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.

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I tend to agree with your summary, distinguishing between the conceptual part and math part of the two theories. Tensors are a bit more of a slug than Hilbert space. And you don't need to know Hilbert space to do many practical calculations with QM.

But a physics theory also has a conceptual part. Either we can figure out when the wave function collapses, or we are all SchrÃ¶dinger's cat.

I took Brad (and Kuznicki, who he was arguing against originally) to be talking about special relativity, which is after all trivial compared to either quantum mechanics or general relativity.

I suspect Kuznicki regards both special and general relativity as hopelessly arcane, but it's a little difficult to tell. The link he gives is to Feynman's

Six Not-So Easy Pieces, which I haven't read, but Amazon suggests includes General Relativity. Sean is, I think, clearly referring to both.I agree, though, that special relativity is relatively (heh) easy, compared to either quantum or general relativity.

Actually, it was Lawrence Krauss who stated, in an interview with Richard Dawkins, that nobody understands quantum mechanics. Feynmans' statement was a bit more elliptical: "if you think you understand quantum mechanics,then you don't understand quantum mechanics".

So your average office drone "understands" computers because they know how to push a key on the keyboard to create the corresponding letter on the screen.

I know how to turn the crank, therefore I understand the machine.

I guess I think that is a remarkably impoverished definition of "understand." It reduces physical understanding to simply understanding the operation of a formal mathematical system.

I'd characterize that more as avoiding understanding because it is too troublesome or inconvenient. When my intro students solve Newtonian problems by selecting equations from the book instead of drawing free body diagrams, I accuse them of relying on mathematics to paper over a lack of understanding. I can't really think of your argument as anything beyond a more sophisticated version of the same thing.

I generally thought that the problem with understanding quantum mechanics had to do with understanding the actual mechanics, not the philosophy or the math. For example it is relatively* easy to calculate and visualize what happens when light reflects off glass, but can you actually describe the physical process that occurs when the photon is absorbed and remitted? Feynman's description of a diffraction grating is pretty clear, but it doesn't really get into what actually happens. And that is the part that is hard to grasp.

In both cases (relativity and quantum mechanics) there is a bit of a disconnect between understanding the math and being able to truly describe what the actual physical process is. I have a vague vision of little bits of coalesced energy alternately rioting and partying, but I can't really get a visual of what happens when they actually confront one another.

*sorry

I tend to agree with you on this... but I echo what's said above. It's hard to tell what people mean when they say "Relativity". Special Relativity can be fully grokked-- both in terms of practically doing stuff with it, and philosophically-- by human minds without even having to be all the way through a first-year physics course. GR is both conceptually more difficult (even if the basic premise is beautiful and can be stated simply) and mathematically more challenging than SR.

My first reaction to reading Sean's post was the same as yours. "But, but, all undergrads do Quantum, and most physicists don't really have much of a clue about GR!"

Adding a bit to Feynman's description in QED: the strange theory of light and matter, say that a particle HAS a complex phase (so it is automatically a local gauge theory) and then we have 'quantized Newton', and the phases from different paths can interfere - and come to think of it, there ought to be 'special orbits' where there are a whole number of phase cycles in an orbit.

@ pjcamp -- there's way more shades of grey and way more subtlety than that.

Consider the computer example. There are people who know how to use word processors and cruise the Internet. Then there are people who know how to administer their systems and configure them to work really the way they want; this is already a small minority of computer users. Then there are people who know how to program computers. If you are somebody who understands both the administration and the programming, I'd argue that you "understand" computers...

...but that doesn't mean you have the first clue how to design a silicon chip packed with transistors that's going to be able to actually create the computer that you can use as a tool to do tremendous numbers of things.

What is "understanding" really? You can fully understand Newton's theory of universal gravitation-- what it says, what it means, the implications of it. But, on one end, you can't calculate what a three-body system will do without resorting to numerical simulation. And, on the other end, even though you fully understand it, it turns out that it's not reality, but just a model, just an approximation to reality.

Probably both GR and QM are the same. So, at some level, knowing how to use the model to predict what reality does is all the more understanding there is to be had!

Clearly many of us physicists understand Quantum Mechanics at a level far better than being given a black box that predicts the outcome of experiments. Clearly we have some insight about how things work, the kinds of things that will happen. We have the enough intuition to know that something's amiss if we make an error in our calculations and get a nonsensical result. This represents a level of understanding better than what you're dismissing... but it is also different from the level of understanding that means you really grok what's going on when a measurement is made and the state of the system you measure is different from what it was just before the measurement.

I agree with the quoted insert from Sean Carroll. Understanding, like purpose, is a relationship - not an absolute. This becomes self evident when you start asking what the purpose of quantum mechanics or general relativity is. The answer clearly depends on who is asking. To an experimentalist, such as yourself, their purpose is to calculate the perihelion shift of Mercury or the energy levels of the hydrogen atom. To a philosopher, their purpose might be to provide an argument against philosophical realism.

Similarly, the questions of which is easier to understand has no absolute answer. It is a question of relationships. To a hair-dresser (at least any hair-dresser I have ever met) quantum mechanics and general relativity are equally opaque. To a cosmologist who has slowly built relativistic intuition, general relativity is easier to understand.

I do recall Feynman saying that no one understands quantum mechanics in one of his talks. To Feynman, quantum mechanics was much more than a calculation tool - it was a fundamental theory. From his perspective, understanding implies a deep knowledge of purpose. He probably would have said that no one understands gravity. Sure, we have equations and laws that predict the effects of gravity, but no one knows why the laws are they way that they are.

In contrast, Stephen Hawking would probably have no interest in asking why gravity acts the way it does. It might simply be explained by the anthropic principal. Either way, it is not within the realm of questions that science can answer, and thus we can not say anything meaningful about it.

It is only by fooling ourselves into thinking there are absolute answers to these questions that we are able to ask them. As Einstein said, "The belief in an external world independent of the percipient subject is the foundation of all science." Take note that he didn't say "An external world independent of the percipient subject is the foundation of all science." (Also note that I've shamelessly stolen this concept from Weinberg's An Introduction to General Systems Thinking.)

I suspect the arguments come down to relativity still being a classical theory (in the classical semi-tautological sense of it not being a quantum theory). Regardless of the difficulty of the math and visualizing it physically, you still get

one answer, rather than mucking about with probabilities and superpositions and interference. Special relativity is egalitarian â nobody's reference frame is better than anyone else's. Once you latch onto that, the concepts are easier to deal with. Nobody seems to fight the notion that many quantities (velocity, momentum, energy) depend on your frame of reference. I think it's a smaller step from that to time and distance also being relative than it is to, say, atoms diffracting and interfering from a world where they don't do that at all.But as I am also an atomic physics person, I agree that QM is a lot less weird and a lot more intuitive when you deal with it on a regular basis.

I would think that in this context, âunderstandâ means how well the model agrees with the underlying physics. There is nothing mysterious about the models. Some equations are more complex than others, but that should be neither here nor there. However, if the model does not match reality, then there is a lack of understanding about whatâs really going on.

âIn contrast, Stephen Hawking would probably have no interest in asking why gravity acts the way it does. It might simply be explained by the anthropic principal. Either way, it is not within the realm of questions that science can answer, and thus we can not say anything meaningful about it.â

â¦and I would have to agree with him.

I think familiarity has much to do with the distinction. General relativity only plays a significant role in one practical application, namely GPS, and even there it is at such a low level that anybody not involved in designing the system doesn't need to know about it. Since people are generally not confronted with the consequences of relativity (either special or general), they don't have to make the effort to understand it. Quantum mechanics has many practical applications: lasers, microelectronics, chemistry, etc. This is reflected in the curriculum (as Chad pointed out) and in the distribution of faculty by field (in most departments, especially at research universities, the condensed matter/AMO faculty outnumber the cosmology faculty, unless you are at an institute which specializes in the latter). So you are much more likely to encounter somebody who is forced to deal with the consequences of quantum mechanics and therefore needs to understand at least part of the edifice.

For the record, de Long was entirely correct in attacking Kuznicki. The latter was trying to plead for understanding creationists on the grounds that while he (Kuznicki) found evolution rational, he felt he had to take relativity on faith, which is a claim creationists make about the state of the theory of evolution.

Being a mathematician, I have always wondered if general relativity would be easier if it was also taught and learned without coordinates, in terms of abstract vector bundles, abstract tensor products, an abstract Riemannian metric, et c. (Certainly it would be easier for me, and just about every other mathematician.)

The very large

The very small

We dwell at

some time and

some space

in between

Never to be certain

when and where we are

until 'gone' from

some time and

some space

in between

Those who claim relativity is easier than QM have simply not understood the full problematic within GR.

"Easier" is a relative term.

Would agree with Sean Carroll rather than this article.

Just because one can calculate well using something doesn't mean he understands it. Every accountant uses real numbers [rational numbers in a strict sense], but that doesn't mean they have an understanding of how unreal real numbers [say given in terms of dedekind cut] really are. Even if we take rational numbers only, I don't think they understand the equivalence class structure behind it, although they might be doing all the cancelling etc.

The problem with QM for me as an informed layman [I am a software engineer], it looks so incomplete in fundamental way that it can't even be understood without more ingredients.Just as Sean Carroll said, measurement process just drives one nuts. There is an unbridged gap between Unitary evolution part and measurement process. Why should it suddenly jump to an Eigen state just because I looked at it? What is the exact definition of measurement anyway? I can always treat me also as part of the system. Then when exactly would this measurement occur for this combined system? If I treat the whole universe as single system when exactly or how will this wavefunction collapse occur?

In summary, It is hard to understand because it is incomplete and how can we understand something [missing part of the theory] which is not even there.

@Rob - >>...but that doesn't mean you have the first clue how to design a silicon chip packed with transistors that's going to be able to actually create the computer that you can use as a tool to do tremendous numbers of things.

By that token, to understand universe I should be able to build an universe, right?

Also I would think one understood the computer, if they understood say Turing machines, uncomputability, Halting problem than how to build one instance of it using Silicon without any understanding of what is computable in principle etc.

peaking as a non-physicist who took physics in college... and thinks of himself as pretty typical, and an informed layman, and someone who writes abut science a lot professionally...

I have a hell of a lot easier time explaining the basics of relativity to people than QM. And when I actually did the math, at the beginner level, a Lorentz transformation was a HECK of a lot easier to do than the fracking schrodinger equation. Christ, I didn't even know bra-ket notation at all, and so was completely lost. (Had I known it... oh well, at that time the curriculum was all out of order :-( ).

But a lot of basic relativistic stuff can be done without even calculus. t= t0/sqrt(1-(v^2/c^2)) is not all that complicated as these things go.

In that sense, for people who are NOT physics people, and who are NOT deeply involved in the math, I have to give the nod to relativity as being easier to grasp -- again, for us non-physics geeks.

But maybe that is just me.

"Speaking as... " arrrgh

Which is a terrible shame, because not only is GR easier to understand and learn than QM, the geometry it's based on will rescue the poor physics students from the hole which the dreadful conceptual and mathematical mess of the âvector calculusâ of earlier courses has put them in. ;-)