100 Years after Bohr's Hydrogen Atom (1913). Entanglement?

The energy level of the hydrogen atom in classical mechanics. The radius is a monotonically decreasing function of time as the accelerated electron radiates energy.

Bohr and Heisenberg (top)
Soren Kierkegaard.

In classical physics, an accelerated electron radiates energy. Since the electron circling around the proton in the hydrogen atom radiates energy, its orbit should shrink. When I was an undergraduate student, I attempted to calculate the radius as a function of time. I do not know whether I succeeded or not, but it is clear that the the energy level will sink, and the radius will decrease. This means that the earth would shrink to the size of a billiard ball, and continue to become smaller.

Bohr and Copenhagen School

One hundred years ago, in 1913, Niels Bohr presented his picture of the hydrogen atom, and present his rule of quantized electron orbits. This aspect is well known.
Bohr then developed the concept of complementarity which constitute the backbone of the Copenhagen interpretation of quantum mechanics, namely the wave-particle duality. This aspect is also well known.
Yet, there remains one intriguing question. How did Bohr get the idea of complementarity? We all know that Einstein was heavily influenced by Immanuel Kant. Who was the philosopher behind Bohr? It is an accepted view that Bohr's philosopher was Soren Kierkegaard. You are invited to the following webpages.
1. Bohr and Kierkegaard.
2. Photos from Copenhagen.
Kierkegaard is known as one of the early pioneers of Existentialism addressed to us by Jean Paul Sartre.
The question then is from where Kierkegaard (1813-1855) get his idea? From Kant (1724-1804)? May be, but there seems to be another important ideological pool which affected many philosophers including Kierkegaard.
In theology, God is Kant's Ding-an-Sich. Since not many people met God personally, different people have different interpretations of God depending on their backgrounds. Egyptians started this debate and came up with the concept of one God. In Christianity, this debate has been a continuing process since the Nicene Creed (325 AD), and became accelerated during the Renaissance period where the God-centered world was transforming itself into an individual-centered world.
On the other hand, the church's role has been and still is to adopt one interpretation and forbid all others. Thus, if there were debates about God among theologians, they were thoroughly hidden by the church.

While I was attending a conference in Rome (2012), I walked into two lesser-known churches just for curiosity. At one of them, I found a statute of Galileo Galilei constructed by T.D.Lee. Click here for my what I saw in that church.

There is another church called "Basiliaca di San Pietro in Vincoli" (Saint Peter in Chains) next to the engineering faculty building of the Uni. di Roma Sapienza near the Colosseum. There I spotted Michelangelo's statue of Moses. Every art piece of Michelangelo has its distinction.
There also is a tomb of a clergy man who was totally unknown to me. His tomb was so elegant that I had a photo of myself there. I later found out he was Nicholas of Cusa (1401–1464). According to Wikipedia, he was a German philosopher, theologian, jurist, mathematician, and astronomer.
Nicolas Cusa proposed a theory that one has to develop his/her "divine" mind to understand God. Since different people can develop different divine minds, Cusa's philosophy was a prelude to Kantianism. In fact, during the 19th century, many Kantian scholars studied Cusa's writings.
This is an indication that Kantian-like logic had been developed among theologians by the Renascence period, 300 years before Kant, but we do not know about it because the church's job has been and still is to insist on one view of God and suppress all other views.
It is safe to say that Kierkegaard's philosophy has a deep root in theology. Kierkegaard was Bohr's philosopher.
Click here for more about the Basiliaca di San Pietro in Vincoli.

Bohr and Einstein

Why was Einstein so against quantum mechanics? I do not think Einstein was against his photo-electric effect. I think he had a great respect for Bohr. I think Einstein was frustrated because Bohr's hydrogen atom did not accommodate Einstein's relativity. Bohr sensed Einstein's frustration and he added "time" whenever he mentioned "space," even though he could not accommodate Einstein's relativity in his mathematical formulas. I am not the first one to think in this way.
Paul A. M. Dirac was not completely happy with the Copenhagen interpretation. However, re-examinations of the present form of quantum mechanics can come only after we examine whether the wave-particle duality is consistent with relativity. As you know, I believe in Dirac.
Then what are the Einstein issues for the hydrogen atom?
1. The electron orbit is now replaced by a standing wave.
2. How would this standing wave appear to a moving observer?
3. Are there hydrogen atoms moving with relativistic speed? The answer to this question is No. The hydrogen atom is a neutral object and cannot be accelerated, even with the present technology.
4. These days, the proton is a bound state of three quarks, and consists of two standing waves. The proton speed can reach 0.999999..(I do not know how many 9s), and it is criminal not to study Lorentz-boosted standing waves. I am not the first one to study the standing waves in the Lorentz-covariant world.
  We know how to deal with standing waves in the Galilean world. We have to impose boundary conditions. What happens to this boundary conditions in Einstein's Lorentz-covariant world? Have you heard anyone mentioning this problem?
5. We do not have to worry about this problem if we use harmonic oscillators with built-in boundary conditions, as noted by Dirac, Yukawa, Feynman, among others.
6. We can construct at least one Lorentz-covariant standing wave if we synthesize the following three papers written by Dirac.
  1. P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 (1927) -- on time-energy uncertainty relations.
  2. P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 (1945) -- on using harmonic oscillator wave functions in the Lorentz covariant world.
  3. P. A. M. Dirac, Rev. Mod. Phys. 21 , 392 (1949) -- on the light-cone coordinate system.
  If we synthesize these three papers, we end up with the result which can be summarized by this cartoon. It has been a pleasure for me to be able to translate Dirac's poems into cartoons. Click here to see the assembly process.
This table summarized how physical theories were developed in the past. It is easier to understand the history of physics if we divide the world into scattering and bound-state problems. In the quantum world, scattering problems are about running waves where all the particles become free particles asymptotically. Feynman diagrams seem to satisfy this need.
For bound-state problems there seems to be one set of wave functions, namely those of harmonic oscillators. Thus, the scattering and bound-state problems take two different mathematical forms. However, the more fundamental question is whether they share the same set of principles in quantum mechanics and relativity. The answer to this question is Yes. Click here for a published paper on this subject.
Squeeze and Entanglement. We all know that Lorentz transformations are not rotations. However, the variable separability is maintained in the light-cone coordinate system. The proton wave function retains its separability, but what happens in the space-time coordinate system. It is a squeeze transformation. As a consequence, the wave function becomes entangled.
1. Click here for an one-page explanation in terms in terms of figure and formulas.
2. Click here for a published review paper on this subject.
There are many people who question the foundations of quantum mechanics. It may help them if they realize the present form of quantum mechanics started from Bohr's hydrogen atom. Go back to his hydrogen atom and find out what went wrong there.

copyright@2013 by Y. S. Kim, unless otherwise specified.
The photo of Bohr and Heisenberg is from the public domain. The photo of Dirac and Heisenberg is from the AIP Emilio Segre Visual Archives.