**Theory of
Everything **

A
short introduction to the history of physics, and string theory as a ¡°Theory of
Everything¡±

The fine tuning problem and the
hierarchy problem

__Comments__:

The first
article explains what string theory is and why many physicists study it. The
second article explains what the first superstring revolution and the second
superstring revolution are in laymen¡¯s terms. I also explain the significance
of my calculation of string coupling constant. The last article derives a
simple mathematical relation that is very important in string theory. fel

**Chemistry**

History of chemistry up until the
beginning of 20^{th} century

The structure of atoms
and the periodic table

In these two articles, I explain the
basics of the basics of chemistry as chemistry partly shares history with
physics up until the early 20^{th }century. Of course, I am not an
expert on chemistry, but having taken AP chemistry, I know chemistry just
enough to explain the basics of its basics.

**Astronomy**

Evidences that the Earth is not
flat, but round

Parallax

History of astronomy up until the mid 17^{th}
century

History of astronomy from the late
17^{th} century to the early 21^{st} century

__Comments:__

In the first article, I provide the
evidences that the Earth is round, as it is alarming that the Flat Earth
proponents are gaining momentum these days. They are idiots who reject
scientific evidences. They don¡¯t deserve to enjoy modern scientific
innovations. In the second article, I provide a brief overview of history of
astronomy from ancient time to the time of Johannes Kepler and Galileo Galilei.
In the third article, I provide a brief overview of history of astronomy from
the time of Sir Isaac Newton to the present. Physics was essentially applied to
and received feedback from astronomy during the time period treated in this
article.

**Bosons and
Fermions **

Supersymmetry: an exposition for laymen

Bosons, Fermions, and Pauli¡¯s exclusion principle

Pauli's
exclusion principle, color charge of quarks, asymptotic freedom and confinement

Bosons,
Fermions and the statistical properties of identical particles

Bosons, Fermions in quantum mechanics picture

__Comments__:

These five articles explain what bosons and fermions are, and how
the concept of these categories of particles is applied in physics. The first
article explains how supersymmetry relates bosons and fermions to one
another. Supersymmetry is a very important topic in the contemporary
particle physics community. First theorized in the early 1970s, many expect
that it will soon be supported by experiments at the LHC
in Geneva, Switzerland. The second article can be read independently
of the first. The third, fourth, and fifth articles can be read independently
of one another, but you may have to read the second article in order to
understand them. The third article explains how the idea of color charge of quarks
was introduced to reconcile the theory with Pauli's exclusion principle,
and goes on to explain some interesting characteristics of the strong force.
The fourth article explains the microscopic statistical properties of identical
particles which may seem bizarre to macroscopic human beings. The fifth article
supplies another derivation of Pauli's exclusion principle via an approach
alternative to that taken in the second article.

**Black hole **

Why time goes more slowly at a lower place and what a black
hole is

__Comments__:

Most people
have probably heard that nothing can get out of a black hole once it has been
sucked into it. The article here explores this assertion in more detail qualitatively.
For a quantitative treatment, read ¡°By how much does time go more slowly at a
lower place?¡± after reading the above article.

**Newton¡¯s Inverse
Square Law of Gravity **

Conic sections and Newton¡¯s law of gravity

The inverse square law and the 3-dimensional world

__Comments__:

These two articles can be read more or less independently of one another.

**Some basic mathematics
and statistics **

Expectation and Standard deviation

Asymptotic
behavior of polynomials

Exponential function vs
polynomial function

__Comments__:

Vector is a very important basic mathematical concept in physics. To learn
more about vectors, read the sections ¡°Dot product¡± and ¡°Linear Algebra and
Quantum Mechanics.¡± The article on vector is the only prerequisite to
¡°Electricity and Magnetism, the first part,¡± which in turn is the only
prerequisite to the section ¡°Special Relativity.¡± Logarithm is often used in physics
and mathematics. It serves as a prerequisite for ¡°What is entropy? From a
microscopic point of view¡± and the articles in the section ¡°Loop Quantum
Gravity (for laymen).¡± ¡°Expectation and Standard deviation¡± serves as a
prerequisite for ¡°A short introduction to quantum mechanics XII: Heisenberg¡¯s
uncertainty principle.¡± ¡°Exponential function vs polynomial function¡± will play
an important role in understanding my research on black hole entropy, which is
reviewed in our article ¡°Approximation of the naïve black hole degeneracy.¡±

**Energy and Entropy **

What
is entropy? From a microscopic point of view

What is entropy? From a macroscopic point of view

__Comments__:

Energy and
entropy are very important concepts in physics. The second article explains what
entropy is and why it ¡°always¡± increases. The third article explains what
entropy is from a macroscopic point of view. It can be read independently of
the first one. These articles serve as prerequisites for the section
¡°Statistical Mechanics.¡±

**Loop Quantum Gravity **

Discrete area spectrum and the black hole entropy II:
Domagala-Lewandowski-Meissner formula

Discrete
area spectrum and the black hole entropy III: Newer variables

Discrete area spectrum and the Hawking radiation spectrum I

Discrete area spectrum and the Hawking radiation spectrum
II: Single unit area deduction

Discrete area spectrum and the Hawking radiation spectrum
III: Maxwell-Boltzmann

Discrete
area spectrum and the Hawking radiation spectrum IV: Single-partition black
hole

__Comments__:

**Basic high school
physics without calculus, the first part **

__Comments__:

I have written ¡°Newton¡¯s first law¡± so that those who have never learned physics
can have a chance to learn about the wonderful ideas of the two great
physicists, Galilei and Newton. To understand ¡°Newton¡¯s second law,¡± you have
to understand what a vector is. The last article explains how one can relate
the distance and the time an object falls due to gravity on Earth. It serves as
a prerequisite for the articles listed in the section ¡°Some basic ideas in
General Relativity.¡±

**Trigonometric
****F****unctions**** **

What are trigonometric functions?

Polar coordinate and trigonometric functions defined over all values

Rotation in the Cartesian coordinate system

Addition
and subtraction rules for trigonometric functions

Inverse trigonometric
functions

__Comments__

Even
though you may naively imagine that trigonometric functions are important only
for geometry, they are actually very important and widely used in mathematics.
For example, trigonometric functions are important in describing waves in
physics. As quantum mechanics is about particles and waves, knowledge of
trigonometric functions is essential in understanding quantum mechanics.

The
purpose of the article ¡°Rotation in Cartesian coordinates¡± is to serve as a
basis to make an interesting comparison with the Lorentz transformation in my
article on that topic in the section ¡°For students learning high school
physics.¡±

**Complex
****N****umbers**** **

Complex
numbers and the trigonometric functions

Fundamental
theorem of algebra

__Comments__

Complex
numbers is a prerequisite to quantum mechanics. Everything in quantum mechanics
is calculated in terms of complex numbers, even though at the end of these
calculations one must obtain an answer in terms of the real numbers to compare
with experimental results, since complex numbers are not ¡°real¡± and can¡¯t be
the values of measurements. The last article explains the beautiful relationship between complex numbers
and the trigonometric functions, which you may appreciate better after reading
¡°Euler¡¯s formula¡± listed in ¡°A crash course in calculus, the second part.¡±

**Electricity and Magnetism, the first
part **

Electric charge
and Coulomb force

Electroscope

Electric current makes compass needle turn

Magnet exerts force on wire through which
electric current passes

The force
between two parallel wires through each of which electric current passes

__Comments__:

These
six articles provide the prerequisites for the articles explaining the relation
between Einstein¡¯s theory of special relativity and electromagnetism presented in
the section ¡°For students learning high school physics.¡± Nevertheless, they
could be interesting on their own as those who did not take physics in high
school do not usually know about the phenomena presented in these articles. ¡°What is a vector?¡± listed in the
section ¡°Some very basic high school physics¡± is the prerequisite to ¡°Electric
charge and Coulomb force.¡±

**Special Relativity **

¡°Why¡± is
the speed of light constant?

Time
dilation in Einstein¡¯s theory of special relativity

Electromagnetic
forces and time dilation in special relativity

Lorentz-Fitzgerald
contraction: Why is a moving object shortened?

Origin
of the magnetic force from the perspective of special relativity

The relativity of simultaneity

Lorentz transformation and Rotation, a
comparison

__Comments__:

This
section groups together eight
articles on special relativity, in a suggested order of reading. (You may also want to read pages
177-209 of ¡°The Evolution of Physics.¡±) While the third and fifth articles
require the basic knowledge on electricity and magnetism, as covered in the
section ¡°Electricity and Magnetism, the first part,¡± others can be read without
these prerequisites. The third and fifth articles show that Einstein's theory
of special relativity is consistent with electromagnetism. Of course, this
should be the case since light is an electromagnetic wave, and Einstein's
theory of special relativity is based on the fact that the speed of light in
vacuum is always constant. Nevertheless, it is exciting to check these
consistencies between electromagnetism and special relativity in easy ways,
since understanding them from the original construction of special relativity
requires advanced knowledge. Moreover, it is always exciting to see that you
arrive at the same conclusion even from very different perspectives.

The
third article makes use of the relationship between electric current and
magnetic force. Later, in the fifth article, this relationship is partly
derived by ¡°using¡± the special theory of relativity, but the relevant facts are
stated in the third article and can be taken for granted for the purpose of
understanding the point of the third article. If you don¡¯t wish to take it for
granted, you may want to read the articles in the section ¡°Electricity and Magnetism, the first part,¡±
which deal with the interplay between electric fields and magnetic fields.

Unlike other articles, the last three
articles related to Lorentz transformation are mathematical to some extent.
Even though you only need to know the concept of square root to comprehend
them, the derivation of Lorentz transformation might be complicated. ¡°Lorentz
transformation and Rotation, a comparison¡± assumes prior knowledge on
"Rotation in Cartesian coordinates" covered in the section
"Trigonometric functions."

**Paradoxes in Special Relativity**

__Comments__:

Theory of relativity is quite
confusing and unintuitive. At first glance, it seems wrong. Therefore, many people
could come up with a lot of paradoxes that seemed to show that theory of
relativity was wrong. However, it isn¡¯t, since these paradoxes can be resolved.
These articles deal with such paradoxes.

**Electricity and Magnetism, the second
part **

Gauss¡¯s law

Why is the electric field inside spherical
shell zero?

Gravitational field on the surface of the
Earth

Magnetic
monopole and Gauss¡¯s law

__Comments__:

The prerequisites to ¡°Electric field¡±
are ¡°What is a vector¡± and ¡°Electric charge and Coulomb¡¯s law.¡± The
prerequisites to ¡°Gauss¡¯s law¡± are ¡°Electric field¡± and ¡°The inverse square law
and the 3-dimensional world.¡± These articles do not use any complicated math,
but we will formulate Gauss¡¯s law mathematically in our later article
¡°Revisiting Gauss¡¯ law and the ¡°derivation¡± of Coulomb¡¯s law¡± listed in the
section ¡°Maxwell¡¯s equations.¡±

**Basic high school physics without
calculus, the second part **

Constant acceleration in 1-dimension

Projectile
motion

Potential energy
and conservation of energy

Newton¡¯s third law and conservation of
momentum

Elastic collision in 1-dimension

Elastic
collision in 1-dimension in center of mass frame

Elastic collision in 2-dimension

Torque

Angular
momentum

Hooke¡¯s
law and harmonic oscillator

Harmonic oscillator and
circular motion

__Comments__:

There are two aims for this section. The first one is completing the
course on very basic high school physics that began in an earlier section. The
second one is presenting the elastic collision problem in 2-dimension, which
plays an important role in our later article ¡°Compton scattering.¡±

**Electricity and Magnetism, the third part **

Faraday¡¯s law of induction

Faraday¡¯s law of induction from the point
of view of magnetic force on moving charge

__Comments__:

Faraday experimentally discovered his
law of induction in the 19^{th} century. The first article explains
Faraday¡¯s law while the second article explains the origin of Faraday¡¯s law;
Faraday¡¯s law nicely fits with the picture presented in that article. These
articles serve as prerequisites for ¡°Faraday¡¯s law of induction in Maxwell¡¯s
equations,¡± in which we present the mathematical equations for the material
described qualitatively in the above articles.

**Dark Matter and
Modified Newtonian Dynamics **

¡°Conformal Gravity,¡± a proposed alternative to the dark matter theory,
falsified

__Comments__:

In the above article, I explain my own research on ¡°conformal gravity.¡± To
this end, I explain here what the dark matter theory is. In our later article ¡°Problems
with Mannheim¡¯s conformal gravity program¡± I will fully explain my own research
on ¡°conformal gravity¡± with all the technical details.

**Dimensional Analysis, the first part **

The power
of dimensional analysis

__Comments__

Dimensional
analysis is widely used in advanced physics. Although it may not be apparent at
first glance, dimensional analysis is essential to understanding nature. There
is a sequel to these articles in the section ¡°Dimensional Analysis, the second
part.¡¯¡¯

**CPT **

The
symmetry of physical laws: the CPT theorem for laymen

CP
violation and the Nobel Prize for Physics 2008

__Comments__:

These two
articles explain what Kobayashi and Maskawa won the Nobel Prizes for. These
articles could be a little bit difficult to understand for beginners.

**Neutrino
oscillation**

__Comments__:

This article
explains at a laymen level what is the neutrino oscillation for which Nobel Prize
in Physics was awarded in 2015. We will revisit it fully in our later article
¡°Neutrino oscillation, clarified¡± as neutrino oscillation seems so bizarre and
cannot be understood without quantum mechanics.

**Wave **

Huygens¡¯ principle

Young¡¯s interference experiment

Interference from thin films

__Comments__:

Familiarity with trigonometric functions is the prerequisite to the above
articles. They serve as prerequisites to ¡°Bohr model,¡± ¡°De Broglie¡¯s matter
waves,¡± and ¡°Schrödinger equation¡± listed in ¡°Historical introduction to
quantum mechanics.¡±

**A ****C****rash ****C****ourse in ****C****alculus, the ****f****irst ****p****art**** **

What are continuous functions?

Derivatives, velocity, and acceleration

Addition,
subtraction rules for differentiation and Leibniz¡¯s rule

Derivatives of the polynomials

The sandwich theorem and the limit of sin
theta/theta

Derivatives of the
trigonometric functions

Velocity
re-visited and extremum

Exponential
functions and natural logs

Differential
and infinitesimal change

__Comments__

Calculus
is an essential tool for physics. It¡¯s a very basic area of mathematics which
you cannot avoid with if you truly want to understand physics. Calculus was
first discovered by Newton to apply it for physics, even though it is widely
believed that Leibniz discovered it independently, despite the fact that Newton
accused Leibniz of plagiarism. Calculus is composed of two parts:
differentiation and integration. Interestingly, integration is
anti-differentiation. If I make an analogy, integration is to differentiation
as subtraction is to addition and division to multiplication. In the first part
of the crash course, I explain differentiation, which is also called ¡°taking
the derivative.¡±

**A ****C****rash ****C****ourse in ****C****alculus, the ****s****econd ****p****art**** **

Integration and the
fundamental theorem of calculus

Euler¡¯s formula and
hyperbolic functions

Even functions and odd
functions

__Comments__

In
the second part, I explain integration and other topics which are usually
covered in the second semester of calculus.

**Applications
of ****C****alculus,
the first part**** **

Area inside a circle, surface
area of a sphere and volume inside a sphere

The derivation of Snell¡¯s law
using calculus

Convexity, concavity and the
point of inflection

Expectation values in quantum field theory (1)

__Comments__

We already
covered Snell¡¯s law in the section ¡°Wave,¡± but we provide an alternative
derivation using calculus in the second article. To appreciate Fourier
transformations, you must know linear algebra well, but it is simple enough to
understand without it. I included the article on Fourier transformations here
because it is not usually covered in freshman mathematics while its
construction is interesting. For more motivations behind Fourier
transformations, please read ¡°What is Fourier series?¡± listed in the section
¡°Trigonometric functions.¡± Actually, the whole book ¡°Who is Fourier?¡± treats
this topic, along with all its prerequisites such as trigonometric functions,
complex numbers, calculus, and vector. I highly recommend the book.
¡°Expectation values in quantum field theory (1)¡± prepares you to understand
Feynman diagram. The last two articles explain some statistics.

**The products of vectors **

The dot product and the law of cosines

The cross
product

__Comments__

There are
two different ways to multiply two three-dimensional vectors: ¡°Dot product¡± and
¡°cross product.¡± These articles assume the familiarity with vectors as treated
in ¡°What is a vector?¡± Unlike cross product, dot product can be defined in any
dimensions, and plays a very important role in physics, math and engineering.

**A ****C****rash ****C****ourse in ****C****alculus, the ****t****hird ****p****art**

Partial derivatives
and the chain-rule

Partial differential equations

Separation of variables method in
partial differential equations

__Comments__

In
the third and fourth parts, I cover the content of the
third semester of calculus, which most science and engineering college students
who have taken a year of calculus in high school take in the first semester of
their freshman year. The first four articles are important in understanding
quantum mechanics.

**Some basic ideas in General Relativity **

By how much does time go more slowly at a
lower place?

__Comments__:

These articles survey two ideas
Einstein discovered in 1907 and found very useful for his final discovery of
the theory of general relativity in 1915. Both articles assume very basic high
school physics knowledge as covered in ¡°The free fall and Newton¡¯s second law.¡±
The second article assumes the knowledge of the first article, familiarity with
the constancy of the speed of light, in addition to very basic high school
physics knowledge. For an alternative approach to the second article, please
read ¡°Why time goes more slowly at a lower place and what a black hole is¡±
listed in the section ¡°Black hole.¡±

**Mathematical Introduction to Physics **

Newton¡¯s first and
second laws

Newton¡¯s third law
and the conservation of momentum with calculus

Kinetic energy and Potential energy
in one dimension

Kinetic energy and Potential energy
in three dimensions, Line Integrals and Gradient

Earth¡¯s Gravity near its
surface

Centripetal force
revisited with calculus

Newton¡¯s law of universal
gravitation and Kepler¡¯s third law

Newton¡¯s proof of Kepler¡¯s second
law

Kinetic energy, Potential energy
and angular momentum in polar coordinate

Re-visiting angular
momentum conservation in central force

Rolling down on an inclined
plane

A pencil rolling down on
an inclined plane, an International Physics Olympiad problem

Reflection and
transmission of travelling wave

Young¡¯s
interference experiment, revisited

Diffraction

I wrote the first four articles for
those who haven't taken high school physics to read before going on to my
articles on quantum mechanics. The articles in listed in this section assume
familiarity with calculus at the level of the section ¡°A Crash Course in
Calculus, the third part.¡± For those who have read the articles in our earlier
sections ¡°Some very basic high school physics¡± the first three articles,
¡°Earth¡¯s Gravity near its surface¡± and ¡°Centripetal force revisited with
calculus¡± will be a review. Nevertheless, it is good to study the same material
for the second time, from a slightly different approach using calculus. In
addition to some physics, ¡°Kinetic energy and Potential energy in three
dimensions, Line Integrals and Gradient¡± explains some basic concepts in
multivariable calculus using physics as an example. The last two articles are
about waves and require the section ¡°Wave¡± as prerequisites.

**Electrodynamics**

Magnetic
force on a current-carrying wire

Magnetic dipole

Relativistically moving
charges around a square loop, an International Physics Olympiad problem

__Comments__:

The main purpose of these articles is to introduce
the concept of the magnetic dipole which will turn out to be crucial in our
later article ¡°Stern-Gerlach experiment.¡± Nevertheless, if you are impatient
and want to jump into ¡°Stern-Gerlach experiment¡± as soon as possible, you can
go ahead and read it without reading these four articles as I explain there the
concept of magnetic dipole needed for ¡°Stern-Gerlach experiment¡± in a light
manner. Nevertheless, if you want a firm basis, you would need to read ¡°Magnetic
dipole.¡±

**Historical Introduction to Quantum
Mechanics **

Tunneling

__Comments__:

I wrote these articles to complement my articles on quantum
mechanics listed in the section ¡°Linear Algebra and Quantum Mechanics,¡± because
I worry that those articles may be too mathematical and allow readers to lose
the physical picture. However, those articles can be read more or less
independently as well without knowing these articles much. The first two
articles do not assume any knowledge of physics. ¡°Bohr model¡± assumes knowledge
of high school physics, such as centripetal force and Coulomb force. ¡°Planck¡¯s
relation¡± and ¡°De Broglie¡¯s matter waves¡± should help to understand my article,
¡°A short introduction to quantum mechanics X: comparison with de Broglie¡¯s
matter waves and time-dependent Schrödinger equation.¡± ¡°Schrödinger equation,¡±
¡°Tunneling,¡± and ¡°Infinite potential well¡± assume knowledge of differential
equations.

**Enumerative Geometry **

Conic
sections in Cartesian coordinate

Conic sections
in polar coordinate

__Comments__:

College
students or even math majors don¡¯t usually learn enumerative geometry, but I
included the second article to give readers a sense of what kind of mathematics
is used in string theory. The first article helps understanding the second
article. The third article is a prerequisite for ¡°Kepler¡¯s laws, revisited.¡¯¡¯

**Dimensional Analysis, the second part **

The Planck length, the
Planck time, the Planck mass and the fine structure constant

__Comments__

Building
on the ideas in our earlier article ¡°Natural units¡± we explain the important
concepts.