Wisdom of Korea in my Research Life
 Koreans are ethnically Mongolians, who speak the
UralAltaic language, and their grammar is quite different
from that of Chinese. On the other hand, Koreans are different
from Mongolians because they adopted the culture of China
extensively from 600 AD.

In this document of 1486, the King of Korea tells his people to use 28 new
letters to express their opinions.

However, the Chinese writings were not consistent with the language of Koreans.
Thus, they developed their own letters based on their sounds during the 15th
Century. The Koreans scholars realized that the sound can be generated by 10
vowels and 18 consonants. The combination of (consonant + vowel + consonant)
can generate all possible sounds humans can produce. For this reason, Koreans
are mighty proud of their own letters.
Yet, until recent years, Korean boys and girls had to study books containing the
words (like School, Democracy, Trade, Science, etc) written in Chinese letters.
These days, they read the books with English words written in English alphabets.
I am an old Korean, and I had to study those Chinese characters during my
highschool years (194854).
 Koreans found Chinese characters very interesting. One character corresponds to
one thing in the world. Sun, Moon, Horse, Mountain, River, Snow, Snake, Country, etc.
All of them have their own characters. Thus, we do not know how many Chinese
characters are in Chinese books.
In the past, the basic education for Korean children started with 1,000 Chinese
characters. I think I can recognize about 5,000 characters.

Ancient Chinese used picture to genarate their letters.
Six hundred years years ago, under the leadership of King Sejong the Great,
Korean scholars used symbols for consonants and vowels to generate sounds.
The order was 1, 2, 3 (leftrightbottom) for consonantvowelconsonant as
shown in this figure,
because Korean sentences were written vertically at that time.


 The point is that each character starts from the picture of a visible object.
Sun and Moon are both visible. The letter consisting of both Sun and Moon leads to
the abstract concept of bright, as illustrated here.
This kind of process is known as the Hegelian Synthesis in the Western world.
 Let us go back to physics. The issue is then how to combine two different
theories (relativity and quantum) into one theory with the higher degree of abstraction.

Richard Phillips Feynman
believed in "one physics." He started constructing quantum field theory in order to
combine quantum mechanics with Einstein's relativity.
 This quantum field theory provides a satisfactory explanation of scattering processes
where all particles are free in the remote past and remote future.
 It is important to note that Feynman provides the tool of quantum field theory
using pictures, known as Feynman diagrams, where all particles are free in the remote
past and in the remote future. We call these pictures "Feynman diagrams."

In order to construct quantum mechanics in Einstein's space and time,
 we note that, for scattering problems, quantum field theory with Feynman
diagrams provides a satisfactory tool for us.
 We still have to construct quantum mechanics for bound states (Step 1).
 We then have to find a mathematical framework that encompasses both
scattering and bound states (Step 2).

 However, this field theory does not provide explanations for bound states. Let us
consider a hydrogen atom, consisting of one electron circling around one proton.
These particles are never free. Thus, it is not possible to draw Feynman diagrams
for the hydrogen atom with its discrete energy levels.
For planets (boundstate), we have to take into account boundary conditions in a
Lorentzcovariant manner, and the problem becomes quite different from those for
scattering processes.
The word "Lorentzcovariant" means valid in the world of Einstein's special relativity
which produces E = mc^{2}.
 For this bound system, Paul A. M. Dirac published the important papers in
1927, 1945, and 1949.
 In 1927, Dirac noted the importance of the timeenergy uncertainty relation.
He pointed out there that there are no quantum excitations along the time
direction. Dirac called it the "cnumber timeenergy uncertainty relation.
 In 1945, Dirac considered fourdimensional harmonic oscillator wave functions
applicable to the fourdimensional Mikowskian space and time.
 In 1949, he noted the Lorentz boost as a squeeze transformation, where a
square becomes a rectangle with the same area in the twodimensional coordinate
of the time and direction of motion.
 I spent time with Dirac in 1962. Click here
for my story.
Yes, they are excellent observations. It is indeed enjoyable to read Dirac's papers.
They are like poems with beautiful mathematical formulas. On the other hand, have you
seen pictures or figures in Dirac's papers?
 We are now interested in integrating all those ideas. We can go back to the
Korean Wisdom (derived from Chinese characters). First, translate Dirac's ideas
into pictures, integrate those pictures into one, and translate the resulting
picture into mathematical formulas.
If we translate Dirac's papers, we end up with the upper two figures given here:
Click here for a detailed explanation of this
figure.
 The question is how I was able to do this while Dirac could not do and nobody
else could do before me. Here is my answer.
It is well known that Chinese characters were derived from pictures of visible
objects such as Sun and Moon. How about invisible abstract ideas? Combine
the letters for those visible objects to produce the concept of Bight.

We can use the same wisdom for combining two theories. Translate the basic mathematical
formulas into pictures. Then combine those pictures into one, and translate this one
picture into a new set of formulas.
Bohr and Einstein were the two scientific giants of the 20th Century, and they met
occasionally to discuss physics. However, did they talk about how the hydrogen
atom appears to moving observers?


 Let us go back to the table given above.
We have settled the issue of quantum bound states in Einstein's Lorentzcovariant
world, namely Step 1 in the table.
 How about Step 2?
The mathematical formulas for quantum field theory and quantum bound states
are quite different. However, they belong to the same group of mathematics called
"representations of the inhomogeneous Lorentz group" formulated by Eugene Wigner
in his paper of 1939.
With my younger colleagues, I wrote many papers and three books on this subject.
Among them, the following two papers directly address this issue.

Representation of the Poncare Group for Relativistic Extended Hadrons(1979)
 Quantum Mechanics of Moving Bound States (2022)
This completes Step 2 specified in this table.
 OK. The theory is beautiful, but does it have anything to do with the
real world. Click here for the experimental
aspect of this theory.
 Next. We can ask whether quantum mechanics and Einstein's Lorentz covariance
can be derived from the same basket of equations.
In other words, is it possible to derive Einstein's E = mc ^{2 }
from Heisenberg's uncertainty brackets?
Crazy? NOT SO.

