The Quantum Pontiff

Michael Nielsen has a nice essay up explaining Why the world needs quantum mechanics:

Conventional wisdom holds that quantum mechanics is hard to learn. This is more or less correct, although often overstated. However, the necessity of abandoning conventional ways of thinking about the world, and finding a radically new way – quantum mechanics – can be understood by any intelligent person willing to spend some time concentrating hard. Conveying that understanding is the purpose of this essay.

For a good explanation of Bell inequalities, jump to Michael’s essay.

At the end of the article, Michael compares his essay, explaining Bell inequality violations, with the traditional manner in which quantum theory is taught:

The standard explanation is based on the historical development of quantum mechanics between 1900 and 1930. During that time there were a series of crises in physics. The pattern was that each time some experimental fact would be noticed that seemed hard to explain with the old “classical” way of viewing the world. Each time, physicists would bandage over the old classical thinking with an ad hoc bandaid. This happened over and over again until, in the mid-1920s, the sick patient of classical physics finally keeled over completely, and was replaced with the new framework of quantum mechanics.

The problem with this style of explanation, and what makes it confusing, is that none of those early crises was entirely clearcut. In each case, there were physicists who argued that the new experimental results could be explained pretty well with a conventional classical picture. And, in fact, with hindsight, we can now see that some of these crises have pretty good explanations that are essentially classical.

Which made me think: what if we take this idea seriously and tried to teach Bell inequalities first (before we tell the students lies about Planck and the Raleigh Jean’s Law)? This is a bit akin to the idea of teaching the basics of quantum computing before teaching the basics of quantum mechanics (i.e. separating the basics of quantum theory from the physics which you put on top of quantum mechanics) but not quite the same. One interesting point about this is that one can’t really explain why quantum theory violates Bell inequalities without building up quantum theory. One can, however explain very early on, in line with Michael’s essay, what a Bell inequality is, and that quantum mechanics does appear to violate the inequality. Thus the course could very nicely form a circle, as later in the course you could do the quantum mechanical calculation.

More speculatively, the way quantum theory appears to be taught, is very close to the 1950s published textbook of David Bohm. At least in my mind, most of the textbooks of quantum theory follow a similar tact to Bohm’s. Now suppose that we build a large scale quantum computer, such that everyone had easy access to these strange machines. Would this change how we would teach quantum theory?

Comments

  1. #1 Sam C
    August 4, 2008

    Now suppose that we build a large scale quantum computer [...]

    Presumably powered by the almost limitless and free energy provided by a fusion reactor? Let’s see a useful quantum computer first, then we can discuss its significance!

  2. #2 Norman Doering
    August 4, 2008

    Dave Bacon asked:

    Would this change how we would teach quantum theory?

    I started with “The Fabric of Reality” by David Deutsch and I might be hopelessly confused.

    I was looking at the sample chapters for “Our Undiscovered Universe” – here:
    http://nullphysics.com/

    And I couldn’t tell if it was revolutionary or crackpot.

    What’s your opinion?

  3. #3 Dave Bacon
    August 4, 2008

    Sam C, it must be difficult to live in a world with no hope, no creativity, and nothing better to do than snark on a blog post.

    Norman: I just glanced at nullphysics, but my first impression is crackpot. David Deutsch has some crazy ideas about physics, but hell he helped invent quantum computing, so I would say not paying attention to him is silly. I don’t know if “The Fabric of Reality” is the best introduction to quantum theory, but many enjoy it. A list of suggestions for popular science intros to quantum theory is here: http://cosmicvariance.com/2006/09/28/quantum-mechanics-made-easy/

  4. #4 Matt
    August 4, 2008

    From my personal rather confusing experience learning QM as an undergraduate, I agree that the way it’s introduced needs to be changed. Things like the Bell inequalities would probably be a good conceptual motivation; along with that I think it might be better to sneak a little QM in during linear algebra class. That way instead of the just the Schrodinger picture, students will already have a better grasp of where things are going in the matrix mechanics representation.

  5. #5 Ian Durham
    August 4, 2008

    Which made me think: what if we take this idea seriously and tried to teach Bell inequalities first (before we tell the students lies about Planck and the Raleigh Jean’s Law)?

    I already do this – in my introductory physics courses (as well as QM). Been doing it for four years now. Originally, I got the idea from this site and then switched to Wigner’s derivation as it appears in Sakurai.

  6. #6 Ian Durham
    August 4, 2008

    P.S. I have a great classical analogy I do to demonstrate the weirdness of it that involves colored marbles and has been given Rob Spekkens’ epistemic stamp of approval.

  7. #7 Michael Bacon
    August 4, 2008

    “This is a bit akin to the idea of teaching the basics of quantum computing before teaching the basics of quantum mechanics . . .”

    I think Deutsch would certainly agree this would be a better way to teach QM than using his book (which I did, however, enjoy very much). :) I recall him touting the approach in one of his talks or papers somewhere and could probably find the quote.

  8. #8 GrayGaffer
    August 4, 2008

    In tribute to the gods of missed opportunities: I was a Physics major undergrad at Birkbeck College, University of London, 1967-73 (why that long is another story …). David Bohm was my professor for Properties of Matter and Quantum Mechanics classes. I really liked him, but had no idea whatsoever at the time of his history or the extent of his contributions to what he taught. But I credit his teaching with pretty much all that has stayed with me on the subject, that helps me have at least some limited understanding of the field today, including my nodding acquaintance with quantum computing.

    I was seduced away from theoretical physics by the Atlas computer accessible through the dark back-rooms of the Maths dept. And by the Elliott 4130 series which it was my pleasure to help bring to life at Elliott Automation in the same time-frame. Now, 40 years later, the two paths cross. Who would’a thunk, eh?

    Topics such as entanglement and the possibility of computational devices dependent on quantum effects were not even fantasies back then, at least not to an undergrad, and not even in the SciFi stories. Here is one field that cannot but benefit from new teaching styles, since the results are bearing real-world fruit that is so much farther from ‘common sense’ than ever before. Which implies that notions of common sense need a lot of revision, and cannot be used as explicit or implicit underpinnings of teaching devices.

    For me the lab was where everything became real, where it entered ones’ notions of common sense via the gut. Double slits, diffraction gratings, etc. But those were simple; I saw a photo of a recent experiment that demonstrated quantum entanglement of photon polarization: the optic bench was an insane-looking rats nest. How does one reduce that to do-able in the three hour session? or even two sessions? Somehow I think there is something unequivocally quantum needed to hit freshmen with early on, preferably hands-on. I could probably say ‘yes’ when I see it, but I am of the audience to this, nowhere near being an author.

  9. #9 JohnQPublic
    August 4, 2008

    I take it the suggestions are intended to guide students into a counter-intuitive world more gently. Is that realistic? You guys are, after all, looking at it through hindsight and often (I know this from training others in computer science) you forget that the mental struggles of a logical progression forward were really helpful. Now you’re attempting to mitigate those bumps believing it creates a smoother transition. To me it’s like saying the concepts of calculus can be easily digested by anyone (they can), but there is a lot of conceptual baggage that is created a long the way that is not there to shape their conceptual model (I’m not talking about just the mechanics). Therefore, the mental model is not as complete as it could be. Basically, it’s shortcutting. Anyway, just a thought.

  10. #10 Blake Stacey
    August 4, 2008

    I have occasionally wondered whether it would be possible to build a first-term quantum physics course out of Feynman’s QED: The Strange Theory of Light and Matter. Assume, for simplicity’s sake, that the students already have some experience with calculus and complex numbers; this would make writing homework exercises considerably easier. Either before or after the chapter on the Standard Model’s particle content, expand the book with two-state systems, the Bell Inequality and entanglement stuff. (I might do it after the Standard Model chapter, so I could lead into it with a little kaon physics.) After entanglement, introduce decoherence. Follow with the model of electrons hopping from atom to atom expounded in the Lectures on Physics, volume 3, and use it to motivate band-gap behavior and, by shrinking the lattice spacing, the Schrödinger Equation. Solve the particle-in-a-box and the harmonic oscillator, and then bid the kids a happy summer vacation.

  11. #11 Blake Stacey
    August 11, 2008

    Norman Doering:

    I was looking at the sample chapters for “Our Undiscovered Universe” [...] And I couldn’t tell if it was revolutionary or crackpot.

    Crackpot.

  12. #12 Jonathan Vos Post
    August 11, 2008

    Blake Stacey is brilliant as usual, starting with the ground rules for Metric Crackpottery, and his assault on Pseudomathematics.

    “Chapter 1 is where Witt lays out a series of ‘proofs’ derived from what he calls the ‘Null Axiom’. That axiom is: ‘Existence sums to nonexistence’ (pg. 28)—something that Witt calls self-evident after a page of invalid set theory. The central mistake, if I had to identify one, is the claim that ‘X does not exist’ is the same as ‘everything except X exists’.”

    That is as basic as the distinction between Solipsism (you other people do not esxist) and Antisolipsism (as I first pointed out roughly 25 years ago in APA-L as “Every person except myself exists.”

    The deluded Witt is not to be confused with the mathematician Witt as in q-Witt algebras, Witt groups of affine three-folds, Picard groups of Witt rings, and the like.

  13. #13 Reality Check
    December 16, 2008

    “Norman Doering:

    I was looking at the sample chapters for “Our Undiscovered Universe” [...] And I couldn’t tell if it was revolutionary or crackpot.”

    Crackpot:
    Also see my review at http://homepages.ihug.co.nz/~fiski/ouu_review.html
    The flaws of this crackpot book are many and include:
    Redefining the concept of infinity as a length with magnitude.
    Defining a line as a series of points written as zeros, treating them as numbers so that they add up to zero and then treating the number zero as a point again!
    A really bad atomic model “proving” that a electron orbiting a proton has a ground state that it cannot decay from by creating a new physical law.
    Using the high school description of a neutron as a proton plus an electron and not realizing that this is just his atomic model!
    Postulating that galaxies have “galactic cores” which are super massive objects that are not quite black holes and not realizing that the centre of the Milky Way is well observed. These recycle stars into hydrogen. Oddly enough astronomers have not noticed dozens of stars vanishing from the galactic centre in the many images that they have taken over the last few decades.

    Conclusion: Bad mathematics and even worse physics.

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