Einstein Story

• There are many books written about Einstein. There are also many webpages dedicated to him, including the Wikipedia page for him.

  I am with Joseph Weber (1988) who pionneered the detection technique of gravitational waves. He was my senior colleague at the Univ. of Maryland. He was a man of courage and was not afraid of being alone in his research eofforts. So was I.

  There are far more scientists in the Washington area than politicians. Those scientists are quiet while the politicians are noisy. I live in this area.

• In this website, I would like to talk about the consequences of his special theory of relativity, not yet widely known. There is a tendency to think his special relativity is out-dated, and his general relativity is the thing to study. This is not the case.

  1. Einstein's E = mc² is a product of his special relativity.

  2. These days, high-energy accelerators produce particles moving with speeds close that of light. We analyze those experimental data using special relativity.

  3. While Einstein's general relativity is concerned with what happens in far-away places in the universe, his special theory deals with what happens on the surface of our Earth.

  4. The Lorentz group is the mathematical language for Einstein's special relativity. It is a beautiful mathematical formalism applicable to other branches of physics, including optical sciences and condensed matter physics.

• The key issue in this special theory is how an object appears to observers moving with a constant velocity. How then did he become interested in this question?

  While he was a high-school student, Einstein became quite enthusiastic about the philosophy of Immanuel Kant. According to Kant, a given object could appear differently depending on the observer's environment or his/her status of mind. The following figures will illustrate how he came to this question.

  Toyotomi Hideyoshi (1536-98) is an important person in Japanese history. He unified Japan by brutally eliminating rival warlords. He is known as O-Saru-San (Mr. Monkey) in Japan. He looks like a monkey to human eyes, but he is a human if monkeys look at him. This Japanese saying could serve as an easy-to-understand illustration of Kant's philosophy. As a Kantianist, Einstein should have asked how Toyotomi appeared to him when he was on his moving bike.

  	Einstein with Hendrik Lorentz (1921).

• For the moving observer, Einstein used the transformation law developed earlier by a Dutch physicist named Hendrik Lorentz (Nobel 1902). He developed this transformation law based on the fact that the speed of light is invariant. The speed of light shined by a stationary lamp is the same as that from a jet plane.

• This transformation is hyperbolic transformation between the longitudinal and time coordinates. If this transformation combined with rotations in the three-dimensional (x, y, z) space is called the Lorentz group, whose transformation matrices are four-by-four applicable to the four-dimensional space of (x, y, z, t).

  If we add translations in this four-dimensional space, it becomes the inhomogeneous Lorentz group known also as the Poincaré group.

• The theory of these groups is a beautiful mathematics, and serves as the language of Einstein's special relativity.

  Einstein's E = mc² belongs to this mathematical framework. Thus, the world to which Einstein's special relativity is applicable is often called

  Einstein's Lorentzian world.

• I love the mathemarics of the Lorentz group and its applications to physics. I wrote many pappers and a number of books on this subject with my younger colleagues. The latest book is available from the Amazon.

• In 1879, Einstein was born in Ulm, Germany, but his family moved to Geneva, Switzerland, and then to Milan, Italy. He went to the Swiss Federal Institute of Technology in Zurich for his higher education
  1. Click here for photos of Ulm.

  2. Click here for Swiss Federal Institute of Technology in Zurich.

• In 1905, Einstein formulated his special theory of relativity resulting in his
  E = mc² ,

  while he was working for the Swiss patent office in Bern, Switzerland.

  In Bern, Switzerland, I am so happy to be at the birth place of E = mc2.

  1. Click here for Einstein's Bern.

  2. Aslo in 1905, Einstein gave his theoretical explanation for the photo-electric effect. Einstein received his Nobel prize for the photo-electric effect, but not for his theories of relativity.

  3. In 1905, in addition, Einstein gave an explantion to the Brownian motion.

• In 1908, Einstein started studying gravitational effects on light lays.
  1. This became the beginning of his general theory of relativity, worrying about the universe and far-away places. The research along this direction led to the discovery of the gravitational wave.

  2. Presumably, Einstein turned his attention to the universe because he could not think of observable effects in the world at his time.

Einstein became a citizen of the United States in 1940.

• In 1933, Einstein immigrated to the United States and settled down in Princeton, New Jersey. He became a citizen of the United States in 1940.
  1. Einstein died in 1955. Until 1965 (ten years after his death), many ambitious students wanted to go to Princeton to study physics and to meet Einstein. He was a God-like figure.

  2. This video talks about a Korean boy who wanted to meet Einstein.

  3. On March 12, 1958, I received a letter from Princeton telling me that I was one of the 15 students admitted to their graduate program in physics. This was the happiest day in my life.
     

  4. How could I talk to a man in Heaven? How did Moses talk to God?
     Click here for a story.

  5. Click here for my Princeton page.

Click here for the first nuclear test on July 16, 1945. A-bomb explosions on Hiroshima (August 6) (left) and on Nagasaki (August 9) in Japan (1945).

• Einstein became known to the world as the inventor of the nuclear bomb after the end of the World War II in 1945. This is not true.

  1. The nuclear bomb was developed by the scientists, engineers, and administrators of the Manhattan Project.

  2. Einstein's name is nowhere in the literature on this project. However, the project needed a huge amount of money, and the president of the United States was the only person who could supply this amount. The president at that time was Franklin Roosevelt.

  3. However, nobody in the Manhattan Project was prominent enough to write a letter which could reach Roosevelt's attention. Thus, they needed a letter from Einstein. Roosevelt would read a letter from Einstein.

     Nazi poster depicting Einstein's immigration to the United States.

  4. Then who could approach Einstein for this letter?

• It is my understanding that John von Neumann and Eugene Paul Wigner wrote the letter and approached Einstein for his signature. They could talk to Einstein, while not many American scientists could approch him.
  1. Wigner and von Neumann were the residents of Princeton as Einstein was.

  2. They were born in Hungary and went to the same high school in Budapest, but they were educated in Germany. Einstein was born and educated in Germany.

  3. Like Einstein, they spoke German, and they could talk about German physicists, including Werner Heisenberg, who could have developed nuclear bombs for Adolf Hitler.

  4. Their reasoning to Einstein was that Hitler and his German physicists were working on the dreadful nuclear bomb. Einstein had to sign the letter to Roosevelt in order to save this world.

  5. I spotted this Nazi poster depicting Einstein's immigration to the United States at the Einstein Museum in Bern, Switzerland (2014). This poster tells Einstein was afraid of Hitler's possible nuclear bombs.

  Wigner and Kim (1986).

• This story is based on what I heard from Eugene Wigner, but he is not responsible if the story is less than 100% accurate.

  I am responsible. It is possible that my understanding of what I heard from Wigner could be less than perfect.

  During the period (1986-90), I went to Princeton often to tell the stories Wigner wanted to hear. He also told me many interesting stories. We published seven papers together.

Einstein with nuclear explosion and his E = mc2 on the cover of the Time magazine (July 1, 1946).

• After the nuclear bombs on Hiroshima and Nagasaki in 1945,

  Einstein's name and his E = mc² became widely known to the world. The nuclear bomb converts the mass of the material into energy, but we cannot do this experiment too often.

  Yet, we can do some fun calculations.

  1. During the second world war (1939-45), the Soviet Union produced many combat tanks to destroy Hitler's German army. Their tank model was called T-34. They were developed in the industrial city of Kharkov (now in Ukraine), and were mass-produced, during the war, at the open-air factories in the city of Chelyabinsk hidden in the Ural Mountains.

     There, 18,000 tanks were produced. Hitler was not aware of this. Indeed, the T-35 tank is a historical machine.

     T-34 tank displayed at the WWII memorial park in Kharkov, Ukraine. I was there in 1999. Nuclear-powered aircraft carrier "Enterprize" of the U.S. Navy commisioned in 1961.

  2. The mass of this tank is about 50 tons (50,000 kg). If we covert its entire mass to energy according to Einstein's formula, it produces enough electrical energy consumed by the entire world for one year.

  3. There are these days many nuclear power generating stations in the world. There are also many nuclear submarines and nuclear aircraft carriers.

     It would be interesting to calculate the mass difference between the nuclear fuel and the nuclear waste, and compare this difference with the energy produced. The produced energy is measurable, but the mass difference could be very small. In any case, this calculation does not seem to serve useful purposes.

• Einstein's E = mc² has been and still is valid in particle decay processes. When one heavy particle decays into several light particles, the sum of those light masses and their kinetic energies are equal to the mass of the initial heavy particle. This formula is valid in all high-energy collision processes.

History Museum in Berlin (Germany). The cover of one of the books I wrote with Marilyn Noz.

• Einstein's E = mc² serves as his nickname. This formula is often used for decorative and comerical purposes.

  As an emeritus professor, my job is to become famous. I am using this formula to become famous.

  • Click here for Further Contents of Einstein's E = mc².

• LORENTZ TRANSFORMATION is the word commonly used for Einstein's special relativity, and its mathematics is well defined.
  1. The issue is how an object looks to an observer on a train with a constant speed. If it remains the same, we call it "Lorentz invariance." if it becomes different, we use the word "Lorentz covariance." For a given particle, it's mass in Lorentz-invariant, but its kinetic energy is Lorentz-covariant.

  2. I am one of a small number of physicists who understand the difference between the Lorentz invariance and the Lorentz covariance, thanks to Paul A. M. Dirac.

     I was very hppy to have a photo of myself at image of Feynman at the Firmilab near Chicago (2003). I respect him.

  3. Richard Feynman was one of the most respected physicists of the 20th Century, and I respect him, and I maintain a website dedicated to him.

     However, according to his 1971 paper he published with his students, Feynman did not understand this difference between "invariance and covariance."

     I realize that this is a very serious statement. Please continue reading this webpage for explanations.

Einstein in the Quantum World

• In 1905, Einstein gave his theoretical interpretation to the photo-electric effect. Here he gave the energy-momentum relation for massless particles, and energy-frequency relation for the electromagnetic wave including light waves. They are the key issues in quantum mechanics.

  Physicists of the Manhattan Project (photo from the Los Alamos National Laboratory). Feynman is in this photo.

• In Einstein's Lorentz-covariant world, the physics of running waves has been well formulated. It is called quantum field theory. The main contributors for this Lorentz-covariant theory are Richard Feynman, Julian Schwinger, and Shinichiro Tomonaga. They shared the Nobel in 1965.

  Among these three distinguished physicists, we mention Feynman most often, due to his Feynman diagrams for scattering processes. Feynman was one of the youngest members of the Manhattan project. He was a graduate student at Princeton, and his thesis advisor was John A. Wheeler.

  I was at Feynman's talk (1970) and took this photo with a telephoto lens. The lecture hall was dark for his slide show.

  1. In 1970, at the Spring Meeting of the American physical Society, Feynman gave a talk telling that quantum field theory is not adequate for dealing with quantum bound states in Einstein's relativistic world. He suggested harmonic oscillator wave functions for the bound states in the quark model.

     In 1971, with his students at Caltech, Feynman published a paper based on his 1970 talk he gave in Washington. Click here for details about what Feynman said.

  2. Indeed, in his 1971 paper with his students, Feynman presents a Lorentz-covariant harmonic oscillator wave function for moving bound states. Yes, the physics of their paper was in the right direction, but their mathematics for the moving oscillator was thoroughly wrong.

     To make things worse, they ignored the attempts made by earlier authors on the same subject. Among those earlier authors was Paul A. M. Dirac (Nobel 1933).

     Dirac and Feynman at the Jablonna Palace in Poland (1962), photo by Marek Holzman, from Caltech Photo Lab.

  3. After reading this 1971 paper, I was able to understand what Dirac told me about American physicists in 1962. I had a privilege of talking with Dirac in 1962. Click here to see how I met Dirac.

     Dirac said American physicists do not understand the difference between the Lorentz invariance and Lorentz covariance.

     Dirac did not talk with too many people, but he met Feynman in July of 1962 at the Jablonna Palace in Poland. By American physicists, he meant Feynman.

• Yet, it is gratifying for Feynman to acknowledge the limitation of quantum field theory and suggest a new approach to understanding bound states in Einstein's world. We can summarize Feynman's picture of the physics world with this table:

  

  Our unified understanding of scattering and bound states has been very brief in history. In the present form of quantum mechanics, there are running waves for scattering states and standing waves for bound states. The present form of quantum field theory takes care of running waves.

  For standing waves, Dirac made his life-long efforts to construct bound state wave functions in Einstein's world. We can integrate his efforts to construct harmonic oscillator wave functions for moving bound states.

• The oscillator wave function so constructed should have the same mathematical base as the present form of quantum field theory, if we wish to insist on the quantum system in Einstein's Lorentz-covariant world.
  1. It is well known that the present form of quantum field theory is a representation of the Poincaré group (inhomogeneous Lorentz group). The covariant harmonic oscillator formalism is also a representation of this group. On this issue, with my younger colleagues, I published my first paper in 1979.

  2. I repeated my discussion of this issue in later publications including a number of books on the Lorentz group. Click here for my list of publications.

• A more ambitious program would be to show that the present form of quantum mechanics and Einstein's Lorentz covariance are derivable from the same basket of equations. Here also Paul A. M. Dirac published a pioneering paper on this subject in 1963. I was indeed fortunate to have an audience with Dirac after he finished this paper in 1962. Click here to read about my meeting with Dirac.

Quantum Mechanics of Moving Bound States

Bohr and Einstein One hundred years ago, Bohr and Einstein met occasionally to discuss physics. Bohr was worrying about why the energy levels of the hydrogen atom are discrete, while Einstein was interested in how things look to moving observers. Did they ever discuss how the hydrogen atom looks to a moving observer? Bohr and Einstein, photo from the AIP Visual Archives. Bohr's worry became the present form of quantum mechanics where the hydrogen atom is a quantum bound state or a standing wave. Thus, the problem becomes that of a moving bound state in Einstein's world. This world of Einstein is called the Lorentz-covariant world. In this covariant world, moving objects appear differently according to Lorentz transformations. Click here for illustrations. Click here for my review article on moving bound states in the Lorentz-covariant world. The question then is how to construct Lorentz-covariant wave functions for bound states. The harmonic oscillator wave function serves as the standard tool for the bound state in quantum mechanics. Paul A. M. Dirac made his life-long efforts to construct Lorentz-covariant oscillator wave functions. We can mention the following four papers. P. A. M. Dirac, The Quantum Theory of the Emission and Absorption of Radiation, Proc. Roy. Soc. (London) A [114], 243 - 265 (1927). P. A. M. Dirac, Unitary Repercussions of the Lorentz Group, Proc. Roy. Soc. (London) A [A183], 284 - 295 (1945). P. A. M. Dirac, Forms of Relativistic Dynamics, Rev. Mod. Phys. [21] 392 - 399 (1949). P. A. M. Dirac, A Remarkable Representation of the 3 + 2 de Sitter Group, J. Math. Phys. [4], 901 - 909 (1963). In 1962, I had the privilege of spending time with Dirac to learn his physics directly from him. I was led to study his papers carefully. Dirac's papers are like poems and enjoyable to read. However, they do not contain figures or illustrations. Another problem is that Dirac never quoted his own papers published earlier on the same subject. Presumably, he thought he was presenting new ideas when he wrote those papers. We can thus translate his poems into cartoons and synthesize those cartoons. The net result is This ellipse (squeezed circle) can provide the resolution of the quark-parton puzzle and thus the Bohr-Einstein issue. Click here for a detailed story. For a published papers on this subject, go to Integration of Dirac’s Efforts to Construct a Lorentz-covariant Quantum Mechanics, with Marilyn E. Noz. Symmetry [12(8)], 1270 (2020), doi:10.3390/sym12081270, Physics of the Lorentz Group, Second Edition, with Sibel Baskal and Marilyn Noz, published by the IOP (British Institute of Physics). Quantum Mechanics of Moving Bound States, J. Modern Physics [13] 138-165 (2022). Poems are written in one-dimensional language. Cartoons constitute a two-dimensional language. Physics can be best explained in this two-dimensional language. Click here for the pioneer of this important language. Physics is an Experimental Science. Yes, it is OK for the description of relativity with a squeezed circle. The essential question is whether this elliptic squeeze can be seen the real world. While there are no observable hydrogen atoms moving with relativistic speeds (speed comparable with the light speed), modern accelerators started producing protons with relativistic speed, after 1950. The question is then what the proton has to do with bound states like the hydrogen atom. According to Gell-Mann (1954), the proton at rest is a bound state of three quarks, sharing the same quantum mechanics of bound states as the hydrogen atom. According to Feynman (1969), the proton moving with the velocity close to that of light appears as a collection of an infinite number partons. Are they talking about the same proton? This question is illustrated in this figure: Indeed, this elliptic squeeze of the proton shows the following observable effects in high-energy labs which produce protons moving with velocities very close that of light. Click here for detailed explanations. By providing the resolution of the quark-parton puzzle, we can settle the Bohr-Einstein issue of the moving hydrogen atom. In order to provide the answer, we had to construct bound-state wave functions that can be Lorentz-boosted. This problem has a long history in physics. It is possible to construct the harmonic oscillator wave functions that can be Lorentz-boosted. We can call them Covariant Harmonic Oscillators and construct the following table. Einstein's World Massive/Slow between Massless/Fast Energy Momentum E = p2/2m Einstein's E=(m2 + p2)1/2 E = p Hadrons, Bound States Gell-Mann's Quark Model Covariant Oscillators Feynman's Parton Picture In addition, the covariant harmonic oscillator can serve as a representation of the Poincaré group (inhomogeneous Lorentz group). Click here for the published paper on this subject. Quantum field theory is an effective theory (with Feynman diagrams) for quantum scattering processes in Einstein's Lorentz-covariant world. This theory is also a representation of the Poincaré group. It is thus possible to combine the oscillator formalism and quantum field theory into the Poincaré (inhomogeneous Lorentz group) as specified in the following table. The last row in the above table asks whether Einstein's Lorentz covariance can be derived from Heisenberg's starting equations for quantum mechanics. This is indeed a crazy question, and Einstein will turn over in his grave. Einstein did not like Heisenberg, who attempted to develop nuclear bombs for Hitler before 1945. Dirac's bust at the Fine Hall Library of Princeton University (2000). The Fine Hall Library was my study place when I was in Princeton (1958-62) as a graduate student and a postdoc. Let us go to Dirac's 1963 paper on the two-oscillator system. He constructed a Lie algebra (closed set of commutation relations for the generators of the group) for the Lorentz group applicable to three space-like dimensions and two time-like dimensions. This group is known as the O(3,2) deSitter group. I heard about this paper directly from Dirac when I met him in 1962. The remarkable fact is that this set was constructed solely from Heisenberg's brackets for his uncertainty relations. How is it possible to derive a set of equations for Einstein's relativity from those for quantum mechanics? The remaining question is to transform the second time variable of the O(3,2) system into a useful variable in the Minkowskian system of three space coordinates and one time. Indeed, it is possible through the group contraction technique. I published a number of papers on this issue. Poincaré Symmetry from Heisenberg's Uncertainty Relations, with S. Baskal and M. E. Noz, Symmetry [11(3)], 236 - 267 (2019), doi:10.3390/sym11030409, Einstein's E = mc2 derivable from Heisenberg's Uncertainty Relations, with Sibel Baskal and Marilyn Noz, Quantum Reports [1(2)], 236 - 251 (2019), doi:10.3390/quantum1020021, Physics of the Lorentz Group, Second Edition, with Sibel Baskal and Marilyn Noz, to be published by the IOP (British Institute of Physics). Two more fundamental issues A massive particle at rest has three rotational degrees of freedom. However, a massless particle has only one degree of freedom, namely around the direction of its momentum. What happens to rotations around the two transverse directions when the particle is Lorentz-boosted? You also have been wondering why massless neutrinos are polarized, while massless photons are not. The answers to these questions are in the bottom row of this table: Einstein's World Massive/Slow between Massless/Fast Energy Momentum E = p2/2m Einstein's E=(m2 + p2)1/2 E =p Hadrons, Bound States Gell-Mann's Quark Model Covariant Oscillators Feynman's Parton Picture Helicity Spin,Gauge S3 S1 S2 Wigner's Little Group Helicity Gauge Trans. Click on the colored items for further explanations. If you are interested in symmetry problems, you should be aware that Wigner's 1939 paper deals with the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. Thus, these subgroups dictate the internal space-time symmetry of the particle. It is generally agreed that Wigner deserved a Nobel prize for this paper alone, but he did not. He got the prize for other issues. Click here for my explanation of where the confusion was. Wigner liked my story. This is the reason why he had photos with me, and I am regarded as Wigner's youngest student, even though my thesis advisor at Princeton was Sam Treiman. I did enough work for Wigner to deserve this genealogy: The scientific content of this table is I was then able to expand my scope of research. Lorentz Group in Other Branches of Physics The Lorentz group is the mathematical language for Einstein's special relativity. Two-by-two matrices are everywhere in physics, and they are representations of the Lorentz group. Thus, the mathematical language from this group serve useful services in other branches of physics. Modern optics is a case in point. With my younger colleagues, I published a book on this subject. If you like modern optics, including coherent and squeezed states, beam transfer matrices, polarization optics, as well as periodic systems, click here. If you are interested in entanglement problems, particularly Gaussian entanglements, click here. If you are interested in entropy problems and Feynman's rest of the universe, click here, and here. Poincaré and Einstein? click here, and here. Poincaré sphere for polarization optics and the Poincaré symmetry for Einstein's relativity. Click here. I am now working the Lorentz group in condensed matter physics.