QM: Interesting View - Get the Inside Scoop

[vanhees71]

What's described in Fig. 1 is the preparation of the system, a trapped ion or a single photon in a cavity. What's measured on this single ion (or in this particular case 3 ions) is the fluorescent light emitted by these ions excited by a laser field. This "image of the fluorescence" is due to many photons emitted in such transitions. So what's measured is rather the reflection of a coherent laser state of light than a single photon. If you'd observe a single transition and a single photon, you'd just excite (at most) one pixel on the CCD cam.

The same holds true for the CQED measurements:

Photons produced by a coherent source are coupled to the cavity via a waveguide. The atoms are sent
one at a time into the cavity at a controlled velocity and thereby have a controlled time of
interaction. In most experiments performed by Haroche’s group, the atom and field have
slightly different frequencies. An atom traveling in the cavity does not absorb photons, but
its energy levels shift due to the dynamical Stark effect, inducing a phase variation of the
microwave field.

In neither of these example you need more than standard statistically interpreted quantum theory to describe the experimental results.

 

[A. Neumaier]

What's measured on this single ion (or in this particular case 3 ions) is the fluorescent light emitted by these ions excited by a laser field. This "image of the fluorescence" is due to many photons emitted in such transitions.

But this does not explain why you are allowed to interpret the result as having measured the state of the ion - which is the object of interest. According to the statistical interpretation, having measured the many photons only tells something about their state!

 

[vanhees71]

Yes, but their state is entangled with the state of the ion in the cavity!

 

[Lord Jestocost]

It may be that it is in principle impossible to describe the quantum properties of an individual quantum system, or even meanigless to talk about them. So, this need not be a deficiency of this interpretation.

When “Statistical interpretation” is used in the way Ballentine means it, there is a fundamental deficiency of this interpretation. In Abner Shimony’s words (in “Symposia on the Foundations of Modern Physics 1992 - The Copenhagen Interpretation and Wolfgang Pauli” (edited by K. V. Laurikainen and C. Montonen)):

“There is, for example, Ballentine, whom I mentioned yesterday. He says: ‘I am not a hidden variable theorist, I am only saying that quantum mechanics applies not to individual systems but to ensembles.’ I didn't put this down separately because I simply do not understand that position. Once you say that the quantum state applies to ensembles and the ensembles are not necessarily homogeneous you cannot help asking what differentiates the members of the ensembles from each other. And whatever are the differentiating characteristics those are the hidden variables. So I fail to see how one can have Ballentine's interpretation consistently. That is, one can always stop talking and not answer questions, but that is not the way to have a coherent formulation of a point of view. But to carry out the coherent formulation of a point of view, as I think Einstein had in mind, you certainly have to supplement the quantum description with some hypothetical extra variables.” [bold by LJ]

 

[A. Neumaier]

Yes, but their state is entangled with the state of the ion in the cavity!

So what? None of your minimal postulates says that when you measure many times observable X (of the photons) it counts as a measurement of the state of the single Y with which it is entangled. Entanglement is not even mentioned in your postulates! You are just handwaving!

 

[A. Neumaier]

None of your minimal postulates says that when you measure many times observable X (of the photons) it counts as a measurement of the state of the single Y with which it is entangled.

The state of the single ion is not even defined since according to your postulates, the state is not a property of the single system but one of the ensemble!

 

[A. Neumaier]

Of course. It strongly suggests it - but as far as I can see, that's all:
https://arxiv.org/pdf/1201.0150.pdf

Actually, the physically correct way to state the dynamical classical limit is as a limit where the ''classical point particles'' are the center of mass of bound states with a large number of protons. Examples are cannon balls or planets. Then the classical dynamics follows without difficulties. I treated it in Section 2.3 of my book

A. Neumaier, Coherent Quantum Physics: A Reinterpretation of the Tradition, de Gruyter, Berlin 2019.

 

[bhobba]

I have had a chance to have a look at a preview on Amazon. I generally like to buy books by Mentors/Science Advisors here. IMHO it is both provocative and good. Written at a nice level that undergrads can generally understand. It is a worthwhile addition to the literature on QM foundations, and I will eventually get a copy. Just have so much reading to catch up on at the moment. Thanks for making me aware of it.

Thanks
Bill

 

[vanhees71]

So what? None of your minimal postulates says that when you measure many times observable X (of the photons) it counts as a measurement of the state of the single Y with which it is entangled. Entanglement is not even mentioned in your postulates! You are just handwaving!

It's not handwaving. Measurements of quantum properties are usually made by observing some macroscopic pointer observable. E.g., in the SG experiment you observe two partial beams of Ag atoms that went through a magnet by observing the corresponding traces on the observation screen. So what's literally meaured is the position of the Ag atoms when hitting this screen. That this is a separation of Ag atoms wrt. the value the corresponding spin component takes is due to the known entanglement between position and this spin component.

The observed pattern of the photons is also related to the state of the atom(s) in the trap through such an entanglement. It's well-described in the Nobel paper.

Of course, I don't mention entanglement in the postulates, because it's a consequence of the postulates. The corresponding observable non-classical properties concerning measurable correlations are not postulates but deduced from the postulates.

 

[A. Neumaier]

So what's literally measured is the position of the Ag atoms when hitting this screen.

I fully agree.

The observed pattern of the photons is also related to the state of the atom(s) in the trap through such an entanglement.

True only by handwaving and experience. But not according to your minimal foundations!

The problem with this begin already in the meaning of your statement.

Does the single atom in the trap have a well-defined state at every time?

If yes, then the state is a property of the single atom, and not of an ensemble of atoms. This flatly contradicts your postulates.

If not, what do you mean by the 'state of the atom'? Only one atom was prepared, so there is no ensemble to refer to. Thus your postulates are not applicable to this system.

Since you claim that everything in your lecture notes (and hence presumably in quantum mechanics) is derived from your minimal postulates, no consequences of entanglement apply to the single atom.

Thus your postulates are too minimal and need to be extended to allow for entangled states of single atoms to be measured by measuring instead an Ag atom.

 

[gentzen]

I'm one of those stupid people, who don't see, where the "puzzle" is.

You seem to assume that there is one single big puzzle, and that it is the same for everyone.

For example, one puzzle for me has been of historical and sociological nature:
Why does popular science get QM so badly wrong? How did it happen that the "consciousness causes collapse" interpretation got associated with the names of John von Neumann and Eugene Wigner? What was the role of Henry P. Stapp in this?

What might be characteristic about this sort of puzzle is that there is some activity I can do for investigating it more seriously, and that this is an activity that I could bear. So my guess is that different people will see various puzzles, and at least some of these puzzles will be choosen such that the one who believes this to be a puzzle also believes that there are ways to make progress on his puzzle.

I personally believe that there will not such new interpretation. It will just confirm the quantum theory as it is.

My intial reaction was that there will be no new interpretation, just improved understanding of certain questions and better (more convincing) approaches to explain them to other people. I fully agree that it will not contradict quantum theory as it is.

However, then I noticed that the quantum computing and quantum information science people basically already converged on the outline of their "new interpretation":

That is not to 'trivialise' those issues - I just think the generalised probability theory viewpoint resolves them.

I also invested effort in the past to better understand this viewpoint (based on a somewhat long series of blog post by Qiaochu Yuan - a nice fit to "bright young researcher") and even tried to explain it to a senior researcher. While doing so, I also mentioned one of my puzzles and that I believed that this viewpoint could help with it: "For quantum mechanics, the question for me is how to use concepts from probability theory for avoiding infinite information content. The first step is to switch to a probability from expectation approach, as outlined in Qiaochu Yuan's post, ..."

 

[vanhees71]

According to quantum theory any system has a state at any time, described by the statistical operator $\hat{\rho}(t)$.

What do you mean by "consequences of entanglement"? The consequences of entanglement are of course again of statistical nature, describing the well-known correlations. Take again the SG experiment, just because it's most simple to discuss this issues.

The preparation of the state is getting an Ag atom out of the oven, let it go through some slits, then letting it go through the magnet. Now there is an entanglement between the position of the atom with the spin component determined by the magnet. So you can be sure when measuring this spin component of the atom at a given place to find with certainty the corresponding value of this spin component. That's the "consequence of entanglement".

Thus by counting many Ag atoms prepared in this specific way (forming an ensemble of equally prepared silver atoms) ending up at the one or the other region of screen is, according to the calculation using the postulates, a way to measure the probabilities for the outcome of a spin measurement though what's indeed is observed is just the position of the Ag atom at the one or the other region on the screen. Of course that's not directly said in the postulates, because its deducable from the postulates.

If you make different postulate for any specific experimental setup you don't have a theory but just a description of one specific application. That's why "old quantum theory" has been abandoned in favor of "new quantum theory". The former just predicted the spectrum of the hydrogen atom and failed for all other atoms if not making additional ad hoc assumptions for these other cases, leading gradually to the discovery of new quantum mechanics which allowed to predict the spectra of all atoms using generally valid concepts.

 

[A. Neumaier]

According to quantum theory any system has a state at any time, described by the statistical operator

I fully agree.

What do you mean by "consequences of entanglement"?

I mean your statement that when you measure the pointer position you actually measured the state of the trapped ion, because of entanglement. This is pure handwaving since it is neither in your postulates nor is it derived from them in your lecture notes (version of July 22, 2019), as far as I can see. If I missed the derivation of such a fundamental claim, please point me to the relevant page.

Take again the SG experiment, just because it's most simple to discuss this issues.

No, take the Nobel prize winning experiment with the single ion in the trap, since there the problem is much more obvious!

Independent of that, your minimal exposition has another flaw. The experimental results (the pointer positions) are compared are independent of anyone's knowledge - one only needs to be able to read the meter. Thus they and the probabilities computed from them are objective in the ordinary sense. On the other hand, according to the minimal interpretation (p.23 of your lecture notes) the state of the trapped ion depends on we's knowledge of the system. The same system may be in a pure or in a mixed state, depending on the knowledge of 'we' who assigns the state. Since the predicted probabilities are a direct consequence of the assigned state they depend on this subjective assignment. But because the measurements are objective, there can be (within the measurement accuracy) at most one correct assignment! Unless augmented with a recipe to assign the correct state independent of what 'we' knows, this smells very fishy...

 

[martinbn]

But experimentalists prepare and measure routinely individual quantum systems called quantum dots, and they analyze their properties using shut-up-and-calculate (i.e., the handwaving interpretation of) quantum mechanics. The Nobel prize 2012 was awarded for this work!

Not sure how this related to the statistical interpretation! They work with representatives of the ensemble, and according to the statistiacl interpretations, they do not analyse their properties, but those of the ensemble. Are you saying that this disproves the statistical interpretation?

 

[vanhees71]

This is again a purely philosophical quibble. How good my description of the preparation in terms of the quantum formalism is, is of course itself subject to experimental test. Obviously for the experiments by Haroche et al our knowledge of the state is sufficient to accurately describe the outcome. This is of course the problem of any theorist using any theory. So it applies as well to your alternative theory you called "thermal interpretation" before. Now it seems to be called "coherent quantum mechanics". So, how do you describe the SG experiment (or the experiments by Haroche and Wineland describe in the Nobel foundation's citations)?

The SG experiment is very well understood in the standard formulation because of its simplicity. You can dynamically calculate how it comes to the said entanglement between position and spin component with sufficient accuracy to understand the outcome of the experiments. So where is the problem?

 

[A. Neumaier]

Not sure how this related to the statistical interpretation! They work with representatives of the ensemble, and according to the statistical interpretations, they do not analyse their properties, but those of the ensemble.

They interpret a single time series as giving evidence of temporal properties of the single ion. No ensemble of ions is involved. This is the whole point of probing individual quantum systems. Being able to control and read the state of a single quantum object is the prerequisite of quantum computing.

Are you saying that this disproves the statistical interpretation?

No, only that the statistical interpretation is incomplete since one cannot infer measurable physical properties of single systems without having a postulate that relates these measurable properties to the state.

 

[A. Neumaier]

How good my description of the preparation in terms of the quantum formalism is, is of course itself subject to experimental test.

Then - like in classical mechanics - the state is an objective property that is matched more or less well by your knowledge. Therefore - like in classical mechanics - you should not talk about knowledge (which is manifestly subjective), since there must be a knower.

So, how do you describe the SG experiment (or the experiments by Haroche and Wineland describe in the Nobel foundation's citations)?

You can read my book to find out. I said it here already many times, without getting it across to you, and won't do it again.

The SG experiment is very well understood [...]So where is the problem?

The problem is that instead of answering my questions you are shifting grounds.

I am not talking about the SG experiment, which is done with n ensemble of many identically prepared systems, so that the minimal interpretation applies.

The Nobel prize winning experiment was instead for measuring a single ion in a trap! You did not explain why

when you measure the pointer position you actually measured the state of the trapped ion, because of entanglement. This is pure handwaving since it is neither in your postulates nor is it derived from them in your lecture notes (version of July 22, 2019), as far as I can see. If I missed the derivation of such a fundamental claim, please point me to the relevant page.

 

[martinbn]

They interpret a single time series as giving evidence of temporal properties of the single ion. No ensemble of ions is involved. This is the whole point of probing individual quantum systems. Being able to control and read the state of a single quantum object is the prerequisite of quantum computing.

Yes, that is a valid interpretation, but is different from the statistical one. And it is not the only possible one.

No, only that the statistical interpretation is incomplete since one cannot infer measurable physical properties of single systems without having a postulate that relates these measurable properties to the state.

But that is something that people insist on. Nature doesn't have to be like that. It could be the way the statistical intepretation descibes it, and questions about the individual system may be meaningless.

 

[A. Neumaier]

It could be the way the statistical interpretation describes it, and questions about the individual system may be meaningless.

The 2012 Nobel prize shows that questions about the individual system are not meaningless but can be probed - sometimes even returning a high prestige and cash value.

 

[martinbn]

The 2012 Nobel prize shows that questions about the individual system are not meaningless but can be probed - sometimes even returning a high prestige and cash value.

How?

 

[A. Neumaier]

How?

The prestige and cash value of a Nobel price is well-known. For the probing of individual systems read this:

the description of the Nobelist's work by the Academy:

https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2012_02.pdf

From the introduction there:

Individual ions can now be manipulated and observed in situ by using photons with only minimal interaction with the environment. In another type of experiment, photons can be trapped in a cavity and manipulated. They can be observed without being destroyed through interactions with atoms in cleverly designed experiments. These techniques have led to pioneering studies that test the basis of quantum mechanics and the transition between the microscopic and macroscopic worlds, not only in thought experiments but in reality. They have advanced the field of quantum computing, as well as led to a new generation of high-precision optical clocks.

 

[martinbn]

The prestige and cash value of a Nobel price is well-known. For the probing of individual systems read this:

From the introduction there:

I still don't get it. Yes, it is phrased using that language, but so is most of QT in a typical text. Are you saying that it cannot be phrased in a statistical intepretation terminology?

 

[A. Neumaier]

I still don't get it. Yes, it is phrased using that language, but so is most of QT in a typical text. Are you saying that it cannot be phrased in a statistical interpretation terminology?

It can be phrased in the language of quantum stochastic processes but not in the language of the minimal statistical interpretation, which has not enough concepts to handle the continuous measurement of individual quantum systems.

 

[martinbn]

It can be phrased in the language of quantum stochastic processes but not in the language of the minimal statistical interpretation, which has not enough concepts to handle the continuous measurement of individual quantum systems.

The minimal statistical interpretation doesn't handle any induvidual systems irrespectively whether there is a continuous measurment or not. What makes this different? Can you easlily describe the actual experiments that cannot be analysed in the statistical interpretation language?

 

[gentzen]

What makes this different?

The meaning of the state is the difference. If the state is only the description of an ensemble of independent identically prepared system, then the state is not able to describe details of an individual system that go beyond what you be true for any identically prepared system.

Can you easlily describe the actual experiments that cannot be analysed in the statistical interpretation language?

Well, an idea could be to distinguish between the state and what you want to assert about the state. Then you could let the unknown state be the description of the individual system, and determine what you can or cannot assert about it based on what you learn from your measurements.

 

[A. Neumaier]

What makes this different? Can you easily describe the actual experiments that cannot be analysed in the statistical interpretation language?

I had said it several times: The fact that only a single ion is observed a large number of times in sequence. A single ion cannot be discussed in a pure ensemble language.

 

[martinbn]

The meaning of the state is the difference. If the state is only the description of an ensemble of independent identically prepared system, then the state is not able to describe details of an individual system that go beyond what you be true for any identically prepared system.

How is that different from any other type of measurment?

Well, an idea could be to distinguish between the state and what you want to assert about the state. Then you could let the unknown state be the description of the individual system, and determine what you can or cannot assert about it based on what you learn from your measurements.

I was asking specifically about the 2012 nobel prize work.

 

[martinbn]

I had said it several times: The fact that only a single ion is observed a large number of times in sequence. A single ion cannot be discussed in a pure ensemble language.

So, you are saying that the statistical interpretation cannot discuss repeated measearments? I disagree.

 

[A. Neumaier]

So, you are saying that the statistical interpretation cannot discuss repeated measurements? I disagree.

No. The statistical interpretation cannot discuss measurements on only a single atom - the same in all measurements. Of course it can discuss repeated measurements on a large ensemble of atoms.

 

[martinbn]

No. The statistical interpretation cannot discuss measurements on only a single atom - the same in all measurements. Of course it can discuss repeated measurements on a large ensemble of atoms.

That's what I meant by repeated measurments. One atom measured more than ones in succession. Say you pass it through a SG and then through another one. Why should this be impossible for the statistical interpretation to handle and why do you need anything more compliated than this, like 2012 nobel, for you to make your point?

 

[gentzen]

I was asking specifically about the 2012 nobel prize work.

The relation to the 2012 nobel prize work is the focus on individual ions or photons:

Individual ions can now be manipulated ... In another type of experiment, photons can be trapped in a cavity and manipulated ...

OK, not sure whether they really mean an individual photon (because they write "photons"), but they definitively mean an individual ion. If they repeat their experiment many times with different individual ions, then they can also use the minimal statistical interpretation, at least if they don't make assertions about the state of individual ions in their experiments.

 

[A. Neumaier]

That's what I meant by repeated measurements. One atom measured more than ones in succession. Say you pass it through a SG and then through another one. Why should this be impossible for the statistical interpretation to handle?

How do you handle it with the minimal statistical interpretation? The latter is only about ensembles, not about individuals!

If they repeat their experiment many times with different individual ions, then they can also use the minimal statistical interpretation, at least if they don't make assertions about the state of individual ions in their experiments.

But instead they repeat their measurements many times on the same ion. Thus they cannot use the minimal statistical interpretation.

 

[*now*]

A fresher foundational look at an old link from btsm might add some thoughts around the topic [gr-qc/0306059] A simple background-independent hamiltonian quantum model (arxiv.org)

 

[PeterDonis]

That's what I meant by repeated measurments. One atom measured more than ones in succession.

That's not what the statistical interpretation is talking about. It is talking about making one measurement on each of a large ensemble of identical systems prepared by the same preparation procedure. It is not talking about making many measurements on a single system which is only prepared once (and then measured many times in succession). Those are two different things and one cannot be substituted for the other.

 

[vanhees71]

They interpret a single time series as giving evidence of temporal properties of the single ion. No ensemble of ions is involved. This is the whole point of probing individual quantum systems. Being able to control and read the state of a single quantum object is the prerequisite of quantum computing.No, only that the statistical interpretation is incomplete since one cannot infer measurable physical properties of single systems without having a postulate that relates these measurable properties to the state.

No, there's no ensemble of ions involved but an ensemble of photons. You can use a single quantum system and repeat your experiment using this single quantum system a lot of times. That's simply done by using a laser field to excite one and the same ion again and again and observe the emitted photons from the deexcitation giving the pattern depicted in the Nobel paper.

The statistical meaning of quantum states is to the best of our knowledge not incomplete, because there's no hint that the described randomness is not a feature of Nature. In other words there's no hint that one needs hidden variables and determinism to describe the phenomena.