Teaching and understanding of quantum interpretations in modern physics courses

[ZapperZ]

It took me a while to finish reading http://prst-per.aps.org/abstract/PRSTPER/v6/i1/e010101" {you can get free access to the paper}, and I still don't have a clear idea of it rather than the conclusion that stated that if the instructor doesn't make any explicit discussion on the interpretation of QM, the student will tend to adopt a realist approach.

Abstract: Just as expert physicists vary in their personal stances on interpretation in quantum mechanics, instructors vary on whether and how to teach interpretations of quantum phenomena in introductory modern physics courses. In this paper, we document variations in instructional approaches with respect to interpretation in two similar modern physics courses recently taught at the University of Colorado, and examine associated impacts on student perspectives regarding quantum physics. We find students are more likely to prefer realist interpretations of quantum-mechanical systems when instructors are less explicit in addressing student ontologies. We also observe contextual variations in student beliefs about quantum systems, indicating that instructors who choose to address questions of ontology in quantum mechanics should do so explicitly across a range of topics.

Most of us here who have physics degrees would have gone through a course like this. So this could easily be an arena for an unscientific poll. Were you introduced to a specific interpretation of QM when you were first introduced to it? How did it affect your interpretation of it then, and now? If you are an instructor, or were once, what was your approach on this? Did you explicitly invoke a particular interpretation?

Zz.

 

[Norman]

I read the first couple of pages of the article - not a lot of time at the moment - but, I don't think after a single modern physics course it is meaningful to even ask a student how to interpret quantum mechanics (or am I missing the point?). Maybe my modern physics class was not up to par (and it was about 10 years ago that I took it), but we just worried about understanding how to use Schrodinger's equation. I mean we only spent 6 weeks on QM in my modern physics class. I know that 6 weeks was not enough for me to even start thinking properly about interpretations of QM. I don't think there was even a mention of interpretations in the class. There might have been some statement about the wave function only containing information (I say this last part simply because I know the instructor of the class fairly well and he is a realist in his interpretation of QM).

But, for my 2 semesters of QM in undergrad (not the modern physics course, but an intro to QM course), I do know we stuck explicitly to the Copenhagen Interpretation of QM. I actually asked the professor about it a few years later and he explained that he did not want to have the students worrying about interpretations when they should be worried about solving problems and getting familiar with the "weirdness" of QM compared to classical physics.

I agree with his analysis, that at the undergrad level you should probably stick with the Copenhagen Interpretation since I think it allows the student to develop the machinery needed to delve into QM more deeply in grad school when one is a little more comfortable with the quantum world. As far as my opinion of the interpretations now, I am fairly agnostic with my default interpretation being a realist one. As far as I am concerned, what matters is physical observables and if my calculation matches experiment or not. Unless a certain interpretation of QM effects the results of my calculation, I am not too worried about which one is right. I will leave those considerations to someone with a lot more time on their hands then I have.

 

[physics girl phd]

Via a quick read (given that my little infant E is in the office with me):

I think what probably lacks notice in the article's analysis is that, even BEFORE a QM course is taken, a student is likely exposed to views such as that expressed by "realist" student 1 on pg 7 (the electron is a tiny particle inside the probability "blob").

Where? Try any high school chemistry class that introduces s,p,d,and f orbitals (and note that in most school systems, a college-prep chemistry course precedes the college prep physics). Typically the orbitals are introduced as probability densities for the location of the electron, not as a "blob" representing the electron itself unit the measurement of it's position is made (as student 2 on pg seven, who holds the "quantum" view would likely say for this simple problem).

Again, note all the education research that says how hard it is to change the students preexisting views -- particularly if those preexisting views aren't appropriately confronted... so I'm not surprised at their conclusion.

For your poll positions:
1) In high school chem, I was introduced to a realist view. Probably was not until my first "junior-level" QM course (I didn't have a "modern physics" course because it was not-required for the degree and considered "holding ground" before QM and EM) where I was met with the "quantum" view... which I most certainly was, but I think my QM professor for that course sequence was simply a fabulous instructor in the subject, and most certainly included interpretive discussions as well as teaching us the general tools of solving quantum problems, though of course this was pre-powerpoint days (so one can't count how many slides he used).

2) As a lecturer I get the lower level courses... so I've never taught our intermediate QM course, but I can say that as a high school chem and physics teacher (years ago) I probably used the realist view. I will have to take special note this term in how I treat the subject in our conceptual "How Things Work" class... though it isn't really until the end where we possibly confront this, spending much more time on light and optics, and simple nuclear physics rather than on matter waves.

 

[ZapperZ]

Via a quick read (given that my little infant E is in the office with me):

I think what probably lacks notice in the article's analysis is that, even BEFORE a QM course is taken, a student is likely exposed to views such as that expressed by "realist" student 1 on pg 7 (the electron is a tiny particle inside the probability "blob").

Where? Try any high school chemistry class that introduces s,p,d,and f orbitals (and note that in most school systems, a college-prep chemistry course precedes the college prep physics). Typically the orbitals are introduced as probability densities for the location of the electron, not as a "blob" representing the electron itself unit the measurement of it's position is made (as student 2 on pg seven, who holds the "quantum" view would likely say for this simple problem).

Ah, that's an excellent point that I completely missed! It would be nice if this was looked at at the very beginning.

Zz.

 

[jtbell]

It's been so long ago, about 35 years, since I took my sophomore-level "intro modern physics course" that I don't remember much about it, except the book: Wehr, Richards and Adair, with a picture of bubble-chamber tracks on the cover. I doubt that we discussed interpretations at all, leaving us each to form our own mental pictures as to what an electron in the hydrogen atom is "really doing."

I've now taught that sort of course many times, and my treatment has evolved somewhat as I've learned more about interpretational issues. I warn students against taking the circular orbits of the Bohr model seriously, in fact, I don't even discuss them in detail the way most textbooks do; I focus on the energy levels, and "derive" them from the Balmer-Rydberg formula for the hydrogen spectrum.

Then when we get to the Schrödinger equation and probabilistic QM, I tell students that QM predicts the outcomes of measurements, but does not address the question of what is "really happening," in detail, before the measurements occur. I say that different groups of physicists have different opinions on the matter and briefly list some of the most common interpretations so students can Google for them if they want. I emphasize that that there is no experimental way to choose between many of these interpretations.

When I have time, I spend a lecture on Bell's Theorem using Mermin's example from his classic Physics Today article, and talk about the limitations that this places on interpretations.

I doubt that much of this really "sinks into" students at this level, but I hope it at least raises doubts about whatever mental pictures they've developed themselves.

 

[Andy Resnick]

I don't understand what the authors are trying to say: all I got out of the article was that teachers that emphasize different aspects of QM produce students with different conceptual perspectives.

Given that the instructors, in their own research, differ fundamentally on how to interpret the wavefunction (page 2, first column) and yet (presumably) have active research programs, it's not clear what any difference in conceptual perspectives means.

As for the assessment tool (the QPCS), the question is the usual: what is being assessed? Especially since there does not appear to be a standard, "correct" interpretation of QM. there was certainly no discussion about any difference in student outcome given differences in instructor emphasis. "Attitude statements" are not measures of proficiency.

The final paragraph of the paper dovetails nicely with Physics girl's comment.

 

[twofish-quant]

My intro to quantum course was very much engineering focused. Here is a problem. This is how you solve it. There was no discussion at all of the interpretation issues, and when I did read up on the different interpretations, I had to go back and try to connect the interpretation with the course. I think this left me with a Cophenhagen interpretation of things (i.e. just do the equations and don't think about what they mean).

One thing that the course on quantum did seem to do is to try to push people out of a "naive realist" approach which doesn't work at all.

As far as teaching. A lot of it involves removing misconceptions. In ordinary physics classes, this involves showing that a naive realist approach just won't work (much of that involves using Feymann).

In talks outside a physics program, it turns out that the people that have the most interest in QM are people that have read something really, really weird.

 

[Astronuc]

It's been so long ago, about 35 years, since I took my sophomore-level "intro modern physics course" that I don't remember much about it, except the book: Wehr, Richards and Adair, with a picture of bubble-chamber tracks on the cover. I doubt that we discussed interpretations at all, leaving us each to form our own mental pictures as to what an electron in the hydrogen atom is "really doing."

I've now taught that sort of course many times, and my treatment has evolved somewhat as I've learned more about interpretational issues. I warn students against taking the circular orbits of the Bohr model seriously, in fact, I don't even discuss them in detail the way most textbooks do; I focus on the energy levels, and "derive" them from the Balmer-Rydberg formula for the hydrogen spectrum.

Then when we get to the Schrödinger equation and probabilistic QM, I tell students that QM predicts the outcomes of measurements, but does not address the question of what is "really happening," in detail, before the measurements occur. I say that different groups of physicists have different opinions on the matter and briefly list some of the most common interpretations so students can Google for them if they want. I emphasize that that there is no experimental way to choose between many of these interpretations.

I have that textbook, which I used in an introductory modern physics (intro QM) course. Adair taught the course, and he more or less adopted the same approach as jtbell mentions, i.e. he cautioned about taking the models too seriously. But that was more than 30 years ago.

 

[Fredrik]

Were you introduced to a specific interpretation of QM when you were first introduced to it? How did it affect your interpretation of it then, and now?

The books I studied for my first two classes (Gasiorowicz and Sakurai) didn't say much about interpretations. The teacher of the first class, mentioned Copenhagen with wavefunction collapse, and the MWI. If he mentioned any of the others at all, it must have been very briefly, because I don't remember it. The presentation of the MWI was pretty weak. It was just the usual stuff about "branches". I think all of us ended up thinking that the wavefunction represents the properties of the system at all times, and that "collapse" was a mysterious physical process that no one really understood.

It took a long time to shake that off. One of the things that made me drift towards an anti-realist position was an article called "Quantum theory needs no interpretation" by a guy named Ulrich Mohrhoff. I don't remember how I found it. This guy has some pretty strange ideas about quantum mechanics, but he was at least able to make me understand a few things that I didn't before, in particular that a theory of physics doesn't have to be anything more than a set of rules that tells us how to calculate probabilities of possibilities. The more I thought about it, the more likely it seemed that this was actually the case.

I tried looking at the MWI a few times, but it looked like complete nonsense. The MWI supporters here certainly weren't able to change my mind about that. The articles I read weren't much better. The best one was an article by Max Tegmark that cleared up a lot of the misunderstandings, but it was clearly wrong about the Born rule, and it dismissed a very solid peer reviewed article that claimed that there's no well-defined MWI as "based on misundersandings". The only justification he provided was a reference to an unpublished article that looked like crackpot nonsense to me. The MWI guys certainly weren't very convincing.

But I eventually came up with a way of thinking about the MWI that made sense to me, and now I don't know what to think. I can't dismiss the MWI as an ill-defined pile of garbage anymore, and I think it might have something to say about the universe that an anti-realist interpretation can't. So I'm definitely going to have to continue to think about this.

Since my definition of "the MWI" is almost synonymous with realism, I think most of the other interpretations are just describing certain aspects of "my" MWI. (I don't mean to imply that I have come up with an original idea. I have seen all of the key ideas in writing somewhere, just not all in the same place).

The de Broglie-Bohm pilot wave theory is probably an exception. I think of that as a "different but equivalent" theory, and not as an "interpretation of QM". But what do I know? I haven't even studied it yet. (I bought Holland's book, but I haven't read it yet).

I have never taught a class on QM, but if I ever do, I will strongly emphasize the anti-realist position, and wait until we're near the end of the course to talk about attempts to interpret QM as a description of what "actually happens" to the system at all times (including times between state preparation and measurement).

 

[dx]

The problem with interpretations is that it's such a subtle topic and most people don't even know what an interpretation is!. For example, twofish-quant said above that copenhagen interpreation is "just do the equations and don't think about what they mean". If Bohr heard that, he would cringe.

An interpretation is the unambiguous clarification of how to relate a mathematical formalism to experience. Without a formalism, experience cannot be discussed. The standard mathematical formalism of quantum mechanics is that of Hilbert vector spaces, linear operators and their spectra (just like the mathematical formalism of Newtonian mechanics is that of second order differential equations). The physical idea of the quantum of action, i.e. the 'individuality' of elementary processes is reflected in the formalism in the occurrence of discrete spectra for operators. The individuality of the processes also precludes a causal description in this formalism. Also, in this formalism, a state with a definite dynamical aspect, called momentum eigenstates, are not localized. An application of conservation laws of momentum and energy precludes a description of the process in spacetime. This is clarified by the idea of complementarity, and the consistency of the description is shown by the Heinsenberg uncertainty relations. One can hope that a different formalism can be found where energy-momentum and spacetime concepts can be used at the same time, but it must be made absolutely clear to the student that the standard formalism precludes this, and also giving an exposition of all possible alternative formalisms is not the role of an introductory course in QM.

So in my view, in an introductory course in qm, which teaches the use of the Hilbert space + linear operator + their spectra formalism must stress exactly the aspects that were stressed by the Copenhagen physicists. The students must learn how to use unambiguously the standard formalism.

The question of whether the formalism can be extended to allow a deterministic basis, or whether the Hilbert space alone can serve as a basis for qm, and the linear operators and probabilities can be derived from it statistically (Everett) can be mentioned, but it must be made absulutely clear that these pictures involve a change in the formalism itself.

 

[Fredrik]

There are at least two different kinds of interpretations in physics. To turn a mathematical structure into a theory of physics, we must interpret the mathematics as predictions about results of experiments. This is the type of interpretation provided by the standard axioms of QM. (The set of axioms that defines a theory is always an interpretation of this kind).

The second kind of interpretation tries to go beyond that, by interpreting the theory (which always includes an interpretation of the first kind) as a "description of what actually happens" to the system, a description that's supposed to be valid at all times, including times between state preparation and measurement. (I will clarify this point a bit in the last two paragraphs).

When I hear the term "quantum mechanics", I think of a theory of physics, not a mathematical structure. Since a "theory" by definition includes an interpretation of the first kind, an "interpretation of quantum mechanics" should definitely be an interpretation of the second kind. But I think most of the people who write about interpretations of QM haven't even thought about this. Most of the articles about Everett's many-worlds interpretation for example are clearly not trying to provide an interpretation of the second kind to quantum mechanics. They are trying to modify the interpretation of the first kind that defines that theory. In other words, they're trying to define a different but equivalent theory. (In my opinion, they're all doing it badly and failing miserably).

In classical theories, the interpretation of the second kind is always obvious. For example in the non-relativistic classical theory of a single point particle, the solution to the equation of motion is always a function x, and its value x(t) at an arbitrary time t has an obvious interpretation as the particle's position at time t. The moon is there even when no one is looking at it. QM on the other hand doesn't have any obvious interpretation of the second kind. (And perhaps more importantly, it's not at all obvious that there exists an interpretation of the second kind that's even approximately correct). Yes, it's very straightforward to just interpret the state vector as a mathematical representation of all the properties of the system, but this seemingly harmless assumption takes us deep into many-worlds territory, and now you can certainly argue that a) this isn't a complete interpretation until we have added axioms that provide the answers to questions like "what exactly is a world?", and b) that there's no good reason to think that any of the other worlds exist.

There is an "interpretation" of the state vector that everyone agrees is accurate: The state vector is a mathematical representation of the statistical properties of an ensemble of identically prepared systems. However, since the members of this ensemble don't exist at the same time, this doesn't qualify as an interpretation of the second kind. It tells us nothing at all about what the system is "doing" between state preparation and measurement.

 

[dx]

There are at least two different kinds of interpretations in physics. To turn a mathematical structure into a theory of physics, we must interpret the mathematics as predictions about results of experiments. This is the type of interpretation provided by the standard axioms of QM. (The set of axioms that defines a theory is always an interpretation of this kind).

The reason I prefer to use the term 'experience' rather than 'results of experiements' is that the latter presumes already a space-time frame of concepts. When we are talking about basic issues in science, like "what is a theory?", we must allow for the possibility that phenomena can transcend any particular set of concepts, i.e. our notion of "theory" cannot be tied to any particular set of physical concepts. In particular, we must allow for the fact that phenomena can transcend description in spacetime. Our notion of 'reality' is connected inextricably with spacetime, and we think of something as 'real' or 'actual' when we can provide a description of it in spacetime or within the spacetime frame of concepts, i.e. in terms of things like worldlines.

The second kind of interpretation tries to go beyond that, by interpreting the theory (which always includes an interpretation of the first kind) as a "description of what actually happens" to the system, a description that's supposed to be valid at all times, including times between state preparation and measurement. (I will clarify this point a bit in the last two paragraphs).

When you say "a description that's supposed to be valid at all times", or "what is the system actually doing before measurement?", you are again demanding a description of this type, but as I explained above, in the quantum mechanical framework, based essentially on the physical ideas of a finite quantum of action and the superposition principle, such a description is excluded*. For example, the very idea of a stationary state excludes a description in time. That is the nature of the formalism. Now, this is so far away from our usual mode of thinking that we persist and ask "but what is really happening?", and we try to design experiments to answer this question, hoping to show that we can actually find out what is 'really happening', and therefore show that the quantum mechanical formalism is inadequate. But, we failed. If we perform an experiment to check the validity of the conservation laws, it works out, but the very nature of the experiment will exclude a spacetime description. On the other hand, if we follow the particle's trajectory accurately, which we can, then the experiment excludes an energy-momentum description. Thinking along these lines, we can show that all possibilities of observation are comprised within the applicability of the quantum mechanical formalism, and the consistency of the complementary pictures is ensured by Heisenberg's uncertainty principle and therefore it cannot be judged as inadequate on that basis.

*not excluded a priori, but excluded by the quantum mechanical framework. So if one still wants something of that sort, a new framework must be found, and it will not longer be an interpretation of quantum mechanics, it will be a new theory, which may contain quantum mechanics as a special case.

 

[Fredrik]

I prefer to have exact definitions of terms like "theory" and "science", even if there's a chance that we might have to change them some day.

Science will always be limited by the fact that the only way we can obtain information about the world around us is through our senses. Space and time will always be in the picture because measuring devices are localized in space, and because the signals they send to our sensory organs to inform us that an interaction has taken place are localized in time.

It looks like you misunderstood what I called an "interpretation of the second kind", or a "description of what actually happens". Everyone seems to do that at first. I wish I knew why. Every time I talk about it I think I've made things clear, but no one ever understands. You seem to think I'm talking about a description in terms of eigenstates. That's certainly not what I'm doing.

 

[dx]

Science will always be limited by the fact that the only way we can obtain information about the world around us is through our senses.

Of course, but that doesn't mean Nature is limited in the same way. That seems to be the assumption that a lot of people make: that since the space-time frame of concepts is used to describe our experience, they must be able to comprise all phenomena. For example, imagine an organism that had only an auditory sense, and no sight. It will describe its experience predominantly using auditory concepts, but that does not mean those concepts are adequate to reflect the basis of its experience. Nature transcends those concepts. In the same way, quantum mechanics has shown us that Nature transcends the space-time frame of concepts. Atomic processes cannot be visualized as continuous processes that occur in time (which seems to be what you are looking for in 'interpretations of the second type'), and visualized in space at each moment. The fact that elementary atomic processes are 'individual' leads almost directly to this conclusion. This does not mean that classical concepts cannot be used in the description of these processes; it just means that we must recognize a limitation in their applicability, and learn to use them correctly. This involves, for example, realizing that when we talk about particles of definite momentum, we cannot simultaneously talk about their position. The two are complementary.

Now this is a very difficult situation, but the difficulty is not with quantum mechanics, but with a deviation from our standard way of thinking. We are just uneasy when the possibility of visualization of 'what is actually happening' is taken away from us. But using this uneasiness as an argument against quantum mechanics is simply denying the limitation of classical concepts in the descriptoion of atomic processes.

It looks like you misunderstood what I called an "interpretation of the second kind", or a "description of what actually happens". Everyone seems to do that at first. I wish I knew why. Every time I talk about it I think I've made things clear, but no one ever understands. You seem to think I'm talking about a description in terms of eigenstates. That's certainly not what I'm doing.

I apologize if I've misunderstood what you mean by 'what is actually happening'. If I did, could you explain more clearly, because everyone who feels the need to know 'what is actually happening' in quantum mechanics seem to mean quite different things by that. I definitely did not interpret it as having anything to do with eigenstates.

 

[Fredrik]

No need to apologize. The fact that no one ever understands what I mean suggests that I haven't figured out the right things to say yet. And I think I misunderstood some of your thoughts too (but I understand them now). I'm working on a reply that I'll post here within a few days. (I've been meaning to write an essay or something like that about these things at some point, and I see this as an opportunity to get some of my thoughts in order before I do that, so the post will be longer than it would have been if I had just been trying to reply to your post).