Einstein, Dirac, Wigner, Feynman One hundred years ago, Niels Bohr was worrying about the electron orbit of the hydrogen atom. Albert Einstein was interested in how things appear to moving observers. How would the hydrogen atom look to moving observers? If they discussed this problem, there are no written records on this aspect. Homework problem for younger generations!  • This is an image of the bridge near Avignon (France) built during the reign of Julius Caesar. This structure is an excellent illustration of what God can do and what humans can to. God created mountains and humans built a bridge.

To me, Bohr and Einstein are like God-like figures. The best I could do was to build a bridge between them.

• Then, am I the first one to recognize this problem? The answer is No.
 Many distinguished physicists worried about this problem. Among them were Dirac, Wigner, and Feynman. Let us review their works and integrate them.
 Three Wise Men from the 20th Century. Why three?   Three papers Click here for detailed references. Dirac 1927. c-number time-energy uncertainty relation. 1945. Harmonic oscillators for the Lorentz group. 1949. Light-cone coordinate system. Combine all three. Wigner 1932. Wigner functions. 1939. Little group for internal space-time symmetries. 1953. Group contractions. Combine 1. and 2. Combine 2. and 3. Feynman 1969. Parton model. 1971. Harmonic oscillators. 1972. Rest of the universe. Combine all three.
 Major contributions c-number time-energy uncertainty, harmonic oscillators, light-cone coordinate system. Little groups defining internal space-time symmetries. Parton model, oscillator model for Regge trajectories, in addition to Feynman diagrams.

 Favorite language Poems. Dirac's writings are like poems. Group theory, and two-by-two matrices. Diagrams and pictures.

 Soft spots Lack of figures and illustrations. Lack of physical examples. Before the age of high-energy accelerators. Lack of concrete physical examples. His 1939 paper could not explain Maxwell's equations. He could not explain his parton picure in terms of the mathematical tools developed by Dirac and Wigner.

 Mathematical Instruments We all know that Einstein's special relativity is best described by a hyperbola, written as t2 - z2 = 1. We can then consider a circle to tangent to this hyperbola and squeeze to produce an ellipse to tangent to the hyperbola. High-school mathematics. Dirac's idea is to use the Gaussian function (the language of quantum mechanics) for the circle. Click here for a paper on this subject. Click here for applications of the same mathematics to modern optics.

If we integrate those nine papers by Dirac, Wigner, and Feynman, we end up with

Further Contents of Einstein's E = mc2.

 Click here for a story. 100 years of contentious history since Bohr (quantum) and Einstein (relativity). Facebook pages on this issue. Click here for my recent publications on this subject.

Einstein's Lorentz-covariant world

 Massive/Slow between Massless/Fast
 Energy Momentum E=p2/2m Einstein's E=(m2 + p2)1/2 E=p
 Spin, Gauge, Helicity S3 S1 S2 Wigner's Little Group S3 Gauge Trans.
 Gell-Mann, Feynman Quark Model Lorentz-covariant Oscillators Parton Picture
We can now be more ambitious.
• Is it possible to derive quantum mechanics (with the Heisenberg brackets) and special relativity (with E = mc2) from one basket of equations? Look at the following papers. 