# Quantum Physics For Everybody

#### kdawson posted about 4 years ago | from the this-time-without-the-math dept.

145
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."*

## Jews for Nerds! (-1, Troll)

## Anonymous Coward | about 4 years ago | (#32817620)

I'm glad I don't have a whole country full of deceitful, greedy kikes stealing all my water and land anywhere near me. Fucking Jews can't just live in peace. They have to steal other people's land. Our national economy is collapsing from the Jewbanks doing their usual Jewthing. You see, with Jews, you lose. That's how THEY win. They WIN by making YOU lose. So let's lose the Jews.

Global warming could be swiftly solved if we incinerated all of the Jews. Their ashes would be ejected into the upper atmosphere, where they would block some sunlight from hitting the earth. The economy would improve thanks to the absence of Jewish predatory lending, and it would buy us time to deal with climate change. Two birds, one stone.

Fun with Facts:

* Isreal has a Jewish population of 5,309,000.

* America has a Jewish population of 5,275,000.

Guess who really owns America? Hint hint, it isn't the Americans.

## No mathematical background? (3, Insightful)

## The_Wilschon (782534) | about 4 years ago | (#32817630)

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? (1)

## eln (21727) | about 4 years ago | (#32817728)

backgroundrequired." Presumably this means they'll be introducing math concepts in this course as well, starting with 8th grade pre-algebra and ending up at advanced calculus. Seems rather ambitious for a 9-part series of PDFs.## Re:No mathematical background? (1)

## Geoffrey.landis (926948) | about 4 years ago | (#32817806)

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

Agree. When you leave the math out, it's not quantum mechanics; it's philosophy.

To be fair, I suppose that they could teach the math as part of the course. (If they take the Dirac abstract-algebra approach, it may be that you have to learn it all from zero anyway.)

## Re:No mathematical background? (2, Insightful)

## Monkeedude1212 (1560403) | about 4 years ago | (#32817840)

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? (4, Insightful)

## frieko (855745) | about 4 years ago | (#32819172)

## Re:No mathematical background? (1)

## commodore64_love (1445365) | about 4 years ago | (#32820434)

That presumes that you like music..... I mean math.

A lot of us don't. Even Stephen Hawking has said he's not thrilled with math, and develops most of his ideas visually in his head (source: his book Black Holes and Baby Universes). He only uses the math as the final step, to describe what he sees in his head, not because he enjoys it.

## Re:No mathematical background? (0, Troll)

## moteyalpha (1228680) | about 4 years ago | (#32817892)

"Intelligence for dummies" by "I. schmel profit".

"Quantum Physics for bears"

citing "Introduction to Trailer Court physics" on your resume for LHC would certainly get you noticed.

## Re:No mathematical background? (1)

## dimeglio (456244) | about 4 years ago | (#32818736)

Physics use mathematical tools and most of its notation. However, this serves as a means to an end. That being said, you can also follow Leonard Susskind Stanford lectures on Quantum Physics and learn how Einstein's worked out that E=mc^2 with grade 13 math.

## Re:No mathematical background? (0)

## Anonymous Coward | about 4 years ago | (#32819126)

And Einstein later showed how you can get E=mc^2 with only grade 7 math, using the fact that electromagnetic waves transfer momentum, Newton's 3rd law of motion (valid if the recoil of the body emitting the electromagnetic waves leaves it moving at a speed much less than c), and the fact that the center of mass of an isolated system initially at rest in some inertial reference frame remains at rest in that frame).

## Re:No mathematical background? (5, Informative)

## fiziko (97143) | about 4 years ago | (#32819378)

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? (1)

## moteyalpha (1228680) | about 4 years ago | (#32819860)

I did work with NASA 40 years ago and so I guess that makes me correct also. Wikipedia already has good reference and has some people that maintain the reference well. No point in muddying the waters.

http://en.wikipedia.org/wiki/Quantum_mechanics [wikipedia.org] It is a difficult science and the relationships are modeled with math. Understanding math is not a suggested dependency it is a prerequisite in any curriculum.

As someone else already said, without math, physics is just philosophy.

Professor Lewin covers the basics better anyway. It requires no math to watch the videos and he has a good knowledge of the subject.

http://videolectures.net/mit801f99_physics_classical_mechanics/ [videolectures.net]

On top of that, math is fun and very interesting in its application. Markov Chains and Monte Carlo methods are so cool.

How is a person supposed to understand even the most important reference on the net [xkcd.com] without math?

## Re:No mathematical background? (1)

## fiziko (97143) | about 4 years ago | (#32821566)

The Bureau 42 authors don't use the site for profits. Most years, ad banner revenue is about the cost of renewing the domain name, and none of us get paid to post our stuff. We just have fun in our spare time. That's where this came from; when doing my M.Sc., I found I enjoyed teaching in labs far more than I enjoyed doing the actual research. That realization and a case of bilateral elbow tendonitis prompted me to switch to education. Now I teach K-12 (along with other tasks) at the private education company everybody in North America has heard of, which I love, but doesn't hit the higher level physics often. I wrote these lessons for fun, and shared this one with Slashdot because I thought the series came out well and that others might enjoy reading them.

## Re:No mathematical background? (1)

## thirtybelow (1755558) | about 4 years ago | (#32817904)

## Re:No mathematical background? (4, Interesting)

## chichilalescu (1647065) | about 4 years ago | (#32817916)

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? (0, Flamebait)

## The_Wilschon (782534) | about 4 years ago | (#32818060)

## Re:No mathematical background? (0, Troll)

## chichilalescu (1647065) | about 4 years ago | (#32818432)

I see your point. the age old problem of deciding what various words mean.

As a sidenote, I went to the page and tried to go through the first PDF. I don't really like it, and i doubt the effort is of any use (anyone unfamiliar with the concepts will not be able to understand them from these lectures --- I think). But the guy trying to do it has to start somewhere.

## Re:No mathematical background? (1)

## lymond01 (314120) | about 4 years ago | (#32819820)

the age old problem of deciding what various words mean.What, exactly, do you mean by mean, in this sense?

Anyway, the person is trying to show the concepts that are generally discussed along with math in Grad School Physics. I'm not sure why Wilschon is trying to so hard to drive home an obvious point.

## Re:No mathematical background? (2, Funny)

## fritsd (924429) | about 4 years ago | (#32818430)

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? (1, Informative)

## chichilalescu (1647065) | about 4 years ago | (#32818810)

A Hilbert space is a complete vector space with a scalar (dot) product. The "complete" just means that any infinite sequence of items such that the distance between two successive ones goes to zero has a limit (the set of rational numbers is NOT complete). A trivial example is normal Euclidian 3D space.

You don't need to explain anything about functions in order to explain Hilbert space, because any Euclidian space is a Hilbert space. When you do know about functions, you just show that any linear differential equation generates a Hilbert space with functions as it's points, and you can show that it is infinite dimensional if you need to. You just have to realize that there is a difference between configuration space ('where', commonly denoted as x, y, z) and wave-function space ('state', commonly denoted as psi or phi in quantum mechanics). The integration is performed in configuration space, and that's always finite-dimensional; the solutions to Schrodinger's equation are vectors in wave-function space, and you can write them as infinite sums.

There will always be problems when you actually have to go through the quantitative stuff. Each generation learns things in a certain order, using certain conventions. And, the fields being so vast, it's very easy to make it hard for the students in some areas, while making it easy in other areas.

## Re:No mathematical background? (0)

## Anonymous Coward | about 4 years ago | (#32820078)

You are an asshole. And your definition of completeness is wrong unless successive is understood in a completely nonstandard way (i.e., $x_{n+k}$ is a successor of $x_n$ for any $k>0$.).

## Re:No mathematical background? (1)

## martin-boundary (547041) | about 4 years ago | (#32820610)

Wrong. You either don't know what completeness means, or you've oversimplified to the point where you're harming readers who might trust you to explain the concept correctly.

Counterexample: Pick a sequence x_1 = 1, x_2 = 3/2, ... x_{n+1} = x_n + 1/(n+1). If you think of these values as angles on the unit circle, then distance(x_n, x_{n+1}) tends to zero, but there is no limiting angle, the sequence just goes around the circle forever.

## Re:No mathematical background? (1)

## FrangoAssado (561740) | about 4 years ago | (#32818920)

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 agree, but to understand why and how a Hilbert space important to QM, you need the features of Hilbert spaces that are

unlikeEuclidean spaces.To see why this is relevant, take the Uncertainty Principle. It can actually be stated for systems described by finite-dimensional Hilbert spaces (for which one could have a nice geometric intuition), but it's not that interesting. The real understanding (at least for me, and I suspect for most people) only comes when you learn the position and momentum operators, which operate in infinite-dimensional Hilbert space states, and realize that the commutator between them is constant no matter what the state they're applied to. To really understand that, you need to get your hands dirty with (very little) functional analysis, the geometric interpretation of a Hilbert space will give no insight over that.

Still, I think there's a lot of value in explaining QM with only very basic math -- and there's a lot that can be done

really wellthat way: entanglement, measurement, Schroedinger's cat, etc. But you also have to understand that a lot of the really interesting bits need advanced vector calculus, linear algebra, funcional analysis, etc. to be done right, otherwise you're only teaching with analogies.## Re:No mathematical background? (1)

## dmartin (235398) | about 4 years ago | (#32821252)

But the fact that we can state the Uncertainty principle in a finite dimensional Hilbert space (as you point out) shows that the Uncertainty principle does rely on properties of infinity. It fact in the finite dimensional case it becomes somewhat easier to understand what is going on. Take the spin-1/2 system which is two dimensional. The eigenvectors any of the operators s_x, s_y or s_z form a basis for the state, however each operator's eigenbasis is not parallel to any other operator's eigenbasis. A vector which "lines up" like (1,0) and (0,1) in one basis cannot in the other two which we can draw on a sheet of paper (and remind students about breaking things into components).

In infinite dimensional cases things are more complicated because there are various subtitles that can arise. But these subtitles are not at the core of the uncertainty principle, merely a technical distraction that needs to be addressed.

And I really don't understand this statement:

you need the features of Hilbert spaces that are unlike Euclidean spaces.All finite dimensional Euclidean spaces, for which we have a reasonable intuition,

areHilbert spaces. In the infinite dimensional case Hilbert spaces are defined to carry over the properties of Euclidean space while eliminating some of the perverse things that can happen in infinite cases (i.e. ensuring Cauchy sequences have limits in the space).## Re:No mathematical background? (1)

## martin-boundary (547041) | about 4 years ago | (#32819324)

But it *isn't* just common sense. Hilbert space is far stranger than ordinary 2D or 3D space, and if your experience is limited to those two examples, then you'll get things wrong.

Here's an example: draw a square in the plane, and fill it randomly (uniformly) with lots of points. They cover the square roughly evenly. This is also true in 3D. But if you go up to ND, something new starts to happen: all the random points get closer and closer to the boundary of the N-cube as N becomes large. That's intuitively unexpected.

Here's another example: in 2D or 3D, take a ball (=sphere + interior), and choose an infinite number of points inside it. Then there's at least one point X inside the ball that gets targeted by your list of points, ie you can always find closer and closer points to that particular X. And that's true regardless of cleverly you pick the infinite list of points. In infinite dimensional Hilbert space (which is used in quantum mechanics), that's no longer true. But you can't see it in 2D or 3D.

Here's another: let's say you pick an axis in Hilbert space, then you pick another axis that's perpendicular, and so on. In 2D, you get a pair of axes, such that every point can be identified from its components along those axes. In 3D, the same is true except you'll have 3 axes. In infinite dimensional Hilbert space, this is false: You can pick a sequence of perpendicular axes forever, and still you won't have enough axes to identify every point in Hilbert space.

There's a lot of strange things happening in Hilbert spaces that can seriously mess up a person's intuition. The above ideas ,for example, have implications such as if you try to find a solution to a problem that minimizes some quantity (eg energy), then it might not exist.

## Re:No mathematical background? (2, Insightful)

## khchung (462899) | about 4 years ago | (#32819672)

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

thinkthey "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? (1, Insightful)

## Anonymous Coward | about 4 years ago | (#32818066)

If you can't explain it simply, you don't understand it well enough.

--Albert Einstein

## No gedanken background (0)

## Anonymous Coward | about 4 years ago | (#32818092)

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.

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

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.

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

## Re:No gedanken background (2, Insightful)

## Anonymous Coward | about 4 years ago | (#32818472)

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:No gedanken background (1)

## by (1706743) (1706744) | about 4 years ago | (#32818676)

That math may be why Quantum Physics waits until the graduate level.

Pretty sure quantum mechanics gets taught to undergrads (for some definition of rigorous). And even at that "elementary" level, some amount of math is invaluable to intuit quantum weirdness. For example, I'm not sure what the conceptual/non-mathematical understanding of the (quantum mechanical) car bouncing off the edge of the (quantum mechanical) very high vertical cliff would look like; however, the only vaguely mathematical explanation is quite simple and concise.

## Re:No gedanken background (2, Interesting)

## fiziko (97143) | about 4 years ago | (#32819430)

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.

## Re:No gedanken background (1)

## by (1706743) (1706744) | about 4 years ago | (#32819700)

...including Dirac notation...

In the interest of gender equality, I tried to introduce Jok-Strap notation. It didn't catch on.

## Re:No mathematical background? (1)

## oliverthered (187439) | about 4 years ago | (#32818138)

it depends on the teaching approach.

more 'theoretical' set theory based stuff, yeh loads of maths.

but you should be able to explain things using concepts, which the audience 'can' grasp without knowing the precise math behind it.

For instance, you could explain Newtonian physics via example and a persons every day experience. You'd get the basic principles behind it accros with no need for maths.

every action has an equal and opposite reaction.

and some clips of experiments to demonstrate this such as newtons cradle or whatever.

vs

well some geometry other measurements and equations (which would be different depending upon exactly what your doing or measuring etc..). to the effect of a a weight of 1kg (or newtons if SI) traveling at a speed of 1 meter / second in the direction of another mass of 3kg etc...

you'd so something similar for measuring stresses on something a bit more static like a bridge.

explaining the physics and laws does not require a full working knowledge of the maths.

## Re:No mathematical background? (0, Troll)

## The_Wilschon (782534) | about 4 years ago | (#32818906)

## Re:No mathematical background? (3, Insightful)

## oliverthered (187439) | about 4 years ago | (#32819566)

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? (2, Insightful)

## adamofgreyskull (640712) | about 4 years ago | (#32821194)

now what was the name of that patent clerk again?

Perhaps you mean Albert Einstein [wikipedia.org] ? 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

canteach someone to drive without knowing all theengineeringbehind 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? (1)

## oliverthered (187439) | about 4 years ago | (#32819626)

I did give a small spin example, but it looks like I may have forgotten to submit after preview.

in brief:

angular momentum. Can be explained to a good degree of understanding without knowing the math.

then but in devisions of 1/4, which relates to spin number (could give formula).

Then spin direction as other component.

then some experimental examples,

and some entanglement, and demonstrations.

touch a bit on the standard model I suppose, but it's known to be a bit of a fudge etc... so is that really teaching physics, or just teaching 'known bad' physics?

I'm sure that it's not going to go into the whole square peg round whole that is QED.

do the rest of it in a similar way and people may well be able to do some research and the like.

## Re:No mathematical background? (5, Insightful)

## memyselfandeye (1849868) | about 4 years ago | (#32818194)

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? (2, Interesting)

## The_Wilschon (782534) | about 4 years ago | (#32818932)

And yes, I do physics for a living.

## Re:No mathematical background? (1)

## lymond01 (314120) | about 4 years ago | (#32819844)

And yes, I do physics for a living.Obviously. :-)

## In the beginning "all particles were packed into (0)

## Anonymous Coward | about 4 years ago | (#32819884)

a small space". I paraphrase from the first section. The section is too short to be helpful. Before the "big bang" there was no space and hence no particles, just energy without space. Give birth to three dimensions and suddenly energy cools and morphs into what we have today, after only ~14 billion years. I look forward to see if the author teaches or preaches and makes sense as we move through the series.

## Re:No mathematical background? (1)

## Keebler71 (520908) | about 4 years ago | (#32819972)

## Re:No mathematical background? (1, Insightful)

## Anonymous Coward | about 4 years ago | (#32818242)

I think graduate level physics simply means this is the type of topics you get in graduate level physics, but it is not a graduate level education of said concepts. Love it or hate it that seems to be what they are trying to do.

This whole issue exposes the Slashdot science paradox. We're disdainful of the general public for being ignorant of science, and then when someone tries to introduce the general public to it all we can say is "it's not really physics without the math." Should we just tell people either understand it completely or don't try? Some people think the LHC will destroy the world. Shouldn't someone try to explain what they are doing and why it won't blow up the earth? Do you have to use math for that? Why can't you just discuss the concepts so they get the gist?

They are trying to teach concepts to educate the general public. You don't really need all the math to describe what's going on. They're not trying to train physicists just help laypeople understand. What's wrong with that? Not everyone needs to be a physicist.

## Re:No mathematical background? (1)

## The_Wilschon (782534) | about 4 years ago | (#32818998)

They're not trying to train physicists just help laypeople understand.

This is precisely what makes it not graduate level physics, because graduate level physics *is* trying to train physicists. I'm all for teaching people about physics on a layperson sort of level; I think it is a phenomenally great thing to do. I'm not in favor of lying to them about just what it is that they are learning.

Car analogy (possibly bad, as always): I think that making people take a driver's ed program so they can get a license is a really good idea. I think that telling them that their driver's ed program is training them to be movie stunt drivers is a really really bad idea. It isn't, and the consequences of so telling them are probably worse than not giving them training at all.

## Re:No mathematical background? (1)

## memyselfandeye (1849868) | about 4 years ago | (#32819386)

This is precisely what makes it not graduate level physics, because graduate level physics *is* trying to train physicists. I'm all for teaching people about physics on a layperson sort of level; I think it is a phenomenally great thing to do. I'm not in favor of lying to them about just what it is that they are learning.

I concede you have a point, for sure a valid one. I kinda ranted because of a similar story to the other one I shared that happened not too long ago, although of an opposite nature.

My cleaning lady told me she needed to find a dentist, and asked for a recommendation. Turns out, she and her previous dentist got into it over X-rays. "What do I care, it's her kid, and who knows maybe she's right?"

But what stuck in my craw, was her explanation that it was 'the frequencies,' and her following rant on microwaves.

I tried to explain that microwave ovens are perfectly safe, that compared to the SEM and XPS machines I work with every day, the radiation is quite minuscule, the exposure in all cases in nill, and I haven't grown and belly button eyes or nipple arms. It didn't work, and I didn't push it for fear of upsetting her, though I did research the dental X-ray on my own and learned that the intensity was less than what I suffered a boy growing up in the Rocky's.

So, my point was more to the nature of, so long as they wont be expecting someone to derive any concepts, to explain them in proofs so to speak, that even if they touched on the basics of QED et. all, then it's all good.

But you are right, this isn't training an engineer of physicist, but it may be a start for someone out there who catches the bug.

## Re:No mathematical background? (2, Funny)

## by (1706743) (1706744) | about 4 years ago | (#32818502)

Hpsi = Epsi

Just divide out psi and you're done!

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

## Re:No mathematical background? (4, Insightful)

## DynaSoar (714234) | about 4 years ago | (#32818578)

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? (1, Insightful)

## The_Wilschon (782534) | about 4 years ago | (#32819082)

But, a graduate level education (in any field) is intended to prepare you to teach and to do novel research. You cannot teach physics, and you certainly can't do novel physics research, if you don't know any more than grade school math. It is simply impossible. So, the people who are creating what might well be a really excellent popsci series should not tell people that it is graduate level physics, because it is in fact something different from graduate level physics.

Argh. You are the last (currently) in a line of about a dozen people who have totally misunderstood my comment.

## Re:No mathematical background? (0)

## Anonymous Coward | about 4 years ago | (#32821240)

While you may be right in one way, you, and most of the scientific establishment, are wrong in the most important ways. Give up.

## Re:No mathematical background? (1)

## Keebler71 (520908) | about 4 years ago | (#32819996)

## Re:No mathematical background? (1)

## mburns (246458) | about 4 years ago | (#32820084)

The best route out of the arcane "math" is the correct geometric representation of physical objects. Physicists have a really bad habit of using the wrong tensor rank - not the same as what operates out there.

Just try calculating Kaluza-Klein charges using the wrong tensor rank. But they can be simply drawn when the right tensor rank is used.

It is quite true though that quantum mechanics can not be drawn like this.

## Re:No mathematical background? (0)

## Anonymous Coward | about 4 years ago | (#32820740)

Utter crap. You may be able to describe in an intuitive way what's going on, but a graduate level student should be able make predictions and determine the precision with which these predictions should match measurements. Otherwise it's simply not science,

## Re:No mathematical background? (1)

## WastedMeat (1103369) | about 4 years ago | (#32821230)

## Einstein (2, Interesting)

## Midnight Thunder (17205) | about 4 years ago | (#32821504)

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.

## Re:No mathematical background? (3, Informative)

## fiziko (97143) | about 4 years ago | (#32819024)

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? (1)

## kurokame (1764228) | about 4 years ago | (#32820336)

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.

Physics that uses no more math than this is not college-level physics, unless you want to count the first week or two of the not-for-majors version of the 100-level stuff. Even that requires a fairly decent grasp of algebra and trigonometry.

You can talk about quite a few

conceptsin college-level physics provided that you do so in relativelybroad terms. But reaching graduate level physics in any honest senserequiresquite a bit of advanced math. Further, it is not something you can learn in any real sense over a period of two months even if you somehow happen to be the smartest human ever born.If you want a look at what college-level quantum mechanics actually entails, the book "Introduction to Quantum Mechanics" [amazon.com] by David Griffiths is commonly used. But note that the lecture component of these classes easily covers more material than you can pick up by reading the book alone. Also note that students taking courses using this book have usually already taken at least 2 to 3 courses covering quantum mechanics and other topics in modern physics beyond the 100-level courses which provide a survey of elementary topics in physics, and that they have a fairly good grounding in things like linear algebra and differential equations.

## Re:No mathematical background? (1)

## fiziko (97143) | about 4 years ago | (#32821606)

Griffiths' text is commonly used, but I wasn't thrilled with it. I'm of the "do the math right or not at all" mentality, and his use of the probability distribution with operators instead of the psi* operator psi proper methodology in the first few chapters forms bad habits with students. It only works because he carefully chooses examples whose operators do not involve derivatives. His electricity and magnetism textbook is fantastic, and his particle text is great, but I'm not happy with his quantum text. Joachain and Bransden made a text I much prefer (in its first edition; I haven't looked at the second edition, ISBN: 0582356911) and would recommend over Griffiths in this case.

## Science w/o math (0, Flamebait)

## SnarfQuest (469614) | about 4 years ago | (#32817646)

Science without mathematics. Sounds like an Al Gore school.

## No math??? (0, Troll)

## stanlyb (1839382) | about 4 years ago | (#32817648)

## oblig XKCD (1)

## ChipMonk (711367) | about 4 years ago | (#32817672)

## Re:oblig XKCD (3, Interesting)

## Relic of the Future (118669) | about 4 years ago | (#32817910)

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

## Re:oblig XKCD (1)

## Monkeedude1212 (1560403) | about 4 years ago | (#32817974)

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

## Re:oblig XKCD (2, Interesting)

## Culture20 (968837) | about 4 years ago | (#32819146)

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:oblig XKCD (1)

## narcc (412956) | about 4 years ago | (#32819238)

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

This is how we know that you're not a mathematician...

## Re:oblig XKCD (0)

## Anonymous Coward | about 4 years ago | (#32819272)

It depends whether or not your philosophy of mathematics is constructivist or platonic. If it is constructivist, mathematics is a sub-field of psychology dealing with the concepts such as sets, quantities, order, etc....which exist only in minds (humans and some other animals).

## Re:oblig XKCD (1)

## martin-boundary (547041) | about 4 years ago | (#32821182)

## Re:oblig XKCD (1)

## Hazelfield (1557317) | about 4 years ago | (#32818116)

## Biggest problem with this course (2, Funny)

## Anonymous Coward | about 4 years ago | (#32817678)

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? (5, Insightful)

## l2718 (514756) | about 4 years ago | (#32817686)

primary languageby 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 (5, Funny)

## eln (21727) | about 4 years ago | (#32817808)

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:How do you talk about physics without mathemati (1)

## fritsd (924429) | about 4 years ago | (#32818342)

## Re:How do you talk about physics without mathemati (1)

## Hazelfield (1557317) | about 4 years ago | (#32818084)

I really can't see an accurate description of quantum mechanics without quite heavy use of mathematics. This web course might very well be a good introduction to the subject, but if you really want to understand where quantum mechanics comes from, you'll need a bigger mathematical toolbox.

## Re:How do you talk about physics without mathemati (2, Interesting)

## blair1q (305137) | about 4 years ago | (#32818168)

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:How do you talk about physics without mathemati (1)

## ebmi (1463935) | about 4 years ago | (#32820328)

Agreed. As Pauli might say, physics without math is "not even wrong."

## Re:How do you talk about physics without mathemati (0)

## Anonymous Coward | about 4 years ago | (#32820838)

+5 Funny???

+5 Insightful: the post is amusing, but primarily it adds to the discussion. Hand out the karma, mods!

## More intellectual rigor than Glenn Beck University (-1, Troll)

## Anonymous Coward | about 4 years ago | (#32817802)

"Quantum physics without math" == pretentious pseudoscience drivel.

But it'll still have more intellectual rigor than the newly opened Glenn Beck University, where "Quantum Mechanics 101" is "Jeebus makes it work. Math is for fags. Buy gold!"

## ,first post (-1, Offtopic)

## Anonymous Coward | about 4 years ago | (#32817830)

## Khan Academy physics? (1)

## mpfife (655916) | about 4 years ago | (#32817912)

"Revenge is a dish best served cold - and it's very cold in the vacuum of space. Around 2.725 Kelvin; which is -270 deg Celcius. That is minus 27 tens, and that's terrible....ly cold."

"KAAAAAAAAAAAAAAAAHN!"

Now that's a school I could go for...

## So far, I'm not impressed (2, Interesting)

## Geoffrey.landis (926948) | about 4 years ago | (#32818038)

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

relativisticquantum 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 actuallyareelectromagnetic in nature... but you need quantum mechanics to really understand that! It sure isn'tobviousthat 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 (4, Insightful)

## blair1q (305137) | about 4 years ago | (#32818180)

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

## Re:So far, I'm not impressed (1)

## chichilalescu (1647065) | about 4 years ago | (#32818984)

actually, someone who knows the subject can tell when a particular line of though will lead you where there be dragons. and they're usually right.

also: "how can I be impressed if what you're saying has no obvious connection to what I understand as reality?"

## Re:So far, I'm not impressed (3, Informative)

## Linux_ho (205887) | about 4 years ago | (#32818208)

With the exception of gravity, of course

## Re:So far, I'm not impressed (1, Flamebait)

## Monkeedude1212 (1560403) | about 4 years ago | (#32818476)

And love.

## Re:So far, I'm not impressed (1, Informative)

## Anonymous Coward | about 4 years ago | (#32819034)

In GR, gravity is not a force.

## Re:So far, I'm not impressed (1)

## mburns (246458) | about 4 years ago | (#32820216)

Electromagnetism alone does not get you a solid surface. Nor does gravity. This is one of the failure points of classical physics, a side effect of the small scale where the premise of spacetime, the existence of the metric, goes out of range.

## Re:So far, I'm not impressed (1)

## zzsmirkzz (974536) | about 4 years ago | (#32819506)

measurethe mass of the components individually and then the nucleus as a whole? Then once I understood that I'd wonder how could the result of this method be affected in ways not originally intended that would could the mass of the nucleus to appear to be less than the masses of its individual components. I don't claim to know much about quantum physics but I do know the masses involved are almost infinitesimally small and any measurement of them is likely to be incorrect as our methods of measuring are far from perfect.## Re:So far, I'm not impressed (1)

## fiziko (97143) | about 4 years ago | (#32821650)

The protons have a mass that's relatively easy to measure. The charge is very well known, as is the interaction of moving charges with magnetic fields. If you fire a proton through a magnetic field, it will be accelerated into a circular motion, and the easily-measured radius of the circle (visible in a bubble chamber) will indicate what the mass is.

For neutrons, it's much harder. Early measurements at the time were imprecise compared to today's. Now that we better understand the mechanism of radioactive decay, we can find it through a roundabout means. When a neutron is not part of a nucleus, it is unstable, and decays into a proton, an electron, and an electron antineutrino. The difference in masses between the neutron and the proton is a significant factor in the half lives of these decays, so that was used in the early days to compute the mass of a free neutron.

## Re:So far, I'm not impressed (1)

## niteshifter (1252200) | about 4 years ago | (#32820912)

... It sure isn't obvious that the force that keeps you from falling through the ground to the center of the Earth is electromagnetic ...

The hell it isn't, and the nature of this force can be readily demonstrated with simple and commonly had objects:

Battery

Wire

Incadescent lamp

Pair of magnets

Compass (the navigational kind)

I'll skip the details one how one uses the above to demonstrate that opposite charges / polarity attract and like repels as most readers of /. are smart enough to figure it out. But those simple demonstrations with a grade school level description of the atom makes it obvious.

And with not a single calculation or equation being used :)

No one is suggesting that after studying materials like this that someone is qualified to do PhD level work. The value in material like this in it's utility in combating the woo-woo purveyors out there.

## Re:So far, I'm not impressed (1)

## FrangoAssado (561740) | about 4 years ago | (#32821458)

So true, I couldn't agree more about the focus on the wrong problems.

I was expecting something like an introduction to really basic quantum stuff, like superposition, entanglement, measurement, etc. This can actually be done the right way with very little math, like this excellent series of lectures from Stanford [youtube.com] , where you can learn something that is actually right, not just analogies.

Instead, based on what's in the first lesson, it looks like it will try to talk about a lot of things, explaining none of them really right.

## Re:So far, I'm not impressed (1)

## fiziko (97143) | about 4 years ago | (#32821662)

Instead, based on what's in the first lesson, it looks like it will try to talk about a lot of things, explaining none of them really right.

So, which parts could I have explained better?

## time, space & circumstance (-1, Offtopic)

## Anonymous Coward | about 4 years ago | (#32818058)

nothing new out there, except to us. if 'jesus' (or anybody like that, including today) were around, he'd be known as a domestic terrorist. nothing new, just change the words a little. the results are the same; from the blank stare, right up to the gas chamber. many still get off on doing (strange reprehensible) things for the queen mother? see you on the other side of it?

the corepirate nazi illuminati is always hunting that patch of red on almost everyones' neck. if they cannot find yours (greed, fear ego etc...) then you can go starve. that's their (slippery) platform now.

never a better time to consult with/trust in our creators. the lights are coming up rapidly all over now. see you there?

greed, fear & ego (in any order) are unprecedented evile's primary weapons. those, along with deception & coercion, helps most of us remain (unwittingly?) dependent on its' life0cidal hired goons' agenda. most of our dwindling resources are being squandered on the 'wars', & continuation of the billionerrors stock markup FraUD/pyramid schemes. nobody ever mentions the real long term costs of those debacles in both life & any notion of prosperity for us, or our children. not to mention the abuse of the consciences of those of us who still have one, & the terminal damage to our atmosphere (see also: manufactured 'weather', hot etc...). see you on the other side of it? the lights are coming up all over now. the fairytail is winding down now. let your conscience be your guide. you can be more helpful than you might have imagined. we now have some choices. meanwhile; don't forget to get a little more oxygen on your brain, & look up in the sky from time to time, starting early in the day. there's lots going on up there.

"The current rate of extinction is around 10 to 100 times the usual background level, and has been elevated above the background level since the Pleistocene. The current extinction rate is more rapid than in any other extinction event in earth history, and 50% of species could be extinct by the end of this century. While the role of humans is unclear in the longer-term extinction pattern, it is clear that factors such as deforestation, habitat destruction, hunting, the introduction of non-native species, pollution and climate change have reduced biodiversity profoundly.' (wiki)

"I think the bottom line is, what kind of a world do you want to leave for your children," Andrew Smith, a professor in the Arizona State University School of Life Sciences, said in a telephone interview. "How impoverished we would be if we lost 25 percent of the world's mammals," said Smith, one of more than 100 co-authors of the report. "Within our lifetime hundreds of species could be lost as a result of our own actions, a frightening sign of what is happening to the ecosystems where they live," added Julia Marton-Lefevre, IUCN director general. "We must now set clear targets for the future to reverse this trend to ensure that our enduring legacy is not to wipe out many of our closest relatives."--

"The wealth of the universe is for me. Every thing is explicable and practical for me .... I am defeated all the time; yet to victory I am born." --emerson

no need to confuse 'religion' with being a spiritual being. our soul purpose here is to care for one another. failing that, we're simply passing through (excess baggage) being distracted/consumed by the guaranteed to fail illusionary trappings of man'kind'. & recently (about 10,000 years ago) it was determined that hoarding & excess by a few, resulted in negative consequences for all.

consult with/trust in your creators. providing more than enough of everything for everyone (without any distracting/spiritdead personal gain motives), whilst badtolling unprecedented evile, using an unlimited supply of newclear power, since/until forever. see you there?

"If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land." )one does not need to agree whois in charge to grasp the notion that there may be some assistance available to us(

boeing, boeing, gone.

## Well, its possible (1)

## BigJClark (1226554) | about 4 years ago | (#32818094)

By abstracting all the mathmatical conjecture. 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.

## Re:Well, its possible (2, Insightful)

## jasomill (186436) | about 4 years ago | (#32819084)

I humbly submit Feynman 1988 [princeton.edu] 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:Well, its possible (1)

## martin-boundary (547041) | about 4 years ago | (#32821262)

Yes, we know this (see here [wikipedia.org] ). But the whole point of complex algebra is to go the other way, namely from geometry and scaling and little arrows to algebra as a way of simplifying calculations and improving understanding.

The status quo before the discovery of analytical geometry was Greek style synthetic calculations, which are much too cumbersome in the presence of viable alternatives.

## I wonder if this is really useful (1)

## aBaldrich (1692238) | about 4 years ago | (#32818150)

At back at school we were taught that physics has laws and mathematical models, which are an (simplified) generalisation of the empirical data. If there's no mathematical description,

whatam I going to learn? 3 years ago I heard about "Schroedinger's equation". I couldn't resist my curiosity and searched it in Wikipedia. Nice greek letters and strange symbols. The teacher told me it's result described an area where it was more probable to find an electron. Wikipedia said it means much more. So now I'm sceptical about this mathless physics: they are going to make a lot of unexplained statements, and in the end I wont get any practical results out of it, and anything they write will be so over simplified that it would have lost all its meaning, just like my teacher. I won't "know" quantum physics.## Re:I wonder if this is really useful (0)

## Anonymous Coward | about 4 years ago | (#32819120)

took his time to write in LaTeX, which automatically made me think it can be trusted

You're halfway to succeeding in academia!

## Re:I wonder if this is really useful (1)

## memyselfandeye (1849868) | about 4 years ago | (#32819608)

The teacher told me it's result described an area where it was more probable to find an electron.

Oddly enough, it makes it less probable to find your car keys :(

Nobody really knows this stuff anyway. I still don't know what the heck an electron or photon is and I blast millions of them at tiny little samples all day.

If you are curious, I'd suggest Mr. Tompkins in Wonderland or Einstein's Dreams... two very small, and very fun books for everyone.

## A good textbook? (0)

## Anonymous Coward | about 4 years ago | (#32818212)

Not to go too far off topic, but can someone recommend a good text book for introductory quantum mechanics? The math I can figure out (most likely...I've been through multivar calc, linear algebra, and diffeq), but I just want to study some of this for fun. While we're at it, an orbital mechanics text would be good, too.

## Re:A good textbook? (1)

## jjsm (895856) | about 4 years ago | (#32818536)

## Sooo... (1)

## dustin_0099 (877013) | about 4 years ago | (#32818372)