Graduate Quantum Mechanics Reform

So I've written a bit on revamping the undergraduate physics laboratory. I believe that many, if not most, of the studies on better teaching and presentation methods have been directed at introductory college, undergraduates, and high school students. We don't hear much about graduate programs that need revamping. I suppose one assume that students at that advanced level can mostly learn on their own even with unequipped instructors and teaching methods that aren't well-developed.

So it is a breath of fresh air that I came across this preprint that actually talked about reforming how graduate level QM is taught.

Abstract: We address four main areas in which graduate quantum mechanics education in the U.S. can be improved: course content; textbook; teaching methods; and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all four of these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, use modern textbooks that include such content, incorporate a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey (QMCS). We find that graduate students respond well to research-based techniques that have previously been tested mainly in introductory courses, and that they learn a great deal of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. On the other hand, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.

It's an interesting reading, and I've gone through it only quickly. I plan on reading it some more when I have the time. In the meantime, why don't you take a whack at it? :)

Zz.

Quantum All The Way

This is from a few weeks ago, but the issue is so important and interesting, I should still mention it on here. This was also the article I was reading on the plane while I was on my most-recent vacation. It was fascinating enough that it didn't put me to sleep and entertained me for several minutes.

This article was written by Phillip Ball in May 1st 2008 issue of Nature. I strongly suggest that, if you haven't read it and have access to it, that you take some time reading it. It deals with the issue of the "transition" or boundary or crossover or whatever between classical and quantum regimes.

To understand what the quantum–classical transition really means, consider that our familiar, classical world is an ‘either/or’ kind of place. A compass needle, say, can’t point both north and south at the same time. The quantum world, by contrast, is ‘both/and’: a magnetic atom, say, has no trouble at all pointing both directions at once. The same is true for other properties such as energy, location or speed; generally speaking, they can take on a range of values simultaneously, so that all you can say is that this value has that probability. When that is the case, physicists say that a quantum object is in a ‘superposition’
of states.

Thus, one of the key questions in understanding the quantum–classical transition is what happens to the superpositions as you go up that atoms-to-apples scale? Exactly when and how does ‘both/and’ become ‘either/or’?

Of course, there is a very good coverage of the leading candidate that tries to connect between the classical-quantum transition - decoherence. One of the important point of the article is the idea that it isn't the SIZE of the object that is important, but rather the time scale for when decoherence sets in.

Decoherence also predicts that the quantum–classical transition isn’t really a matter of size, but of time. The stronger a quantum object’s interactions are with its surroundings, the faster decoherence kicks in. So larger objects, which generally have more ways of interacting, decohere almost instantaneously, transforming their quantum character into classical behaviour just as quickly. For example, if a large molecule could be prepared in a superposition of two positions just 10 ångstroms apart, it would decohere because of collisions with the surrounding air molecules in about 10−17 seconds. Decoherence is unavoidable to some degree. Even in a perfect vacuum, particles will decohere through interactions with photons in the omnipresent cosmic microwave background.

So that's why we can still get interference pattern when particles as large as buckyballs are used, or that we can still see superposition effects in 10^11 particles, as in the SQUID experiments from Delft/Stony Brook.

The article also pointed out the alternative idea from Penrose that the coupling of the system to gravity (or gravitons to be exact) might be responsible for the emergence of our classical observation. I mentioned this earlier in another blog entry, including the upcoming tests being proposed Dirk Bouwmeester.

A great article, even if only for the wealth of the references given. A highly-recommended reading.

Zz.

A Historical Derivation of Heisenberg’s Uncertainty Relation is Flawed

This is a rather interesting paper published in the current issue of AJP[1]. It narrates the historical account of the rigorous derivation of Heisenberg's uncertainty principle and claims that some of the derivation used after Heisenberg's presentation of it may have been flawed.

However, what caught my eye was the single author of this paper. It is John. H. Marburger III. When I checked his affiliation, I was correct. This is THE John Marburger who is currently the embattled "Science Adviser" to President's George W. Bush.

Immediately, 2 things came to my mind. First, at least he still gets to continue to explore scholarly topics, even in the historical sense, while he holds this position. But secondly, he must be bored in his current job to actually have some time to do such in-depth research. :) That last comment, of course, is purely speculative on my part.

Zz.

[1] J.H. Marburger III, Am. J. Phys. v.76, p.585 (2008).

Willis E. Lamb Jr., Died at Age of 94

Anyone who has studied quantum mechanics would have come across his name and the "Lamb shift" named after him. Willis Lamb died this past week at the age of 94.

A professor emeritus at the University of Arizona, Dr. Lamb received a 1955 Nobel Prize in physics for his experimental work on the fine structure of the hydrogen atom and for the discovery of what came to be called "the Lamb shift," a tiny deviation in the energy of an electron orbiting a hydrogen atom's nucleus. The discovery had enormous implications for the quantum theory of matter.

Zz.

Just Because You Say It Is Based On Quantum Physics, Doesn't Make It So

So many pseudoscience are so damn quick to attach themselves to "quantum physics", as if they know what quantum physics is. I've already mentioned several instances of the bastardization of quantum mechanics by a few people who are using it to validate whatever it is that they are claiming. Well, count this one as one of them. It is the "ancient medical treatment" called Shirodhara.

I honestly don't care at all what people wish to do with their bodies. However, when they tried to justified it by saying some nonsense to the effect that it is verified by some aspects from physics, then that gets my goat.

Ayurveda, the primary health system in India, and western biomedicine, the primary system in North America, differ in their view of the body. "It needs to be emphasized that ayurveda is very much a science," Dr. Gupta stresses. "The foundation of ayurveda is based on quantum physics instead of molecules, cells and gross structure.

What the hell does that mean? And why is "molecules" different from quantum physics?

First of all, there's some inconsistencies here. This practice has been going on for "5,000 years". If it is true, how can it be "based on quantum physics", when quantum physics was only formulated in the early 20th century? Did someone from 5,000 years ago time-traveled to the time or Bohr, Einstein, Schrodinger, Heisenberg, etc. and got the knowledge about quantum physics and then got back to 5,000 years ago to form the Ayurveda medical treatment? Sure, I'll buy that!

OK, so maybe it isn't that. Does that mean that they realize that, like Chemistry, which came way before quantum physics, that what they are using can actually be "explained" by quantum physics? Really? Such as what? In Chemistry, many aspects of what is measured (as in QUANTITIVE MEASUREMENT), can be explained in terms of the formulation of quantum physics. The energy state of the hydrogen atom, the nature and strength of chemical bonds, the behavior of molecules, etc. In other words, a lot of things that were measured can be quantitatively derived from quantum mechanics.

Now I would bet you no such comparison has ever been made with this Ayurveda. Oh sure, they might bastardize various aspects of the superficial idea of "entanglement" (this seems to be a popular effect to be bastardized - refer to "The Secret"), but this is FAR from claiming that you have a foundation based on quantum physics.

What these crackpots do not realize is that to be able to say that something is based on quantum physics, one must DERIVE the effect for THAT PARTICULAR SYSTEM, using quantum physics. Start with the Hamiltonian, and use whatever means one has to drive both the QUALITATIVE AND QUANTITATIVE result that agrees with whatever it is one is trying to show an agreement of. One simply cannot use "superficial induction". Just because the phenomenon of entanglement has been shown to work in 2 photons does NOT mean that such phenomenon is valid for 2 apples! It isn't! But that is why these crackpots are doing.

I really don't know how the Edmonton Journal could have seriously published this with a straight face.

Zz.

Towards A No-Loophole Bell-Type Experiment?

Looks like we are well on our way to achieving that and nailing the coffin shut on Local Realism..... or are we?

The paper published last week in PRL[1] seems to point to the possibility of a loophole-free Bell experiment. While entanglement experiments with photons have closed down the locality loophole, and experiments with "particles" such as protons, neutrons, etc... have closed down the detection loophole, no experiments have managed to close both of them simultaneously.

This experiment with Yb+ atoms is well on its way to getting there. While they have certainly closed the detection loophole, they have reduced the possibility of the locality loophole by separating the atoms by 1 m (previously, the spatial separation was of the order of microns). So this is a tremendous improvement.

Eventually, it will be convincing enough, if it isn't already.

Zz.

[1] D.N. Matsukevich et al., PRL v.100, p.150404 (2008).

Interpretation of Quantum Mechanics - The New Religion

First of all, a clarification and a qualification. Most physicists (at least the ones that I come in contact with throughout my years as a student and as a physicist) don't really care about the various interpretations of quantum mechanics. It really is a non-issues 99.9% of the time. So essentially, we practice Feynman's "Shut Up And Calculate" philosophy where the formalism and what empirical evidence that it can produce is what we care about.

Now, in one of my rants in "Imagination Without Knowledge is Ignorance Waiting to Happen", I mention about many crackpots who have argued that physicists simply want to keep the status quo as far as our understanding of the universe goes, that all we care about is upholding the current laws and theories. We can't, as some put it, work "outside the box". Some even compare to our "devotion" towards not wanting to drop our current understanding as a "religion".

This, of course, is stupid, and false, on many different levels, as I've mentioned in that blog entry. Still, there is one aspect of physics in which, I hate to say, is starting to look like a religion, and it has nothing to do whatsoever with what these crackpots have in mind. In fact, I don't think any of them could even comprehend these things well enough to know any better.

What I find in physics to be no different than a religion is the rabid devotion of some people, physicists included, to the various interpretation of quantum mechanics. These interpretations could range from the "popular" Copenhagen Interpretation (CI), to Many-World Interpretation (MWI), to Bohm Pilot Wave (BPW), etc.. etc. Now, again, to be fair, this issue comes up only in a very small percentage of practicing physicists. I tend to find more of these discussions on physics forums rather than in prominent physics journals. And certainly, amateurs and philosophers tend to be more fascinated by this issue than the overwhelming majority of physicists. So in physics, this "religion problem" isn't a widespread epidemic.

Still, those who are devoted to this is not doing physics any favor. I find that the rabid devotion to such various interpretation (rather than just a casual attitude about it) rather puzzling and contrary to how one accepts something to be valid in physics. This is why I find that the devotion to any such interpretation as being no different than a religion:

1. There's no empirical evidence that shows one being "better" than the other. All of them come up with the same analytical form within the formal QM. The similarities with religion is obvious here. This means that there's nothing to support which is better, and they all come up with the same answer, at best, so far.

2. Yet, the devotees in each camp tout why such-and-such is more "logical" or "rational" or "conceptually sensible", etc. Without empirical evidence to support such claim, this is nothing more than a preference based on a matter of tastes! We might as well argue for our favorite color, or, in this case, our favorite religion. This is no different than the different religions and the many followers that they have. Each one will tout the superiority of its belief system, or why it is the "truth", etc. Yet, in none of these are there any empirical evidence to separate and support these claims.

Now one could argue that isn't what is being taught in QM classes more along the lines of adopting the CI? I don't believe so, because in the end, it is the formalism that is more important, and there's no ambiguity at all there. And if it really is CI that is being instilled into these students, how come most of them grow up and adopt the "Shut Up and Calculate" point of view and not become a CI devotee?

I'm not saying that at some point, there won't be a "tie-breaker", be it a further refinement to these various interpretations that make them distinctly different from each other, and/or new tests would come out to allow for direct verification of each one. But until then, why are people "believing" in something that, at the very foundation, is simply a matter of tastes?

Zz.

More Challenges Against Non-Local Hidden Variables Theory

Science Daily is reporting a new experimental measurement out of NIST and Maryland that challenges the validity of a certain aspect of non-local hidden variables theory.

Experiments so far have ruled out locality and realism as a combination. But could a theory assuming only one of them be correct" Nonlocal hidden variables (NLHV) theories would allow for the possibility of hidden variables but would concede nonlocality, the idea that a measurement on a particle at one location may have an immediate effect on a particle at a separate location.

Measuring the polarizations of the pairs of entangled particles in their setup, the researchers showed that the results did not agree with the predictions of certain NLHV theories but did agree with the predictions of quantum mechanics. In this way, they were able to rule out certain NLHV theories. Their results agree with other groups that have performed similar experiments.

I may have missed it, but I don't recall ever seeing any experiment on entanglement that hasn't produced any result that's consistent with QM. One can argue that such-and-such an experiment doesn't rule out that and that theory, but QM is batting with 100% hits here with zero strike-out. I find that rather impressive, and impressively convincing.

Zz.

How Fundamental Particles Lose Track Of Quantum Mechanical Properties

We have another report on the study on the mechanism of the differences between the quantum world and our classical world. This is another study on the effect of decoherence on a quantum system that couples to an external "bath".

It would be interesting to compare this to an earlier report on the emergence of a classical system from a single-particle state after just one interaction. It is also interesting to see how Roger Penrose would handle this. He seems to think that our classical world emerges due to some coupling or interaction between the quantum systems and gravity, and that eventually destroys the quantum system and out comes the classical system. These two papers above seems to indicate that the mere act of decoherence might be sufficient to produce the classical world.

Zz.

The Wave-Particle Duality of Light: A Demonstration Experiment

Other than the fact that I don't quite like the title, this is an excellent demonstration paper that was published recently in AJP. Very much like the J.J. Thorn et al. paper on the which-way experiment, these profound phenomena can actually be performed in an undergraduate physics lab.

First, the exact citation:

T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

They basically performed a Mach-Zehnder interferometer experiment using very low intensity light so much so that only one photon is in the apparatus at any given time. They also have a second stronger laser beam that traverse the same apparatus, but slightly displaced that exhibit the clear wave-like interference pattern.

So far, this is fine and dandy, and it would not have caught my eye because it would be a nice, undergraduate physics lab exercise. But at they end, they did something simple, yet, can be quite profound to a student. I'll quote what they said:

The demonstration, whose result is astonishing for students, is realized in the following way. First the fringe pattern is locked to a photodiode as explained in Sec. IV B, and the photomultiplier is moved to a fringe minimum, as characterized by a low photon count rate which can also be displayed acoustically. If now path A of beam 1 is blocked inside the interferometer, it is possible to hear (and see) a distinct increase of the click rate. This result demonstrates that if we give each photon the choice of taking either path A or path B, it has a low probability to appear at the detector. In contrast, if we force the photon to follow a specific path by blocking the other path, then the probability to arrive at the detector is much higher. The puzzling fact that a two-path alternative for each photon prevents it from reaching the detector, while blocking one of the paths leads to a revival of the clicks, is most intriguing for beginning students. This experiment is well suited for illustrating this remarkable quantum mechanical effect, which can be explained only if we assume that each photon simultaneously takes both paths A and B; that is, each photon, in the phrasing of Dirac, "interferes with itself."

Gorgeous!

It is something we know would happen, but the way this is demonstrated is so clear that I would say this is an experiment worth doing at every undergraduate level. Well done to the authors!!

Zz.

Physicists Successfully Store and Retrieve Nothing

This could easily fit in as an episode of the Jerry Seinfeld series.

It appears that there is such a thing as a "squeezed vacuum", and it takes some effort to store and retrieve this "nothingness".

To see what this is, begin with a normal light wave. Classically, this is a smooth wave of electromagnetic fields with equally spaced peaks and dips. But throw in quantum mechanics and things get more complicated. The precise height of the wave becomes uncertain, so the wave gets fuzzy (see figure). Physicists have learned how to manipulate that inevitable uncertainty--for example, making it smaller at the peaks and larger in between. That makes "phase-squeezed light." Now imagine turning down the intensity of the phase-squeezed light to zero. The wave itself goes away, but the waxing and waning uncertainty remains, creating a squeezed vacuum.

It's interesting that two separate groups produced work on this at almost the same time. This, of course, is not unusual, and PRL, Nature, and Science have been known to put such things in the same issue. It serves to reinforce the discovery.

Zz.

A Deeper Look at Student Learning of Quantum Mechanics: the Case of Tunneling

This preprint, co-authored by Nobel Laureate Carl Wieman, looks at the difficulties that students had in understanding quantum tunneling.

Abstract: We report on a qualitative study of student learning of quantum tunneling in traditional and reformed modern physics courses. In the reformed courses, which were designed to address student difficulties found in previous research, students still struggle with many of the same issues found in other courses, but the reasons for these difficulties are more subtle, and many new issues are brought to the surface. By explicitly discussing how to build models of potential energy and relate these models to real physical systems, we have opened up a floodgate of deep and difficult questions as students struggle to make sense of these models. We conclude that the difficulties found in previous research are the tip of the iceberg, and the real issue at the heart of student difficulties in learning quantum tunneling is the struggle to build the complex models that are implicit in experts' understanding but often not discussed explicitly with students.

It's a lengthy paper, and I'm still reading it. But it is interesting that you get to learn quite a bit more about quantum tunneling in here, especially on aspects that are quite subtle.

Let me know what you think...

Zz.

American Institute of Physics Announces Awards for Best Science Writing

This is a press release from the AIP announcing the winners of the awards for best science writing. There are some really good science essays here. I would bring your attention to Tim Folger and his award in the Journalist category. The article, published in Discover, is actually quite interesting and provocative. It was based on an interview with Roger Penrose, and of course dealt with one of the most fundamental issues surrounding quantum mechanics. It also contains a description of one of his proposed experiment at detecting the quantum superposition using mirrors, which is currently being tested by Dirk Bouwmeester at UCSD.

The proposal for this experiment was published a while back in PRL, and you can find the arXiv version here.

Zz.

Thesis - Students` Depictions of Quantum Mechanics

This is a rather "entertaining" thesis (when was the last time you could say that about a thesis?) by someone going for a degree in the Philosophy of Science. It studies the teaching and learning process of students in the subject of quantum mechanics.

Not sure if this person would find a tracking link back to this blog entry. But if he does, I would certainly welcome any additional comments that he would have.

Zz.

Direct Measurement of Critical Casimir Forces

This is an amazing work. A group of physicists in Germany has made a "direct" measurement of the critical Casimir forces[1]. I suppose this is as direct as it can get, as of now.

There is a News and Views coverage of this paper in the same issue of Nature, and also on the Physics World website.

Zz.

[1] C. Hertlein et al, Nature v.451, p.172 (2008).

Quantum Behavior of Light In Undergraduate Laboratory

While the Compton effect and the photoelectric effect are often used as "evidence" of photons, they actually cannot rule out completely the wave picture. The more definitive experiment would be the which-way experiment or the coincidence experiment. I find it rather amazing that such experiments are now within the realm of an undergraduate laboratory exercise.

There were 2 papers published in the American Journal of Physics that provided a very detailed description of such experiments suitable for such undergraduate laboratory. The first one is by J.J. Thorn et al. Here, they did the coincidence measurement that basically reproduced (with better equipment) an earlier Graingier et al. experiment. The second one by C.H. Holbrow et al. describes 5 different possible experiments (and theory to accompany them) to illustrate the photon pictures. No experimental result was reported in this paper.

Both papers contain a wealth of references, especially to other similar experiments that have already been done. That alone is worth keeping these two papers handy.

Zz.

Physics of Information: From Entanglement to Black Holes

So, if you're in Waterloo, Canada tomorrow (Dec. 5th, 2007), you might want to see if you can attend this. It sounds like such a fun thing to do for physics geeks! :)

Do ideas about information and reality inspire fruitful new approaches to the hardest problems of modern physics? What can we learn about the paradoxes of quantum mechanics, the beginning of the universe and our understanding of black holes by thinking about the very essence of information? The answers to these questions are surprising and enlightening, but also controversial. The topic of information within physics has involved some of the 20th century’s greatest scientists in long-running intellectual battles that continue to the present day. In this special debate, hosted by the CBC’s Bob McDonald of ‘Quirks and Quarks’, you will enjoy a lively discussion between four prominent physicists who have thought long and hard about these questions.

With a high-powered panalist consisting of Anthony Leggett, Leonard Susskind, Seth Lloyd, and Chris Fuchs, this discussion could be very fascinating.

Zz.

Schrodinger's Kittens Enter The Classical World

This is a rather fascinating angle on the quantum to classical transition. The traditional explanation on the cause of the difference between quantum world and the classical world is the onset of decoherence, where the system interacts with its environment. That interaction with the large degree of freedom causes the emergence of our familiar classical world. We have seen several experiments that showed that the onset of such decoherence gave us back the familiar classical description. In fact, it has been shown that even with just ONE interaction, a single-particle system can quickly lose its quantum coherence.

However, a new theoretical research has taken a different angle. Two physicists in Austria has published a paper[1] showing that the emergence of classical observation can be also be obtained without having any decoherence effect, but rather due to the "coarse-grained" measurement that we make. A review of this work was reported in Nature Daily News (the link may be available for a limited time and may require registration and/or subscription).

Johannes Kofler and Časlav Brukner of the University of Vienna and the Institute of Quantum Optics and Quantum Information, also in Vienna, say that the emergence of the 'classical' laws of physics, deduced by the likes of Galileo and Newton, from quantum rules happens not as objects get bigger, but because of the ways we measure these objects. If we could make every measurement with as much precision as we liked, there would be no classical world at all, they say.

We know that "size" isn't the issue here, especially with the recent SQUID experiments of Delft and Stony Brook. However, the conventional thinking is that the larger the size, the more difficult it is to maintain coherence of all the parts of the system. What the new approach here has tried to explain is that with the larger size, the precision of our measurement also tends to get worse. Unfortunately, their proposal to measure and detect the quantum effects on large system appears to be rather daunting, if not almost-impossible.

Kofler says that we should be able to see this transition between classical and quantum behaviour. The transition would be curious: classical behaviour would be punctuated by occasional quantum jumps, so that, say, the compass needle would mostly rotate smoothly, but sometimes jump instantaneously.

But watching such quantum jumps between life and death for Schrödinger’s cat would require that we be able to measure precisely an impractically large number of quantum states. For a 'cat' containing 1020 quantum particles, say, we would need to be able to tell the difference between 1010 states – too many to be feasible.

Still, I wouldn't put it past some experimentalists coming up with an ingenious way to test this.

Zz.

[1] J. Kofler and C. Brukner, Phys. Rev. Lett. v.99, p.180403 (2007).

More Tests of Leggett Inequality

Earlier, I highlighted the paper by the Zeilinger's group that rules out a class of realism model via the violation of the Leggett inequality. Now comes two more papers in last week's Phys. Rev. Lett. that made further tests of such violation.

The first one is more of a refinement of their earlier work from the Zeilinger's group. This one supposedly rules out a larger class of local realism model without the assumed rotational symmetry of the earlier tests.

T. Paterek et al. "Experimental Test of Non-Local Realistic Theories Without The Rotational Symmetry Assumption", Phys. Rev. Lett. 99, 210406 (2007).

The second paper in the same issue also tests the Leggett inequality and finds a clear violation of it.

Cyril Branciard et al. " Experimental Falsification of Leggett's Nonlocal Variable Model", Phys. Rev. Lett. 99, 210407 (2007).

It is amazing that tests after tests all produce a consistent result that are in full agreement with quantum mechanics. At some point, this will become a very convincing body of evidence.

Zz.

The Most Accurate Measurement Ever Made

Would you ever think that using single photons and an interferometer, one could get the most accurate measurement ever made up to now? One certainly can, as shown by this very elegant experiment (link may be available for free for a limited time). In fact, they got close to the Heisenberg Uncertainty limit!

But Pryde and his coworkers in Australia have demonstrated a way of reaching the Heisenberg limit of measurement precision without needing these elusive states: by looking at photons traversing an interferometer's arms one at a time. The key is to avoid making measurements that determine which arm the photon is in, until the beams are recombined at the end. This allows the shot noise to be more or less smoothed away.

Another very clever experiment. Way to go, people!

Zz.