuring the small system in quantum terms then you need another external observer to observe the detector. One needs to end this after finitely meany steps, not to run into the paradox of Wigner's friend.

 

[A. Neumaier]

I've not found the time to read these papers.

Maybe reading Section 7 of http://arxiv.org/abs/1511.01069 is enough to understand how the state of single atoms can be continuously monitored and shows jump of diffusion properties depending on the kind of measurement it is subjected to.

This justifies the collapse as an instantaneous approximation on the system-only level to what happens in an interaction with an appropriate measurement device on the system+detector level.

 

[vanhees71]

Are you saying that quantum dynamics cannot discribe this "jump", but that it necessarily have to be described by classical physics or something outside of any model/theory? That's what "collapse" means as I understand it. It may of course be that there are other definitions of collapse than this. I'll have a look at the paper.

 

[vanhees71]

Ok, Sect. 7 of the above paper answers my question satisfactorily! It's NOT a collapse but good old Wigner-Weisskopf. There are no jumps but rapid exponential decays (which are of course an approximation as is well known for decades, because strictly exponential decay is imcompatible with quantum theory; see Sakurai, Modern quantum Mechanics, but in many cases a very good approximation) with the usual probabilistic meaning of transition matrix elements. It's all very well compatible with the minimal interpretation!

 

[A. Neumaier]

Are you saying that quantum dynamics cannot discribe this "jump", but that it necessarily have to be described by classical physics or something outside of any model/theory?

Not quite. I answered this a moment ago in a new thread.