Quantum Physics For Everybody

fiziko writes in with a self-described "blatant self-promotion" of a worthwhile service for those wishing to go beyond Khan Academy physics: namely Bureau 42's Summer School. "As those who subscribe to the 'Sci-Fi News' slashbox may know, Bureau 42 has launched its first Summer School. This year we're doing a nine-part series (every Monday in July and August) taking readers from high school physics to graduate level physics, with no particular mathematical background required. Follow the link for part 1."

Comments

No mathematical background?

[The_Wilschon]

Grade school level math. The most complicated math in the series is this: “if a times b is less than 6, and we measure a to be 2, then b must be less than 3.” If you can follow that, you’ll be fine.

Physics that uses no more math than this is not graduate-level physics.

Re:No mathematical background?

[Monkeedude1212]

Perhaps they mean teaching the theory and not the applied physics?

I mean there was a whole lot of high school physics that didn't need any math whatsoever to understand, but the math simply helped its application.

And as a side note, All they layed out was a puzzle in Linear Algebra. Essentially, linear algebra branches off into some complex systems like encryption and game-theory, but in essence the math behind it is not any more complex than using constants to define variables.

Re:No mathematical background?

[chichilalescu]

My personal opinion is that you CAN discuss the principles without going into more details. I think it's pretty easy to explain the concept of a Hilbert space with absolutely no knowledge of calculus, because it's just geometry and common sense.
It is problematic to teach physics without math, because you can get it horribly wrong. But you can explain graduate level concepts without math, and you can certainly describe the experiments that prove a formula works, even if you don't go through the complicated math involved in connecting the theory, formula and experiment.
It took some time to get from quantum physics to the specific heat of metals in the statistical physics course. But I can tell anyone on the street "look, if we measure the way metals conduct heat, we find that they behave in a certain way. we are only able to explain that if we use quantum physics to describe part of the electrons as a gas moving around inside the metal. classical physics fails.", and that should be enough for a basic idea.

Re:No mathematical background?

[memyselfandeye]

What's with all the negative comments? Anyone look at the lecture 1 PDF? Anyone actually do physics for a living?

As I write this, I'm staring at a whiteboard drawing of three equations in my den; E=mc^2, E=hc/lambda, r=2GM/c^2. They are there show my 13 year old niece how much energy a human body is equal to, a question she asked after watching K-PAX two nights ago on Netflix. Then she asked how much energy is in a single photon, then she asked how much energy is in a black hole. All questions a little girl might ask had she been exposed to basic ideas in modern physics, aka television.

Does she fully understand quantum mechanics, probably not. Does she she understand the jist with her pre-algebra background, sort of. Did she learn something and does she feel 'smarter' now... you betchya!

She annoyed my sister for hours about how a tree could power the whole world, or a tiny little bug could drive her car for years. My explanations, her worlds, and now a scientist in the making.

My point, you don't need to be able to derive Maxwell from F=ma, as my advisor's advisor did while backpacking across the Rocky Mts., to understand nature at its most simple, what you see is what you get, level. You also don't need to be some bearded mystic holed up in a university to appreciate, understand, or even contribute to our vastly poor knowledge of nature.

Re:No mathematical background?

[fritsd]

I think it's pretty easy to explain the concept of a Hilbert space with absolutely no knowledge of calculus, because it's just geometry and common sense.

I don't know about you, but lacking a background in Physics, I found it *very* confusing to jump from integration in 3-D over a Hydrogen probability density wavefunction, to suddenly talking about the *infinite-dimensional* Hilbert function space. Besides, if the students have a problem visualising that if a < b then a+x < b+x, they may also lack the basic tricks of integrating exponential and trigonometric functions. Maybe you only need those in quantum chemistry, not in quantum physics.. dunno..

Re:No mathematical background?

[by (1706743)]

Well, the time-independent Schrödinger equation requires nothing more than high-school math:

Hpsi = Epsi

Just divide out psi and you're done!

* Thanks, Slashdot, for allowing Greek letters...

Re:No mathematical background?

[DynaSoar]

Physics that uses no more math than this is not graduate-level physics.

I call bullshit, politely though. Not only can it be done, you've got to understand what you're doing well enough to step out of the higher level math. One of the most spectacular instances teaching I ever witnessed was at Purdue, where a class on relativity for non-science students was held, using nothing more than F = ma and a^2 + b^2 = c^2. Anyone can become an expert and talk expert to other experts and future experts. The higher the level the more jargonized and incomprehensible it becomes to everyone else. Worse, it becomes a sign of rite-of-passage, a badge of membership and a competition among its adherents, who constantly push the envelope on this. In doing so they become more and more isolated and insulated, viewing others as outsiders, people to stay away from if not look down on. They become socialized to not speaking outside their box, and pressure is applied from the group ion any member who does try to talk outside.

Anyone who can understand a field at the expert level but can explain it in non-specialized language without polysyballic words probably understands it far better than those in the specialists' club. An often misstated (but flexible enough to still work) quote from Ernest Rutherford is "An alleged scientific discovery has no merit unless it can be explained to a barmaid." There's people out there doing this thing which 'can't' be done. Go listen to them.

Re:No mathematical background?

[The_Wilschon]

I don't disagree with you, and I was not intending to claim that the lecture PDFs are not worthwhile. But I stand by my claim that they do not teach *graduate level* physics. They may teach the concepts that are dealt with in graduate level physics courses, but a graduate level physics education prepares one to teach or do research, which this sort of physics-without-much-math most certainly does not do.

And yes, I do physics for a living.

Re:No mathematical background?

[fiziko]

It's hit the concepts dealt with at the graduate level, but I left the math out to make those concepts accessible to people who don't have the heavy mathematical background. I'm half way through writing next year's summer school (linear algebra, full mathematical glory, ending with tensors), and the 2012 curriculum will be Einstein's Relativity and have two parts to each lesson. The first part will be all conceptual, like this, and the second part will have all of the math. 2013 will be real analysis, 2014 assessment theory, and years beyond that haven't been pinned down. The "Bureau 42 teaches" link at the side has everything along these lines listed, with links if they've already been posted.

Re:No mathematical background?

[frieko]

I disagree. I didn't realize it until college, but physics without calculus is about is as satisfying as having someone describe a piece of music to you.

Re:No mathematical background?

[fiziko]

Actually, I was working on the ATLAS detector that is in place at the LHC when I started writing for Bureau 42 almost 10 years ago. And I don't know how we profit off of something that's free...

My philosophy (which is in lesson nine, and probably should have come sooner; lesson one is more focused on why we need quantum mechanics, and the rest develops over time) is that the concepts and ideas of physics are represented by the math, but not defined by them. Math can certainly point out directions to look at and avenues to explore, and indicate connections between ideas we hadn't previously noticed, but as a student, I always found that the worst possible reason for a physics phenomenon was "because the math says so." This is about getting those ideas across for people who want to learn about the ideas. The ideas covered in the last two lessons are not typically introduced before grad school. (Lesson one starts at the high school level, which is all I wanted to assume from my audience.) Will you be a researcher when you're done? No. Will you have a better understanding of popular science articles relating to quantum physics? I certainly hope so.

Re:No mathematical background?

[oliverthered]

you've spent far to long in school.

A driving instructor can teach someone to drive without knowing all the math behind it.

They can also do some amount of research, perhaps learning the math as they go along.

given that physics is still a theoretical part of science, by not teaching the current application and instead focusing on the more fundamentals you may well be equipping people far better to then go on to push physics in new directions that 'indoctrinated' individuals wouldn't even think of, because they don't even know that there is a box to think outside of.

now what was the name of that patent clerk again?

Re:No mathematical background?

[khchung]

My personal opinion is that you CAN discuss the principles without going into more details

And that discussion would be as useful as discussing topics like OO-programming principles with someone who has never written a line of code. Or like discussing the issues with MySQL with someone who has never used a database or written a line of SQL.

You can make someone think they "understood" the physics, when, in fact, he haven't understood anything. Much like how you "explain" how you fixed a particular tricky bug to the upper management.

Re:No mathematical background?

[adamofgreyskull]

now what was the name of that patent clerk again?

Perhaps you mean Albert Einstein? He was exceptionally gifted in mathematics and physics, from an early age, and studied both at the Polytechnic in Zurich. If you mean to imply that Einstein was just some schmo with only grade-school level ability in maths then you are barking up the wrong tree. You could also say that he was fairly "indoctrinated", in that he had knowledge of current (har-dy-har ;) Physics theories, so your implication that ignorance of prevailing theories freed him to embrace novel ideas more readily is also on somewhat shaky ground.

Also, your car analogy is pitiful, even for slashdot. A driving instructor can teach someone to drive without knowing all the engineering behind it, but his students aren't expected to know how to design cars at the end of his tuition. If they are capable of learning engineering outside of their driving lessons, then what benefit really did the driving instructor provide?

I do see some value in this middle-ground, teaching more advanced Physics concepts in a way that high-school educated people could understand. Your assertion that it is possible to teach Physics concepts without backing it up with maths is, I believe correct, and I was willing to defend your point of view but I think you pushed it too far. GP is correct, in order to describe any new theory they may come up with, based on the "physics"/philosophical education they've received, they will have to learn to back their physics up with maths. Which a math-less physics education will not give them. They could come up with some fantastical new theory, that "dark matter" is actually made of meringue and toffee, but unless they can back it up with maths, how can they expect to be taken seriously?

Similarly, they could go on to teach a math-less physics course, but without maths, their students would be just as encumbered as they were. Like the driving instructor's students, they would be able to teach what they had learned, but no more.

Re:No mathematical background?

[fiziko]

Okay, I can see that point. I admit the language used was imprecise; I was trying to balance between describing what I was doing and keeping it short enough to work as a Slashdot snippet. Perhaps I leaned too far one way. The source article specifies "graduate level physics concepts" instead of just "graduate level physics." This was a submission issue, rather than a source material issue.

Biggest problem with this course

[Anonymous Coward]

What they don't tell you is the course is a superposition of a nine-part series, and that you can't know what course you are going to get until you actually open the pdf file, which is a pretty dicey proposition these days.

How do you talk about physics without mathematics?

[l2718]

Mathematics is the primary language by which physicists describe the world around us. Discussing post-16th century physics in any other terms is like discussing poetry purely by means of interpretive dance.

Re:How do you talk about physics without mathemati

[eln]

discussing poetry purely by means of interpretive dance.

I don't know how you found out about their next lecture series, but I think it would be best if you kept that information to yourself until they get closer to releasing it.

Let me just say, though, that it's almost impossible to truly understand French Medieval poetry until you've seen it performed by a dude in a black unitard.

Re:oblig XKCD

[Relic of the Future]

I loved that one.

Of course, he neglected to point out that mathematics is applied philosophy, and that philosophy is applied sociology...

So far, I'm not impressed

[Geoffrey.landis]

I read the first lesson, and while it's interesting, so far I'm not impressed.
It presents some of the problems with classical physics, but it seems to focus on the wrong problems. The first problem it mentions is that information can't travel faster than the speed of light-- but to address that problem you need more than just introductory quantum mechanics, you need relativistic quantum mechanics, and I just don't think you can get to Dirac's equation in a nine part series without math. Then they ask a question about nuclear physics ("what holds the nucleus together?"), for which, to even understand the question correctly, you need some information that the reader doesn't have yet (for example, what do they mean when they say that the only macroscopic force is electromagnetic? In fact, all the forces you do experience in everyday life actually are electromagnetic in nature... but you need quantum mechanics to really understand that! It sure isn't obvious that the force that keeps you from falling through the ground to the center of the Earth is electromagnetic). And this really isn't fundamental to quantum mechanics, either. Next, the nucleus mass question is, once again, a question of relativity and not quantum mechanics (although at least one that can be answered without resorting to the Dirac equation!). And the final question seems to require addressing the equation of state in ultradense matter at the beginning of the universe! Good luck with explaining that with grade school math.

Re:So far, I'm not impressed

[blair1q]

Would you be impressed if you didn't already know the subject?

Re:So far, I'm not impressed

[Linux_ho]

for example, what do they mean when they say that the only macroscopic force is electromagnetic? In fact, all the forces you do experience in everyday life actually are electromagnetic in nature...

With the exception of gravity, of course

Re:How do you talk about physics without mathemati

[blair1q]

It's more like discussing modern dance by performing it as a sequence of ballet moves.

Or deconstructing poetry.

Or using your words instead of your numbers.

In the end, mathematics is a means of manipulating facts to reveal other facts in a deterministic manner (even if they're facts about non-deterministic things). If you can't subsequently describe both sets of facts in terms a non-mathematician can understand, you haven't reached a result that non-mathematicians will know about, much less be able to form the idea that they should ask what it means.

Physics, being the means of describing the natural world, can be conducted in non-mathematical terms, since the math is just a symbolic model of the physical features, which exist regardless of the shorthand you used to reason about it.

Math will help you turn one symbolic model into another, but unless you understand what the subsequent model means when turned back from symbols into physical concepts, you haven't done any physics.

Re:No gedanken background

[Anonymous Coward]

That math may be why Quantum Physics waits until the graduate level. I've seen more people lost in the formulas than those who understood the concept without the math.

I'm going to be charitable and assume that the rest of the post is provided as a counterexample to this statement, and therefore not call you a fucktard for what follows.

Clearly, "Relativity" means "E = mc^2".

No, it does not. Perhaps you meant the longer "E = mc^2/sqrt(1-v^2/c^2)". Even that, however is wrong. There are two core principles to relativity:

- light always travels at c in a vacuum, independent of reference frame
- the laws of physics are the same in every non-accelerated reference frame

Everything else follows from this; even the specific form of the Lorentz transformation can be determined (using these assumptions) with some simple math and thought experiments.

Very few people can explain the E, m, c, & what they represent. I'd like to hear someone say "Matter has energy proportional to its mass.", which is still not the most import aspect of Relativity.

This was true even before relativity; "0.5mv^2", remember?

For example, the speed limit c on particles insures that kinetic energy (K = 1/2*mv^2) cannot grow forever. Otherwise, energy could be created.

I rescind my opening statement. You, sir, are a fucktard. That isn't even CLOSE to what's going on. "Kinetic energy" (by the modern definition, total energy - rest mass) can and does grow without bound. Particles are regularly created in labs with "kinetic energy" vastly in excess of their rest mass. *Velocity* on the other hand, is strictly limited.

BTW, particles CAN be created via this process - hard X-rays (somewhat above 1 MeV energy) can photoproduce electron-positron pairs when interacting with matter.

These ideas help one to understand the Physics and the math that describes it.

Maybe for some people. You, on the other hand, fail it.

Re:Well, its possible

[jasomill]

But then, you're left with "A brief history of the universe", and I suppose, tack an exam (of course, abstracting from the math), and you now have a "graduate-level" course.

I humbly submit Feynman 1988 as a counterexample. Therein, the author describes the basics of quantum electrodynamics using what appears to be little more than grade school mathematics.

I write "appears to be" because his presentation amounts to an extremely casual exposition of elementary ideas from rather more advanced mathematics (complex and even functional analysis) in terms of "adding arrows."

This book stands out in my mind as perhaps the best "popular science book" ever written, precisely because Feynman understands, here as elsewhere, the difference between glazing over the mathematics — modulo mathematics, there's not really much "modern theoretical physics" to speak of — and glazing over the inessential (to casual exposition, certainly not to understanding, application, or development of theories!) calculational details.

Incidentally, complex algebra is, in a sense, "the algebra of scaling and rotating little arrows" Feynman describes. Put this way, it comes as no surprise that the things have so many practical applications. Forget "square roots of negative one," rotations often arise in applications, as do "functions of circular (periodic) variables."

Re:oblig XKCD

[Culture20]

I disagree in that mathematics is applied philosophy, I think its a fundamental law of the universe.

Mathematics is applied Logic, which is a subset of Philosophy.

Re:No gedanken background

[fiziko]

Yeah, introductory quantum mechanics is introduced typically in second year, and then more detailed versions including Dirac notation show up in third and fourth year. The graduate level is where relativistic implications are usually taken into account, unless you take senior undergraduate particle physics.

Einstein

[Midnight Thunder]

I will add to this one of the greatest physicists around, Albert Einstein, did not know the necessary maths when he wrote his first theory. The maths was done for him, though he did later learn to do mathematics.

Science as we know it is not about the maths, but being able to produce a solid theory that stands up under scrutiny. Using scientific process helps add weight and often mathematics can provide a calculable way of showing numerical relationships, but if the reasoning for the theory is sound then these are just bonuses, IMHO.