Statistical ensemble interpretation done right

[gentzen]

No. The system defines the observables I can measure on it.

That is just playing with words. What defines what you consider to be the system? Good, you may prefer the word "the system" over my "The degrees of freedom and the Hilbert space you choose", but in the end you have chosen what you consider to be your system.

 

[Haborix]

It is unclear to me what you mean. (Are you a Bayesian or a Dutch bookie from those Dutch book arguments?)

If you look at SEI from an operational verification perspective, then yes, you must associate a single system with a state before you know the results of the non-preparation measurements. This allows it to take part in some verification. Of course, no statistical verification can ever fully reject your state assignments, at most it can tell you that winning the jackpot of a lottery would have been more probable than your obtained measurement results given your previous state assignments.

The "my" should have been the royal "our." I didn't mean anything technical by bookkeeping. It was my first try at getting at the different states you might think about as you go about the preparation procedure and eventual experiments. How each of the preparation procedure and experimental measurements would change the knowledge of the state. I think I made too much of the use of the word "associate" when I initially commented, or at least I latched onto it as a bad proxy for what I was trying to get at.

 

[vanhees71]

The system is what I'm investigating, e.g., an electron.

In non-relativistic physics the observable algebra of an electron is generated by the position, momentum and the spin observables, $\vec{x}$, $\vec{p}$, and $\vec{s}$. Each of these observables is represented by an essentially self-adjoint operator $\hat{\vec{x}}$, $\hat{\vec{p}}$, and $\hat{\vec{s}}$. The Hilbert space can be represented by Pauli-spinor valued wave functions, $\psi_{\sigma}(\vec{x})$, choosing the set $\vec{x}$ and $s_z$ as a complete minimal set of compatible observables, defining a (generalized) basis $|\vec{x},\sigma \rangle$. For $|\psi \rangle$ then you have the wave function $\psi_{\sigma}(\vec{x}) = \langle \vec{x},\sigma|\psi \rangle$. The scalar product is defined as
$$\langle \psi_1|\psi_2 \rangle=\int_{\mathbb{R}^3} \sum_{\sigma=\pm 1/2} \psi_{1 \sigma}^*(\vec{x}) \psi_{2 \sigma}(x).$$

A state of the electron, i.e., a preparation procedure, is described by a statistical operator $\hat{\rho}$, which is a positive semidefinite operator obeying $\mathrm{Tr} \hat{\rho}=1$. Having prepared the system in this state, you can measure any observable $A$, represented by a self-adjoint operator $\hat{A}=\hat{A}(\hat{\vec{x}},\hat{\vec{p}},\hat{\vec{s}})$, which defines a (generalized) complete orthonormal set of eigen vectors $|a,\alpha \rangle$. The possible values the observable can take are the eigenvalues $a$, and $\alpha$ labels the orthornomal vectors spanning the subspace of eigenvectors of this eigenvalue.

In the minimal statistical interpretation the meaning of the system being prepared in the state $\hat{\rho}$ is (exclusively!) that the probability (density) for finding the value $a$, when measuring $A$ is given by
$$P(a|\hat{\rho})=\sum_{\alpha} \langle a,\alpha|\hat{\rho}|a,\alpha \rangle,$$
where the sum over $\alpha$ can also contain integrals if there are continuous parts in the parameters written as $\alpha$. You can think of $\alpha$ given by the common eigenvalues making $\hat{A}$ and some other observables $\hat{A}_k$ ($k \in \{1,2,3\}$) with eigenvalues $\alpha=(\alpha_1,\ldots,\alpha_{3})$ a complete set of independent compatible observables.

Since these probabilities can only be experimentally verified by preparing a large ensemble of electrons, each being prepared in the state $\hat{\rho}$ through a corresponding appropriate preparation procedure, concerning the outcome of measurements on an arbitrary observable, the state only describes such an ensemble. For the single electron prepared in this state the observable $A$ only takes a determined value if there is one eigenvalue $a_0$ of $\hat{A}$ for which $P(a_0|\hat{\rho})=1$, which implies that $P(a|\hat{\rho})=0$ for all eigenvalues $a \neq a_0$ of $\hat{A}$.

Last but not least it should be clear that a generalized eigenvector for an "eigenvalue" in the continuous part of the spectrum, is not normalizable and thus there's no state (preparation), for which the observable can take this determined value.

 

[vanhees71]

It's probably written somewhere in a way I would be satisfied, but I don't know where exactly. In any case, I wanted to write it by myself, in a way I would like someone explained it to me.

Maybe

A. Peres, Quantum Theory: Concepts and Methods, Kluwer
Academic Publishers, New York, Boston, Dordrecht, London,
Moscow (2002).

 

[martinbn]

Can you be more explicit, what exactly do I deny? In the first post I wrote about several versions of SEI, is there a possibility that I didn't mention there?

You said that if the preparation procedure is known, then the state is associated with the individual system. If the preparation procedure is not known, then you need many systems to be able to figure out what the sate is. So for you the ensemble interpretation associates a state to an ensemble only because of lack of knowledge. You do not list the possibility that the preparation is fully known and yet the ensemble is in the corresponding state not each member. You also seem to think of the ensemble in a very practical way and not the abstract equivalence class of systems.

 

[Morbert]

Let us consider a classical analogy, in which preparation is a coin flipping. The flipping prepares the state
$$S=[p({\rm heads})=1/2,p({\rm tails})=1/2]$$
where $p$ is the probability. What is the distinction between the following claims?
1. We consider an ensemble of coins, each prepared in the state $S$.
2. We consider an ensemble $S$ of similarly prepared coins.
3. We consider a class of preparation procedures $S$.

Only 2. frames the state as an ensemble of similarly prepared systems. I do not see this framing in 1. or 3.

 

[PeterDonis]

So for you the ensemble interpretation associates a state to an ensemble only because of lack of knowledge. You do not list the possibility that the preparation is fully known and yet the ensemble is in the corresponding state not each member.

Also not included is that in order to test the predictions of the theory, you need to make the same measurement on a large number of similarly prepared systems, because the theory predicts probabilities. That is how Ballentine justifies thinking of the state as referring to an ensemble (but note that this is an addition to what he calls the primary meaning of the state, which is that it describes the probabilities of measurement results associated with a given preparation procedure).

 

[gentzen]

The system is what I'm investigating, e.g., an electron.

You are just switching the focus to the next word. Now you prefer your "what I'm investigating" over my "what you intent to measure":

The degrees of freedom and the Hilbert space you choose to describe them says something about what you intent to measure on the system.

Or maybe you are unhappy because I also used the word "system" in that sentence.

But in the end, this is a fight over words, or perhaps about "how to talk about that stuff". It seems mostly unrelated to the physics.

In non-relativistic physics the observable algebra of an electron is generated by the position, momentum and the spin observables, ...

Not sure whether talking about physics is helpful at that point.

 

[Demystifier]

Only 2. frames the state as an ensemble of similarly prepared systems. I do not see this framing in 1. or 3.

But the difference is only in rhetoric, I don't see any substantial physical difference, at least in the classical case. Do you see a substantial physical difference? Or maybe, as an adherent of consistent histories, you see framing, i.e. rhetoric, as physical?

 

[PeterDonis]

I don't see any substantial physical difference, at least in the classical case.

Since we're talking about QM here, the classical case is irrelevant.

Do you see a substantial physical difference?

We are talking about interpretations of QM, which is a model, not reality. If there were a physical difference involved at all here, it would mean we would have different "interpretations" making different predictions for experimental results, which would make them not different interpretations of QM, but different theories.

In other words, the whole concept of an interpretation "done right", which is the phrase you chose in the title of this thread, cannot involve any physical difference; it is purely a matter of personal preference and opinion. Or "rhetoric", if you want to call it that. (The guidelines for this subforum explicitly recognize this.)

 

[Demystifier]

You said that if the preparation procedure is known, then the state is associated with the individual system. If the preparation procedure is not known, then you need many systems to be able to figure out what the sate is. So for you the ensemble interpretation associates a state to an ensemble only because of lack of knowledge. You do not list the possibility that the preparation is fully known and yet the ensemble is in the corresponding state not each member. You also seem to think of the ensemble in a very practical way and not the abstract equivalence class of systems.

Yes, you summarized it very well. I see SEI as a rather practical approach, it always seemed to me that SEI is an attempt to formulate QM with a minimal amount of philosophy. Now I am becoming aware that not everybody sees SEI that way.

 

[Demystifier]

Since we're talking about QM here, the classical case is irrelevant.

It's relevant, if we want to understand how exactly statistical aspects of QM differ from statistical aspects of classical physics. In my opinion, the former cannot be understood correctly before first understanding the latter.

We are talking about interpretations of QM, which is a model, not reality. If there were a physical difference involved at all here, it would mean we would have different "interpretations" making different predictions for experimental results, which would make them not different interpretations of QM, but different theories.

In the context of quantum interpretations, the word "physical" has a wider meaning than that. By "physical", realists often mean ontological, qbists often mean informational, and consistent-historians perhaps often mean something related to framing.

In other words, the whole concept of an interpretation "done right", which is the phrase you chose in the title of this thread, cannot involve any physical difference; it is purely a matter of personal preference and opinion. (The guidelines for this subforum explicitly recognize this.)

In the first post of this thread, my intention was to clearly separate the non-controversial parts of SEI, from its philosophical/interpretational controversial parts. Both parts need to be discussed, but in such a discussion one needs to be aware which is which, that's what I meant by "done right". It was not my intention to say which philosophical/interpretational version of SEI is "right".

 

[PeterDonis]

I see SEI as a rather practical approach, it always seemed to me that SEI is an attempt to formulate QM with a minimal amount of philosophy. Now I am becoming aware that not everybody sees SEI that way.

I think Ballentine does see his formulation of SEI that way. He explicitly links the interpretation directly to the practical fact that QM predicts probabilities and the only way to test those predictions is to run the same experiment on a large number of similarly prepared systems so you can do statistics. The reason he defines an ensemble using an abstraction is that the ensemble is a thing in the model, not reality: an ensemble as he defines it is part of the theoretical framework we use to make predictions, not the experimental framework we use to test them.

But apparently you don't agree with Ballentine's formulation or see it as he does. So I don't think there is even agreement on what "a minimal amount of philosophy" means.

 

[Demystifier]

But apparently you don't agree with Ballentine's formulation or see it as he does.

My impression (which could be wrong) is that my view of SEI is very similar to that of Ballentine, but that he sometimes uses wording that creates more confusion than clarity, so I tried to further simplify the explanation of SEI in a way which avoids confusion. Now it seems that I wasn't very successful in my intentions, but at least I tried.

 

[PeterDonis]

My impression (which could be wrong) is that my view of SEI is very similar to that of Ballentine

If that is the case, then I'm not sure why you had to ask this in your OP:

within SEI, does it make sense to say that we have one particle in the state $\ket{\psi}$?

Ballentine is quite clear that the answer to this is "no". I've already quoted several passages showing that.

he sometimes uses wording that creates more confusion than clarity

Some specific examples would help. The ones I gave, as I noted just now, seem to imply the opposite.

 

[Demystifier]

If that is the case, then I'm not sure why you had to ask this in your OP:

Ballentine is quite clear that the answer to this is "no". I've already quoted several passages showing that.

Some specific examples would help. The ones I gave, as I noted just now, seem to imply the opposite.

Here is one example. At page 207 of his book he writes:

"It is possible to prepare the lowest energy state of a system simply by waiting for the system to decay to its ground state."

He says "system", not "ensemble". To me, it looks as confirmation of my claim that in the case of known preparation he associates the state with a single system, not with an ensemble. But he is not perfectly clear and explicit about that, which I think creates confusion, so I wanted in this thread to make such things clear and explicit.

One should also have in mind what he says at page 46 (boldings are mine):

"The empirical content of a probability statement is revealed only in the
relative frequencies in a sequence of events that result from the same (or an
equivalent) state preparation procedure. Thus, although the primary definition of a state is the abstract set of probabilities for the various observables, it is also possible to associate a state with an ensemble of similarly prepared systems. However, it is important to remember that this ensemble is the conceptual infinite set of all such systems that may potentially result from the state preparation procedure, and not a concrete set of systems that coexist in space. In the example of the scattering experiment, the system is a single particle, and the ensemble is the conceptual set of replicas of one particle in its surroundings. The ensemble should not be confused with a beam of particles, which is another kind of (many-particle) system. Strictly speaking, the accelerating and collimating apparatus of the scattering experiment can be regarded as a preparation procedure for a one-particle state only if the density of the particle beam is so low that only one particle at a time is in flight between the accelerator and the detectors, and there are no correlations between successive particles."

Thus he makes clear that the ensemble interpretation of the state is not the only (in fact, not even the primary) interpretation of the state, and also that "system" is not the ensemble.

 

[Morbert]

But the difference is only in rhetoric, I don't see any substantial physical difference, at least in the classical case. Do you see a substantial physical difference? Or maybe, as an adherent of consistent histories, you see framing, i.e. rhetoric, as physical?

The difference would be the conceptualizations and intuitions invoked to reason about the single system. In all three statements, an ensemble is conceptualized, so they are quite similar, but only in 2. is this conceptualization insisted upon, in the sense that 1. and 3. imply we could discuss the state, divorced from the context of an ensemble. This is not necessarily a bad thing of course.

If by physical we mean real, there is no difference. What is real is the single system of interest.

As an aside: You could apply a statistical ensemble interpretation to the CH formalism. Given a set of histories, the probability of a history would be the relative frequency of that history in an ensemble of similarly prepared systems. Gell-Mann and Hartle went one step further and published an "extended probability ensemble decoherent histories" which embeds the real fine-grained history of a system in an ensemble of alternatives.

 

[Demystifier]

Gell-Mann and Hartle went one step further and published an "extended probability ensemble decoherent histories"

They lost me when they said that probability can be negative or larger than one.

 

[martinbn]

Yes, you summarized it very well. I see SEI as a rather practical approach, it always seemed to me that SEI is an attempt to formulate QM with a minimal amount of philosophy. Now I am becoming aware that not everybody sees SEI that way.

Then why did you start this thread?! You agreed with me, that you did not describe any interpretation of QM, and that what you wrote is not even specific to QM. So your view is that the ensemble interpretation is not really an interpretation of QM, it is just statistics. Now you have become aware that some people view the ensemble interpretation as an actual interprwtation!

 

[Demystifier]

Then why did you start this thread?!

See my post #47, the last paragraph. And also #49.

 

[martinbn]

Here is one example. At page 207 of his book he writes:

"It is possible to prepare the lowest energy state of a system simply by waiting for the system to decay to its ground state."

He says "system", not "ensemble". To me, it looks as confirmation of my claim that in the case of known preparation he associates the state with a single system, not with an ensemble. But he is not perfectly clear and explicit about that, which I think creates confusion, so I wanted in this thread to make such things clear and explicit.

He could have been more pedantic, but he probable thought it wouldnt cause a confusion.

One should also have in mind what he says at page 46 (boldings are mine):

"The empirical content of a probability statement is revealed only in the
relative frequencies in a sequence of events that result from the same (or an
equivalent) state preparation procedure. Thus, although the primary definition of a state is the abstract set of probabilities for the various observables, it is also possible to associate a state with an ensemble of similarly prepared systems. However, it is important to remember that this ensemble is the conceptual infinite set of all such systems that may potentially result from the state preparation procedure, and not a concrete set of systems that coexist in space. In the example of the scattering experiment, the system is a single particle, and the ensemble is the conceptual set of replicas of one particle in its surroundings. The ensemble should not be confused with a beam of particles, which is another kind of (many-particle) system. Strictly speaking, the accelerating and collimating apparatus of the scattering experiment can be regarded as a preparation procedure for a one-particle state only if the density of the particle beam is so low that only one particle at a time is in flight between the accelerator and the detectors, and there are no correlations between successive particles."

Thus he makes clear that the ensemble interpretation of the state is not the only (in fact, not even the primary) interpretation of the state, and also that "system" is not the ensemble.

Exactly! This show the difference between your view and his.

 

[martinbn]

See my post #47, the last paragraph. And also #49.

Yes, you say that, but it seems that you were cometely unaware of the interpretation itself!

 

[Demystifier]

Exactly! This show the difference between your view and his.

How? I see this as a confirmation that his view agrees with mine.

 

[vanhees71]

You are just switching the focus to the next word. Now you prefer your "what I'm investigating" over my "what you intent to measure":

By "investigating" I meant of course "doing an experiment".

Or maybe you are unhappy because I also used the word "system" in that sentence.

I'm unhappy about your formulation

The degrees of freedom and the Hilbert space you choose to describe them says something about what you intent to measure on the system.

because it seems to state a very common misconception about quantum mechanics. It seems as if you have an interpretation of the Heisenberg uncertainty relations in mind as if it would prevent from meausring the one or the other observable with arbitrary precision. This is, however, in no way what's implied by the uncertainty relation. I can always measure any observable of a system with as high a precision I want, and I'm not in any way restricted in the ability to choose to measure any observable of the system I like due to the state preparation.

The uncertainty relation also does not say anything about the disturbance of the system by measurement. It can't, because it's a fundamental principle derived without any reference to a specific measurement procedure, and how the system is disturbed by the interaction with the measurement apparatus of course depends on the specific device.

But in the end, this is a fight over words, or perhaps about "how to talk about that stuff". It seems mostly unrelated to the physics.

The above is of utmost significance for the correct interpretation of the formalism, and it doesn't in any way depend on the specific interpretation you prefer. It's one of the objective scientific properties of the theory.

 

[PeterDonis]

He says "system", not "ensemble". To me, it looks as confirmation of my claim that in the case of known preparation he associates the state with a single system

No, he associates the state with the preparation procedure that was used, exactly as he said in what you quoted from his p. 46. He uses "system" to refer to the thingie that comes out of the preparation procedure, precisely in order to distinguish that thingie from the preparation procedure and the abstract ensemble that results from it, which are what he says on p. 46 that the state describes.

Thus he makes clear that the ensemble interpretation of the state is not the only (in fact, not even the primary) interpretation of the state

I don't think so. See above.

 

[Morbert]

But in both cases, the "state as an ensemble" will be tested by a series of individual measurements events, that cannot be reduced nor averaged.

"equivalence class of preparations" is quite vague, as it cannot be equivalent as defined by QM itself (no cloning). Either way that ensemble is the most non-local thing there is in physics.

There's no issue with cloning. We can sketch a theory of a preparation procedure to better understand its meaning by extending our theory to include laboratory degrees of freedom. Consider a microscopic system $s$ in a lab $L$, and a desired quantum state $\rho_s(t_0)$. A preparation procedure $P$ is characterised by $$P:= (\rho_{s+L}(t_{-1}), \{C_i\})$$ such that $$\rho_s(t_0) = \frac{\mathrm{tr}_L C_i \rho_{s+L}(t_{-1})C^\dagger_i}{\mathrm{tr}_{s+L}C_i \rho_{s+L}(t_{-1})C^\dagger_i}$$where $\rho_{s+L}(t_{-1})$ is an earlier state of the system + lab and $\{C_i\}$ is an appropriate set of operators. And when we say the state represents a class of procedures, we mean there are many such $P$ that would satisfy the above desired $\rho_s(t_0)$.

Of course, if we extend our theory to include lab degrees of freedom, it can lead to some peculiar interpretations. The preparation can be associated with a POVM on the lab. Or we might consider an infinite ensemble of similarly prepared labs, of which a subensemble is associated with $\rho_s$. Some interpretations might even reject such a macroscopic application of Lueder's rule.

 

[vanhees71]

The latter idea may be expensive. Fortunately we don't need a million CERNs all doing once the same scattering experiments. It's fine to have one CERN and using its equipment to perform a million pp collisions ;-)).

 

[Morbert]

But by reading the many interpretation (of SEI flavors) explained by many people here, I am still looking for at least once factual problem that it addresses (except maybe the strong embedded denial that could help someone sleep at night), or only the vaguest way that map would relate to the territory.

Ballentine argues that it eliminates assumptions that i) play no role in the application of quantum theory, and ii) lead to conceptual difficulties with measurement processes.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

After some cleanup, the thread is reopened.

 

[gentzen]

Or maybe you are unhappy because I also used the word "system" in that sentence.

I'm unhappy about your formulation

The degrees of freedom and the Hilbert space you choose to describe them says something about what you intent to measure on the system.

because it seems to state a very common misconception about quantum mechanics. It seems as if you have an interpretation of the Heisenberg uncertainty relations in mind as if it would prevent from meausring the one or the other observable with arbitrary precision. This is, however, in no way what's implied by the uncertainty relation. I can always measure any observable of a system with as high a precision I want, and I'm not in any way restricted in the ability to choose to measure any observable of the system I like due to the state preparation.

On rereading this, I see again why I didn't know how to respond. One thing I could do is to explain the concrete example I had in mind:
When you describe a Stern-Gerlach experiment, your magnet may be described as fixed such that the magnetic field (except for its inhomogenity) points in z-direction, or you may describe it such that the magnet can be rotated around the particle beam. In the second case, you probably need to allow density matrices to describe the actual state of the incoming particles. But most introductory QM textbooks have not yet introduced density matrices at the point where they describe and analyse SG, so they typically go with the description using a fixed magnet. Independent of this, the silver atoms have more degrees of freedom in their quantum state than just the spin of the unpaired electron in the outer shell. But we won't describe those in our Hilbert-space for analyzing SG, because we don't intent to measure anything for which they would be relevant.
Another thing I could do is to explain why I participated in this unhappy discussion at all:
Morbert tried to explain some distinctions, and because we both have some "background" in the consistent histories interpretation, I thought I could help. Or at least, I didn't want to distance myself (more than I already did here and here) from that interpretation by staying silent.

The uncertainty relation also does not say anything about the disturbance of the system by measurement. It can't, because it's a fundamental principle derived without any reference to a specific measurement procedure, and how the system is disturbed by the interaction with the measurement apparatus of course depends on the specific device.

This was the actual reason why I still wanted to respond, because here you highlight a specific misconception of Heisenberg from his paper "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". I noticed that I never asked you whether you have any concrete papers (like the one above or his Solvay paper with Born) or books (like "Physics and Philosophy" or "Physics and Beyond") in mind when you say that Heisenberg is responsible for much of the confusion about QM. Here is a summary of some of his works, maybe it simplifies your "selection process":
https://www.informationphilosopher.com/solutions/scientists/heisenberg/

My own interpretation what you dislike about Heisenberg was his focus on the role of the observer (to which I can agree to the extent that it neglects the role of preparation and control), and also quite general his passion for philosophy.

 

[vanhees71]

On rereading this, I see again why I didn't know how to respond. One thing I could do is to explain the concrete example I had in mind:
When you describe a Stern-Gerlach experiment, your magnet may be described as fixed such that the magnetic field (except for its inhomogenity) points in z-direction, or you may describe it such that the magnet can be rotated around the particle beam. In the second case, you probably need to allow density matrices to describe the actual state of the incoming particles. But most introductory QM textbooks have not yet introduced density matrices at the point where they describe and analyse SG, so they typically go with the description using a fixed magnet. Independent of this, the silver atoms have more degrees of freedom in their quantum state than just the spin of the unpaired electron in the outer shell. But we won't describe those in our Hilbert-space for analyzing SG, because we don't intent to measure anything for which they would be relevant.

Once more, this is a misconception of the quantum state. The quantum state of the system you want to observe has nothing to do with the measurement device but with the preparation of this system. E.g., in the original Stern-Gerlach experiment the Ag atoms were prepared by letting Ag vapor stream out of a small hole in an oven. Indeed, this preparation procedure is described by a corresponding mixed state of Ag atoms.

You can direct your magnet independent of how you prepare the Ag atoms and thus you can measure its spin component in any direction given by the magnetic field you like. The state in this specific experiment indeed has to be described by a Ag-atom beam, prepared in a mixed state, no matter whether you fix the field in one direction or another.

Another thing I could do is to explain why I participated in this unhappy discussion at all:
Morbert tried to explain some distinctions, and because we both have some "background" in the consistent histories interpretation, I thought I could help. Or at least, I didn't want to distance myself (more than I already did here and here) from that interpretation by staying silent.

I don't know enough about the consistent-history interpretation to comment on this. I've once read about it and didn't find it in any way convincing compared to the minimal statistical interpretation, which reflects how QT is used in the physics community when discussing real-world experiments and not some philsophical isms...

This was the actual reason why I still wanted to respond, because here you highlight a specific misconception of Heisenberg from his paper "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". I noticed that I never asked you whether you have any concrete papers (like the one above or his Solvay paper with Born) or books (like "Physics and Philosophy" or "Physics and Beyond") in mind when you say that Heisenberg is responsible for much of the confusion about QM. Here is a summary of some of his works, maybe it simplifies your "selection process":
https://www.informationphilosopher.com/solutions/scientists/heisenberg/

For me Heisenberg and Bohr wrote the most incomprehensible papers compared to the other "founding fathers" of QT. Particularly matrix mechanics has been worked out by Born and Jordan in crystal-clear mathematical form, quickly followed by Pauli's derivation of the hydrogen spectrum using matrix mechanics. These authors are a much better read than Heisenberg and Bohr if you like to investigate the early development of this branch of the first discovery of modern quantum theory. This also includes the famous 2nd part, the "Dreimännerarbeit", written together by Born, Jordan, and Heisenberg. Heisenberg had ingenious ideas but always needed translators to clarify his insights for the normal physicist. This usually were Born and Jordan but also very much Pauli.

The most underrated of all these was Born, who was really the one recognizing the mathematics behind Heisenberg's weird Helgoland paper, which reflects the discovery process of the Göttingen group pretty nicely. Also see

https://arxiv.org/abs/2306.00842
https://doi.org/10.1140/epjh/s13129-023-00056-1

My own interpretation what you dislike about Heisenberg was his focus on the role of the observer (to which I can agree to the extent that it neglects the role of preparation and control), and also quite general his passion for philosophy.

What I dislike is his nebulous writing and overemphasizing philosophy over physics. He also had many misconceptions, which for some reason unfortunately still stuck in modern textbooks (although they don't play much of a role anymore in contemporary research), e.g., his first paper about the meaning of the uncertainty relation, which he first published claiming it were about the disturbance of the system by interaction with the measurement device, which leads to the misconception discussed in the first part of this posting. This was corrected immediately thereafter by Bohr, who was even more nebulous in his writing but often had the better physical instinct.

The disturbance of the system by measurement is of course also an important point following from the atomistic structure of matter. E.g., you cannot have an arbitrary small "test charge" to measure an electromagnetic field. You need at least one particle with 1e charge to probe the field, which inevitably disturbs it on these "microscopic scales". To describe this is much more complicated an after all can only be done for specific experimental setups analyzing the dynamics of the measurement process under investigation.

 

[Fra]

My own interpretation what you dislike about Heisenberg was his focus on the role of the observer (to which I can agree to the extent that it neglects the role of preparation and control)

As far as I recall reading som the historical descriptions, there was a early internal tension in the Copenhagen group, where Heisenberg focused more on the individual "observer", but while Bohr suggested that it's all of the classical reality taken together, that is the foundation for preparation, control and observeation. This doesn't mean Heisenberg was wrong and Bohr was right, as I understand it both views were unified because the internal communication within the classical domain is "trivial" as information can be copied/shared at least in principle, and that all different classical observes supposedly will AGREE on what actual records are. So Bohr and Heisenbergs views was consistent. (The dispersion of observations within classical world, is that due to special relativity, which of course wasnt what Bohr worried about, but to the extent QFT solves this, the conceptual idea of CI still holds).

So as I see it the idea is that the macroscopic measurement device is always "in tune" with the information implicit in the preparation and control of the source; as well as any prior information from process tomograpghy to determine hamiltonians etc. Changing of a dial at the detector, does not change the preparation. In this case the observer is always in principle "informed" about the preparation - via the classical communication channels. There is nothing that prevents this. Any issue between difference classical measurement devices are if nothing is wrong, supposed to be resolved by the state transformation of SR.

This is all conceptually fine, as long as we have the classical background spacetime and macrocsopic reality to back this up. I think of the "statistical interpretaion" as beeing litteraly processed and encoded in the macroscopic environment as well. So for me, the statistical interpretation are not really at face with CI. I think they get alon fine. The statistcal information, is the "knowledge of the obsever", and it is encoded in the macroscopic environment?

/Fredrik

 

[PeterDonis]

this preparation procedure is described by a corresponding mixed state of Ag atoms

Not really, since, as @gentzen correctly pointed out, the usual description only includes the outermost electron of the Ag atoms and leaves out the other degrees of freedom. So really the usual description of the state is a mixed state of qubits. (I say "qubits" instead of electrons because the description does make use of the fact that the Ag atoms are electrically neutral so there is no Lorentz force term in the Hamiltonian describing the interaction with the SG magnets, and therefore the only relevant interaction is the magnetic coupling to the spin-1/2 degree of freedom; for actual electrons that would not be the case.)

 

[lodbrok]

The system is what I'm investigating, e.g., an electron.

Is the system "an electron" or "an ensemble of similarly prepared electrons"? Whether you use a single CERN or one million CERNS, do the results of the measurements tell you about "an electron" or "an ensemble of similarly prepared electrons." (or preparation procedure).