Barnacle, my first suggestion would be that he separate the two topics and just pick one of them. There’s not really any particular connection between relativity and quantum mechanics, beyond the fact that a lot of people don’t understand either. Specifically, I would recommend that he go with the relativity: Special relativity can be understood, nearly in its entirety, by a bright 7th-grader who’s had algebra. Quantum mechanics can’t be understood by anyone.
Oh, and this is the best introduction to special relativity I’ve ever seen. It’s long, but if he takes it slowly, piece by piece, he’s probably competent to process most of it.
General relativity is more complicated, and he won’t have the math to do it justice, but nobody expects that of a 7th-grader.
FOR YOURSELF, or even folks who have retired from school many many years ago, there is the way in which a full understanding of Special Relativity can fit in your mind in an almost purely visual manner. To discover Special Relativity on your own in this manner, all you need to be able to do is think.
If you can simply analyze the concept of “motion” in your head, even with your eyes closed, then you can independently discover Special Relativity all by yourself. If, however, thinking is no your thing, and thus you have to be taught instead, then there are plenty of websites that will “Teach” you about Special Relativity.
Too see the thought method in action, watch the 9 mini videos at http://goo.gl/fz4R0I ( total time = 1 hour 39 min. )
I’m not so sure. I mean, I agree quantum mechanics is difficult and certainly the mathematics is well past a 7th grader (past most undergrads too I’d think). But do you really need the math to have a basic grasp of any of it? Especially for 7th graders?
I think the concepts can be grasped just fine. Enough to let the implications blow their minds. Richard Feynman said that the double-slit experiment “has in it the heart of quantum mechanics". I think a good explanation of the double slit experiment to 7th graders is very doable and sets the stage for why QM is mind blowing.
Yeah, he may insist on keeping to his plan of doing both. I probably shouldn’t worry too much- it’s really an English paper, not a science paper. I imagine that he could paint with a broad brush, bring out the weird highlights of each, and finish with a description of their mutual incompatabilities and a mention of efforts to unify them with quantum gravity. It might look more like newspaper science writing.
That is still pretty complicated. I still that he will get more out of focusing on just one of these (such as special relativity) and getting a deeper understanding. But all I can do is guide…
On the subject of incompatabilities, I thought that relativity was accounted for in QED (and QCD?). Am I wrong about this? Or is it the wrong kind of relativity (special, not general)?
Special relativity plus quantum mechanics is fine and their combination indeed serves as the basis for QED and more. General relativity, which introduces dynamics into spacetime itself, has not been successfully handled by any quantum theory.
How long is this report meant to be? A few options, depending on length:
Pick one of QM, SR, or GR (in that preference order) to give a “gee-whiz” report about the weird stuff that happens. There would be no understanding conveyed, just a magic show to excite the masses.
Pick SR and discuss both the weird stuff and its underpinnings. The two postulates of special relativity are very easy to understand, and all the weird stuff that falls out from these can be demonstrated quantitatively without much work. (Contrast: the postulates of quantum mechanics.)
Pick one or two or three of the topics and treat them together in a report about new physics of the 20th century. This would be a history paper more than a science paper discussing the historical contexts surrounding the development of these ideas. If the treatment were cursory, one could hint about what new physics might be on the horizon for the 21st century. If the treatment were in depth, than just a single topic could fill the whole report easily.
Yes. There are four different things you can hope to do with quantum mechanics. First, you can do the math. This is beyond the scope of a 7th-grader, or even of most adults, but it can be done. Second, you can seek out analogies for quantum behavior. This can be done, in some cases, but most of the analogies suck, and either fail to convey anything interesting, or require your audience to already understand the thing you’re trying to explain. Third, you can develop an intuitive understanding of it. Or rather, you can hope to do that, but nobody, even including the physicists who are comfortable with the calculations, ever really has much luck with it. Absent any of these first three, about all you’re left with is what amounts to just reciting trivia facts. Anyone can do this, if they find some source for the facts, but this is mind-numbingly boring.
From my naive point of view, I don’t see what makes the basic math of quantum mechanics (that of vector spaces with a positive-definite complex inner product?) intrinsically more difficult than the basic math of special relativity (that of vector spaces with a (3, 1)-signature real inner product?). But then again, I don’t understand any physics…
Well, I’m not sure there’s much to the idea that quantum mechanics is intrinsically more difficult—you can certainly treat even classical mechanics with mathematics of great complexity, i.e. the full formalism of Poisson manifolds, symplectic structures, etc.; it’s just that usually, you can do useful things in classical mechanics (or special relativity) using simpler math than you need to do anything useful in quantum mechanics. Part of that is certainly that we don’t yet know how to do the same things in a simpler way—QM is still a relatively new subject, and while there has already been some great simplifications regarding things that were done early on, much of it is still somewhat rough-and-ready pioneer work. But in general, you need to delve more deeply into the subjects to make progress—in SR, you can basically get away with thinking of the Lorentz group as being a set of matrices acting on vectors by multiplication, while if you’re doing, say, particle physics, you need to look somewhat more seriously at the attendant group- and representation theory.
Also, since the fundamental equation of QM is a partial differential equation which can get quite complicated even for simple problems, you need to know a bit about the attendant theory; and depending on what you’re interested in, and how you approach these subjects, you’ll need at least some passing familiarity with things like operator algebras, functional integration (for solving Feynman integrals), of course linear algebra, and so on. There’s even people working out a category theoretic formulation of QM. So I don’t think it’s really the case that you can say ‘you need to know this math for SR, and that math for QM’, with this math being in some sense less complex than that math, and either being some fixed field of study, but rather, that you have your own mathematical toolbox that you apply to your field of study in whatever way you can—with the observation being that typically, nontrivial things can be done using simpler tools in SR than in QM, and equally or even more complex tools being needed for general relativity, quantum field theory or string-/M-theory etc.
To start with, you’re not going to get very far in QM without calculus, while you can do most of SR without it. Remember, the question is in the context of a seventh-grader.
Fair enough. I am thinking of how, for example, in discussions of quantum computing, all that seem to be used are finite-dimensional spaces (no calculus! Just the manipulation of complex matrices). But perhaps looking only at that cannot be considered going very far into the actual physics.
I disagree it is boring or that examples without math are uninteresting or not of much use.
There are many successful books and TV shows from the likes of Carl Sagan and Stephen Hawking and Brian Greene and Brian Cox (to name a few) that suggest explaining these complex subjects to the public in an understandable way and without advanced (or even any) math are very popular. More, these scientists felt it is important to explain the complex things to the public in a way the public can understand (doesn’t hurt they make money on it too).
These are 7th graders so the math is out. What you can do is excite them about the fascinating world that is around us and how it really works. I think that is a worthwhile endeavor and can be interesting for them. While some refinement and a true, deep understanding is lost without the math there is still plenty there to intrigue people.
For example, the perspective given by Scott Aaronson here could be introduced and discussed in substantial depth without any calculus. But, sure, one wouldn’t be able to solve the Schroedinger equation for specific Hamiltonians or such things.
I look at the issue (i.e., the 7th grader context) from the other direction: what is the simplest thing you can do that demonstrates a non-intuitive physical consequence of SR or QM using only the tools and the “classical” (“intuitive”?) knowledge the student already has. For QM and a 7th grade student, you get the empty set here. For SR and a 7th grade student, you can take the postulates of SR and demonstrate quickly (and with nothing more complex than the Pythagorean theorem) the consequences of time dilation and length contraction. In principle you could go much further still, but it would get tedious quickly without more advanced tools.
Note that it’s GR that’s significant in Interstellar, not SR. One plot point (this is not a spoiler) involves the passage of time near the event horizon of a black hole. Put simply, under GR, being close to a massive object has effects similar to accelerating in empty space under SR.
