# Physics as an Art of building Bridges

Let us look at the history of physics.
• Galileo Galilei came up with the concept of acceleration in while building a bridge between speed and time. Click here for a story.

• Isaac Newton built a bridge between force and acceleration. Well known!

• William Thomson (Lord Kelvin) built a bridge between Heat and Energy.

2. Here for Maxwell.

3. Here for Wireless Communication for the present world of TVs and cell phones.

 He was a great bridge builder. They need a bridge. They need a bridge.

• Einstein built many bridges. Bridges between

1. Massive Particles and Massless Particles.

2. Frequency and Energy.

3. Mass and Energy.

4. Specific Heat and Discrete Energy Levels.

• Heisenberg built a bridge between Particles and Waves. He attempted to talk to Einstein. Click here for a story.

• Bohr and Einstein talked to each other often. Bohr was interested in the electron orbit of the hydrogen atom, while Einstein was interested in how things look to moving observers. However, they never talked about how the hydrogen atom looks to a moving observer. Click here for the definition of the problem. This is still one of the most outstanding problems in physics.

1. Click here for the evolution of the way in which we look at the hydrogen atom.

2. Click here for this problem as a further contents of Einstein's E = mc2.

• Dirac and Feynman met in Poland (1962). They were not communicating. Someone has to build a bridge for them. They are talking about the same thing, but their languages are different. Dirac was a poet while Feynman was a cartoonist. It is a great challenge to translate Dirac's poems into Feynman's cartoons.

• According to Murray Gell-Mann, the proton is a bound state of more fundamental particles called "quarks." He was talking about the proton sitting on the desk. According to Richard Feynman, the proton moving with a speed close to that of light is a collection of an infinite number of free particles called "partons." Is it possible to build a bridge between these two different ways of looking at the same particle?

You may be surprised to hear that, with Marilyn Noz, I published my first paper on this issue in 1977, before realizing it was an Wigner issue.

You will also be surprised to hear that the mathematical technique developed in this program is directly applicable to the entanglement problems of current interest. Click here for a story.

• Speaking of the role of mathematics in physics, the second-order differential equation plays an essential role in resonances in mechanics and electronics. Thus, it builds a bridge between mechanics and electronics.

Likewise, with the Lorentz group, you can build many bridges in physics.

1. The above-mentioned quark-parton puzzle is a Lorentz-group issue.

2. The optics book written by Jenkins and White still serves as an old testament. These authors did optics without two-by-two matrices and Fourier transformations. They did OK. However, with a degree of exaggeration, optics is the physics two-by-two matrices and Fourier transformations.

3. These days, there are tons of paper on optics and entanglements. It is fun to realize that the Lorentz group is an underlying scientific language for the current trend in physics.

4. Is the Lorentz group a difficult subject? No. Is the algebra of two-by-two matrices difficult for you? There are three Pauli matrices which generate the rotation group. The Pauli matrices are Hermitian. Thus, we may consider three anti-Hermitian matrices. We can therefore consider the two-by-two matrices generated by the three Hermitian and three anti-Hermitian matrices. The algebra of these simple matrices is the same as the algebra of the Lorentz group. In the language of group theory, it is an expansion of the group SU(2) to SL(2,c).

5. Did you know that this expansion could build a bridge between Heisenberg's uncertainty relations and Maxwell's electromagnetic four-vector and four-tensor. Click here if you are interested.

## Bridges around the World

• London's Tower Bridge is the most famous bridge in the world. It is a challenge to take a photo of this bridge while opening.

1. This bridge is often called the London Bridge. The London Bridge is somewhere else.

2. This is the Tower Bridge because it is near the Tower of London. Click here for photos of the London Tower and the Tower Bridge.

3. The Thames River runs through the city of London. There are many many bridges across this river. You are invited to my London page. I love London, and I go there often.

• The Pont du Gard is a bridge Romans completed during the period of Augustus. It is located near Avignon, in southern France.
1. I was there in February of 2017, and became convinced that physics is really an art of building bridges.

2. I met there a Chinese historian and talked about the Great Wall Emperor Chin started building in 300 BC.

3. These two projects had different purposes with different engineering bases. However, there was one thing in common. They needed enormous amounts of manual labors. It took humans 2,000 years to realize that the labor is an essential variable in economics. Karl Marx found out from his variable called "surplus value," meaning the price difference between the finished products and the raw materials.

4. These days, human intelligence (inventiveness) affects our economics. I assume many people are worrying about quantitative approaches to this problem. Great opportunities for physicists!

• The Dandong Bridge across the Yalu River is the most talked-about bridge in the mass media. This bridge connects North Korea to the Chinese mainland. The trade sanction against North Korea crucially depends on the traffic across this bridge.

This bridge was built by Japanese expansionists. Its first span was built in 1935, and the second span was completed in 1939.

1. The southern halves of these spans were destroyed by the U.S. Air Force during the Korean War (1950-3).

2. Chinese and North Koreans reconstructed one of the spans and the other still remains half-destroyed and unusable, as shown in this this photo.

Many people go to the end of this broken bridge and take photos. I was there in April of 2014. This is a photo of myself standing there. In the background is the reconstructed span which Chinese and N. Koreans use for their trade purposes.

• I have photos of many other bridges in the world, including

1. Many bridges in Pittsuburgh.

2. Golden Gate Bridge in San Francisco.

3. Verzano-Narowa Brige in the New Yrok Harbor.

4. Charles Bridge in Prague.

5. Across the Bospherus Channel in Istanbul.

6. Anachikov Bridge in Saint Petersburg.

7. Pont Vechia (old bridge) in Florence.

8. Realto Bridge in Venice.

• I have many more photos, and I would love to add stories to those bridges. I would do so when I have time. Please come again.