Brad DeLong, in the course of something completely different, suggests that the theory of relativity really isn’t all that hard. At least, if your standard of comparison is quantum mechanics.
He’s completely right, of course. While relativity has a reputation for being intimidatingly difficult, it’s a peculiar kind of difficulty. Coming at the subject without any preparation, you hear all kinds of crazy things about time dilating and space stretching, and it seems all very recondite and baffling. But anyone who studies the subject appreciates that it’s a series of epiphanies: once you get it, you can’t help but wonder what was supposed to be so all-fired difficult about this stuff. Applications can still be very complicated, of course (just as they are in classical mechanics or electrodynamics or whatever), but the basic pillars of the theory are models of clarity.
Quantum mechanics is not like that. The most on-point Feynman quote is this one, from The Character of Physical Law:
There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics.
“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 tend to tie quantum mechanics with relativity, just because it seems natural that one really leads you to the other, rather, that was my experence with quantum mecanics and then relativity. It’s nice some one notes that connection just this once.
I once tried to understand quantum mechanics, but I couldn’t find this damn “Hilbert space” where it all seems to happen.
I would rank the hardness by the math involved. General relativity (you need new symbols and techniques just to get the basics), quantum mechanics (mostly calculus), and special relativity (mostly algebra). I am simplifying but that’s where most people start off.
My shortened version :
GR : you change the equations of motion of “stuff”.
QM : you change the notion of what you think is “stuff”.
A series of epiphanies, yes that is a great description. I remember the first time I calculated and completely understood a set of Christofell symbols for a given metric. After that, I never quite understood why I thought it was hard.
Blunt Instrument @2: I think that’s the point at which you should just say “Fock it” and move on to quantum field theory…
I actually found quantum mechanics near impenetrable and finally after self studying for a while (Using Griffith’s and Shankar’s books) gave up altogether. Just this past December I bought a copy of Schutz’s A First Course Course In General Relativity and have been able to get through the first quarter of it with very few troubles. In fact, it’s the most enjoyment I have ever had using a textbook! So yes, I agree that on some level GR is much easier to understand than QM – if only because I find the math a lot more “elegant” and the assumptions that lead up to it are much more open to intuitive reasoning.
In fact, my next purchase is going to be a copy of Spacetime and Geometry: An Introduction to General Relativity (I was planning on going: Schutz, Carroll and then Wald. Hopefully), but I was actually wondering if there was any plans for a second edition on the horizon? I’m going to order a copy either way, I just didn’t to shell out the cash and then not long after see that an updated version is coming out! Sorry, I hope that’s not too off topic!
What’s really hard is understanding why there’s an advertisement for some new-age snake medicine on this page. Quantum Pendant, indeed! (It’s not always there: it shuffled out on a reload.)
Relativity is not that hard if in classical mechanics some typical examples of “relativity” are considered first. A tree from a distance looks smaller and needs calculations to get the right (proper) size, for example. In relativity such calculations involve time intervals too but the principle is the same: one obtains different raw experimental data in different RFs and needs recalculations to get the “proper” data.
Yeah, I thought the deal with GR isn’t so much conceptual, it’s just that solving realistic metrics is incredibly difficult. Of course, calculating the complete electronic structure of ammonia, or the mass of a proton straight from the equations of QCD, is also incredibly difficult, so they say.
As for the conceptual stuff, I agree. If the fact that all observers, no matter where, what, how, measure the same speed of light (in a vacuum, of course) sinks in, a lot that’s important about relativity (so I’m told) sinks in too. Throw in the equivalence principle, and you’re pretty much the rest of the way, at a pop-sci level of understanding.
All discussion of QM is strange and metaphorical. One could as justifiably say “weird shit happens in Hilbert Space, and out pops the world you at least think you’re seeing” as “God throws dice where you can’t see them!” It’s all pretty much meaningless. There are these equations, with the most profound symmetries, built at times from the most abstract and unintuitive (to me, anyway) mathematical objects, and they seem to describe nature as precisely as humans could ever hope to measure it.
But is that really any more hard to get?
Another difference is that, while surprising, relativity fits firmly within the tradition of ‘classical’ physics, whereas qt clearly doesn’t
Relativity is only “hard” because we don’t teach classical mechanics properly.
In my opinion, classical and quantum mechanics are equally easy to understand if we point out that in any case we study complex objects needing many bits of information. One point on a photo film is not sufficient in both cases. Only many-many points give an idea what the “object” is.
“Hardness” is not a property that inheres in a theory itself
You mean “hardness” isn’t a quantitative measure of a particular quality of: metal, rock, elements, etc? I am so easily confused.
Well, I would say it depends upon whether you’re talking about General Relativity of Special Relativity. Special Relativity, of course, is quite easy. But General Relativity, not so much. I’d rank it as roughly on par with Quantum Mechanics, with no definitive way of saying which is harder.
The reason I’d rank GR up there is the concept of general covariance, which leads to all sorts of weird behavior that, to a lot of people, doesn’t seem to make any sense. Examples include things which apparently move at faster than the speed of light (as is the case with the usual definition of recession velocity and most of the visible galaxies), or an apparent failure of conservation of energy (which happens for anything that has any sort of pressure in an expanding universe).
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If you surf around on the web, you can find fun little movies of gravitational waves, what you might see if you fell into a black hole, etc. These graphical depictions may not have the horsepower to provide total realism, but they are “realistic” in that they’re not metaphorical depictions.
There’s a fun little app. I have called “Atom in a Box”. This lets you fiddle with quantum numbers, and shows you the probability density of various excited states of an electron in a hydrogen atom. “Superposition” is especially cool, giving you a look of sorts at hybrid orbitals.
However, if I understand things correctly, these pictures I see are pure fantasy. True, they accurately describe the odds, but the “real” picture at any given time is rather boring: A point. All those beautiful lobed shapes don’t “exist” anywhere. That’s not “really” what’s happening to the electron when I’m not looking at it. In fact, the whole idea that I can “not look” and thus see what the electron is “really” up to when I’m not observing it is an utter contradiction, right?
Sure, it’s difficult at first to get your head around the fact that while quasar X has only been receding from us for some number of billions of years, it’s really some-or-other-many billions of light years away right now. But, by God, it’s a big ancient glob of stars and whatever’s left of that young galaxy we can see in our telescope is right where we say it is in spacetime. If you can get all the light cones straight in your head, it’ll make sense eventually.
What the heck am I legitimately supposed to say about a picture of a d orbital? It’s in there somewhere? It’s smeared out? It’s discrete, yet everywhere at once? All of those things might be legitimate so long as you preface each statement with “It’s as if…” We can describe what electrons can be thought of as doing whenever we’re not looking, but taking the square of the absolute value of a (complex) amplitude to even call the odds does seem more than a tad mysterious when it gets down to what’s “actually” going on. I get that the numbers work out, but what, exactly, is being worked out?
The premise of Greg Egan’s Incandescence was that relativity’s not that hard, so a neolithic-level insect species figures it out because of their asteroid’s unusual dynamics.
GRT hard, SRT not.
>> GRT hard, SRT not.
Not really – replace n by g and , by ; and carry on.
LM, WI: “What the heck am I legitimately supposed to say about a picture of a d orbital? It’s in there somewhere? It’s smeared out? It’s discrete, yet everywhere at once? All of those things might be legitimate so long as you preface each statement with “It’s as if…” We can describe what electrons can be thought of as doing whenever we’re not looking, but taking the square of the absolute value of a (complex) amplitude to even call the odds does seem more than a tad mysterious when it gets down to what’s “actually” going on. I get that the numbers work out, but what, exactly, is being worked out?”
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Tout le monde interprets the wavefunction as a probability distribution.
But there is another interpretation that was favored by Schroedinger: that the electron, after it is bound in the atom, is decomposed into myriad virtually infinitessimal particles which are physically distributed throughout the atom, and the wavefunction is then interpreted as the actual physical distribution of the electron’s mass/charge.
Schroedinger said he much preferred changes in excitation to be viewed as deterministic changes in the vibrational properties of the envelope, rather than as a point-like electron jumping from orbit to orbit acausally, and the probability smoke and mirrors.
A.O. Barut and others have made attempts along these lines, but with limited success. Some would say that the approach is destined to fail. Others say that this highly intuitive approach, with its pictorial/conceptual potential and lack of black-box magic, has never been adequately explored.
Bottom line: A new physics that unifies GR and QM in a way that makes both of them equally easy to understand, at least conceptually, is quite possible. But before physicists can make their own “jump” into the new paradigm, they will need to admit that some of their most cherished assumptions are only limited approximations, such as: differentiability, reversibility, strict reductionism, non-dissipative systems, and all the other Platonic fantasies that are holding us back.
Albert Zwiestein
“Hard” is the operative word. I think we need to separate “conceptually hard” from “computationally hard.
e.
Relativity is “hard” because there’s like one million books full of confusing stories about spaceships and lasers and somebody observing somebody’s something, which is all completely irrelevant decoration. As a teenager I read a whole stack of these books and failed to make much sense out of them because one starts asking all sorts of questions about the construction of clocks and what it means to actually ‘see’ something etc. Then, hallelujah, somebody handed me a book in which it said the Poincaré-group is the symmetry group of Minkowski-space.
Yes, I know, you’ve written one of these math-less books. I’m just saying I believe that pop sci shouldn’t shy away from mathematical definitions and equations to accompany the blabla. We all know the math is clearer and sometimes I think lack of it doesn’t only give the average reader a completely wrong impression about theoretical physics, it actually makes matters more complicated.
Yes, but with a Complete Set of Commuting Observables I can completely describe a state. What QM tells us is that it is nonsensical to talk of position and momentum as absolutes, instead we must talk of states. QFT tells us that we can only talk about input and output particles and the states of those particles. These things are not hard.
As someone who qualitatively understands a heck of a lot, but hasn’t bothered to learn the math and isn’t likely to, I can’t say that I’d be in the faintest way pleased to learn that the Minkowski-group is the symmetry space of the Poincare group. I topped out at Calc II in HS, and the underlying foundations that would have to be learned for me to make heads or tails of most mathematical equations wouldn’t exactly be satisfying.
As for what’s “harder,” I find special relativity totally nonintuitive. I mean, I still “get it,” in that once I conceive of c being the same in all frames, I can intellectually see why length shrinks and time dilates. But I haven’t really internalized it; every time I envision it I have to think through the individual steps each time.
QM, on the other hand, I feel like I get pretty well, because I decided long ago that “wave/particle duality” is simply our failure to properly perceive the underlying probabilistic nature of reality. Discovering that there are wave equations for everything that “entangle” or whatever only reinforced that. It’s quite possible I’m getting something horribly wrong, but it’s not difficult for me to conceive of “things” as bounded by no more than their likelihood of being in that spot at that time.
But if I had to work with the MATH of it? Good gracious, no please.