Quantum Mechanics Made Easy?

By Sean Carroll | September 28, 2006 2:48 am

I was recently asked to recommend a good popular-level book on quantum mechanics. I don’t think I know of any, at least not first hand. We had a whole thread on the Greatest Popular Science Book, filled with good suggestions, but none specifically about quantum mechanics. A quick glance through amazon.com reveals plenty of books on particle physics, or even specific notions like quantum computing, but not one book that I could recommend in good conscience to someone who just wants to know what quantum mechanics is all about. It is the greatest intellectual achievement of the twentieth century, after all.

There are some books that either come close, or might very well be perfect but I’m not familiar with them. In the latter category we have The Quantum World by Ken Ford, and David Lindley’s Where Does the Weirdness Go? These might be great, I just haven’t read them. I’m sure that the Mr. Tompkins books by George Gamow are good, since I love One, Two, Three… Infinity (and Gamow was a genius), but I haven’t actually read them. Feynman’s QED is another classic, but focuses more on quantum electrodynamics (duh) than on QM more generally. David Deutsch’s The Fabric of Reality is a fantastic book, especially if you are curious about the Many-Worlds Interpretation of quantum mechanics; but I’m not sure if it’s the best first introduction (I haven’t looked at it closely in years). And David Albert’s Quantum Mechanics and Experience is great for a careful philosophical account of what QM is all about, but again maybe not the best first exposure.

Any suggestions? Not for a good book that is related to quantum mechanics or perhaps mentions it in a chapter or two, but for something whose major goal is to provide a clear account of QM. Surely there is something?

  • http://members.cruzio.com/~quanta Nick Herbert

    When Australian consciousness philosopher David Chalmers was teaching a course on the physical basis of consciousness a few years ago he sent out a call to his friends to vote on the most user-friendly first book on quantum theory. My own book “Quantum Reality” was considered too technical for a naive reader. The vote went to “Ghost in the Atom” edited by Paul Davies which is a collection of BBC interviews with quantum-mechanical greats about the foundational questions prefaced by a wonderfully clear summary of QM by Paul Davies himself. I voted for GITA too. Short and snappy–a good book to whet your appetite for stronger stuff. Heinz Pagels’s “Cosmic Code” is also a fine popularization.

  • http://airminded.org/ Brett

    I second the nomination of Heinz Pagels’s The Cosmic Code. The Mr Tompkins books are very good, though.

  • Fran

    In Search of Schrodingers Cat by John Gribbin is an excellent book. It covers everything from the basics up to the many worlds interpretation and the spin paradox. No previous knowledge is assumed (I read it when I was 16) and explains evertyhing clearly.

    It is this book which made me start my undergraduate degree!

  • Johan Couder

    the best introduction to Quantum Mechanics for laypersons I have ever read unfortunately exists only in Dutch:
    Lijnse, PL : Kwantummechanica, Het Spectrum – Antwerpen, 1981
    This book contains the best description of the (in)famous 2 slit expiment I’ve ever seen, and moreover, the author doesn’t shy away from simple mathematics, such as (single variable) calculus. The book is actually aimed at last year secondary school / high school students.

    But if you want something in English:
    J.P. McEvoy, Oscar Zarate, Introducing Quantum Theory,
    Icon Books, 1999
    Extremely funny (including Schrodinger’s sexual escapades) and surprisingly good.

    just my 2 eurocents

  • nc

    Feynman’s Character of Physical Law and his QED books introduce the double slit experiment, which is at the heart of the weirdness, without hyping the assumed interpretations. Feynman also has a passage in the former book saying that path-integrals become infinitely complex on the smallest of distance scales (he was clearly thinking about the ultraviolet cutoff in quantum field theory), so he concludes that part of the “weirdness” problem in quantum mechanics and field theory may be artefacts of the complex mathematical modelling, and the underlying physics is probably simple if you can ever discover the deep simplicity, “like the chequer board with all of its apparent complexities”.

    In the QED book, Feynman mentions that the reason for the wavy orbital (Schroedinger probability distribution) when electrons are confined on the atomic scale is simply that the space is so small that interference occurs with particle loops created in the ground state of the quantum vacuum, and the same accounts for the double slit experiment.

    Most popular books focus on speculative interpretations (if they are bad hype books) or focus on mathematics alone.

    It depends what you want to learn about quantum mechanics. If you want to know the deep meaning, steer away from religious hype and read Feynman, and study quantum field theory because that underlies QM and is still incomplete. If you want to use quantum mechanics, there are many good books with titles like Introduction to Quantum Mechanics. A beautifully clear and accurate explanation without mathematical details (he uses graphs of propability distributions to explain the Schroedinger equation) of how the periodic table of elements follows from the four quantum numbers (and where those numbers come from) is given by Professor Samuel Glasstone’s 1972 book “Inner Space: the Structure of the Atom”.

  • http://www.pieterkok.com/index.html PK

    For me also the first to spring to mind was the Dutch book by Piet Lijnse, but it has been out of print for many years now. I read it in my last year as a high-school student and was blown away. I suspect Lijnse is emeritus professor now (he is/was professor of physics education at Utrecht University), so perhaps he can be convinced to write an updated (English) version.

  • http://christinedantas.blogspot.com Christine Dantas

    – What Is Quantum Mechanics?: A Physics Adventure (Paperback)
    by Transnational College of Lex (Editor)

    But start first with their:

    – Who Is Fourier?: A Mathematical Adventure

    It was written by Japanese students who knew nothing about the subject! So they report what they have learned (under the advise of a senior physics tutor). The books have a very unusual style with Japanese cartoons all over, but THEY ARE GREAT BOOKS. One could start them without even knowing what a trigonometric function or complex number is. They construct all concepts needed and reach a reasonable advanced level. Highly recommended.


  • http://www.twistedphysics.typepad.com Jennifer Ouellette

    I really enjoyed Robert Gilmore’s “Alice in Quantumland,” an allegory explaining quantum mechanics a la Lewis Carroll. Very amusing and clever, and quite accessible to a non-scientist…

  • Navneeth


    In Search of Schrodingers Cat by John Gribbin is an excellent book. It covers everything from the basics up to the many worlds interpretation and the spin paradox. No previous knowledge is assumed (I read it when I was 16) and explains evertyhing clearly.

    It is this book which made me start my undergraduate degree!

    That could’ve easily been my reply if I had seen this post sooner. :) John Gribbin is one of my favourite pop-sci authors; I own and have read quite a few of his books.

    This particular book was published in the mid 80’s. There is a sequel to it – In Search of Schrodinger’s Kittens, which covers supersymmetry and more esoteric stuff, although I haven’t read that book yet.

    is a fun to read, though it may not be as “rigourous” pop-sci book. 😀

  • Navneeth

    Not for a good book that is related to quantum mechanics or perhaps mentions it in a chapter or two, but for something whose major goal is to provide a clear account of QM.

    Gribbin’s introduction to the book starts as follows:

    If all the books and articles written for the layman on relativity theory were laid end to end, they’d probably reach from here to the moon. …But if all the books and articles written for the layman on quantum theory were laid end to end, they’d just about cover my desk.

    You can also find an extensive bibliography on nothing but quantum theory/mechanics mostly at a non-technical level and the end of the book.

  • JoeK



    In Search of Schrodingers Cat by John Gribbin is an excellent book. It covers everything from the basics up to the many worlds interpretation and the spin paradox. No previous knowledge is assumed (I read it when I was 16) and explains evertyhing clearly.

    It is this book which made me start my undergraduate degree!

    That could’ve easily been my reply if I had seen this post sooner. :) John Gribbin is one of my favourite pop-sci authors; I own and have read quite a few of his books.

    That could’ve easily been my reply if I had seen this post sooner. :) John Gribbin is one of my favourite pop-sci authors; I own and have read quite a few of his books.

  • http://students.rockefeller.edu/fross/ Fred Ross

    Maybe I’m a bit off base, but I recall Sir Nevill Mott wrote an ‘Outline of Wave Mechanics’ (which may be hard to come by these days) intended for high school students. It wasn’t a pop science book though.

  • nc


    Gribbin changes his tune a bit between “In Search of Schroedinger’s Cat” and “In Search of … Kittens”.

    In the first (80s) book he explains the Copenhagen Interpretation but says he is most taken with the “many world’s” interpretation, and sees the weirdness as definite evidence that “nothing is real” (but then how to you clearly define the word real, so this is just obfuscating).

    In the more recent (90s) “Kittens” book he is keen on Cramer’s transactional interpretation of quantum mechanics, but still doesn’t seem to appreciate that quantum field theory is the essence of it all. In a Yang-Mills quantum field theory, a static field is actually an ongoing exchange of gauge bosons between charges.

    Recently (2004) he wrote “Deep Simplicity” which starts off promisingly with an important quotation from Feynman concerning quantum mechanics, but then the rest of the book is just essays about chaos theory, and steers clear of quantum mechanics. (When I emailed him last year with some suggestions, it led to arguments. It seems he is nowadays happy with publishing contracts for writing books on topics already popular, and doesn’t have any enthusiasm for breaking new ground.)

  • Hiranya

    I read Mr Tompkins as a kid and it make a huge impression on me. I think it would be great for a teenage reader.

  • http://www.farrellmedia.com/lemaitre.html John Farrell

    Nick Herbert, count me among the readers of Quantum Reality (which I still have in hard cover); enjoyed it very much! I seem to recall Owen Gingerich once recommending Zukav’s book–although from the cover it strikes me as a little too ‘hey, wow, quantum weirdness, man!’…


  • Chinmaya Sheth

    Someone who knows some basic Physics concepts (maybe high school physics) would find a substantive and fun introduction in D. F. Styer “The Strange World of Quantum Mechanics”

  • http://www.philipdowney.com/weblog/ Philip Downey

    I think Brian Greene’s “The Fabric of the Cosmos” is the best description of the double-slit experiment and other phenomena that I have come across. He goes through it slowly and clearly.

    I will temper that by saying I have not read many of the other books that have mentioned.

  • J

    I hate to be pedantic, but nc, QFT does not “underlie” QM in any reasonable
    sense of the word. You don’t derive QM as some approximation to QFT and
    you don’t have to understand QFT to understand QM. QFT is simply QM as applied to relativistic fields.

  • Elliot

    “The Quantum World” by J. C. Polkinghorne.

    A short easy read. Very accessible.


  • nc

    Hi J,

    You’ve got it back to front! QFT is the general theory valid in all situations, and QM (although it came first by historical accident) is merely an approximation to it, obtained by assuming non-relativistic cases. Schroedinger’s equation is a non-relativistic Dirac equation, and in fact you can in theory apply QFT path integrals to the atom, ie QM.

    If you examine QFT, polarized pair production occurs in the vacuum where the electric field is over about 10^16 volts/metre, which is the field strength within about 10^-15 metre from an electron. The loops of charges randomly being produced within 10^-15 m of an electron cause small scale deflections to the motion of the electron.

    Over a large distances, the random interferences cancel out and so a beta particle in a vacuum appears to go in a straight line, but on the atomic scale the interference spoils its closed elliptical orbital into chaos which is described by Schroedinger’s equation. (Although his hidden variables theory is wrong, Bohm did show in 1952 that an electron suffering effectively from a kind of Brownian motion interference from a chaotic gas of charges reuslts in Schroedinger’s equation. However, be warned that Bohm’s infinite potential theory is wrong.)

  • Johan Couder


    However, be warned that Bohm’s infinite potential theory is wrong

    Why do you insist that Bohm’s theory is wrong ? I always thought physicists didn’t like it only because his theory made things unnecessarily complicated, not because it was wrong per se ?
    Is your remark perhaps in some way related to it being a truly non-local theory ?

  • http://aspoonfulweighsaton.blogspot.com/ Spoonful

    “In Search of Schrodingers Cat by John Gribbin is an excellent book. It covers everything from the basics up to the many worlds interpretation and the spin paradox. No previous knowledge is assumed (I read it when I was 16) and explains evertyhing clearly.

    It is this book which made me start my undergraduate degree!”

    Did I post as Fran earlier and not remember?

    I agree, this book blew my mind when I read it. I haven’t read it since I’ve “really” learned QM, so I’m not sure if I can judge it accurately, but it definitely was life-altering.

  • nc

    Hi Johan, Bell set up an inequality to test Bohm’s class of hidden variable theories experimentally. Aspect did it around 1982: photon spin correlation indicated that either the wavefunction collapse doesn’t occur at the time of the measurement, or else that there is quantum entanglement involving instantaneous action at a distance (the photons were metres apart, going in different directions when their polarization was measured and found to rule out Bohm’s theories).

    Either way, this seems to rule out Bohm’s hidden variables which invents unobserved/unobservables (hidden variables) instead of building on established QFT facts (pair production polarization effects are observable in high energy scattering) which do have lots of evidence:

    ‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ — I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

    ‘… the effect of the polarization of the vacuum … amounts to the creation of a plethora of electron-positron pairs around the location of the charge. These virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (i.e. lower energies).’ – http://arxiv.org/abs/hep-th/0510040 p 71.

    If you look at equation 8.20 on p 85 of http://arxiv.org/PS_cache/hep-th/pdf/0510/0510040.pdf you will see that pair production occurs when the electric field strength exceeds ~10^18 v/m. This occurs at roughly 10^-15 m from a fundamental charge, corresponding to the distance of closest approach in head on collisions of 0.5 MeV electrons, which is the energy taken as the infrared cutoff in equation 7.15 on page 70 of that text. This vacuum polarization effect leads to renormalization of charge. Obviously gravitational charge (mass) can’t be polarized as there is only one type of gravitational charge, so therefore quantum gravity must be non-renormalizable!

    It is a shame that quantum field theory is buried deeply in technical jargon and math, instead of being popularized. There is loads of evidence for it from particle physics.

  • Brett

    Quantum field theory really has nothing to do with the difficult interpretational questions of quantum mechanics. It does have a lot to say about what quantum mechanics means in general, however. Yet QFT, despite what it may say e.g. in the introduction to Peskin and Schroder, is a very difficult subject to understand. For one thing, it is most ephatically NOT simply quantum mechanics applied to fields. We build up QFT using the notation of QM, and this works quite well until one goes about calculating loop corrections. Then one must introduce infinite renormalizations. The renormalization of infinities is is a basic component of QFT that exists nowhere in the QM framework.

  • thm

    What about Introducing Quantum Theory from Totem Books’ Introducing… series? (The blog software is choking on my attempt to link to the book’s page.)

    I’ve generally been a fan of Oxford University Press’s A Very Short Introduction series, but the Quantum Theory book isn’t getting good reviews on Amazon. An anthropologist friend of mine discussed the series on his blog.

  • bw

    I read this in high school so it is probably a little dated, but very readable. Takes the Flatland approach to explaining science. Alice in Quantumland.


  • Gavin Polhemus

    Feynman’s QED is the book I recommend. Feynman teaches quantum mechanics to the interested lay person. Every other book I’ve seen is either for scientists or talks about quantum mechanics without actually teaching quantum mechanics. Feynman uses the path integral approach, but he is teaching quantum mechanics, not quantum field theory. In addition to having the best content, QED is also cheep, small, and widely available. I loaned my copy to a high school student yesterday.

    If you want a book that talks about the weirdness without actually doing the math, then John Gribbin’s In Search of Schrodingers Cat would be my recommendation. This book addresses the interpretation issues with seriousness, and without wallowing in them as many books do. Even so, I would only recommend this book with QED, not as an alternative.


  • nc

    Hi Brett,

    Renormalization physically is just the effect of taking cutoffs on the energy range for vacuum polarization. The key thing about how QFT differs from QM is pair production. The interference to the motion of the electron from the randomly produced pairs is the source of the chaotic motion of an electron inside the atom.

    The infinite renormalization involves two limits on the polarization, a lower limit so-called ‘infrared’ cutoff which occurs at the threshold electric field strength needed for pair production, and an upper limit ‘ultraviolet’ cutoff.

    The 0.5 MeV infrared cutoff sets a distance limit on polarization, preventing the entire vacuum becoming polarized for an infinite distance around an electron (this infinite polarization would completely cancel all real charges, which we know simply doesn’t happen). The higher energy or ultraviolet cutoff prevents the pair production/annihilation loops containing infinite momenta at zero distance from the electron. It is obvious that as you get to smaller volumes, closer to the electron, the space isn’t big enough to contain massive loops. The ground state of the vacuum is energised by the field, so a strong field produces heavier loops, but there is a physical limit on this when you get so close to the electron that the space is so small that there are simply no ground state particles in that that volume that can be energised and polarized by the field’s gauge bosons. At that distance (and not at zero distance or infinite collision energy!), a cutoff is needed to make the equation work, see eq. 7.13 on p 70 of http://arxiv.org/PS_cache/hep-th/pdf/0510/0510040.pdf

  • Dick Thompson

    Nick Herbert’s Quantum Reality was the first popularization of Quantum Mechanics that really gave me a feeling of what was going on. All the others, including the Gamow books had this flavor of talking down to the peasants, simple explanations for simple folks. Herbert’s on the other hand felt like the kind of explanations the grad student would come up in his own mind as he covered these topics in class.

    I’ve looked as What is the Quantum and Who is Fourier in bookstores and they look like a good introduction for somebody say in AP calculus in high school.

  • qm

    maybe you should write a book on qm too…make it fun…because it is the coolest ideas ever

  • http://countiblis.blogspot.com Count Iblis

    nc, I don’t see how Bohm’s theory is ruled out by Aspects experiment, as it is a non-local theory.

    I read Pagel’s Cosmic Code when I was in high school. I agree with Nick and Brett that this is a very good book. Pagel does a good job of explaining the Bell inequalities in his book.

    I don’t like books that are somewhere inbetween popular books and real textbooks. The best textbook on quantum mechanics is The Principles of Quantum Mechanics.

  • http://snews.bnl.gov/popsci/contents.html Blake Stacey

    My early encounters with QM were a mishmash with no ulterior organization: Asimov’s Chronology of Science and Discovery, then Gleick’s Genius and Feynman’s QED a couple years later. I’d still recommend all of those, although only the last one is really focused upon the topic of this post. I also picked up a bit from the Mechanical Universe TV series, which I first saw and loved during first grade (no joke) and periodically re-watched later, thanks to VHS tapes dubbed off the Public Broadcasting System.

    Somewhere in there, I read Schroedinger’s Kittens by Gribbin. The material up to the Epilogue was pretty good, I vaguely recall, though the transactional interpretation stuff in the Epilogue didn’t really stir me, let alone persuade.

    In high school, I knew enough to tell when the statements in our textbooks were ludicrously wrong. For example, I believe it was my ninth-grade bio book which, in presenting some chemistry background, said that electrons could not be precisely located within atoms because they move too fast.

    (That book also came with a sticker from the State Board of Education: “This book discusses evolution, a controversial theory which some scientists propose . . .” Pretty much exactly the Cobb County phrasing.)

    I look forward to seeing which books this thread eventually chooses.

  • nc

    Count Iblis,

    See http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XI

    “This subject was assessed by the NSF of the USA as follows [Cushing, J. T., review of Bohm, D., and Hiley, B., The Undivided Universe, Foundations of Physics, 25, 507, 1995.] “…The causal interpretation [of Bohm] is inconsistent with experiments which test Bell’s inequalities. Consequently…funding…a research programme in this area would be unwise”.

  • Cynthia

    If you’re looking for a fun, cartoon-like read, I’d recommend Jim Al-Khalili’s “Quantum: A Guide for the Perplexed.” However, if you want a little more depth as well as historial content, I’d suggest Tony Hey’s “The New Quantum Universe.” While John Gribbon’s books cover quantum interpretation in greater detail, Al-Khalili does an admirable job with this aspect of quantum mechanics.

  • http://eskesthai.blogspot.com/2006/09/cosmic-rays-in-atlas.html Plato

    Of course I am partial to “cosmic rays cascading” with Alice, in regards to Atlas as measure. The picture of Alice on name leads to early implications from study?

    The Slides of Gerard Hooft may be helpful?

    Schrodinger’s Kittens and the Search for Reality, John Gribbin was good.

  • http://countiblis.blogspot.com Count Iblis

    nc, I’m not really a fan of the Bohm interpretation. But it does reproduce quantum mechanics exactly. One can object about nonlocality etc. but it doesn’t contradict tests of Bell inequality unless you put in extra constraints. That seems to be the case in the article you quote.

    Note that you can even have local hidden variables, see e.g. here:




    ‘t Hooft says that this is possible because of the “small print” in the proof that local hidden variables are ruled out, e.g. predeterminsm (all the possible loopholes were identified by Bell himself and can be found in his original papers).

    In the proof of Bell’s theorem it is assumed that the experimentator can arbitrarily decide which component of the spin to measure. However, in a deteministic theory the observer is also completely deterministic and has no choice whatsoever about what he/she is going to measure.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Thanks for all the good suggestions. For those who are interested: quantum field theory really is just a particular example of quantum mechanics. Honestly. (It’s not, obviously, a particular example of non-relativistic quantum mechanics.)

    Quantum mechanics is (on one telling) the idea that things are described by wave functions that live in a Hilbert space, evolving according to Schrodinger’s equation, such that the probability of observing something is given by the wave function squared. All of those things are perfectly true in quantum field theory.

  • Elliot


    Ah yes the old “Superdeterminism” loophole. And if you start to believe in superdeterminism doesn’t it inevitably lead to …


  • http://www.quantumenigma.com Fred Kuttner

    If I can toot my own horn, my colleague Bruce Rosenblum and I have written a book just published by Oxford University Press titled “Quantum Enigma:Physics Encounters Consciousness.” The blurbs on the back cover quote an author of an older, excellent popularization calling our book “…the simplest, correct demonstration of the Great Quantum Dilemma that I have ever seen….” In another blurb on the back cover, a physics Nobel laureate called it “A remarkable and readable presentation….” There is web site about the book, http://www.quantumenigma.com.

  • raj

    The first 100 or so pages of Greene’s book The Elegant Universe gives a pretty good introduction to quantum theory and to general relativity. The problem is that the rest of the book is devoted to string theory, and, quite frankly, that portion is horrible.

    My favorite PopSci physics book is Jonathan Allday’s Quarks, Leptons And The Big Bang, which I bought at the MIT Coop a few years ago. Not only does it lay out relativity, quantum theory, particle theory and cosmology, it also goes into detail regaring experiments and experimental set-ups that provide evidence for the various theories that are discussed. The latter is one thing that I found severerly lacking in most science texts.

  • AR

    “We build up QFT using the notation of QM, and this works quite well until one goes about calculating loop corrections. Then one must introduce infinite renormalizations. The renormalization of infinities is is a basic component of QFT that exists nowhere in the QM framework.”

    Brett this is not true, though in practice this statement will usually hold. Renormalization does not require infinities. Regularization of infinities requires renormalizing the parameters of the theory, but one could renormalize the parameters in the theory without any infinities anywhere. Also in quantum mechanics one can and one needs to renormalize– even in the simplest nondegenrate time independent perturbation theory one needs to do wave function renormalization. I think Sakurai’s Q. Mech text has a good description of it. As Sean pointed out QFT is Q.Mech system for infinite degrees of freedom.

    “Renormalization physically is just the effect of taking cutoffs on the energy range for vacuum polarization.”(post#28)

    Again, renormalization is the redefinition of parameters. UV cut-off(regularization) is one way of redefining your parameters. But one could do something completely different– for example prescribe the values for some n-point functions at some energy scales. Coleman’s lecture notes and his Symmetries have the best discussion of renormalization anywhere. It is a wonder why such a fantastic set of lecture notes have not been turned into a text!

  • http://countiblis.blogspot.com Count Iblis

    The remormalization procedure was also used in classical electrodynamics in an attempt to treat the problem of an accelerated charge in a consistent way in the late 1800s.

    Suppose you accelerate a charge by switching on an electric field. The accelerated charge will emit radiation and the backreaction of that radiation will cause the acceleration to be less than the applied electric field times the charge divided by the mass.

    The backreaction is due to the interaction of the charge with its own electromagnetic field. The problem is that for point charges the local electric field is singular. So, you must regularize the problem by replacing the point charge by a small sphere, introduce a bare mass that yields the correct experimental mass etc.

    I don’t think that the renormalization problem of classical electrodynamics was ever solved in a satisfactory way.

  • J


    QFT is a complicated subject and abounds with conceptual difficulites.
    In attempt to clarify things I will add two points to what Sean said.

    1. It is simply not true that “Schroedinger’s equation is a non-relativistic Dirac equation.” This is an old point of view that one sometime encounters at
    the end of bad (or old) books on QM, but it is not true. The two equations have
    completely different meanings. If you would like to understand the details
    I recommend the historical introduction from Vol I of Weinberg’s book on
    QFT. He says “the wave fields phi, psi etc. [refering to solutions to the
    Klein-Gordon and Dirac equations] are not probability amplitudes at all,
    but operators which create and destroy particles in the various normal modes.
    It would be a good thing if the misleading expression `second quantization’
    were permanently retired.”

    2. It is also not true that “The key thing about how QFT differs from QM is pair production.” In QFT the Hilbert space has a vacuum, one particle states,
    two particle states, one particle and one anti-particle states and so on. Pair production involves transitions from one of these QM states to another and
    is perfectly well described by QM.

    That’s it for my attempt at pedagogy. I must now go prepare for more serious
    things like the friday night poker game.

  • http://world.std.com/~mmcirvin/ Matt McIrvin

    My own major pop introduction to quantum mechanics was one that, later, I realized was actually very bad: Fred Alan Wolf’s Taking the Quantum Leap, which neologistically muddies various issues so that it can get into all sorts of wooly speculations about the quantum nature of consciousness near the end. But it got me interested enough to learn enough to realize that it was full of nonsense, so maybe it did its job well anyway.

    The first really good book on the subject I read was the Pagels.

  • http://countiblis.blogspot.com Count Iblis

    J, there is nothing wrong with second quantization. In a sense, you can consider the Dirac equation, Klein Gorden equation as classical field equations and quantize them. There is nothing wrong with that procedure.

    You can argue that the classical system is not physical, but in case of bosons, you can give a physical meaning to the classical field equations. Take e.g. the Classical Maxwell equations.

    Another example is the Gross-Pitayevski equation that describes a Bose-Einsten gas. It is essentially a classical equation for the density of a Bose Einstein gas that you can obtain from a full quantum mechanical treatment by ignoring certain commutators in the large N-limit. If you quantise this system again you can calculate certain excitations that you could also obtain directly.

  • http://thisquantumworld.com Ulrich Mohrhoff

    I am surprised that so far no one has suggested the excellent text “The Quantum Challenge” by Greenstein and Zajonc.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Count Iblis, I think J’s point (and one that I have made a billion times) is that, when you “consider the Dirac equation, Klein Gorden equation as classical field equations and quantize them,” you’ve only quantized something once. It’s not the procedure of “second quantization” that is an antiquated relic, it’s just the nomenclature. You start with some classical degrees of freedom and you quantize them; whether or not you start with a finite or infinite number doesn’t change the heart and soul of the procedure.

    (In the late ’80’s, when people were thinking about wormholes and Euclidean quantum gravity, there was some talk about “third quantization.” Ick.)

  • Paul Valletta

    A good place to start is at the begining:


    The interpretations contained are detailed in historical value, as well as intepretational value.

    One reason there is very few books detailing QM, is that there are limitations to the understanding, hence a Feynman quote:
    Anyone who STATES they understand Quantum Mechanics, knows nothing or very little of Quantum Mechanics.

    One of the driving forces of QM, HUP, is that you cannot KNOW with absolute certainty, that your interpretation is the correct one?

    QM, at its heart as a number of variables, all open to intepretations, many hidden variables could be given first choice.

    Quantum Mechanics is really still an “OPEN_BOOK”, yet to be completed and formulated into precise and Universal intepretation!

    Quite simply, a book on QM has yet to be written.

  • Jimbo

    To paraphrase Feynman, “Nobody really understands QM”. He was referring to scientists. If THEY can’t, how can the average Jack `n Jill, devoid of math skills ? As someone who’s taught college physics for 10 yrs, I can certify that most young people cannot wield a = F/m, much less H[psi> = ihd[psi>/dt . Such pop books on QM exist only to earn royalties for their authors from physics `wannabees’, and convey little else except buzz words. Best to tell them Sean, “View Google’s Quantum Physics Double-Slit Expt.-What-the-Bleep movie”. Check it out everybody !

  • nc


    your first comment contradicts your second, and both are completely wrong:

    “1. It is simply not true that “Schroedinger’s equation is a non-relativistic Dirac equation.” … If you would like to understand the details … “the wave fields phi, psi etc. [refering to solutions to the
    Klein-Gordon and Dirac equations] are not probability amplitudes at all, but operators which create and destroy particles in the various normal modes….’

    “2. It is also not true that “The key thing about how QFT differs from QM is pair production.” … Pair production involves transitions from one of these QM states to another and is perfectly well described by QM.”

    1. is wrong because the non-relativistic Hamiltonian in Schroedinger’s time-dependent equation is H = ½ (p^2)/m.

    But the relativistic Hamiltonian for Dirac’s equation is H = apc + bmc^2. The values of a and b form the Dirac spinor, which allow two solutions to the energy of the particle, E = ± mc^2. Hence it predicts antimatter. Pair production is the production of a particle of matter and its antiparticle.

    The Dirac equation predicts antimatter, which QM doesn’t. Pair production is antimatter + matter production. This relies on Dirac’s sea, which is the physical interpretation of Dirac’s equation for the negative energy states. This is unique to Dirac’s equation. I explained that QFT deals with pair production/ annihilation, operators which create and destroy particles, and how indirectly this controls QM.

    2. Your second point is pretty disingenuous, since having in your first point pointed out that the key difference between QFT and QM is pair production/annihilation, you in the second point refute this. You also say that QM predicts describes the Dirac sea. No, QM doesn’t unless you modify it which is EXACTLY what what I’d like to see: the injection of the Dirac sea into QM to explain physically the basis for the probabilistic nature of QM as depending on the QFT field occuring loops randomly around the electron and deflecting its motion erratically on small scales.

  • J

    Thank you nc. I now understand your point of view perfectly and see that it
    was an error to engage you on this topic. And I won’t chase flush draws.

  • http://thisquantumworld.com Ulrich Mohrhoff

    “Quite simply, a book on QM has yet to be written.” — How true. And thanks to Paul Valletta for the precious link. It says in the abstract that

    The proceedings contain much unexpected material, including extensive discussions of de Broglie’s pilot-wave theory… and a “quantum mechanics” apparently lacking in wave function collapse or fundamental time evolution.

    I am pleased as a punch, for I keep reiterating till I’m blue in the face that the transmogrification of a probability algorithm into an evolving instantaneous state is at the root of the whole semantic mess.

  • Philip

    How about The Dancing Wu-Ii Masters by Gary Zukov?

  • http://quantumnonsense.blogspot.com/ Qubit

    All beginners should read the 1857 version of rumpelstilskin, the stories always come before the equations, it’s easier to understand and it’s from the point of view of Schrödinger cat http://www.pitt.edu/~dash/grimm055.html. “CURIOSITY KILLED THE CAT” just before Schrödinger did, The Washington Post on 4 March 1916. Coincidences?


  • dearieme

    When I studied freshman physics and chemistry (admittedly a million years ago) I was glad I’d read “The Strange Story of the Quantum” by Banesh Hoffman.

  • Joseph

    For laymen, I would recomend a less technical or complex book such as The Strange Theory Of the Quantum, but if you feel you must challenge your mental capacity then read The Universe in a Nutshell by Dr. Hawking. I would advise taking notes in some chapters because of the complexity of the equations, such as Hawking radiation or as it can be used to Find black hole entropy properties, which i attempted to solve for myself and ended up with a negative value so i believe i have either accidentally reproduced Hawking’s time travel theory or just mistook G for the wrong quantitive value….

  • http://watered-down-physics.blogspot.com Alan Reifman

    I have a website called Watered Down Physics, where I — a non-physicist — try to explain physics concepts for a general audience. I do a lot of reading in physics and the entries on my webpage represent my distillation of this material. Because I’m not a trained physicist, I make sure to stick closely to original source material.


    In the summer and fall of 2005, I wrote a series of essays on quantum mechanics, with plenty of external links. My writings on quantum mechanics appear on the following 2005 entry dates (see the archives section on my site):

    July 27: Intro to Quantum Mechanics

    August 2: Double-Slit Experiments

    August 13: Heisenberg Uncertainty Principle

    September 3: Quantum Entanglement

    September 10: Probabilistic Elements, Copenhagen Interpretation, Many Worlds Interpretation

    September 22: Discrete Units, Bohr Atom Model

  • http://www.markfay.id.au Mark

    The Quantum Zoo by Marcus Chown is a fantastic and very interesting read for the total-non-physicist.

    Chown begins each chapter with a paragraph story, and then starts walking you through the very basic theory, leading right up to an “AHA” moment where the reader spots the connection between the story at the beginning of the chapter and the theory that has been presented. Just to be sure you got it, Chown spells it out, and then goes deeper into the theory once the reader has grasped it.

  • Pingback: Kepler’s law (following on from previous post) « Gravity()

  • http://virtuallyshocking.com Brock Tice

    Leon Lederman’s “The God Particle”. I thought it was fascinating and entertaining, even if the name is unfortunate.

  • http://www.cathodixx.com Prince

    I am not a high fallutin theoretician. Just a simple Materials Scientist; however, since I have read Feynman’s lectures and especially his analysis of the electrical self-energy of an electron; I have been perturbed by this problem. I believe that it also lies at the root of renormalisation in QED. It seems to me that one will never be able to really understand QM or QED if one cannot solve this problem without requiring renormalisation; and this I believe could lead to a reinterpretation of QM and QED.

    The question I would like to ask is the following: How do one knows that there exists an electric energy field around a solitary charge. As Heisenberg has argued, if you cannot measure it, it probably does not exist. So how do you measure the existence of this field? One cannot do so by using a “test charge”, because then you do not have a solitary charge anymore! Furthermore according to Coulomb’s law you only have an interaction between seperated charges. When you set one of the charges equal to zero, the force goes to zero. Could it be that there is NO electric field energy around a solitary charge, and that by calculating this energy around an electron charge one calculates something that does not exist. My humble experience has led my to believe that when one finds infinities in a theory you are, most probably, calculating something that does not exist. Any comments to redirect, or renormalise, me?

  • http://www.myspace.com/djedeye Usama Dafaalla

    Parallel Worlds by Michio Kaku is brilliant…it’ll take you from the beginning to the end of time and back again whilst using all types of physics including QP to illustrate the journey…

  • Luccas Raine

    “Quantum Mechanics for Dummies,” is a great place to start when first trying to understand QM. Here is a link.


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .


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