Adventures in Ethics and Science

I had my kids with me at my office and needed to keep them occupied for a small chunk of time while I attended to business.

The younger offspring immediately called dibs on the “Celebrating Chemistry” markerboard.

The elder offspring, creeping up on 9 years old, asked plaintively, “What can I do?”

I scanned my office bookshelves. Given that I am trying to minimize the number of frustrating parent-teacher conferences in the coming school year, I passed right by the Nietzsche. After a moment’s hesitation, I pulled down my copy of David Z. Albert’s Quantum Mechanics and Experience. Handing it to my elder offspring, I said, “Try reading Chapter 1. I’m pretty sure you know all the words in it, and maybe you’ll find it interesting.”

The verdict, 16 pages later:

“This is cool! Can we try to build these devices for measuring the properties of electrons?”

So, the chapter on superposition has my kid really interested in quantum mechanics (or at least, interested in the nature of quantum particles like electrons, and curious about how people can set up experiments to find out more about them). But the challenge is that the second chapter of the Albert book takes up mathematical formalism … and my offspring has not as yet learned how to do math with vectors and matrices (nor to tackle trigonometry).

What’s the best way to move forward from here?

Can the physicists recommend other resources that lay out the distinctive behaviors of quantum-level entities without getting too mathematically complicated? (Tremendous Luddite that I am, my preference would be for written descriptions of these entities and their behaviors, but I could tolerate an animation if it did a good job of conveying the wonders of the quantum world).

Alternatively, are there good resources out there for teaching vectors and matrices to a kid who hasn’t taken algebra yet? (I’m actually fairly confident that I can teach the basic trigonometry — the unit circle is my close personal friend.)

Thanks in advance for your recommendations!


  1. #1 Evan Berkowtz
    July 8, 2008

    You could wait for “Bunnies Made Of Cheese”…

  2. #2 Greg Ladeng
    July 8, 2008

    You should investigate Mr. Tomkins books. I don’t know if they are at the right level.

    You are facing several problems. 1) quantum mechanics IS formal mathy stuff. That is how they know all the stuff they know. It isn’t like you can see a planet spinning around a star, get an intuitive grasp of then, and then if you want do some math. Rather, you do some math, and then the math tells you something you did not know, which makes you do more math, which tells you something else you don’t know. The seeing, feeling, intuitive (non math) understanding of mechanics is not something that actually exists beyond an initial trivial level.

    2) Maybe the above is wrong, and there is a way to do it, but so far not very much has been done. For instance, you COULD look at a high school textbook and see if you can work your way back from, say, 8th or 9th grade physical science. But guess what. They don’t teach QM at that level. It is barely present in Senior/AP level, as I understand it. (at least, I think that is true).

    3) so even when you see QB being discussed, there is almost always the “then a miracle happened” bit (not literally, of course) …. the spooky part where you just have to believe some conclusion.

    I could be totally wrong about the above. I hope I am, and I hope someone will correct me right now because I have the same exact question you do.

  3. #3 Chris
    July 8, 2008

    “The Cartoon Guide to Physics”, by Larry Gonick, would’ve probably worked great in this situation.

  4. #4 mathie
    July 8, 2008

    Well, there is a pretty obvious direction to go from there.

    Teach him the math. It’s really not as hard as it seems as long as you skip over a few pointless parts and just try to explain the basic concepts. In fact, since your kid is already interested, you may even be able to use the math that is in the next chapter to teach him those basic concepts to some degree. Just don’t sugar coat it by trying to make it so you understand it, the kid is the one learning it. Simply, explain the math abstractly and clearly and help the kid when they hiccup on some concept.

    Include some fun and simple experiments, and your kid is well on their way to doing some interesting physics.

    I have been teaching for a long time, and I’m continually surprised how much kids can absorb advanced math. I’d argue that it’s the parents with the problem, since most of the kids seem to be able to understand a ton more math than their parents give them credit for. So much so, in fact, that their parents get mad at me for teaching them it.

  5. #5 DA
    July 8, 2008

    Having a PhD in physics (quantum optics), I remember reading Richard Feynman’s “QED: The Strange Theory of Light and Matter” as a high school student and thinking it was a great, basic intro to the concepts that make quantum mechanics so facinating.

    Read the reviews on Amazon…as the top review there says, part of what makes it great is that Feynman does not create analogies to explain things. Rather, he takes the mathematical and physical concepts behind the quantum mechanics and breaks them down into basic concepts like clocks and arrows. By doing this, you are essentially dealing with vectors and superposition without ever realizing that is what you are doing.

    If your offspring is excited by quantum mechanics, I bet that Feynman would be a great read. And it’s only $4 used on Amazon.

  6. #6 Jen
    July 8, 2008

    I also read Feynman’s QED in high school (before I learned about vectors) and I loved it. I absolutely recommend it to your elder offspring.

    I think the only other non-mathematical treatment of quantum mechanics I’ve read is a book called Beyond Measure: Modern Physics, Philosophy and the Meaning of Quantum Mechanics, by Jim Baggott. It’s a good book, but it goes into a lot more detail than QED, so I suspect a nine year old would have to be pretty motivated to read it (although I don’t actually know anybody who is currently 9 years old). There is actually a little math in this book, but almost all of it is confined to the appendices, and Baggott does a good job of explaining & contextualizing the math that is necessary in the main text.

    With that said, I think the best tool for explaining quantum mechanics is a nice matching set of 3 polarizers…

  7. #7 ec
    July 9, 2008

    This was my intro to QM, in 10th grade, but I think it would be understandable to someone significantly younger. Very little math, maybe some very basic algebra at most.

  8. #8 JYB
    July 9, 2008

    There are these great Sherlock Holmes books by Colin Bruce where Holmes solves all these mysteries using science and math paradoxes. One has physics stuff and is called the Einstein Paradox. I know it has a Many Worlds story. There’s another one about math called Conned Again Watson and has things like the Monty Hall problem and Drunkard’s Walk.

    I love those books.

  9. #9 madarab
    July 9, 2008

    It’s now somewhat dated, but “Quantum Reality” by Nick Herbert will probably fascinate him. It’s pretty light on the math. The only part he might have trouble with is the discussion of complementarity and spherical harmonics.

  10. #10 Alex
    July 9, 2008

    I was a big fan of Alice in Quantumland back in my time. I think I read it around the end of middle school or start of high school, so your Elder Offspring should be able to handle it. There’s no math, it’s all analogies describing things at the quantum level.

  11. #11 Matt Heath
    July 9, 2008

    The Mr. Thompson stories by George Gamow are pretty good. It has trips countries where the physical constants are different, so you can see quantum effects on a pool table (or relativistic ones affecting a cyclist). Between the stories there is more serious explanations but without any heavy maths.

  12. #12 aatish
    July 9, 2008

    What a cool kid! I agree with the QED recommendation. It’s really a fabulous explanation of quantum mechanics (and in fact later on of quantum electrodynamics) using nothing much but little pictures with spinning clock dials. There are some neat lectures to go along with available here:

    It’s certainly a good book to have around. I read it in high school when I’d already learned about vectors, but as a previous poster said, this is really the perfect introduction to them (“you just draw arrows!”). The Mr. Tompkins books are supposedly pretty good pop. sci. books for building some intuition for these things, so that may also be a good idea, though I’ve never read them myself. Many of the above recommendations look quite excellent as well!

  13. #13 ganv
    July 9, 2008

    The best non-mathematical introduction to QM that I know of is “The strange world of Quantum Mechanics” by Daniel Styer. However, it is aimed at non-science college students, and focuses on the deep issues, so probably isn’t right for a 9 year old.

    BTW, I think what he really wants in an experiment. You can do an experiment that gives a hint of QM with three optical polarizers–cheap polaroid sheets work fine. Two crossed polarizers pass no light. But a third placed in between and rotated at 45 degrees to the others allows light to pass through. The first polarizer chooses the quantum polarization state of the photons. A crossed polarizer passes none of these. But the intermediate polarizer ‘projects’ the initial polarization state onto the 45 degree state–which can then be projected onto the 90 degree state. It can’t happen if polarization was a property of particles, but it works for quantum particle-waves (and other kinds of waves). Maybe you want to introduce polarizers first and only bring up Quantum Mechanics later.

  14. #14 Super Sally
    July 9, 2008

    Thanks to all for great recommendations, just in time for b’day shopping…watch the mail next week.

  15. #15 Matthew
    July 9, 2008

    I second the Alice in Quantumland suggestion. I just read it as an adult (with just about no background in quantum mechanics, but enough in the neurosciences and philosophy to get me interested).

  16. #16 Sena
    July 9, 2008


    “The Cartoon Guide to Physics”, by Larry Gonick, would’ve probably worked great in this situation.

    I second this idea!!

    Great stuff.

  17. #17 LO
    July 9, 2008

    You might find something useful in
    * SLAC Virtual Visitors Center
    * The Particle Adventure

    Let me know if you want me to sponsor her for Kids Day at SLAC. None of her age group options include QM, but Option C looks the most interesting to me (actually the older age groups don’t include QM either). She could definitely find someone there to ask though.

  18. #18 Tony Jeremiah
    July 10, 2008

    Physlet Quantum Physics might be useful.

  19. #19 Anna
    July 11, 2008

    (I’ve been thoroughly enjoying this blog for quite a while, partly because I was raised by physical chemists who made science a fun part of everyday life. Thanks for rocking, Janet!) I bet the older sprog could handle the mathy mechanics of vectors and matrices without much trouble–Dad taught me how to multiply matrices in elementary school as essentially a condensed bunch of arithmetic practice problems. Graphically working with vectors should also be possible, a la QED, although grokking the connection between the arrows and the arithmetic is nontrivial. I learned about the Born-Oppenheimer approximation as analogous to my sister and me sitting on the floor playing cards while my brother ran in circles around us. Also, I highly recommend drawing the hats on operators as baseball caps, party hats, etc.

  20. #20 Jonathan Vos Post
    July 12, 2008

    I showed my son when he was about 5 that multiplication of rotation operators in 3-space is noncommutative by giving him a book, approximately an a x b x c rectangular parallelopiped with very different values of a, b, c — and index cards with printed instructions such as: “rotate the book 1/4 turn about the up-down axis.”

    One finds, by randomly drawing cards and following instructions, that a x b is not necessarily equal to b x a.

    So, yes, yay vector space instruction at early ages!

    Oh, and skateboard experts and gymnasts and diving experts, and those who play those on videogames, intutively know the same thing…

    Quantum Mechnics via games. Fun!

  21. #21 penguindreams
    July 13, 2008

    I found myself explaining zero point energy to my 10 year old, so I sympathize. (She’s now debating a physics PhD.)

    I’ll second the QED and Alice in Quantumland suggestions.

    But a good one to bring in the fact that science is done by people, while explaining a lot about quantum, is _30 Years that Shook Physics_ by George Gamow.

  22. #22 LB
    July 13, 2008

    Even the third book of Feynman lectures would do. He introduces the entire concept of quantum mechanics not with mathematics and vectors but rather with particles going through magnets. You get a very good feel for how the operators work on the states and an introduction to bras and kets without any real mathematics at all. But all the basics of quantum mechanics are there.

  23. #23 Lisa
    July 21, 2008

    You might try “From Atoms to Quarks” written in 1980 by James Trefil. It starts with the discovery of the electron and nucleus and tries to take non-scientists through the development of quantum mechanics and particle accelerators and up to the formulation of the standard quark model of particle physics. It uses qualitative black-and-white sketches instead of colorful illustrations, though.

  24. #24 peter zimmerman
    August 8, 2008

    I read Gamow’s “One, Two, Three, Infinity” at around age 10 or 11, so it should be accessible. The Mr. Tompkins (correct spelling; C.G.H. Tompkins, Gamow’s fictional “bank clerk interested in modern physics”)(an exercise for the student to explain the initials) books are still charming and surely readable by a bright 9 year old.

    For a different view suited to a bright 13 year old, Einstein & Infeld’s classic “The Evolution of Physics”.

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