I think I can safely say that nobody understands quantum mechanics. ~ Richard Feynman
I can safely say that, since your modern electronics work, a lot of people "understands" quantum mechanics.
Feynman's comment should be taken in context.
It appears, for instance, in QED lectures, where he emphasizes the ability of QED to predict the outcome of experiments but still asserts that nobody understands it, painting it as a method of doing the maths analogous to ancient peoples predicting eclipses by moving stones between bowls. All that has happened since then is that "predicting the outcome of experiments to high reliability" has become what we mean by "understand". Similarly, those ancient peoples would have said the same thing. Did they understand eclipses?
The success of modern electronic components (the macroscopic devices don't need QM to put together) illustrates the success of QM as a calculation method.
Considering that science is a work in progress, I'm not sure that "understanding" is a useful way to describe our state of knowledge - hence the emphasis on "predicting outcomes". It's "thems the rules" -- also Feynman. However, it is often useful as a loose distinction in teaching undergraduate physics.
Caveat: What we mean when we say we understand something is, in this context, somewhat over-subject to philosophy ... so there is a limit to how much we can discuss it here.
We could debate all day wether QM calculations to predict, say, half-lives, are the same sort of understanding as moving stones to predict eclipses ... but I think that sort of debate is more usefully resolved via pistols at dawn so I decline. What is clear is that there are different sorts of "understanding" (or the debate wouldn't arise) and we need to be careful not to mix them up.
Different people different standards, which are also different in different situations. Just as the statement is vague about what "explaining" entails, I was consciously vague about what "understanding" entails. In a way - being able to explain to someone else, could be treated as a definitive result. After all, we have a reasonable idea what to expect when someone says they understand something, and, if we don't believe them, we would challenge them to explain it to us, would we not?
When we are addressing questions from the lay public, we have to be careful not to read scientific meanings into the common-use words they use. When a layman refers to "understanding", what is usually wanted is some narrative in terms of cause and effect ... they want us to tell them a story that they can cope with.
To a physicist, this would usually mean "classical mechanics".
That is just not possible with quantum mechanics as it is a superset of the classical.
If we knew how to put it in classical terms, we would not need modern physics.
So, in that sense, it is safe to say that, "nobody understands quantum mechanics".
 QED lectures
 I'm hoping these quotes are sufficiently famous not to require full citation.
 As use by Feynman in "The Character of Physical Law lectures".
I've always taken it to mean nobody has really developed an intuition for QM phenomena. Yeah, after you look at some equations you can understand tunneling will happen, electrons will stay at certain energy levels, etc., but how many people can make those sorts of predictions before going through the math? What conceptual understanding do we have which lets us relatively consistently predict what's going to happen?
Feynman meant he did not understand quantum mechanics. Here are two of his errors in http://www.feynmanlectures.caltech.edu/III_01.html#Ch1-S7. (I would like to stress that the lectures are very marvelous and full of insight, and well worth reading.)
Error 1: We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by “explaining” how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.
Feynman was referring to the double slit experiment. Why is it mysterious? It is natural that different experiments can give different results. You can find a discussion of this error in the introductory section of http://arxiv.org/abs/1301.3274.
Error 2: “Well,” you say, “what about Proposition A? Is it true, or is it not true, that the electron either goes through hole 1 or it goes through hole 2?” The only answer that can be given is that we have found from experiment that there is a certain special way that we have to think in order that we do not get into inconsistencies. What we must say (to avoid making wrong predictions) is the following. If one looks at the holes or, more accurately, if one has a piece of apparatus which is capable of determining whether the electrons go through hole 1 or hole 2, then one can say that it goes either through hole 1 or hole 2. But, when one does not try to tell which way the electron goes, when there is nothing in the experiment to disturb the electrons, then one may not say that an electron goes either through hole 1 or hole 2. If one does say that, and starts to make any deductions from the statement, he will make errors in the analysis. This is the logical tightrope on which we must walk if we wish to describe nature successfully.
Bohmian Mechanics provides a counterexample to Feynman's reasoning. It is not an error that was unique to Feynman, since Bohm himself made the mistake in his textbook which was published a year before he discovered an explicit example of a hidden variable theory. Historically, von Neumann made the error also. Although von Neumann's error was known to a few, including Grete Hermann, the error was not widely known until Bell's 1966 article.
Another example of Feynman making the same error is found in the following video at 49:00.
Despite Feynman's errors, there are certainly things in which quantum mechanics differs from classical mechanics.
1. In the orthodox quantum formalism, a quantum pure state can be considered the complete state of a physical system. More mathematically, a pure state is an extremal point in the space of density matrices. What is different between quantum and classical extremal points is that the quantum state space is not a simplex.
2. A classical relativistic theory is a theory of causality - correlations are explained by causes that are within the past light cones of each event. However, a quantum mechanical theory that is relativistic does not satisfy this, showing (to my surprise) that relativity can tolerate a degree of nonlocality. Surprisingly, Popescu and Rohrlich showed that relativity can tolerate much more nonlocality than even quantum mechanics allows.
He meant in terms of pictures developed from everyday experience and part of our intuition.
As you get experience in it and become familiar with its weirdness you understand it - Feynman most certainly did.
I'm confused about why Feynman's statement is seen as an error. The context was that he was talking about the double slit experiment with electrons to an audience who had (presumably for the most part) only ever seen classical mechanics and possibly classical wave theory, but for whom an electron was a particle, with a trajectory. To them, the double slit experiment would surely seem mysterious.
With the state of understanding today, you would probably say, that "it contains the only mystery" is no longer true. When I attended QM lectures (~30yrs ago), there was no mention of entanglement issues or any of the modern quantum foundations thinking, so to us much of the "mysterious" part of QM would have been encapsulated in the double slit behaviour.
The Fuchs/Schack reference looks very good though, I look forward to reading it...
The meaning of things generally, not just this statement, but generally, is usually contextual. The issue here is what context you think the statement was made in. The different answers all have a different take on context.
@atyy: Feynman most definitely did not mean that he was the one that didn't understand QM. He would have said so. If he said nobody he meant nobody. It is another question what he meant by "understand". I also don't understand what you mean by errors! It seems that you are suggesting that he really didn't understand and made errors about the most basic experiment in QM! In fact it seems that you are suggesting that only Bohm (and people who like bohmian mechanics) understand QM!
Well, I'm being a bit cheeky there. It's not as clear cut an error as his second statement that the particle cannot have a trajectory, and that hidden variables are impossible.
But what I'm thinking here is that I don't see why the double slit is mysterious at all. Why should particles have trajectories? Why shouldn't one have a theory whose only predictions are random? Why shouldn't different experiments give different results?
Anyway, the Fuchs/Schack reference starts off by saying that it seems that Feynman made an error here, giving the same criticism as me: 'Without such a guarantee for underwriting a belief that some matter of fact stays constant in the consideration of two experiments, one—it might seem—would be quite justified in responding, “Of course, you change an experiment, and you get a different probability distribution arising from it. So what?”'. They cite in footnote 4 Koopman and Ballentine who also think the same way (wow, I'm agreeing with Ballentine?). But interestingly they go on and try to argue that maybe he was right in some sense. But let me quote bhobba first:
Now I want to take bhobba out of context - but maybe for good reason - bhobba stresses *context*. Maybe quantum mechanics is strange because the formalism is *non-contextual* via Gleason's, but it is *contextuality* that lies behind the intuition that different experiments give different results! Comment on this point welcomed!
Incidentally, while most nowadays would say that it is the Bell tests and nonlocality that is the mystery, apart from the Quantum Bayesian defence of Feynman's "only mystery", I believe Griffith's Consistent Histories also does the same, because that interpretation weakens reality so much that Griffith can reasonably argue that quantum mechanics is local (I'm not sure he is right, but I think his argyument is at least very reasonable).
Yes, I am saying the Feynman did not understand the most basic experiment. First he claimed mystery where there is none - it is simply that different experiments give different results. That is not so clear cut an error, as he might have been referring to something else. However, it is part of the reasoning that eventually leads him to a clear error - that trajectories are impossible, and that hidden variables are impossible. I think it is worth discussing that Feynman's mystery, rejection of trajectories and hidden variables all come from his wrong underlying assumption that because the formalism is "non-contextual", reality must therefore also be "non-contextual".
Just asking to make sure I understood what you were saying. Well, then if Feynman didn't understand the most basic experiment, then I don't see what I could possible contribute to this discusion.
"Mystery" is itself somewhat contextual.
It will, however, appear if you dig deeply enough into just about anything... and Feynman was one of the all-time great deep diggers.
Yes, so how's this for an attempt to make Feynman's mystery correct? In general things should be contextual. Different experiments should give different results. The mystery of quantum mechanics is that its formalism is non-contextual, although reality is contextual.
I think this is more or less what Fuchs and Schack argue in the introduction of http://arxiv.org/abs/1301.3274 (left column of p3, including footnotes 4 and 5)?
I think there are different standards of "understanding". Able to use something to get sensible and useful results is a kind of understanding. I wouldn't say it's the full story, though.
Sure: Feynman was describing the standard interpretation of quantum mechanics. I suppose he could have pointed out that there are other interpretations... going into them each in detail would have been beyond the scope of the lecture series.
To my knowledge, nobody has ever measured the pilot waves of bohemian mechanics, and there is stil some fitting to do in terms of lorentz invariance and non-locaity. However, it remains an intreguing classical analogy to quantum phenomena.
We don't need to go into the various failings of different interpretations in this thread, anyway there's a sticky somewhere...
Anyway, the pilot waves seem to be outside of classical mechanics so, even if we were to accept the Bohemian mechanics view, it still does not invalidate the observation: we still don't "understand" QM in the sense usually intended by the layman and in the sense Feynman spells out in numerous sources (recall he was adressing a lay audience in both examples I gave). Just the usual observations on interpretations (none is more empirically true than any other etc) kinda underlines the point.
Perhaps "nobody understands quantum mechanics" means "there is no place under quantum mechanics" - in the sense that, within physics, QM itself must be the most basic framework of understanding...
Makes you wonder...
Ever play 20 questions? The underlying premise is like classical realism - it assumes the person has actually chosen, well defined, and isolated the object you are to guess and you then proceed to ask questions about the object that they must answer "yes" or "no". The premise of realism implies and entails that with sufficient time (and faster using various strategies) one could determine the object they have selected. A brute force approach would be to ask of each of the 10^90 or so particles of the observable universe, "Is this one part of it?"... there are better strategies to speed this up... but the idea is that eventually you will find the object in question.
Ever play 20 questions with a child? Sometimes they will randomly answer your first question "yes" or "no", and then answer all subsequent questions in such a way that all previous answers remain always self-consistent... the narrowing class of possibilities containing the object you seek to identify continues to have the appearance of realism but in fact there is no real chosen selected object at all, only a formal procedural process - a series of crafted questions always met with consistent answers...
The first time my little niece pulled this on me it kinda blew my mind.
Since your niece is classical, this means quantum mechanics is classical. But I don't know whether your niece is nonlocal!
Or maybe Wheeler learnt it fron his niece too, and there is only one niece in the whole universe, like Wheeler's electron - that might count as nonlocality
In case that was too cryptic, one can try this description of Wheeler's "it from bit" http://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ or Leifer's wonderful essay on Wheeler's aphorism http://arxiv.org/abs/1311.0857.
Separate names with a comma.