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

Jews for Nerds!

[Anonymous Coward]

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?

[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?

[eln]

Well, it doesn't say "no math", it says "no math background required." 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?

[Geoffrey.landis]

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?

[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?

[moteyalpha]

I agree.
"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?

[thirtybelow]

You can get basic points in physics across without using math, but in general if you want to get to the interesting bits you have to be willing to write down some equations. For instance, I can tell you that gravity pulls things together, which is the basic idea, but if you want to know why planetary orbits are elliptical or what the escape velocity from earth is, then you have to do some calculus. In quantum mechanics, the math involved gets deep rather quickly.

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?

[The_Wilschon]

Oh certainly. I do agree with you. But discussing the concepts and principles is not graduate level physics, it's conceptual physics, which is what you teach to undergraduate poets and business majors. Nothing wrong with it, and it certainly is very important and worthwhile, but it is not graduate level physics, which is intended to prepare you to do actual novel physics research on your own.

Re:No mathematical background?

[Anonymous Coward]

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

Re:No mathematical background?

[oliverthered]

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?

[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?

[Anonymous Coward]

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?

[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?

[chichilalescu]

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?

[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?

[dimeglio]

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?

[chichilalescu]

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?

[The_Wilschon]

True. And the people who received and understood your explanation would in no way be equipped to either teach physics themselves or to do novel physics research of their own. So, I stand by my point: physics without math is not *graduate level* physics, which prepares one to either teach or do research (or both).

Re:No mathematical background?

[FrangoAssado]

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 unlike Euclidean 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 well that 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?

[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?

[The_Wilschon]

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?

[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?

[The_Wilschon]

I'm not saying that it isn't physics because you aren't using math. I'm not saying it shouldn't be done. I think that explaining physics on a conceptual level to non-scientists is a really, really good plan.

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?

[Anonymous Coward]

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?

[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?

[martin-boundary]

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.

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?

[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?

[memyselfandeye]

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?

[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?

[oliverthered]

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?

[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?

[lymond01]

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?

[lymond01]

And yes, I do physics for a living.

Obviously. :-)

Re:No mathematical background?

[moteyalpha]

People profit on free things in the same way that Google profits from giving away free search.
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 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/
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 without math?

Re:No mathematical background?

[Keebler71]

if your advisor could derive Maxwell's equations from F=ma I'd be awfully impressed... now if you mean F=ma as a metonym for "first principles" then maybe...

Re:No mathematical background?

[Keebler71]

double bullshit. Yes,... you can talk about TOPICS covered in graduate physics but not at a graduate LEVEL.

Re:No mathematical background?

[Anonymous Coward]

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?

[mburns]

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?

[kurokame]

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 concepts in college-level physics provided that you do so in relatively broad terms. But reaching graduate level physics in any honest sense requires quite 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" 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?

[commodore64_love]

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?

[martin-boundary]

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).

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?

[Anonymous Coward]

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?

[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?

[WastedMeat]

Expert...you keep using that word. I do not think it means what you think it means. I know plenty of 'experts' on relativity. I had some of them on my candidacy exam committee. An expert on relativity can program a GPS receiver with full corrections, write a numerical simulation of black hole accretion, or at the very least show that the precession of the perihelion of Mercury is incompatible with Newtonian gravity, and use it to validate general relativity. True, an expert should be able to explain things at a basic level, but another criterion is certainly the ability to actually use the subject to some end other than talking about it.

Re:No mathematical background?

[Anonymous Coward]

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?

[dmartin]

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, are Hilbert 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?

[fiziko]

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?

[fiziko]

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.

Re:No mathematical background?

[oliverthered]

"gifted in mathematics and physics, from an early age"

so, what your saying is, that he most probably had a good idea of how things worked, far beyond what he was taught and most probably before he was taught it?

he may well have taken a lot of stuff on board, thought 'interesting' somewhat useful, but best broken at best, so don't do to much with it. lets go do some patent checking instead. and while I'm at it, seeing as it all looks a bit to crap to really bother with the rest of them, I'll just do some stuff with bromine motion on my tod.

I've got 4 GCSE's, so on book I can do a bit of simple trig (no sign-cosine rules or anything interesting), and a bit of algebra.

little more physics than something like specific heating capacity.

I could work out things like best value smallest of (price/weight) across a number of products when I was pre-school (just under 4)

Oh, I also past the maths extension paper without even bothering to look what was supposed to be in it. and only used any form of aid when taking my math exams when having to do trig (it was as bit late in the day for lookup tables). only 1 question incorrect across 4 papers, and was on the 'easiest' paper.

I should be able to construct things like log or sin tables using Taylor series if you like, though I'd have to work out the Taylor series for them. (log would just be so that the angle and gradient are equal, and sin would be related to Pythagoras, which would relate the length to the squares.)

Oh what's that, you can actually work the maths out just by knowing the basic principals behind things. My god, it's like you don't even need to go to school.

infact the majority of people with aspergers are said to have some kind of 'savant' abilities.

most of the really sucessfull people are dropouts.

people with ADHD/ADD have more startup businesses (at least in the UK), that their so called none disabled counterparts.

and who says that any kind of 'grand' theory of everything is going to be a typical maths / set theory based one. after all maths is still theoretical and based on commonly held assumptions. it's going to be quite a task without that illusive set of all sets.

so, quite possibly a mathematical (as it currently stands) education in physics, may well be the poorest education you get.

the car anology was fine, to use a car and to teach how to use a car doesn't require that you know how to make one.
(although I know a number of people who could and don't know squat about maths)

That's like saying all physics is pointless unless you can make a universe.

Re:No mathematical background?

[FrangoAssado]

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.

I disagree that it's merely a distraction. Yes, when teaching the Uncertainty principle for the first time, it may be a good idea to show it for finite dimensional Hilbert space (in fact, I wish it was done this way, it's so much simpler, like you said!). For your example of a spin-1/2 particle:

delta(s_x)*delta(s_y) >= abs(<[s_x,s_y]>)/2

It's very nice for an introduction, and it can be derived with very simple math, but you can't honestly say it's graduate-level Physics if you can't even do it for position and momentum, and show that the commutator becomes constant, like so:

delta(x)*delta(p) >= abs(<[x,p]>)/2 = hbar/2

Which is the usual statement, and shows that you can't really expect the state to be exactly an eigenstate of either position or momentum, etc. (but by the time you get to this point you already know that, because things get very fishy with the eigenstate being a Dirac delta, and so on. Or maybe that's just the way I learned, but it seemed fishy to me :)).

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, are Hilbert 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).

Sure, but not all Hilbert spaces are Euclidean. Some properties can't carry from finite to infinite dimensional, like I've wrote above: in the finite dimensional case, you can't have unbounded operators, you can't have operators A and B for which [A,B] is constant, and a lot more, things that you do need in physics.

Like I said before, I think there's a lot of value in learning things with simple math, using finite dimensional Hilbert spaces, etc. In fact, I'm mostly interested in Quantum Computing, where there's no need for infinite dimensional spaces. But I have no illusions that this is full graduate level Quantum Physics.

Re:No mathematical background?

[oliverthered]

by the way, I derived the math for the newton physics only knowing the law.

(didn't bother to complete it, because well all kinds of things like friction and inertia and center of gravity and density and viscosity and .......)

there's a good reason why you can't patent things such as maths.

Re:No mathematical background?

[oliverthered]

physics is a set of excremental data and laws, math is just a convenient (at times) way to work with them, and can easily be derived or looked up if needed.

you can also perform 'thought' experiments intuitively, without even reaching for a calculator. and then turn them into real world experiments.

Re:No mathematical background?

[oliverthered]

I should say that you could use a axiom based on a subset of the axiom of choice to provide injection into set theory from nothing, not even a set.

but I'll save that for another day.

Re:No mathematical background?

[oliverthered]

ok, lets take the following.

at a base level, you can easily show that everything must be at least comparable, thought equal and opposite and interface.

so you can show that there is up and down and their for there must be something that is neither up nor down (even the grand old duke of York knows that one).

you now can have a set of axioms, which can then be related to mathematics.

mathematics need not be the basis of you axioms, it can be derived.

try applying that to say, matter and space, energy and time, matter /energy and space/ time and see what happens. it get's quite interesting.

you'll need something a bit more than just a ab b for space time. and working out where space comes from in the first place... well it's all a bit random if you ask me.

Re:No mathematical background?

[oliverthered]

Yeh, all those basket ball / socker / snooker etc.. players spend all their time brushing up on their calculus between games to make sure their equipped to work the with physics.

apparently they don't teach limits properly in the UK, which is probably why we dropped out soon. Best give the education system a kick up the ass and get them teaching limits properly for the next world cup or away game.

Re:No mathematical background?

[Roger W Moore]

My philosophy...is that the concepts and ideas of physics are represented by the math, but not defined by them.

Correct - maths is the language of physics and just like any language it is used to express ideas and concepts. As such you can certainly, albeit it crudely, explain the concepts in other languages such as English which lack the precision of maths, in much the same way that you lose a lot of the beauty and depth of Shakespeare if the bard is translated into, say, French. Similarly you are fooling yourself, and more importantly your readers, if you think you have communicated those concepts at the graduate level: that requires maths for a full and deep understanding of the ideas involved which is why certain topics are regarded as 'graduate level'.

I might as well say that I've covered graduate level physics concepts after giving an ATLAS outreach talk since Higgs, Supersymmetry etc are all topics covered in grad school. However it would be a pretty horrendous outreach talk if I covered those concepts in the same level as I would when teaching a grad course so it would be wrong and misleading to claim that I'd covered graduate level topics.

Re:No mathematical background?

[chichilalescu]

you're right, of course. I was just trying to explain what a Cauchy sequence is, and I didn't do it properly...

Re:No mathematical background?

[Anonymous Coward]

Actually, you've gone a long wy to prove GP's point: you did a pretty good job of conveying the essential concepts without a bit of actual math.

Re:No mathematical background?

[Have Brain Will Rent]

I'd say even more than that. My 1st year of physics I found if painfully difficult to learn what the text was trying to teach... in large part because they special cased everything to keep the required level of math down (otoh at the very same time the Feynman Lectures seemed fairly easy to follow by comparison). Then I took a course in ODE's and PDE's and just about everything I had come across in all of 1st year Physics dropped/popped out as simple examples in this one course.

My advice to anyone wanting to study Physics: first go take as much math as you can; basic calculus of one and several variables, PDE's ODE's and numerical analysis courses, algebra, linear algebra, complex numbers, topology... then start taking the Physics courses... the Physics part will be way easier and way faster.

Re:No mathematical background?

[tenco]

Considering that their first PDF is only 6 pages long and only text, I don't expect any serious physics thaught in that course.

Re:No mathematical background?

[tenco]

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

It's the other way around: theoretical physics is even more concerned with math than applied physics. There's a reason why theoretical physics is also called mathematical physics. And I guess you confuse working the numbers with math.

Furthermore, you can't separate physics and mathematics because the latter is the formers language.

Re:No mathematical background?

[tenco]

How the hell is this flamebait?

Re:No mathematical background?

[chichilalescu]

well, there is a mistake in my definition of a complete space. and fritsd was modded funny for some reason.

i'm relatively new, so I assumed this was a "welcome to slashdot" kind of thing. there's also an AC that called me an asshole for this same post. something must be wrong with it.

Re:No mathematical background?

[chichilalescu]

Well, by "graduate level physics" Wischon understands "final preparation for research", while I understood "concepts that you don't hear about in school till you get your batchelor's degree".
He was saying you can't do research without the math, and I was saying that you can understand a lot of the concepts without the math. Now we agree that we're both right.

Re:No mathematical background?

[chichilalescu]

Maybe he was referring to Maxwell's distribution.

Re:No mathematical background?

[tenco]

What about:

F=ma --> lagrange formalism --> lagrange density for the electromagnetic field --> maxwell equations

Re:No mathematical background?

[fritsd]

Welcome to Slashdot! :-) It can be somewhat harsh sometimes.
I was not the AC who called you asshole, just to clear that up.
I don't know why my posting was marked funny, maybe I made a mistake in it (getting rusty). I understand and agree with your explanation that the "where" is 3-D space and the superposition of n different orthogonal wavefunctions Psi(x,y,z) = \sum_i^n C_i psi_i(x,y,z) is a "point coordinate" in n-D (function-)space, all I wanted to whine about in my original posting is, that for a student learning the basics of quantum mechanics this sudden jump in perspective from the familiar "space" space to n-dimensional function space can be baffling. Well it was for me.
There is another point that I wanted to convey, and that is that when you managed to calculate a result out of your first crude estimation of the ground-state energy of a Hydrogen atom with 1 GTO orbital, and it's only one order of magnitude out of whack with the real value, only *then* you start to get the idea that maybe you are getting somewhere with this quantum thingy. There is a strong sense of empowerment the first time you get something useful with your own brain (and a calculator or computer); comparable to writing your first working "hello world" in a for you unfamiliar computer language. I think maybe you can convey a sense of awe and wonder for QM without use of maths, but I doubt it will be as strong as when the students realize they can calculate things *themselves* that are crude approximations of molecules and spectra *in the observable world*. Otherwise it's a bit of a spectator sport.

Re:No mathematical background?

[T.E.D.]

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."

That was just Ernest trying to explain how all that time he spent talking to barmaids he was actually working.

Occasionally it pays off to be smart...

Re:No mathematical background?

[Anonymous Coward]

To offset all the negative comments here a bit: I hope your effort gives you and your students great joy and understanding.

Re:No mathematical background?

[skids]

Personally I've read so much "math free" stuff about Physics and especially QM and gained very little from the experience.

You're better off finding better ways of teaching people math.

Re:No mathematical background?

[The_Wilschon]

Sorry, I did not mean to degrade your wonderful efforts. I think that a well written accounting of conceptual physics is an excellent thing to have.

However, I would caution you to take great care not to overstate what your students are receiving. There are already way too many people out there who think that you don't really need math and rigor, that they can do physics if they just think really hard about weird things, and that "the scientific establishment" only uses math in order to maintain some imaginary level of power and control over the "outsiders". Please try very hard not to contribute to this mentality, as I think it is much more harmful than a lack of a conceptual understanding in the first place. This is why I took issue with your characterization of your work as teaching "graduate level" physics.

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.

Re:No mathematical background?

[The_Wilschon]

Conceded. Best of luck!

Science w/o math

[SnarfQuest]

Science without mathematics. Sounds like an Al Gore school.

No math???

[stanlyb]

What? No math? Do you really believe that you could learn any science without math? And not only any kind of math but university degree math?

oblig XKCD

[ChipMonk]

Here.

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...

Re:oblig XKCD

[Monkeedude1212]

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

Re:oblig XKCD

[Hazelfield]

Actually one discipline is missing in that strip. There should be a philosopher to the right of the mathematician.

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:oblig XKCD

[narcc]

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

[Anonymous Coward]

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

[martin-boundary]

No, because pi is not a matter of mere mental interpretation: it is a fundamental constant which can be observed in nature.

Re:oblig XKCD

[shazie]

me also like this

Re:oblig XKCD

[Anonymous Coward]

Philosophy is the study of declaring your field responsible for all human achievements without actually contributing anything to them.

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.

More intellectual rigor than Glenn Beck University

[Anonymous Coward]

"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!"

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.

,first post

[Anonymous Coward]

Irc.easynew5.com This post brought

Khan Academy physics?

[mpfife]

How do the classes go? Something like this I imagine:
"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

[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:So far, I'm not impressed

[Monkeedude1212]

And love.

Re:So far, I'm not impressed

[chichilalescu]

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

[Anonymous Coward]

In GR, gravity is not a force.

Re:So far, I'm not impressed

[zzsmirkzz]

The thing that didn't impress me (with all the questions being asked and all) is that they state the mass of the nucleus is not equal to the sum of the components and in fact is usually less. Okay, good observation but my immediate question is how did they measure the 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

[mburns]

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

[niteshifter]

... 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

[FrangoAssado]

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, 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

[fiziko]

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

[fiziko]

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?

Re:So far, I'm not impressed

[khallow]

Electromagnetism alone does not get you a solid surface.

What is a "solid surface"? It's not clear to me why you think this is relevant.

Re:So far, I'm not impressed

[FrangoAssado]

So far, for an introduction, there's no bad explanation. But it seems they're promising to explain a lot more that is reasonable to expect: are they really planning to go all the way up to relativistic QM without math? If not, why bring up relativity at all?

There's a lot of QM to explain before getting into that: superposition, entanglement, Bell states (to see what's really weird with entanglement), measurement, uncertainty principle, etc. And that's just the foundation, then (based on Lesson 1) it seems they'll explain photons, electrons and maybe other fundamental particles. That's really hard to explain right (and with simple math!) in only 9 lessons. I don't see how you can do that and still squeeze in the relation of QM with relativity.

Re:So far, I'm not impressed

[Anonymous Coward]

I'm in complete agreement with you. This 'lesson' is too brief about virtually every problem it mentions; At the level of exposition given it is not clear if there is a problem, and where the resolution comes from. Is this supposed to be a lesson in relativity or quantum mechanics?

Furthermore, even the starting point of 'classical thinking' is not clearly defined; How are we to know, then, if the stated problems are problems with classical physics?

My take on the pieces:

First off, the hard sphere force transmission problem. This contradiction is a house divided against itself; It appears that the information will travel faster than the speed of light, but our theory is not relativistically compatible; We built this 'hard-sphere' theory without any recourse to the relativistic idea. So, if we believe the relativistic principles, we should reject this 'hard-sphere' picture outright, regardless of quantum mechanics. The lesson says that this idealization is 'structureless', but it's not; The structure is that of a sphere. If you thought particles were made of hard spheres, you could try lining them up in different ways or bouncing them off each other with different trajectories and measuring the angles involved to test the idea that they have that shape. 'Structureless' means that the particles are (0-d) points with no spatial extent. The end of this section poses questions about contact forces and is maybe drawing from the collapse of the classical atom- however, it kindof begs (entirely classical) questions like "How can light travel through an object if the light and the object must be 'on top' of each other (ie in the same space)?" Why can an electric field exist outside of a vacuum?

Interaction problems: This section is moving too quickly to properly pose its own questions, in my opinion. It starts out only frighteningly fast, and then jumps to talking about DNA strands. In addition, questions like "what is the nucleus made of?" are relevant to this conversation. (The neutron was not discovered until after quantum mechanics, and one good reason to believe in it is the -quantum mechanical- puzzles it helps solve.)
Here's a question for you: Is there some special reason that the force which holds a nucleus together cannot be a classical force? (Maybe the force goes like 1/r^5 or something so that it appears short ranged; My point is that without any mathematical tools available to us, we are unable to analyze a question like this in classical mechanics, much less in quantum mechanics)

Nuclear mass problem:
There are two questions posed in this section: What holds Nuclei together, and how come a nucleus weighs less than the things that appear to comprise it? The first question has already been asked in the previous section, and the second is answered -entirely- within the domain of relativity. According to relativity, the resulting object has less mass -because- the two objects are bound together. Why? The mass of the system is the total energy of the system, which is greater if the system is free than if it is bound. Why, you might ask, is E=MC^2? Believe it or not this is no postulate of relativity- it's a conclusion. Unfortunately, I do not think this question is so easily answered without any math whatsoever. The physics is not terribly difficult, but when you shun mathematics, you shun understanding.
Also, again, is this a course on relativity or quantum mechanics?

"Particle Creation problems", this section is just outright confusing. It is not clear what the questions are, really! Clearly a theory of hard spheres would not predict that time and space came from a singularity. The big bang theory is based on cosmological observations and extrapolation of general relativity (Whaoaoa, I thought this was a class on quantum mechanics?), though, in my mind an entirely separate endeavor from "what is the basics of quantum mechanics?" (This piece of physics, in my mind, is a descendent of modern physics, not a piece of it). Physics has given us insight into big questions, bu

Re:So far, I'm not impressed

[kaneod]

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.

The mass defect is the basis of both nuclear fission and nuclear fusion power generation, and the atomic masses are known to quite a high accuracy these days. Go look at NIST, their physical reference data has the electron, proton, neutron and various atomic masses with the uncertainties, with references to the data sources.

Re:So far, I'm not impressed

[mburns]

It is a response to the assertion that all ordinary forces are electromagnetic. Without Pauli exclusion, there are no solid bodies, but only points neutralized out of the plasma.

Re:So far, I'm not impressed

[khallow]

It is a response to the assertion that all ordinary forces are electromagnetic. Without Pauli exclusion, there are no solid bodies, but only points neutralized out of the plasma.

Then perhaps you should have said this instead. My view is that Pauli exclusion is not even similar to the claim "where the premise of spacetime, the existence of the metric, goes out of range". I believe modern physics claims that the spacetime metric is good down to the so-called Planck scale, which is considerably smaller than the scale of the electron clouds of atoms. Instead Pauli exclusion is a feature of quantum models which differ from classic models not in the spacetime metric, but in the mathematics of the system.

Having said that, the most distinctive difference between the two models is in the structure of phase space (which is combined spacetime and momentum space). In classical systems, positions and momenta "commute", that is, it doesn't matter what order you consider these things in when evaluating properties of your system. In quantum systems, they do not. You still have spacetime and a corresponding metric in momentum space, but the order of positions and momenta matter when calculating properties of the overall phase space and observables in the model.

time, space & circumstance

[Anonymous Coward]

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.

Re:How do you talk about physics without mathemati

[Hazelfield]

This. To grasp even basic quantum mechanics you need to know about linear algebra (to understand the bra/ket notation and why a*b doesn't equal b*a), improper integrals and complex functions (to understand the wave function) and preferably partial differential equations too (to derive the solutions of some simple cases). And that's just the beginning of it.

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.

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.

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

[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:No gedanken background

[by (1706743)]

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

[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.

Re:No gedanken background

[by (1706743)]

...including Dirac notation...

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

Re:No gedanken background

[tendrousbeastie]

That is by far the funniest joke that no-one will get that I have read all day.

Well, its possible

[BigJClark]

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

[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:Well, its possible

[martin-boundary]

Incidentally, complex algebra is, in a sense, "the algebra of scaling and rotating little arrows" Feynman describes.

Yes, we know this (see here). 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

[aBaldrich]

As a CS student I have not studied much physics; but I'm a very curious guy so I could not resist to follow the link. Their requirements are: average level intelligence, basic maths and a PDF reader. Sounds like perfect for me... or too perfect? W. Blaine Dowler took his time to write in LaTeX, which automatically made me think it can be trusted - don't ask me why. But, on second thoughts, this doesn't sound right.
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, what am 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

[Anonymous Coward]

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

[memyselfandeye]

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.

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.

A good textbook?

[Anonymous Coward]

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?

[jjsm]

With your math background I think that the book 'Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles' by R. Eisberg and R. Resnick would be a good read. That's the book I am reading for a one year class on modern physics.

Re:A good textbook?

[The_Wilschon]

I would absolutely recommend David J. Griffiths' "Introduction to Quantum Mechanics". It's blue and has a cat on the cover (and a dead cat on the back), hence it is sometimes known to physicists as "the cat book". Multivariable calculus, linear algebra (with a small emphasis on abstract algebra if possible), and diffeq (partial, not just ordinary), are exactly the math that you need to grok everything in Griffiths. It is one of a few standard undergrad (usually sophomore or junior level) texts, and, in my opinion, the best written among them.

Another poster recommended a modern physics text, but I would disagree that that is your best choice. Modern physics texts tend to be great at going "wooee! look at how weird the universe is!" and touching briefly on a whole bunch of the seminal experiments and theories, but without really going into much of anything in any sort of depth.

Re:How do you talk about physics without mathemati

[fritsd]

You tell 'em, you "villain", you!

Sooo...

[dustin_0099]

This is just a reprinting of Fred Wolf's 15 chapter "Taking the Quantum Leap" as 9 chapters?

In the beginning "all particles were packed into

[Anonymous Coward]

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:How do you talk about physics without mathemati

[ebmi]

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

Re:How do you talk about physics without mathemati

[Anonymous Coward]

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

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.

The ivory tower syndrome

[rsborg]

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.

Even worse than what happens for the insiders is what is left for the outsiders: demagogues, televangelists and industry funded anti-science groups convince those outsiders that the insiders are elitist and despise the outsiders' lack of knowledge... also poisoning the well of understanding while gaining their trust "against the elite science crowd".

Making advanced knowledge as accessible (without reductionism) as possible is the best hope for our continued development as a society and species.

Like it or not maths is still needed

[Roger W Moore]

He only uses the math as the final step, to describe what he sees in his head, not because he enjoys it.

Exactly - in order to describe physics you have to use maths. It is certainly possible to teach the basic concepts but if you think you are learning "graduate level" physics you clearly have no idea what graduate level physics is because that requires maths in order to communicate a full understanding even though the understanding in your head will be in "pictures".

For example I can simply tell you that in nature every symmetry produces a conserved quantity. You can think about it for a while and perhaps convince yourself that this is true. However without understanding Noether's theorem and basic Lagrangian mechanics your understanding will be far from complete and, worse, you will have no way to be able to calculate what the conserved quantity is given a particular symmetry or vice verse....and this isn't even graduate level, its second year undergrad!

Re:Like it or not maths is still needed

[oliverthered]

'Noether's theorem'

looks like she's saying things must be in a transient/flux state.

or each action must also be symmetrical and have an 'interface'

and indeed, each symmetry must also have an asymmetry and interface.

this requires latent 'constants' (I can't remember if the laws of super duper symmetry required some things to be constant absolute and some things to be relatively constant) within the system and means that the system must be in a status of continuous flux.

conservation laws (and their a/symmetries) then ensure that the system remains a/symmetrical transcendently.

Wrong : love is based on EM force

[aepervius]

Love is the behavior which is the result of chemical reaction in the brain and the body (neurotransmitter, hormone, neuron state etc...). Love *IS* based on chemistry , and therefore fully based on electromagnetic force, QM. All our emotion are based on chemistry. A complicated system, surely, one for which we have only superficial model definitively, but in absence of evidence to the contrary, those are definitively system where only biochemistry is at play.

I disagree

[aepervius]

Logic at his purest form is not dependent on *ANY* material. Philosophy involve more than logic is dependent on logic, the same way physic involve more than math but is dependent on math. So philosophy is applied logic to idea and existence etc... Logic is not a subset of philosophy, philosophy is USING logic. Otherwise you could declare math a subset of physic. So at the core of EVERYTHING, logic, is there present and the most purest of all material.

Remove the fallacies first

[Chemisor]

The paper is simply packed with logical fallacies. Yes, many of these are commonly accepted in the physics community, and are indeed the cause of the current pithy state of physics research, that continues to leap from one absurd conclusion to the next, discarding logic in the process. But is it really a good idea to pollute the minds of the next generation with them? The paper starts with a misconception right from the start:

> Nothing, not even information, can travel faster than the speed of light.

Here is a fine example of the mind projection fallacy: failure to distinguish between reality and what you think about reality. Information is not a physical object. A physical signal varying in an informative (to you) way is indeed limited by the speed of light, but the transfer of information is not necessarily limited to a direct transfer of measurements through a physical signal. An obvious example are the current research into "entangled" particles, where you can create two particles with correlated properties and by measuring the parameters of one know the parameters of the other. Because of the mind projection fallacy, physicists still think of this as "spooky action at a distance", even though no "action" has occured except in the experimenter's mind. No physical signal was sent from one particle to the other, only information was "sent" from the experimenter's mental model of one particle to the mental model of the other. Such virtual "transfers" are limited only by the size of the containing brain. Understand this, and you'll see why we must always make the distinction between what we think and what is. Unfortunately, the very formulation of quantum theory forbids such questions. In section 2.4 we see a continuation of this insanity:

> If we have an electron orbiting a nucleus, then the electron "knows" of an opposing electrical charge of the nucleus.

Quantum theory models all interactions as particle exchanges and thus has mostly lost the concept of a field of force. We could, for instance ask the very same question about the earth orbiting the sun and receive an answer that the gravitational field deforms the space around the sun and the earth, and that the interaction of their curvatures produces the gravitational force. Likewise, we could imagine charge curving some "electromagnetic space" and causing protons and electrons to interact in the same manner. (Interestingly, the old ether theories were "disproved" because we could not find effects of motion through it, even though the gravitational space does not appear to manifest any absolute velocity either)

> In other words, information about that charge has been received. In order to manage that, energy must be transmitted away from one or the other. How does the energy get replenished?

How does the "energy" get replenished when the earth moves around the sun? The answer, of course, is that there is no energy transmission, or information transmission. Neither the electron nor the earth is an intelligent entity capable of processing information in the same way we do. Physical objects merely interact with local space, creating gravitational deformation, and space then arranges those deformations into a minimal energy configuration, which, in the case of the earth, just happens to be an orbit around the sun. The same happens in the nucleus, except that the minimum energy levels are limited by quantum effects (why they are limited is a whole different discussion, and one that quantum mechanics simply postulates without any explanation whatsoever).

> In a world of absolutes, where particles are immutable and indivisible, the particles also become invincible.

Where the heck did he get that? Particles and antiparticles can annihilate into electromagnetic radiation, and radiation can create particle-antiparticle pairs. No, we don't know why that is so. Quantum mechanics has a mathematical model that can calculate the parameters of the interaction, but offers no explanation of how it actually happens (nor c

Re:Remove the fallacies first

[fiziko]

Funny, you are criticizing the lesson for the questions raised in this lesson, and then providing many of the exact answers that are coming in later lessons...

Re:Remove the fallacies first

[Anonymous Coward]

Re: information and quantum entanglement: I challenge you to send a message, even just a single bit, from point A to point B, faster than the speed of light, using entangled states. If you decide that you want to send a 1, does your collaborator on the other side the lab, who you aren't talking to, see a 1 every time? The fact is, if you study how the entangled state experiments work, you will see that, while the measurements of the two entangled particles are exactly correlated, there is no way for you to choose what value you will get from your measurement of your entangled particle, and thus no way for you to decide what measurement your collaborator will get on the other particle. Thus, you cannot use wavefunction collapse in entangled states to transmit information from one place to another faster than the speed of light.

The rest of your post displays a similar lack of understanding of the "fallacies" you decry, but it's late, so I'm going to go to bed instead of dealing with them.

Stating sentences in the subject and continuing th

[alexo]

em in the body stopped being novel years ago.
Now it is just annoying.

obvious answers can often hide plain sight

[Anonymous Coward]

There is a fundamental problem with Quantum Physics. The math definitions put forth only describe arbitrary states of matter and pay little attention to spacial shapes, though there has been some concept of shapes proposed through math (strings for example).

There has been very little done to try to extrapolate state shapes from math. Einstein tried most of his career to find some mathematical correlation between shape and state (his search for a Unified Field Theory). Since his death there has been essentially a lack of real effort to continue this line of investigation. The slightest mention of a unity between Newtonian Physics and Quantum Physics causes poo-hoos and heckles and huge headaches for Professors in the Ivory Towers.

It will take some high school grad with no predisposition to exclude any mathematical possibility (for example using an equation that uses the speed of light as a positive multiplicative factor) to discover how matter and energy can create gravity.

A good example is the fact that most who perceive space as three dimensional do not understand that physical space can be defined only with four points. Two points describe a line, three points describe a plane and four points describe space. From this simple fact all spacial shapes can be extrapolated with math. Because a point is defined as a sphere, the equation 4/3*pi*r(3) becomes the single most important equation to learn.

Big question is if you have four congruent points that intersect and are enclosed within a circle then is all the math possible from this basic shape defined? For instance what are the mathematical relationships between the enclosure and the four congruent and equal circles defining the enclosure? Is it possible that wave lengths and gain (wave energy) can be quantified from equations that define shapes within the field of the enclosing circle? From simple mathematical questions like this the answers to Einstein's big unanswered question about unity and much more about unified field physics will be found.