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Photos from Trier, Saint Helena,
Karl Marx, and E = mc2.

Have you been or heard about a small German city called Trier? . This city is in Germany but is very close to Luxemburg. I assume you know where Luxemburg is. Trier is one-hour train ride from Luxemburg.

    Saint Helena in Saint Peter's Basilica
    in Rome.
  • Why should we talk about this city. Karl Marx was born and raised in this city. Earlier in history, Saint Helena built the first Christian church north of the Alps. Saint Helena was Emperor Constantine's mother, and regarded as the mother of the Christian Empire. Constantine later built a larger church in Trier, but this church was destroyed and rebuilt severl times due to armed conflict in that area. In addition, new buildings were addes in the same area.

  • I am not a religious person, but my Korean background includes a strong Christian background. You may be interested in the following webpages baased on my Christian background.

    1. Herod Complex. This deals with psychological problem for every self-respecting physicist.

    2. How did Moses to talk to God? How can we talk to Einstein?




  • Let us look at some photos from Trier.

    1. The first notable object is the gate to the city constructed by Romans. Here is a photo of the the Roman Gate.

    2. I then visited the tourist office. Next to this office was a giant statue of Karl Marx.

      I went to Trier to learn about Saint Helena, but I met this person responsible for God-less communist empire. The question is whether I should give up and leave the city, or study why Marx is there.

    3. Marx's statue is there because he was born and raised in this city. He was born in a Jewish family, and his family belonged to an upper-middle class in Germany.

    4. These days, the political ideology called "communism" is forgotten and irrelevant, but the city of Trier is quite proud of Marx as their distinguished son, and his childhood house is now a Marx museum.

    5. The Marx Museum contains many Marx items, including his bust at the flower-filled quadrangle.

    6. Needless to say, the Museum shows a list of prominent communists who played their role in the 20th Century.

    7. The Museum also shows the books Marx wrote including Das Kapital. Have you read this book. I read this book in the summer of 1956 between my sophomore and junior years in college. In Volume IV of this book, Marx introduces a new variable in economics: Surplus Value.

  • I did not have enough time to find out how the the life style of the people in this city, but they seem to be very happy.

    1. Their town square is beautiful,
    2. with interesting groups of people,
    3. also with locally grown farm products and flowers.

    4. The Trier ladies enjoy their afternoon teas.

    5. Click here for more photos and stories of this interesting city.




  • Let us go to the Basilica of Constantine. This church was first built by Constantine the Great of the Roman Empire, and has a complicated history. It is said that he built this church on the place where his mother, Saint Helena, worshipped before Constantine declared the Edict of Milan in 313 AD.

    The original building was destroyed by armed conflicts in this area, and the building was rebuilt several times.

    In addition, a new administrative building called Electoral Palace was built next to this church. I am not able to explain the role of this shiny building. You may click on this Wiki page for details. Thus, the area is now a pleasant park. Let us look at some photos. s

    1. This is the Basilica building.
    2. Plate on the outside wall telling this building is the Constantine Basilica.
    3. This is a side view of the Basilica.
    4. Inside the Basilica. This photo is from the Wikipedia.

    5. The Electoral Palace is an stylish modern building. The building behind with a triangular roof is the Constantine Basilica.
    6. Front of this building is a serene park with this kind of maze, and a reflection pond with statues of 12 Apostles.
    7. There is also a portrait of Karl Marx in this Christian park.

  • Let us return to Karl Marx, and let us ignore his communism issues. There are still many important items to talk about him.

    Before Hitler, Humboldt University of Berlin was one of the most respected learning places in the world. Bismarck, Hegel, Marx, Planck, Einstein, and many others studied and/or taught there. As soon as you enter the main building, you see what Karl Marx said about on a marble plate.

    What does he say in English? Let us go to his grave at the Highgate Cemetery in London.

  • Here, Marx was taking about changing the world. We know how he wanted to change the world. Politically? We are not interested in this aspect.

    Throughout his writings, he talks about manual labors and manual laborers. After all those struggles in writings, Marx formulated the concept of "surplus value" in Volume IV of his book "Das Kapital." Marx died before this volume was published.

      This is a bridge built by Romans at the time of Julius Caeser near Avignon, France. Did they worry about the cost of labors?
    Before Marx, money and price were important variables in economics, but labor was not. Marx noted that there is a price differences between raw materials and finished products. He called this difference "surplus value." He then concluded that this difference in value comes from the labor contributed by manual workers. Thus, he formulated the formula

      Labor = Money .

    This is one of the most important formulas in the industrial world, it was a totally strange concept before Karl Marx. When Egyptians built their pyramids, and when Romans built their water bridges, did they have this concept?

    More recently, according to Mrs. Michelle Obama, the White House was built by slaves (laborers without compensation).

  • Let us come back to physics. We all know Einstein formulated the concept

      Do they know what this formula means?
      E = mc2, or

      Mass = Energy.

    This formula serves as Einstein's nickname these days, but it was so strange at his time that his Nobel prize (1921) was NOT for his special relativity leading to this formula.

    This formula sometimes is used as an advertising purpose for being electrically powered (a car ad in Shanghai, China), or being nuclear powered (the flght deck of the nuclear aircraft carrier called USS Enterprise).

  • Let us do a quantitaive analysis of this formula. You all know how much your automobile weighs, and you think combat tanks are much heavier. Let us look at two tanks which played their important roles in history.

    The mass of each tank is about 50 metric tons. Using E = mc2 , it is possible to convert tons to joules. Indeed, one of these tanks can satisfy the total energy need for humans for one year.

In spite of the urgent energy need, physicists are trained to look into a smaller world.

  • Let us see whether Einstein's reasoning for E = mc2 is applicable to the interior of the hydrogen atom.

    Bohr and Einstein

  • In 1913 (more than one hundred years ago), Bohr was worrying about why the energy levels of the hydrogen atom are discrete.

    Einstein was worrying about how things look to moving overseers.

    Did Bohr and Einstein worry about how the hydrogen atom looks to a moving observer?

    There are no records to indicate that they discussed this issue. Who started worrying about this problem? His name is Paul A. Dirac.

  • While quantum field theory deals with running waves with the S-matrix as the main calculational tool, Dirac was concerned with localized standing waves. He wrote three important papers on this subject, but he was not able to integrate them. The reason is very simple.

    1. His writings are like beautiful poems, but he never attempted draw figures.

    2. In the hydrogen atom, the distance between the proton and election is the space separation. In dealing with the time-variable, Dirac does not specify the time separation.

      Dirac and Wigner,
      brothers-in-law.

    3. In his 1927 paper, Dirac complained that the time-energy uncertainty relation is a c-number relation (no excitations along the time-like direction). He did not know this issue was later addressed by Wigner in 1939 who introduced his little groups. The space-time symmetry of the hydrogen atom (localized wave) is like that of the three-dimensional rotation group, with no-time-like excitations.

  • If we make up these deficiencies, we can integrate Dirac's works in the following manner.

    Can we observe this effect in the real world?

    This figure integrate the following three papers written by Dirac.

    1. P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 - 265 (1927).
    2. P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 -295 (1945).
    3. P. A. M. Dirac, Rev. Mod. Phys. 21, 392 - 399 (1949).

  • Yes, the above figure indeed integrates these three papers. The question is whether there are hydrogen atoms moving with relativistic speed? The answer is No. The question then is what I said above is only a science fiction. The answer is again No.

    1. The hydrogen atom is neutral, and cannot be accelerated by a strong external electric field, but we can accelerate protons because they are charged particles.

    2. During the last half of the past century, countries spent billions of dollars to build particle accelerators. These accelerators produce protons moving with speeds close to the speed of light.

    However, the proton is not a hydrogen atom. Atccording Gell-Mann, it is a bound state of the more fundamental particles called "quarks." This bound state shares the same quantum mechanics as the hydrogen atom.

  • If the proton moves with its speed close to that of light, it appears like a collection of partons (Feynman), whose properties are quite different from those of the quarks. The question is whether this difference can be explained in terms of Einstein's special relativity and the standing-wave picture of the quantum bound state.

  • These questions constitute further contents of Einstein's

      E = mc2.

    Click here for a story, and Click here for another story.


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This webpage was constructed by Y.S.Kim (May 2020).