This Week's Finds in Mathematical Physics (Week 271)
John Baez
October 26, 2008
This Week's Finds in Mathematical Physics (Week 271)
John Baez
This week I'll talk about quasicrystals and how they arise from
the interplay between crystallographic and noncrystallographic
Coxeter groups. I'll describe Jeffrey Morton's new paper on
groupoids and 2-vector spaces, and Stephen Summers' review of
new work on constructive quantum field theory. But first - more
pictures of Jupiter's moon Io!
Here's a great photo of volcanic activity on Io - the "Masubi plume":
1) NASA Photojournal, Masubi plume on Io,
http://photojournal.jpl.nasa.gov/catalog/PIA02502
You can see hot gas and dust shooting 100 kilometers up into the
atmosphere!
Here's another:
2) Solarviews, Pele volcano and Pillan Patera,
http://www.solarviews.com/eng/iopele.htm
In front we see a volcanic feature called Pillan Patera. Over the
horizon we see an enormous eruption 300 kilometers high coming from
the most intense persistent hot spot on Io: Pele. This seems to be
an active lava lake inside a volcanic depression, or "patera", about
20 x 30 kilometers in size.
But Pillan Patera is no slouch either when it comes to eruptions.
Look at these "before and after" pictures taken 5 months apart in 1997:
3) NASA Photojournal, Arizona-sized Io eruption,
http://photojournal.jpl.nasa.gov/catalog/PIA00744
The big red ring is sulfur spewed out by Pele. But the exciting new
feature in the "after" picture is the dark blotch centered at Pillan
Patera. It's 400 kilometers in diameter, roughly the size of Arizona.
It consists of about 50 cubic kilometers of lava laid down by a big
eruption. At the peak of the activity, 10,000 cubic meters of lava
were spewing out each second. This was the largest volcanic eruption
ever seen, anywhere!
For more, try these:
4) A.G. Davies et al, Thermal signature, eruption style and eruption
evolution at Pele and Pillan on Io, Jour. Geophys. Research 106
(2001), 33,079-33,103. Also available at
http://europa.la.asu.edu/pgg/associates/members/williams/gw/pdf/2001Daviesetal.pdf
5) Jani Radebaugh et al, Observations and temperatures of Io's
Pele Patera from Cassini and Galileo spacecraft images,
Icarus 169 (2004), 65-79.
In case you're wondering about the red sulfur around Pele versus
the yellow sulfur you saw last week, let me say a bit about that.
Sulfur comes in an incredible number of forms, or allotropes:
6) Wikipedia, Allotropes of sulfur,
http://en.wikipedia.org/wiki/Allotropes_of_sulfur
It can form different molecules consisting of 2 to 20 atoms. The most
common form on Earth is alpha-sulfur: rhombic crystals made of
ring-shaped molecules containing 8 atoms each. Alpha-sulfur is lemon
yellow, but above 95 degrees Celsius it gradually turns into paler
yellow beta-sulfur: the ring-shaped molecules reorganize to form
crystals with less symmetry - monoclinic crystals, to be precise.
Sulfur melts around 115 Celsius. But when you heat it above 160
Celsius, something weird happens: contrary to the usual pattern for
liquids, it gets more viscous as it gets hotter! The reason: the
atoms start forming long chain polymers, called "catena sulfur".
As these predominate, the stuff gets darker in color: first orange,
then red, then dark red, and finally almost black. Blecch! If you
then cool it suddenly, it can form a red amorphous solid. And that,
presumably, is what we see in the ring around Pele.
Now, from crystals to quasicrystals...
Last week I asked if quasicrystals with approximate 5-fold symmetry
could be obtained by slicing lattices in higher dimensions. Greg
Egan answered - yes! He even has a beautiful Java applet that
demonstrates it:
7) Greg Egan, deBruijn,
http://www.gregegan.net/APPLETS/12/12.html
It shows some nice quasiperiodic tilings of the plane with approximate
n-fold symmetry, made by cleverly slicing a cubical lattice in
n-dimensional space. The idea comes from this paper:
8) N. G. deBruijn, Algebraic theory of Penrose's nonperiodic tilings
of the plane, I, II, Nederl. Akad. Wetensch. Indag. Math. 43 (1981),
39-52, 53-66.
When n is odd, we can also get deBruijn's tiling by slicing the
A_{n-1} lattice in (n-1)-dimensional space. You're probably most
familiar with the A_3 lattice, which shows up when you stack oranges.
You'll notice this pattern has tetrahedral symmetry. The symmetry
group of the tetrahedron is also called the A_3 Coxeter group.
It's the group of all permutations of 4 things (the corners of the
tetrahedron). This contains the symmetry group of the square, since
that group contains some but not all permutations of the 4 corners of
the square. Indeed, if you view a regular tetrahedron from the
correct angle, it looks like a square!
This pattern goes on for higher n. Last week I spoke about the A_4
lattice, whose symmetry group consists of all permutations of 5 things
- namely the 5 corners of a 4-simplex, which is the 4d analogue of a
tetrahedron. I explained how this group contains the symmetry group
of the pentagon. Indeed, if you view a 4-simplex from the right
correct angle, it looks like a pentagon!
DeBruijn exploited this to get a quasiperiodic tiling of the plane
with approximate 5-fold symmetry by taking a 2d slice of the
A_5 lattice and doing a few other tricks.
But this generalizes: the symmetries of an (n-1)-simplex include the
symmetries of a regular n-gon. Just as this Coxeter group, the
symmetry group of the pentagon:
5
o---o
sits inside the A_4 Coxeter group:
o---o---o---o
similarly the symmetries of a hexagon:
6
o---o
sit inside the A_5 Coxeter group:
o---o---o---o---o
and so on: the noncrystallographic Coxeter groups I_2(n)
sit nicely inside the Coxeter groups A_{n+1}. But the really
cool part is how deBruijn uses these to get quasiperiodic tilings
of the plane!
And this idea generalizes to the *other* two noncrystallographic
Coxeter groups. Remember, there are just two more:
H_3, the symmetry group of the dodecahedron, with 120 elements;
H_4, the symmetry group of the 120-cell, with 120 x 120 elements.
We can get 3d quasicrystals with approximate dodecahedral symmetry by
cleverly slicing the 6-dimensional D_6 lattice. This is actually
practical, since there really *are* such quasicrystals in nature. And
we can get 4d quasicrystals with approximate 120-cell symmetry by
cleverly slicing the E_8 lattice! This is just incredibly cool as
pure mathematics:
9) Veit Elser and Neil Sloane, A highly symmetric four-dimensional
quasicrystal, J. Phys. A 20 (1987), 6161-6168.
Also available at http://akpublic.research.att.com/~njas/doc/Elser.ps
10) J. F. Sadoc and R. Mosseri, The E8 lattice and quasicrystals:
geometry, number theory and quasicrystals, J. Phys. A 26 (1993),
1789-1809.
11) Robert V. Moody and J. Patera, Quasicrystals and icosians,
J. Phys. A. 26 (1993), 2829-2853.
Yes, this is the same Moody who helped invent Kac-Moody algebras! For
the last decade or so he's been working on quasicrystals. In "week20"
I explained the "icosians" - a subring of the quaternions built from
the symmetries of a dodecahedron - and how Conway and Sloane used them
to construct the E8 lattice. Moody's article uses the icosians to
study the 4d quasicrystals that we get by slicing the E8 lattice.
While they may seem remote from the real world, these 4d quasicrystals
can be further sliced to give 3d quasicrytals with approximate
dodecahedral symmetry. So in some sense, the quasicrystals we find
in nature are "shadows" of the E_8 lattice... trying their best to
have a symmetry that can only exist in 8 dimensions, but never quite
succeeding.
I love this idea, because it's gotten me over my fear of quasicrystals.
They look unruly and complicated, but now I see that some of them
have close ties to the beautiful, perfectly symmetrical world of
Dynkin diagrams. The "noncrystallographic" Coxeter groups are really
"quasicrystallographic"!
Next let me discuss this paper by Jeffrey Morton:
12) Jeffrey Morton, 2-vector spaces and groupoids, available as
arXiv:0810.2361.
It's an important new twist in the Tale of Groupoidification! As
part of this tale, in "week256" I described a functor from the
category with
finite groupoids as objects,
equivalence classes of spans of finite groupoids as morphisms
to the category with
finite-dimensional vector spaces as objects,
linear operators as morphisms.
I called this "degroupoidification". The idea is that a lot of linear
algebra has an underlying purely combinatorial "skeleton" that doesn't
involve the complex numbers - just symmetry in its purest form.
Groupoidification is quest to strip the fat off linear algebra and
do it using groupoids.
Jeffrey boosts this idea up one notch, getting a 2-functor from the
2-category with:
finite groupoids as objects,
spans of finite groupoids as morphisms,
equivalence classes of spans of spans finite groupoids as morphisms
to the 2-category with
finite-dimensional 2-vector spaces as objects,
linear functors as morphisms,
natural transformations as 2-morphisms.
Here by "finite-dimensional 2-vector space" I really mean a
"Kapranov-Voevodsky 2-vector space". That's a category equivalent to
Vect^n for some n, where Vect is the category of finite-dimensional
vector spaces. A "linear functor" is one that's linear on each
homset. More concretely, we can describe a linear functor
F: Vect^n -> Vect^m
as an m x n matrix of finite-dimensional vector spaces, just as we
can describe a linear operator
F: C^n -> C^m
as a m x n matrix of complex numbers.
This suggests that Jeffrey is secretly talking about a categorified
version of Heisenberg's "matrix mechanics" - and that's true.
I want to explain that. But I'm getting really sick of saying
"finite" and "finite-dimensional". So, henceforth I'll leave out
those adjectives... but they're really always there. Okay?
Degroupoidification turns each groupoid into a vector space... but
in fact it gives more: a Hilbert space! Similarly, Jeffrey's process
actually turns each groupoid into a 2-Hilbert space. I proved that
a long time ago:
12) John Baez, Higher-dimensional algebra II: 2-Hilbert spaces,
Adv. Math. 127 (1997), 125-189. Also available as arXiv:q-alg/9609018.
So, just as degroupoidification reveals that a fair amount of
quantum mechanics can be done with groupoids instead of vector spaces,
Jeffrey's process reveals that a fair amount of *categorified*
quantum mechanics can also be done with groupoids!
Categorified quantum mechanics becomes important when we go from the
physics of particles (which is really field theory on 1d spacetimes)
to the physics of strings (which is really field theory on 2d
spacetimes). The simplest case is "topological string theory",
also known as "extended 2d topological quantum field theory". And
the simplest example of such a theory is the "Dijkgraaf-Witten model":
a gauge theory with a finite gauge group.
In his thesis:
13) Jeffrey Morton, Extended TQFT's and Quantum Gravity, Ph.D.
thesis, U. C. Riverside, 2007. Available at arXiv:0710.0032.
Jeffrey showed that a special case, the "untwisted" Dijkgraaf-Witten
model, gives a 2-functor from the 2-category with
0d manifolds as objects,
1d cobordisms between these as morphisms,
equivalence classes of 2d cobordisms between these as 2-morphisms
to the 2-category with
finite groupoids as objects,
spans of finite groupoids as morphisms,
equivalence classes of spans of spans finite groupoids as morphisms.
Composing this 2-functor with the 2-functor I just described,
he gets the untwisted Dijkgraaf-Witten model as an extended TQFT!
And in fact, he does it in all dimensions, not just dimension 2.
By the way, most of the 2-categories and 2-functors here are "weak".
Also by the way, Jeffrey constructed the above cobordism 2-category in
an earlier paper, which I discussed in "week242". He recently
polished up this paper, changing the title to make it focus on
the algebraic essence of his construction:
14) Jeffrey Morton, Double bicategories and double cospans,
available as arXiv:math/0611930.
There's a lot more I could say about this, but not a lot more time.
So, let me wrap up with a pointer to Stephen Summers' review of new
work on constructive quantum field theory.
Constructive quantum field theory is the branch of mathematical
physics where you try to rigorously construct examples of quantum
field theories. I did my Ph.D. thesis on this subject under Irving
Segal, but it was too hard for me, and my heart was never really in
it, so I soon fled - first to classical field theory, and then further.
I recently met Stephen Summers at a conference in honor of von
Neumann, and he tried to call me back to my roots. It turns out
there's been a lot of interesting progress in constructive quantum
field theory! I'll probably keep working on topological quantum field
theory and other wimpy subjects - but it's great to hear someone out
there is doing the hard work of getting physically realistic quantum
field theories to make rigorous mathematical sense.
Here's some of what he has to say:
The development of the tools and techniques of algebraic quantum
field theory (AQFT) has reached the point where they can be turned
upon the question of existence of quantum field models. Although
the program of constructing models via AQFT is still in its infancy
and only a few researchers are working in the field, already some
encouraging successes can be displayed. I personally find it
stimulating that the ideas employed go well beyond the range of the
semiclassical ideas which were mathematically developed by
researchers in constructive quantum field theory in the 70's and
80's. There is no appeal to Lagrangians, actions and perturbation
theory, nor does one "work in the Euclidean realm", and one
generally avoids a direct construction of strictly local quantum
field operators (as these either do not exist or are prohibitively
difficult to construct), preferring to construct more physically
relevant quantities such as the scattering amplitudes and local
"observables". Some of the constructed models are local and free,
some are local and have nontrivial S-matrices, and yet others
manifest only certain remnants of locality, although these remnants
suffice to enable the computation of nontrivial two-particle
S-matrix elements. This includes models with nontrivial scattering
in four spacetime dimensions.
This is just the beginning of a fascinating review. Check it out:
15) Stephen J. Summers, Constructive AQFT,
http://www.math.ufl.edu/~sjs/construction.html
Also check out his big AQFT page, which lists textbooks and
many more references:
16) Stephen J. Summers, Algebraic quantum field theory,
http://www.math.ufl.edu/~sjs/aqft.html
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Quote of the Week:
During the journey we commonly forget its goal. Almost every
profession is chosen as a means to an end but continued as an
end in itself. Forgetting our objectives is the most frequent
act of stupidity. - Friedrich Nietzsche
-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at
http://math.ucr.edu/home/baez/
For a table of contents of all the issues of This Week's Finds, try
http://math.ucr.edu/home/baez/twfcontents.html
A simple jumping-off point to the old issues is available at
http://math.ucr.edu/home/baez/twfshort.html
If you just want the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html
Uncle Al
>
> Also available at http://math.ucr.edu/home/baez/week271.html
>
> October 26, 2008
> This Week's Finds in Mathematical Physics (Week 271)
> 7) Greg Egan, deBruijn,
> http://www.gregegan.net/APPLETS/12/12.html
>
> It shows some nice quasiperiodic tilings of the plane with approximate
> n-fold symmetry, made by cleverly slicing a cubical lattice in
> n-dimensional space. The idea comes from this paper:
>
> 8) N. G. deBruijn, Algebraic theory of Penrose's nonperiodic tilings
> of the plane, I, II, Nederl. Akad. Wetensch. Indag. Math. 43 (1981),
> 39-52, 53-66.
>
> When n is odd, we can also get deBruijn's tiling by slicing the
> A_{n-1} lattice in (n-1)-dimensional space. You're probably most
> familiar with the A_3 lattice, which shows up when you stack oranges.
> You'll notice this pattern has tetrahedral symmetry. The symmetry
> group of the tetrahedron is also called the A_3 Coxeter group.
> It's the group of all permutations of 4 things (the corners of the
> tetrahedron). This contains the symmetry group of the square, since
> that group contains some but not all permutations of the 4 corners of
> the square. Indeed, if you view a regular tetrahedron from the
> correct angle, it looks like a square!
[snip]
http://www.geom.uiuc.edu/apps/quasitiler/
http://www.scienceu.com/geometry/
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Gerard Westendorp
[..]
> Sulfur melts around 115 Celsius. But when you heat it above 160
> Celsius, something weird happens: contrary to the usual pattern for
> liquids, it gets more viscous as it gets hotter! The reason: the
> atoms start forming long chain polymers, called "catena sulfur".
If you don't have a chemistry set, you can always watch
it on Youtube:
http://www.youtube.com/watch?v=JtPbHL5gFKw&NR=1
This one is also fun:
http://www.youtube.com/watch?v=mGMR72X8V-U
Gerard
Ivica Kolar
I have a few questions, hoping not completely off topic:
Where is the best on-line source to start with Categories,
something like "Introduction to Categories for complete dummies" ?
Where is the best place to post some (novice) questions ?
I'm dealing with (n!)!, my main model with permutation as basic element
is 3d body shown below:
Cardinality: 1 n n! (n!)!
-------------------------------------------------------
point perm Sn all Sn orderings
............. ---------- 3d body -------------
I have noticed that I should be able to express product of permutations
(function composition) additively i.e.:
AoB = A[B] == (a+b) + f(a,b)
Where I can read more about such approach (Phase Space Of Function
Composition) ?
Best regards,
--
ivica
JohnF
> Where is the best on-line source to start with Categories,
> something like "Introduction to Categories for complete dummies" ?
Jaap Van Oosten's "Basic Category Theory"
http://www.math.uu.nl/people/jvoosten/syllabi/catsmoeder.pdf
http://www.math.uu.nl/people/jvoosten/syllabi/catsmoeder.ps.gz
is pretty good.
--
John Forkosh ( mailto: j...@f.com where j=john and f=forkosh )
Archimedes Plutonium
> Also available at http://math.ucr.edu/home/baez/week271.html
> October 26, 2008
> This Week's Finds in Mathematical Physics (Week 271)
> John Baez
TEACHING TRUE PHYSICS// 1st year College// Physics textbook series, book 4
by Archimedes Plutonium
Preface: This is AP's 151st book of science published. It is one of my most important books of science because 1st year college physics is so impressionable on students, if they should continue with physics, or look elsewhere for a career. And also, physics is a crossroad to all the other hard core sciences, where physics course is mandatory such as in chemistry or even biology. I have endeavored to make physics 1st year college to be as easy and simple to learn. In this endeavor to make physics super easy, I have made the writing such that you will see core ideas in all capital letters as single sentences as a educational tool. And I have made this textbook chapter writing follow a logical pattern of both algebra and geometry concepts, throughout. The utmost importance of logic in physics needs to be seen and understood. For I have never seen a physics book, prior to this one that is logical. Every Old Physics textbook I have seen is scatter-brained in topics and in writing. I use as template book of Halliday & Resnick because a edition of H&R was one I was taught physics at University of Cincinnati in 1969. And in 1969, I had a choice of majors, do I major in geology, or mathematics, or in physics, for I will graduate from UC in 1972. For me, geology was too easy, but physics was too tough, so I ended up majoring in mathematics. If I had been taught in 1969 using this textbook that I have written, I would have ended up majoring in physics, my first love. For physics is not hard, not hard at all, once you clear out the mistakes and the obnoxious worthless mathematics that clutters up Old Physics, and the illogic that smothers much of Old Physics.
Maybe it was good that I had those impressions of physics education of poor education, which still exists throughout physics today. Because maybe I am forced to write this book, because of that awful experience of learning physics in 1969. Without that awful experience, maybe this textbook would have never been written by me.
Cover picture is the template book of Halliday & Resnick, 1988, 3rd edition Fundamentals of Physics and sitting on top are cut outs of "half bent circles, bent at 90 degrees" to imitate magnetic monopoles. Magnetic Monopoles revolutionizes physics education, and separates-out, what is Old Physics from what is New Physics.
The world needs a new standard in physics education since Feynman set the standard in 1960s with his "Lectures on Physics" that lasted until about 1990 and then AP's Atom Totality theory caused Feynman's Lectures to be completely outdated. And so much has changed in physics since 1960s that AP now sets the new world standard in physics education with this series of textbooks.
To be a Master of physics or Calculus or Mathematics, has to be seen in "signs and signals". Can you correct the mistakes and errors of Old Physics, of Old Calculus, of Old Math? If you cannot clean up the fakery of Old Physics, of Old Calculus, of Old Math, you have no business, no reason to write a physics, calculus or math textbook. There is an old legend in England about King Arthur, and the legend goes, that the King is the one who pulls Excalibur out of the iron anvil. Pulling the sword out of the anvil is a metaphor for Cleaning up all the mistakes and errors of Old Physics, of Old Calculus, of Old Math. You have to clean up and clear out the mistakes and errors of the past, for Physics to move forward.
Should you write a textbook on Calculus, if you cannot see that the slant cut in a cone is a oval, never the ellipse? Of course not. Should you write a Calculus textbook if you cannot do a geometry proof of Fundamental Theorem of Calculus? Of course not. Should you write a physics textbook if you cannot ask the question, which is the atom's real true electron, is it the muon or the 0.5MeV particle that AP says is the Dirac magnetic monopole.
Feynman was the prior King of Physics before AP showed up. Feynman wrote the last textbook in 1960s to guide physics forward, and although Feynman did not clean up much of Old Physics, he did direct the way forward in that Electricity and Magnetism in his Quantum Electrodynamics was the way forward. It would have been nice for Feynman to have found that it is impossible for a 0.5MeV particle to be the atom's electron moving near the speed of light outside the proton of hydrogen and still remain an atom, thus all atoms collapse. It would have been nice for Feynman to say the muon is the real atom's electron and that the 0.5MeV particle was Dirac's magnetic monopole. But it just was not in the fated cards of Feynman's physics. Yet, his textbook served the leadership of physics from 1960 to 1990. Time we have the new replacement of physics textbook.
Now, in 2021, we need a new textbook that carries all of physics forward into the future for the next 100 years, and that is what this textbook is. I predict this textbook will carry physics forward to at least year 2100, and if I am lucky, perhaps my book will last for thousands of years as the standard bearer of Physics education.
I will use Halliday and Resnick textbook as template to garner work exercise problems for 1st year and 2nd year college. For 3rd and senior year college physics I will directly use Feynman's Lectures and QED, quantum electrodynamics. Correcting Feynman and setting the stage that all of physics is-- All is Atom and Atoms are nothing but Electricity and Magnetism.
Much and most of 20th century physics was error filled and illogical physics, dead end , stupid paths such as General Relativity, Big Bang, Black holes, gravity waves, etc etc. Dead end stupidity is much of Old Physics of the 20th century. What distinguishes Feynman, is he kept his head above the water by concentrating almost exclusively on Electrodynamics. He remarked words to the effect== "QED is the most precise, most accurate theory in all of physics". And, that is true, given All is Atom, and Atoms are nothing but Electricity and Magnetism.
This textbook is going to set the world standard on college physics education. Because I have reduced the burden of mathematics, reduced it to be almost what I call -- difficult-free-math. I mean, easy-math. Meaning that all functions and equations of math and physics are just polynomials. All functions of math and physics are polynomials. Making calculus super super easy because all you ever do is plug in the Power rules for derivative and integral, so that physics math is able to be taught in High School. In other words, physics with almost no math at all-- so to speak, or what can be called as easy as learning add, subtract, multiply, divide.
What makes both math and physics extremely hard to learn and understand is when mathematics never cleans itself up, and never tries to make itself easy. If all of math can be made as easy as add, subtract, multiply, divide, no one would really complain about math or physics. But because math is overrun by kooks (definition of kook: is a person who cares more about fame and fortune than about truth in science), that math has become a incomprehensible trash pile and the worst of all the sciences, and because the math is so difficult, it carried over into physics, making physics difficult.
And that may sound like a contradiction that AP ended up majoring in mathematics, rather than his first love of physics. But not a contradiction in truth. Because in Old Physics, you have not only a use of the messed up dirty Old Math, but you have use of what I call "idealisms" in Old Physics. Idealisms are "suppose this and that.... " "imagine a ball of mass moving in space....." So Old Physics not only had the tangled mess of kook math of trigonometry everywhere and thousands of silly rules for calculus. But Old Physics had a fakery contraption of "idealism". I ended up majoring in mathematics, although math was a mess, but at least I could still navigate in that mess. But I just could not navigate in physics with their math mess plus, their idealism mess. If you closely examine all Old Physics textbooks, even the latest recent ones, they are all "idealism physics". Idealism is a nice and better term for "fake physics".
You see, one of the greatest omissions of science in the 20th and 21st century was the idea that both math and physics can be reduced to a Simplicity of education. That math need not be hard and difficult. That physics can be made logical, not full of idealisms. Yet no-one in the 20th and 21st century ever had that idea of simplicity, (with the possible exception of Harold Jacobs in mathematics) that math had run out-of-bounds as a science and was more of a science fiction subject for kook mathematicians. Math had become absurdly difficult because of the reason that kooks gain fame and fortune on making math difficult. Mathematicians never thought their job was to make math simple and easy, instead, the kooks of math piled on more trash and garbage to make math a twilight zone of science. The same in physics with idealism run amok. And this is easily proven true about the sociology of math and physics education for it is no secret to anyone in education that college professors are paid not for their teaching so much, no, they are recognized and paid for their research, and this means the simplification of math or physics is secondary, not of first importance. College professor research is of more importance to them, than their failure to make physics or mathematics clear and easy to learn.
When you make all of math be just polynomial equations and functions, you make math the easiest of the major sciences, which then follows up by making physics easy as possible. For there is no longer trigonometry to cloud the mind in everything you do in physics. There is no longer hundreds of calculus rules you must learn just to do Faraday's law or Ampere's law.
So I end up writing this textbook, keeping in mind of AP way back in 1969 in a huge classroom of 1st year college physics, and how AP, the King of Science, especially Physics, would have majored in physics and not mathematics, if physics had been properly taught.
--------------------------
Table of Contents
--------------------------
Part I, Introduction, and about physics.
a) About this textbook and series of Physics textbooks.
b) Brief history lesson of 20th century physics.
c) How we make the mathematics super easy.
d) Horrible error-filled concept of "charge" in Old Physics, and thrown out of New Physics.
e) We increasingly have to use Biology DNA knowledge to unravel the physics of light waves and EM theory.
Part II, 6 Laws of EM theory.
f) The 6 laws of EM, ElectroMagnetic theory and their Units.
g) Matrix of the 6 EM laws.
h) Fixing the horrible mistake of Old Physics units of Magnetic field compared to Electric field.
i) The four differential equations laws of EM theory.
j) Defining the units of Coulomb and Ampere as C = A*seconds; and the Elementary-Coulomb.
k) Faraday Constant Experiment in classroom.
l) Matching the physics Algebra of units with the physics Geometry of units.
m) The EM Spectrum, Electromagnetic Spectrum where electricity is placed between X-rays and gamma rays.
Part III, 1st Law of EM theory.
n) 1st Law of EM theory; law of Magnetic Monopole and units are B = m^2 / A*s^2 = m^2/ C*s.
Part IV, 2nd Law of EM theory.
o) 2nd Law of EM theory; New Ohm's Law V = CBE, the Capacitor-battery law.
p) Short Circuit.
q) Series versus Parallel Circuits connection of closed loop.
r) Review of Geometry volume in 3D and path in 2D.
Part V, 3rd Law of EM theory.
s) 3rd law of EM theory, Faraday's law, C' = (V/(BE))'.
t) Short history lesson of Old Physics, 1860s Maxwell Equations.
u) New Rutherford-Geiger-Marsden Experiment observing Faraday Law.
v) Math Algebra for making one physical concept be perpendicular to another physical concept.
w) EM laws derive the Fundamental Theorem of Calculus.
x) Principle of Maximum Electricity and Torus geometry so essential in Atomic Physics.
Part VI
y) 4th law of EM theory; Ampere-Maxwell law B' = (V/(CE))'.
Part VII
z) 5th law of EM theory; Coulomb-gravity law; E' = (V/(CB))'.
aa) Centripetal versus Centrifugal force explained.
Part VIII
bb) 6th Law of EM theory, Transformer law; differential equation of New Ohm's Law V' = (CBE)'.
cc) Reinventing the Multivariable Calculus.
dd) Atomic bomb physics comes directly out of short circuit of V'=(CBE)', for atoms have no nucleus, just a thrusting muon inside a 840MeV proton torus.
ee) Electric Permittivity and Magnetic Permeability explained.
ff) Two proofs that electricity is not the flow of 0.5MeV particles but is waves between X-rays and gamma rays.
AP, King of Science, especially Physics