This Week's Finds in Mathematical Physics (Week 276)
John Baez
Also available at http://math.ucr.edu/home/baez/week276.html
June 20, 2009
This Week's Finds in Mathematical Physics (Week 276)
John Baez
Math is eternal, but I'll start with some news that may be
time-sensitive. Betelgeuse is shrinking!
1) Stefan Scherer, Shrinking Betelgeuse,
http://backreaction.blogspot.com/2009/06/shrinking-betelgeuse.html
Betelgeuse is that big red star in the shoulder of Orion. It's a red
supergiant, one of the largest stars known. It's only 20 times the
mass of the Sun, but it's about 1000 times as big across - about 5
times the size of the Earth's orbit. For more of a sense of what that
means, watch this video:
2) Hansie0Slim, Largest stars this side of the Milky Way,
http://www.youtube.com/watch?v=u70UBs7BWY8
But, it's shrinking. These authors claim its radius has shrunk 15%
since 1993:
3) C. H. Townes, E. H. Wishnow, D. D. S. Hale and B. Walp, A
systematic change with time in the size of Betelgeuse, The
Astrophysical Journal Letters 697 (2009), L127-L128.
That's about 1000 kilometers per hour!
Of course, it's a bit tricky to estimate the size of Betelgeuse -
besides being rather far, it's so diffuse that its surface isn't very
precisely defined. And it's a variable star, so maybe a little
shrinkage isn't a big deal. But the two known cycles governing its
oscillations have periods of one year and 6 years. So, the authors of
the above paper think this longer-term shrinkage has some other cause.
It could be just another cycle, with a longer period. But there's
another possibility that's a lot more exciting. Maybe Betelgeuse is
about to collapse and go supernova!
Indeed this seems likely in the long term, since that's the usual fate
of such massive stars. And the long term may not even be so long,
since Betelgeuse is about 8.5 million years old - quite old for stars
this big, which live fast and go out in a blaze of glory.
What if Betelgeuse went supernova? How would it affect the US
economy, and the next Presidential election? Could this be the
Republican party's best hope?
Sorry, I'm being a bit parochial... let me try that again. How would
it affect the insignificant inhabitants of a puny speck called Earth,
located about 500 or 600 light years away from Betelgeuse? According
to Brad Schaefer at Louisiana State University, it would be "brighter
than a million full moons", but it wouldn't hurt us - in part because of
the distance, and in part because we're not lined up with its pole.
(Perhaps just to build up the suspense, Schaefer added that Betelgeuse
could already have gone supernova, in which case we're just waiting
for its light to reach us.)
It would be nice to see some calculations of just how much power we'd
get from a supernova at that distance. I must admit that "brighter
than a million moons" doesn't really do it for me. Does anyone out
there have what it takes to crunch the numbers?
It's worth recalling that not too long ago, a supernova exploded at a
roughly comparable distance from us, forming the "Local Bubble" - a
peanut-shaped region of hot thin gas about 300 light years across,
containing our Sun. The gas in the Local Bubble is about 1000 times
less dense than ordinary interstellar space, and vastly hotter.
What do I mean by "not too long ago"? Well, nobody is sure, but back
in "week144" I reported a bunch of evidence for a theory that the
Local Bubble was formed just 340,000 years ago, when a star called
Geminga went supernova, perhaps 180 light years away.
Now I'm getting a sense that the situation is more complex. It seems
our Sun is near the boundary of the Local Bubble and another one,
called the "Loop I Bubble". This other bubble seems to have formed
earlier - perhaps 2 million years ago, at the Pliocene-Pleistocene
transition, when a bunch of ultraviolet-sensitive marine creatures
mysteriously died:
4) NASA, Near-earth supernovas,
http://science.nasa.gov/headlines/y2003/06jan_bubble.htm
The Loop I Bubble may have been caused by a supernova in "Sco-Cen",
a cloud in the directions of Scorpius and Centaurus. It's about
450 light years away now, but it used to be considerably closer.
In the last few million years, some wisps of interstellar gas have
drifted into the Local Bubble. Our solar system is immersed in one of
these filaments, charmingly dubbed the "local fluff". It's much cooler
than the hot gas of the Local Bubble: 7000 Kelvin instead of roughly
1 million. It's also much denser - about 0.1 atoms per cubic centimeter
instead of 0.05 or so. But Sco-Cen is sending interstellar cloudlets
in our direction that are denser still, by a factor of 100. These might
actually have some effect on the Sun's magnetic field when they reach us.
I'm sure we'll get a clearer story as time goes by. In 2003, NASA launched
a satellite called the Cosmic Hot Interstellar Plasma Spectrometer, or
CHIPS for short, to study this sort of thing:
5) NASA/UC Berkeley, Overview of CHIPS Science,
http://chips.ssl.berkeley.edu/science.html
It sounds pretty interesting. Unfortunately the latest news on the
CHIPS homepage dates back to 2005, before they'd done much science.
What's up?
You can't do much about Betelgeuse. But you can do something about
mathematics! For example, if you're into categories or n-categories,
you can help out the nLab:
6) nLab, http://ncatlab.org/nlab
The nLab is like the library, or laboratory, in the back room of the
n-Category Caf�. The nCaf� is a place to chat: it's a blog. The nLab
is a place to work: it's a wiki. It's operating since November 2008.
There's quite a lot there by now, but it's really just getting
started. Check it out! You'll find a lot of explanations of a lot
of concepts, and the beginnings of some big projects.
So far the main contributors include Urs Schreiber, Mike Shulman, Toby
Bartels, Tim Porter, Todd Trimble, David Roberts, Andrew Stacey, Bruce
Bartlett and myself. Jim Dolan recently joined in with a page on
algebraic geometry for category theorists - I'll say more about this
someday. And like the nCaf�, technical aspects of the nLab are
largely run by Jacques Distler - it uses some wiki software called
Instiki which he is helping develop.
Finally, a bit of actual math. Here's a paper by the fellow I'm
working with here in Paris, and a grad student of this:
7) Paul-Andr� Mellies and Nicolas Tabareau, Free models of T-algebraic
theories computed as Kan extensions, available at
http://hal.archives-ouvertes.fr/hal-00339331/fr/
I really need to understand this for my work with Mike Stay.
In "week200" I talked about Lawvere's work on algebraic theories; I'll
assume you read that and pick up from there. In its narrowest sense,
an "algebraic theory" is a category with finite products where every
object is a product of copies of some fixed object c. We use
algebraic theories to describe various types of mathematical gadgets:
to be precise, any type of gadget that consists of a set with a bunch
of n-ary operations satisfying a bunch of purely equational laws.
For any type of gadget like this, there's an algebraic theory C; I
explained how you get this back in "week200". If we have a functor
F: C -> Set
that preserves finite products, then F(c) becomes a specific gadget of the
given type. Conversely, any specific gadget of the given type determines
a functor like this.
So, we define a "model" of the theory C to be a functor
F: C -> Set
that preserves finite products. But actually, this is just a model of
C in the world of sets! We could replace Set by any other category
with finite products, say X, and define a "model of the theory C in
the environment X" to be a functor
F: C -> X
that preserves finite products.
For example, if C is the theory of groups and X is Set, a model of C
in X is a group. If instead X is the category of topological spaces,
a model of C in X is a topological group. And so on. In general
people call a model of this particular theory C in any old X a
"group object in X".
But as you might fear, we want to understand more than a single model
of C in X. As category theorists, we want to understand the whole
*category* of models of C in X. This category, which I'll call
Mod(C,X), has:
functors F: C -> X that preserve finite products as its objects;
natural transformations as its morphisms.
For example, if C is the theory of groups and X is the category of
topological spaces, Mod(C,X) is the category of topological groups
and continuous homomorphisms.
So far I've just been reviewing at a fast pace. What happens next?
Well, there's always a forgetful functor
R: Mod(C,X) -> X
sending any model to its underlying object in X. But what we'd really
like is for R to have a left adjoint
L: X -> Mod(C,X)
sending any object of X to the free gadget on that object. Then we
could follow L by R to get a functor
RL: X -> X
called a "monad". One reason this would be great is that monads are
another popular way to study algebraic gadgets. I explained monads
very generally back in "week89", and said how to get them from adjoint
functors in "week92"; in "week257" I gave some links to some great
videos by the Catsters explaining monads and what they're good for.
So, I won't say more about monads now: I'll just assume you love them.
Given this, you must be dying to know when the functor R has a left
adjoint.
In fact it does whenever X has colimits that distribute over the
finite products! For example, it does when X = Set. And Mellies and
Tabareau give a very nice modern explanation of this fact before
generalizing the heck out of it.
The key is to note that
R: Mod(C,X) -> X
is just an extreme case of forgetting *some* of the structure on an
algebraic gadget: namely, forgetting *all* of it. More generally,
suppose we have any map of algebraic theories
Q: B -> C
that is, a finite-product-preserving functor that sends the special
object b in B to the special object c in C. Then composition with
Q gives a functor
Q*: Mod(C,X) -> Mod(B,X)
For example, if B is the theory of groups and C is the theory of rings,
C is "bigger", so we get an inclusion
Q: B -> C
and then Q* is the functor that takes a ring object in X and forgets
some of its structure, leaving us a group object in X. But when B is
is the most boring algebraic theory in the world, the "theory
of a bare object", then Q* forgets everything: it's our forgetful functor
R: Mod(C,X) -> Mod(B,X) = X
So, we should ask quite generally when any functor like
Q*: Mod(C,X) -> Mod(B,X)
has a left adjoint. And, the answer is: it always does!
The proof uses a left Kan extension followed by what Mellies and
Tabaraeu call a "miracle" - see page 5 of their paper. And, it's
this miracle they want to understand and generalize.
They generalize it by replacing "algebraic theories" by "T-algebraic
theories" where T is any pseudomonad on Cat. I already said that
monads are a trick for studying very general algebraic gadgets.
Similarly, pseudomonads are a trick for studying very general
*categorified* algebraic gadgets, like "categories with finite
products" or "monoidal categories" or "braided monoidal categories" of
"symmetric monoidal categories".
Each of these types of categories allows us to define a type of
"theory":
monoidal categories let us define "PROs"
braided monoidal categories let us define "PROBs"
symmetric monoidal categories let us define "PROPs"
categories with finite products let us define "algebraic theories"
I explained all these, along with monads, here:
8) John Baez, Universal algebra and diagrammatic reasoning, available
as http://math.ucr.edu/home/baez/universal/
Take my word for it: they're great. So, we would like to generalize
Lawvere's original results to these other kinds of theories, which are
all examples of "T-algebraic theories". But, it's not automatic! For
example, it doesn't always work with PROPs.
A typical kind of algebraic gadget we could define with a PROP is a
"bialgebra". While there's always a free group on a set, there's not
usually a free bialgebra on a vector space! The problem is not the
category of vector spaces: it's that bialgebras have not only
"operations" like multiplication, but also "co-operations" like
comultiplication.
So, Mellies and Tabareau have their work cut out for them. But they
tackle it very elegantly, using profunctors and a certain generalization
thereof: Richard Wood's concept of "proarrow equipment".
That sounds pretty scary when you first hear about it, so I'll stop
here, right around page 12 of the paper - right when the fun is getting
started.
----------------------------------------------------------------------
Quote of the Week:
The question you raise, "how can such a formulation lead to
computations?" doesn't bother me in the least! Throughout my whole
life as a mathematician, the possibility of making explicit, elegant
computations has always come out by itself, as a byproduct of a
thorough conceptual understanding of what was going on. Thus I never
bothered about whether what would come out would be suitable for this
or that, but just tried to understand - and it always turned out that
understanding was all that mattered. - Grothendieck
-----------------------------------------------------------------------
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Phillip Helbig---remove CLOTHES to reply
ba...@math.removethis.ucr.andthis.edu (John Baez) writes:
> It would be nice to see some calculations of just how much power
> we'd get from a supernova at that distance. I must admit that
> "brighter than a million moons" doesn't really do it for me. Does
> anyone out there have what it takes to crunch the numbers?
We don't know enough about how Betelgeuse will behave exactly to do
better than an order of magnitude, but that's good enough.
A rule of thumb is that a supernova is about as bright as a galaxy. A
galaxy has about 10**11 stars, but on average they are not as luminous
as the Sun. Say a galaxy is a few times 10**10 times as bright as the
Sun. 5 magnitudes is a factor of 100. (The absolute magnitude of an L*
galaxy (a "typical" galaxy, luminosity-wise) is about -21.5, that of the
Sun about 5.5. That makes 27 magnitudes, or a few times 10**10. So
that looks consistent.) 10**10 is 25 magnitudes. Say a typical star
has an absolute magnitude of 6. Increase that by 27 magnitudes and we
arrive at -21. The absolute magnitude of Betelgeuse is about -5. So
that means that as a supernova Betelgeuse will be about 16 magnitudes
brighter than it is now. Its apparent magnitude now is about 0.5 (it's
variable), so as a supernova its apparent magnitude would be about
-16.5.
The Sun has an apparent magnitude of about -27. So we are looking at
something about 10.5 magnitudes fainter than the Sun, say roughly
one-ten-thousandth the brightness of the Sun.
At night, though, it will seem even brighter than that, since a) the eye
is dark-adapted and b) the contrast to the dark nighttime sky is greater
than that of the Sun to the blue daytime sky. (Of course, at its
brightest phase as a supernova Begelgeuse might not be in the nighttime
sky.)
The apparent magnitude of the full moon is about -12.5, so Betelgeuse as
a supernova would be about 4 magnitudes brighter. That's less than a
factor of 100, not "brighter than a million moons". (One could arrive
at "brighter than a million moons" if one assumes that Betelgeuse as a
supernova would be 27 magnitudes brighter than it is now, rather than 27
magnitudes brighter than a typical star. A factor of a million
corresponds to a difference of 15 magnitudes. That would be -27.5.
That is brighter than the Sun! Betelgeuse as a supernova will be
bright, but not that bright!)
Uncle Al
The full moon subtends an angle of 0.491 degrees at apogee and 0.546
degrees at perigee - significant radiating surface area either way and
boosted by reflectance of glass spherules in lunar regolith (re 3M
reflective tapes) for the sun being behind your head (and planet).
Betelgeuse subtends an angle of 0.047" or 1.3x10^(-5) degree. The
supernova fireball might be a factor of 10 wider, cooling as it
expands and its nickel and cobalt decay.
The proffered number then may refer not to the objects' astronomic
brigthnesses as such but to the amount of light shed total.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Phillip Helbig---remove CLOTHES to reply
<Uncl...@hate.spam.net> writes:
> The full moon subtends an angle of 0.491 degrees at apogee and 0.546
> degrees at perigee - significant radiating surface area either way and
> boosted by reflectance of glass spherules in lunar regolith (re 3M
> reflective tapes) for the sun being behind your head (and planet).
> Betelgeuse subtends an angle of 0.047" or 1.3x10^(-5) degree. The
> supernova fireball might be a factor of 10 wider, cooling as it
> expands and its nickel and cobalt decay.
Right, but all this really doesn't matter. The apparent magnitude
(apparent brightness on a logarithmic scale) is concerned with the total
brightness of the object, whatever its angular size. (Of course, an
object with a smaller angular size will, for the same total brightness,
be brighter per angular area. This might make it seem somewhat
brighter, subjectively.) The full moon is more than twice as bright as
a quarter moon (i.e. half-lit as seen from Earth) due to the effect you
mention and also due to the fact that a full moon has essentially no
shadows whereas other phases have shadows in the otherwise illuminated
portion. Interesting, but not relevant here---the value I quoted for
the apparent magnitude of the Moon is for the full Moon.
> The proffered number then may refer not to the objects' astronomic
> brigthnesses as such but to the amount of light shed total.
No, since the apparent magnitude refers to the brightness, regardless of
the angular size.
SUBJECTIVE brightness is another matter---I mentioned a couple of
effects, but it also depends on the colour, varies from person to
person, is influenced by angular size (see above), comparison to nearby
objects, departure from familiarity etc.
Dr J R Stockton
2009 22:42:26, Phillip Helbig---remove CLOTHES to reply <hel...@astro.mu
ltiCLOTHESvax.de> posted:
>In article <h1jgpm$ikn$1...@glue.ucr.edu>,
>ba...@math.removethis.ucr.andthis.edu (John Baez) writes:
>> It would be nice to see some calculations of just how much power
>> we'd get from a supernova at that distance. I must admit that
>> "brighter than a million moons" doesn't really do it for me. Does
>> anyone out there have what it takes to crunch the numbers?
>
>We don't know enough about how Betelgeuse will behave exactly to do
>better than an order of magnitude, but that's good enough.
>At night, though, it will seem even brighter than that, since a) the eye
>is dark-adapted and b) the contrast to the dark nighttime sky is greater
>than that of the Sun to the blue daytime sky. (Of course, at its
>brightest phase as a supernova Begelgeuse might not be in the nighttime
>sky.)
Betelgeuse is about 15 degrees from the Ecliptic, so it is necessarily
always visible in Nautical Twilight or darker from at least some part of
the Earth, ignoring weather. I think.
--
--
(c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.
John Baez
>According to Brad Schaefer at Louisiana State University, [if
>Betelgeuse went supernova] it would be "brighter
>than a million full moons", but it wouldn't hurt us - in part because of
>the distance, and in part because we're not lined up with its pole.
>It would be nice to see some calculations of just how much power we'd
>get from a supernova at that distance. I must admit that "brighter
>than a million moons" doesn't really do it for me. Does anyone out
>there have what it takes to crunch the numbers?
Charles McElwain kindly responded to this plea. He wrote:
As you mention, there's not a lot of (quality) work out there. Most of
what I found briefly would score fairly high on the "crank index".
Of course, near supernovas have a positive and essential role in life on
earth, in there *being* an earth, rather than just a star...
A few that I found that weren't immediately eliminated as cranks, that
might repay further investigation:
9) Michael Richmond, Will a nearby supernova endanger life on Earth?,
Available at http://stupendous.rit.edu/richmond/answers/snrisks.txt
Perhaps the closest to the number-crunching you're looking for.
10) S. E Thorsett, Terrestrial implications of cosmological gamma-ray
burst models, Astrophys. J. 444 (1995), L53. Also available as
arXiv:astro-ph/9501019
Specifically, nitric oxide increases/ozone decreases.
11) Steven I. Dutch, Life (briefly) near a supernova, Journal
of Geoscience Education, 2005. Available at
http://nagt.org/files/nagt/jge/abstracts/Dutch_v53n1.pdf
The conceit here is what would happen if the Sun went supernova;
acknowledged as impossible, but a very interesting exercise almost
as a "Fermi problem", spinning out the real implications of the
classic Arthur C. Clarke story "Rescue Party", and interesting also
pedagogically.
Using this and other information, I decided to check the claim
that supernova Betelgeuse would be "brighter than a million full
moons".
First of all, the full moon is 1/449,000 times as bright as the Sun.
So, "brighter than a million full moons" is just an obscure
way of saying "more than twice as bright as the Sun."
Second, let's try the calculation ourselves. There are various kinds
of supernovae, with different luminosities. I guess Betelgeuse is
most likely to become a type II supernova. Such supernovae show quite
a bit of variation in their behavior. But anyway, it seems they get
to be 1 billion times as bright as the Sun, or maybe at most - let's
look at a worst-case scenario - 10 billion times as bright. So,
between 10^9 and ten times that.
On the other hand, Betelgeuse is about 600 light years away, and there
are 63,239 astronomical units in a light year, so it's about
600 x 63,000 ~ 4 x 10^7
times as far away as the Sun - no point trying to be too precise
here. Brightness scales as one over distance squared, so
supernova Betelgeuse should look between
10^9 / (4 x 10^7)^2 ~ 7 x 10^{-7}
as bright as the Sun, and ten times that bright.
As I mentioned, the full Moon is about 2 x 10^{-6} times as bright as
the Sun. So, supernova Betelgeuse should be roughly between 1/3 as
bright as the full Moon, and 3 times as bright. This is a rough
calculation, but I've done it a few different ways and gotten similar
answers. So have some other people.
So, it's safe to say that "brighter than a million full moons" is a
vast exaggeration.
Whew.
Christopher Henrich
ba...@math.removethis.ucr.andthis.edu (John Baez) wrote:
> Using this and other information, I decided to check the claim
> that supernova Betelgeuse would be "brighter than a million full
> moons".
>
>snip
> But anyway, it seems they get
> to be 1 billion times as bright as the Sun, or maybe at most - let's
> look at a worst-case scenario - 10 billion times as bright. So,
> between 10^9 and ten times that.
>
> On the other hand, Betelgeuse is about 600 light years away, and there
> are 63,239 astronomical units in a light year, so it's about
>
> 600 x 63,000 ~ 4 x 10^7
>
> times as far away as the Sun - no point trying to be too precise
> here. Brightness scales as one over distance squared, so
> supernova Betelgeuse should look between
>
> 10^9 / (4 x 10^7)^2 ~ 7 x 10^{-7}
>
> as bright as the Sun, and ten times that bright.
>
> So, it's safe to say that "brighter than a million full moons" is a
> vast exaggeration.
>
OK, but here's a quibble.
You have calculated the total illumination shed by Supernova Betelgeuse.
There is also the intensity - illumination per steradian - to consider.
This is independent of distance, up until the apparent diameter of the
light source is less than the diameter of a single retinal receptor.
Then, (thank God) it starts to diminish by an inverse-square rule.
--
Christopher J. Henrich
chen...@monmouth.com
http://www.mathinteract.com
"A bad analogy is like a leaky screwdriver." -- Boon
John Baez
Christopher Henrich <chen...@monmouth.com> wrote:
>In article <h1t0ep$92k$1...@glue.ucr.edu>,
> ba...@math.removethis.ucr.andthis.edu (John Baez) wrote:
>> supernova Betelgeuse should look between
>>
>> 10^9 / (4 x 10^7)^2 ~ 7 x 10^{-7}
>>
>> as bright as the Sun, and ten times that bright.
>You have calculated the total illumination shed by Supernova Betelgeuse.
>
>There is also the intensity - illumination per steradian - to consider.
>This is independent of distance, up until the apparent diameter of the
>light source is less than the diameter of a single retinal receptor.
>Then, (thank God) it starts to diminish by an inverse-square rule.
Yes - and I'm curious whether Supernova Betelgeuse could be dangerous
to look at. Say its illumination is 4 times that of a full moon, but
it's essentially a point source, except for the twinkling of starlight.
Would it blind you to look at it?
People who know the safety issues concerning lasers might be able to
help us answer this.
David Bernier
Just before or after totality in a solar eclipse, the sun
looks like a very bright spotlight in the sky.
I'm not sure about the time interval between negligible illumination
and an illumination equal to four times a full moon, but I think
it should be a matter of no more than a few seconds
after totality (or before).
Whether an almost eclipsed sun as bright as 4 full moons
is a good substitute for Supernova Betelgeuse is
another question ...
David Bernier
Dirk Bruere at NeoPax
Since it is possible to look at the sun for a few seconds without eye
damage I assume it would be safe to look at the supernova for a similar
time. The ratio between sunlight and moonlight is around half a million
to one, so "compressed moonlight" won't exceed the intensity of the sun
until the area of the spot on the retina is reduced by a similar ratio.
I doubt whether that is possible.
--
Dirk
http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff
johnd...@iprimus.com.au
> So, it's safe to say that "brighter than a million full moons" is a
> vast exaggeration.
>
"Brighter" may not be the safest word to use as APOD refers to the
Moon as being "brighter" than the Sun.
http://apod.nasa.gov/apod/ap060527.html
[[Mod. note -- That's in gamma rays, not in the visible or in total
luminosity. The Earth's atmosphere is opaque to gamma rays, so we
could only observe supernova gamma rays from space.
-- jt]]
How bright would the supernova be in Gamma rays?
Archimedes Plutonium
> Also available at http://math.ucr.edu/home/baez/week276.html
> June 20, 2009
> This Week's Finds in Mathematical Physics (Week 276)
> John Baez
Why in Old Physics they knew that you could send light waves down the electric line and receive information from the light waves, and they knew you could send electricity wirelessly from the Tesla experiments, yet, not a single physics professor had the lights come, in his mind that electricity belongs as a region of the EM Spectrum range.
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.
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Table of Contents
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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.
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Archimedes Plutonium