Could someone recommend books on quantum electrodynamics and/or quantum field theory that are understandible to the nonspecialist? By that I mean people well versed in undergraduate physics and math but specializing in some other field. A PhD chemist would be a good example. It seems there are only two kinds of QED and QFT books available. There are the dumbed-down ones for laymen found in shopping mall bookstores that are hopelessly vague and superficial, and there are the opaque tomes full of equations that fill half a page. This is in sharp contrast to books on pre-QFT quantum mechanics that deal with Schrodinger equations, orbitals and so on. There are lots of good books at that level. Why the discrepancy? Is QFT so difficult that it is impossible for anyone but a professional physicist to understand? Any recommendations?
Well, QFT is more complicated than QM, so you’re going to have to expect that any books on it would be more complicated as well. That said, if you’re interested in heuristics rather than foundations, you might try a book on particle physics instead of a full-fledged QFT text; Griffiths is a particularly good one. Zee’s QFT in a Nutshell is supposed to be quite good, too, though I haven’t had a chance to look at it myself.
I’d second Zee’s book. I had a tough time making it through the more high level text used in class (Peskin and Schroder), until I read QFT in a nutshell and was able to get a better grasp on the core ideas of the theory.
The basic non-technical text on the topic of quantum electrodynamics (the quantum field theory of electrodynamics) is Richard Feynman’s QED: The Strange Theory of Light and Matter. Feynman was, of course, one of the founders of modern QED theory and it is usually identified specifically with him in the public consciousness (or at least, the tiny minority of the public that is conscious of it at all) because of his eponymous diagrams, although many others, including Freeman Dyson, John Wheeler, Eugene Wigner, Pascual Jordan, Robert Oppenheimer, Hans Bethe, and of course Julian Schwinger and Sin-Itiro Tomonaga contributed substantially to the theory as well. QED is about the clearest non-technical treatment, which is not to say that it makes the topic completely clear, as I detail more below.
Tony Zee’s Quantum Field Theory in a Nutshell is certainly an easier read than most textbooks I’ve found on QFT, but I wouldn’t describe it as being for the nonspecialist; it still covers the material at a graduate student level (although shifting quickly past some of the uglier mathematics). Murray Gell-Mann and Yuvan Ne’eman’s The Eightfold Way is probably somewhat more accessible as essentially a reprint of the fundamental papers that led to the development of the Standard Model with explanations and clarifications by the book authors. The canonical reference for QFT is, of course, Steven Weinberg’s three volume The Theory of Quantum Fields, but these are definitely texts for the physicist.
As for the difficulty in describing QFT in “layman’s terms”: whereas discrete particle quantum mechanics can at least be described as at least roughly analogous to something we experience everyday–waves in water, for instance–QFT gives rise to a whole host of phenomena that are completely and utterly absurd. This is because any field will have a very large, possibly infinite number of degrees of freedom, making the problem seemingly unsoluable. Feynman et al did an end run around this problem by essentially declaring it to be a purely mathematical construct and that by quantizing the “self-energy” of the field around a particle locus–that is, in the case of QED the cloud of virtual photons swimming around an electron which makes up its EM field–can only have certain quanta of energies. This and the need for rotationaly symmetry gives rise to a limit to the number of quanta that can have any “real” energy, conceptually not dissimilar to Planck’s solution to the ultraviolet catastrophe (i.e. that per the Rayleigh-Jeans classical formulation a blackbody should radiate all the way up to infinity with increasing energy in each little bit of the spectrum, summing to infinite energy). This is the “second quantitization” in QFT, and it basically allows you to cancel out all the impossibilities using a method called renormalization until you are left with not only a real quantity, but precisely–to our limit of measurement–the exact quantity that occurs, which is an phenominally accurate prediction.
The only problem is that you end up doing some mathematical handwaving to get to the solution which. Just as Planck assumed his quantization of light was nothing more than a mathematical formalism describing some more complex and (to him) hopefully continuous phenomena, Feynman and others doubted that QED, despite its predictions, was a complete theory; that hidden behind renormalization was some actual mechanism that doesn’t require cutting space up in bits or dividing out the infinities to get a finite result. When you try to explain all this in terms of someone whose mathematical grounding goes only up to integral calculus and differential equations (pretty much everyone except for mathematicians and physicists) it comes out as complete gibberish that would get you a big red “0” on an algebra exam.
And that’s QED; quantum chromodynamics–the interactions between nucleon particles and their components–is even worse, with particles that can’t be found or played with except in prohibitively energetic reactions, and gauge boson force carriers that don’t even function on any distance we can observe. Photons at least have a manifestation that we can literally see; gluons and quarks may, as far as we can actually measure, be as fictional as the characters in Finnegan’s Wake, and the theory nearly as impenetrable. (Gell-Mann once made the mistake of referring to quarks as “fictitious”, meaning that their binding energies were such that they could not exist in an unconfined state; this was unfortunately taken out of context and intrepreted that Gell-Mann didn’t believe in their existence at all.) The only good thing one can say about QCD is that the math gives very consistent results and has permitted the formulation of a coherent quantum theory of fields for the subnuclear interactions. It has even led to unification between electrodynamics and the weak nuclear interaction, and gone quite a way toward integrating the strong nuclear force to give a unified field theory. (Gravity, on the other hand, hangs way out there like the black sheep ex-felon brother that everybody invites to Chrismas dinner hoping that he won’t show up.)
It’s tough stuff, especially if you want to explain it nonmathematically in a way that doesn’t make you seem like wandering madman.
Stranger
Thanks Stranger for the Advice. We’ve met before, in the thread about the glass prism.
You seem knowledgeable about QFT, so may I ask you a few questions?
What is the metaphysical status of virtual particles? They seem to be just a mathematical artifice which arises only because we have used perturbation theory to describe a perturbed field as a superposition of unperturbed fields. Do they have physical reality or not?
What does it mean to say a particle is equivalent to the corresponding antiparticle moving backward in time?
I can understand how a normal mode of a wave field is mathematically equivalent to a harmonic oscillator, and the nth energy level of that oscillator is equivalent to a beam of n photons. But what about the static field around a stationary charge? That has nothing to do with harmonic oscillators. Why do we say that field consists of virtual photons coming out of and going into the charge?
What is the justification for second quantization? In the early days of QM when they were arguing about the meaning of the wave function, I thought it was settled when Born said the wave function was just a “map” of the electrons amplitude to be found at various points of “configuration space”, which has as many dimensions as there are degrees of freedom. The electron was real, and the wave was just a description of its liklihood of being found with properties a, b, c etc. What happened? Why do we now regard an orbital as a real wave in 3D space?
Thank You
Before reading the other replies, I, too, was going to recommend the Griffiths and Zee books. While Zee is still a graduate-level text, I found that he did a lot better job of explaining the concepts, rather than just presenting wall-of-text pages of calculations.
What is the metaphysical status of anything, for that matter? Assuming that virtual particles exist enables you to perform certain calculations, and make correct predictions about real particles that we can directly observe. If you want to call that “really existing”, then go right ahead. On the other hand, virtual particles can’t themselves be observed, by definition. If you want to call that “not really existing”, then go right ahead with that, too. If you want to say on alternate Tuesdays of months rhyming with “December” that virtual particles exist, but say at other times that they don’t exist, that’s fine, too.
Yes, but you can make them real by observing them. When a particle is tunneling through a potential barrier we say it is virtual because it violates energy conservation by being there. But if you stick a geiger counter there and find it, we say you have exchanged energy with it, giving it enough energy to pay off its energy debt and become real. Does that mean I bring things into existence by observing them, and until then they are virtual?
As to why there’s the discrepency in the sort of simplified books people have published, a lot of it is down to the widespread view that the transition from quantum mechanics to QFT doesn’t really introduce any new physical ideas. Quantising fields necessitates working with all sorts of tricks and technicalities, but the usual view is that none of these rises to the status of a new law of nature. (Personally, I’m not entirely convinced by this minimisation viewpoint in most textbooks and histories, but I recognise that I’m in a minority here.) Which isn’t to say that those technicalilties or the new wrinkles that QFT introduces aren’t endlessly fascinating. But there’s nothing as profoundly startling as, say, the philosophical issues introduced by just quantum mechanics.
I distinguish here - as any quantum field theorist would do - between the methods of QFT and the fact that specific QFTs have proven to be spectacularly good models of nature. Stuff like quarks, QCD and electroweak unification can be popularised without getting bogged down in all those technicalities of QFT and so there are plenty of accessable books discussing such discoveries.
Stranger has already mentioned Feynman’s QED and that is the obvious attempt to discuss QFT in a popular manner. While it’s donkeys years since I read it, I thought it was commendable as the attempt and not misleading, but still bore little relation to how theorists actually think about such matters. I don’t visualise such processes like that - to the extent that I can - and I don’t believe that Feynman did normally either. Very much worth reading, but it is (deliberately) limited.
The closest book to what you seem to want is probably Paul Teller’s An Interpretive Introduction to Quantum Field Theory (Princeton, 1995). He’s writing as a philosopher, rather than as a physicist, and there’s at least one equation on most pages. Yet the aim is to understand the basic ideas in terms of prose rather than algebra. It does assume undergraduate physics and mathematics, but that doesn’t seem to be a problem in your case.
That said, I have reservations. It’s view of QFT was already very, very old fashioned at the time it was published. And, though as someone who wasn’t novice in the subject, the book seemed to me rather pedestrian. It is ultimately just the slowed down, plodding step-by-step through canonical quantisation for non-specialists. Which may, of course, be exactly what you’re looking for.
It’s pretty typical that the actual stepping stone up for anyone wanting to formally pursue the subject to be a course/book that primarily teaches you the mechanics of calculating Feynman diagrams without paying too much attention to the underlying concepts. Just developing the basic muscles. Classic textbooks at that level are the likes of Mandl and Shaw or Halzen and Martin. Books you work through the calculations in as much as read. I get the feeling that that’s probably not what you’re looking for. Something like Ryder or Itzykson and Zuber was the traditional step after that. These days, Peskin and Schroder.
I’ve heard good things about both Griffiths and Zee, but haven’t read them myself.
Incidentally …
The consensus is that it’s much, much worse than that. The vast majority of experts have come to suspect that QED is possibly trivial. In other words that by itself the full theory basically has no content whatsoever.
As far as the claim that QFT adds nothing new to QM, I must disagree, ignorant as I am. It seems to me that there are metaphysical implications, possibly even mystical ones, in the world view it presents. The zero-point energy, for example, that pervades all space. If you probe really closely into a very small portion of space your very interaction brings into existance a cornucopia of particles and their corresponding antiparticles. The more energy you pour in, the more particles come out. It means there is no such thing as empty space! The number of particles in the world is variable. One photon can disappear and be replaced by an electron and a positron, which can then recombine to give two or three photons, depencing on how much energy you put in. Material bodies-things-can multiply and interconvert among themselves. It’s almost as if matter is alive! The distinction between matter and fields breaks down. And, anything that can happen will happen. Any process not forbidden by a conservation law is possible. It’s as if a beer can could suddenly turn into a rabbit if there was no reason why it couldn’t happen. Instead of being dead and inert, matter is unpredictible and creative.
This is why I want to learn it. You could even try to make a religion out of it.
I’d also put in a vote for Zee’s book, supplemented by his Fearful Symmetry
All of which follow as direct consequences of just applying quantum mechanics to classical field theories. There are no magical extra ingredients involved.
One has to be careful to do things consistently and there are all sorts of beartraps, but those are usually regarded as mere technicalities. Well, awkward but doable technicalities.
The answer to all of these questions (no offense intended) is, “Shut up and calculate!” That is to say, when physics students ask these questions, old embittered professors tell them to just do the math and it all falls out from there. The justifications for these approachs, insofar as it exists at all, is that they work to a very high degree of precision. The actual behavior of fundamental particles on the quantum level is subject to interpretation because we can’t directly observe the phenomena in a classical sense of watching them or measuring without significantly influencing the results. The problem with any approach that speaks of electrons or photons being just points (with a bit of weirdly wavelike behavior) is that in some ways that don’t act at all like points particles. And the converse is true as well; they don’t function as waves (waves in what?) because they’re discrete in their interactions. If, as you note in the last question, “the electron was real, and the wave was just a description of its liklihood of being found…” then we have to cope with the fact that it is able to occasionally exceed binding energy barriers or demonstrate diffraction behavior that makes it distinctly wave-like.
The real reality, if I may be excused for using such a term, is that fundamental “particles” are really nothing like particles of stuff that we see everyday, and so of course their behavior is wild and wacky and completely impossible to relate to. Or as Raymond Hall put it, “Stuff is made of particles. Therefore, particles cannot be made of stuff.” Wave/particle duality is another way of saying that we don’t actually know what color the elephant is.
You could easily make a religion out of it, but only by sheltering it from the critical approach of science (which has to be honest and say, “Uhnuhno?” when theory cannot provide an answer) and stuffing all the gaps with manufactured mysticism and made-up mumbo-jumbo. Many people, including some of the leading figures in quantum theory and conceptual physics like David Bohm and Roger Penrose, have tried to extend their theorizing into the metaphysical realm, and all have come off looking pretty silly for the effort, not even because they were necessarily wrong, but because their claims weren’t even testable. (Looking silly is a professional risk of any scientist who seeks to advance a new theory, but the Gallery of Regrettable Foolishness is saved for scientists to make claims that are beyond proof in any sense.) I enjoyed Bohm’s essays on the “implicate and explicate order”, and have to admit an esthetic fondness for his particular interpretation of quantum mechanical basis, but I didn’t walk away with any greater understanding of how things work on any level that can relate back to real, physical experiments. And people like Fritjof Capra and Deepak Chopra are just pitching drivel by making facile and non sequitor-ish analogies between the QM and Eastern mysticism, although I suppose it has made them a lot of money over the years.
The first thing you have to cope with about quantum mechanics, must less quantum field theory, is nobody really knows how it all works, a point Feynman makes repeatedly in QED. (The book is actually an editted transcript of four public lectures Feynman gave on the topic, and he starts each lecture by reminding people that they won’t understand, and that’s okay because he doesn’t either.) All we know is a set of rules that predicts the results (statistically, of course) with a high degree of accuracy. Everything else is beyond the scope for science to address, and I don’t have much faith in the Philosophy or Theology departments to add anything substantial to the discussion. (Although I do think philosophers often ask some of the most beautiful questions about completely inane and obtuse subjects, and come up with some inspired gibberish to address but never answer them. Except Heidegger, the fascist jerk; I can’t abide him.)
Heh, this reminds me of a passage from another Feynman book, “Surely You’re Joking, Mr. Feynman!”: *I still remember a guy sitting on the couch, thinking very hard, and another guy standing in front of him, saying, “And therefore such-and-such is true.”
“Why is that?” the guy on the couch asks.
“It’s trivial! It’s trivial!” the standing guy says, and he rapidly reels off a series of logical steps: “First you assume thus-and-so, then we have Kerchoff’s this-and-that; then there’s Waffenstoffer’s Theorem, and we substitute this and construct that. Now you put the vector which goes around here and then thus-and-so…” The guy on the couch is struggling to understand all this stuff, which goes on at high speed for about fifteen minutes!
Finally the standing guy comes out the other end, and the guy on the couch says, “Yeah, yeah. It’s trivial.”*
QED might be wrong–it might be completely and utterly, without question, wrong in its basic premises and assumptions about how things work–but any theory that replaces it will probably reduce down to something very similar if not identical when dealing with strictly electrodynamic phenomena. Of course, it doesn’t really tell us what is going on, and the whole business of a photon taking all paths and averaging them out is almost certainly a stand-in for some other, possibly even stranger and more inexplicable (in everyday terms) mechanism. But it does have the virtue that it works, and works far better than Eastern mysticism or spacey New Age flurble.
Stranger