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?
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.
http://www.amazon.com/Alice-Quantumland-Allegory-Quantum-Physics/dp/0387914951/sr=8-1/qid=1159459457/ref=pd_bbs_1/103-9288903-4086239?ie=UTF8&s=books
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.
Gavin
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
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.
maybe you should write a book on qm too…make it fun…because it is the coolest ideas ever
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.
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.
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”.
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.
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.
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:
http://arxiv.org/abs/gr-qc/9903084
http://arxiv.org/abs/hep-th/0104219
http://arxiv.org/abs/quant-ph/0604008
‘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.
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.
Count,
Ah yes the old “Superdeterminism” loophole. And if you start to believe in superdeterminism doesn’t it inevitably lead to …
Elliot
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.
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.
“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!
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.
nc,
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.
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.
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.
I am surprised that so far no one has suggested the excellent text “The Quantum Challenge” by Greenstein and Zajonc.
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.)
A good place to start is at the begining:
http://arxiv.org/abs/quant-ph/0609184
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.
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 !
J,
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.