Sean Carroll and Brad DeLong have each recently asserted that relativity is easier to understand than quantum mechanics. Both quote Feynman saying that nobody understands quantum mechanics, but Sean gives more detail:
“Hardness” is not a property that inheres in a theory itself; it’s a statement about the relationship between the theory and the human beings trying to understand it. Quantum mechanics and relativity both seem hard because they feature phenomena that are outside the everyday understanding we grow up with. But for relativity, it’s really just a matter of re-arranging the concepts we already have. Space and time merge into spacetime; clocks behave a bit differently; a rigid background becomes able to move and breathe. Deep, certainly; inscrutable, no.
In the case of quantum mechanics, the sticky step is the measurement process. Unlike in other theories, in quantum mechanics “what we measure” is not the same as “what exists.” This is the source of all the problems (not that recognizing this makes them go away). Our brains have a very tough time separating what we see from what is real; so we keep on talking about the position of the electron, even though quantum mechanics keeps trying to tell us that there’s no such thing.
I disagree slightly, for the usual reason that I find myself disagreeing with Sean (and Feynman). I think he’s absolutely right in a philosophical sort of sense, but that’s not the only way to look at the problem. In an operational sense (which is my normal inclination, being an experimentalist by training), I think it’s probably true that more people understand quantum mechanics than (general) relativity.
Of course, the key item here is the definition of “understand.” If you take “understand” to mean “have a solid grasp of the philosophical foundations of the theory,” then it’s true that relativity is a lot simpler than quantum mechanics. The philosophical foundation of relativity is really a single idea (“The laws of physics appear the same to all observers regardless of their motion.”), and everything follows from that. The philosophical foundation of quantum mechanics is a mess– there are still active and contentious debates about what, exactly, a wavefunction is, whether it represents a real physical thing or just the state of our knowledge about reality.
However, there’s more to the world than philosophy, Horatio, and there is a sense in which I think it’s true that more people understand quantum mechanics than relativity. That is, if you take “understand” to mean “have enough grasp of the mechanics of the theory to calculate something,” then the number of people who understand quantum mechanics is vastly greater than the number of people who understand general relativity. Every undergraduate physics major takes quantum mechanics and does at least some calculations with it; a great many physicists never take general relativity, even in graduate school.
The mathematical situation of the two theories is the mirror image of their philosophical condition. General relativity, while philosophically simple, is fearsomely complex mathematically. I couldn’t begin to tell you how to calculate the perihelion shift of Mercury, and I read about it in a textbook not three days ago. Quantum mechanics, on the other hand, is relatively simple. I’m not an ace theorist by any stretch, but I can tell you how to calculate a whole bunch of atomic energy levels and other properties.
Which of these you regard as more important is a matter of taste, and familiarity. Sean’s first quoted paragraph above strikes me as an excellent example of familiarity breeding… not contempt, exactly, but an underestimate of the difficulty of the subject. Sean is a cosmologist and thus spends lots of time thinking about general relativity, so of course it seems easy to him. My comments are probably something of the same thing in the other direction– I don’t do wavefunction calculations every day, by any stretch, but my experimental background is in what might broadly be termed quantum optics, so I’ve spent a lot of time reading papers about quantum phenomena, which means I’m not that troubled by them.
None of this, of course, means that whatever Brad DeLong was arguing against wasn’t stupid– I’m not sure what kicked this off, and life is too short for me to go find and read whatever it was– but as someone who wrote a popular book on quantum physics with relative ease, and is now mired in trying to explain general relativity to his dog, I don’t think you can so blithely assert the simplicity of relativity compared to quantum mechanics. There’s a very practical sense in which quantum mechanics is far better understood than general relativity, and my own inclination is to value practicality over philosophy.