Monday, January 21, 2013


Although amber (electrostatics) and lodestone (magnetism) were known to the ancient Greeks, electrodynamics developed as a quantitative subject in less than a hundred years. Cavendish's remarkable experiments in electrostatics were done from 1771 to 1773. Coulomb's monumental researches began to be published in 1785. This marked the beginning of scientific research in electricity and magnetism on a worldwide scale.

Our own Benjamin Franklin contributed to the understanding of electricity during these years. Fifty years later Faraday was studying the effects of time-varying currents and magnetic fields. By 1864 Maxwell had published his famous paper on a dynamic theory of the electromagnetic field. Twenty-four years later (1888) Hertz published his discovery of transverse electromagnetic waves, which propagated at the same speed as light, and placed Maxwell's theory on a firm experimental footing. 

Find more in A Treatise on Light (and Color)

That takes us up to Quantum Electrodynamics (QED) that was developed in the latter half of the twentieth century.

Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interacts and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. 

One of the founding fathers of QED, Richard Feynman, has called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron, and the Lamb shift of the energy levels of hydrogen. (The Lamb shift, named after Willis Lamb, is a small difference in energy between two energy levels in electrons around an atom.)

In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Mysterious things happen in the space and time within the limits of Heisenberg's Uncertainty Principle. Complex violations of well known limits can occur and energy and matter can appear out of nothing, as long as it is gone again within the time and space constraints given by Heisenberg. Sort of like Cinderella at midnight … the coach returns to a pumpkin.

The first formulation of a quantum theory describing radiation and matter interaction came from British scientist Paul Dirac, who (during the 1920s) was first able to compute the coefficient of spontaneous emission of an atom. Dirac described the quantization of the electromagnetic field as an ensemble of harmonic oscillators with the introduction of the concept of creation and annihilation operators of particles. 

In the following years, with contributions from Wolfgang Pauli, Eugene Wigner, Pascual Jordan, and Werner Heisenberg and an elegant formulation of quantum electrodynamics due to Enrico Fermi, physicists came to believe that, in principle, it would be possible to perform any computation for any physical process involving photons and charged particles. However, further studies by Felix Bloch with Arnold Nordsieck and Victor Weisskopf in 1937 and 1939, revealed that such computations were reliable only at a first order of perturbation theory, a problem already pointed out by Feynman’s boss at Los Alamos, Robert Oppenheimer. 

At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself. With no solution for this problem known at the time, it appeared that a fundamental incompatibility existed between special relativity and quantum mechanics. 

(These problems with “infinities” continue to crop up in much of quantum physics and have resulted in many solutions and methods that have some doubt as to their correctness. Usually an attempt to "cancel out" the infinities is performed, although the correctness of treating infinities in this manner has not been established. Feynman developed a brilliant solution that not only eliminated the problems with infinity “blow ups,” but also yielded the most accurate results of any known physical theory.)

Near the end of his life, Richard Feynman gave a series of lectures on QED intended for the lay public. These lectures were transcribed and published as Feynman (1985), “QED: The Strange Theory of Light and Matter,” a classic non-mathematical exposition of QED from the point of view articulated below.

The key components of Feynman's presentation of QED are three basic actions.

  • A photon goes from one place and time to another place and time.
  • An electron goes from one place and time to another place and time.
  • An electron emits or absorbs a photon at a certain place and time.
These actions are represented in a form of visual shorthand by the three basic elements of Feynman diagrams: a wavy line for the photon, a straight line for the electron and a junction of two straight lines and a wavy one for a vertex representing emission or absorption of a photon by an electron. Such a diagram is shown at the top of this article. As the diagram suggests, these interactions do follow the classical physical laws in the same manner as the balls on a pool table. Newton would be proud.

Mathematically, QED is an Abelian gauge theory with the symmetry group U. The gauge field, which mediates the interaction between the charged spin-1/2 fields, is the electromagnetic field. Using the Lagrangian method to describe the interaction was a brilliant solution. In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations. The Lagrangian of a dynamic system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was introduced in a reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, known as Lagrangian mechanics.

Here we see a powerful method from classical (non-quantum) physics being used to clarify the complex details of quantum physics. This goes a long way toward resolving issues between these areas of physics, issues that even bothered the great Albert Einstein.

Richard Phillips Feynman (May 11, 1918 – February 15, 1988) was an American theoretical physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics. (He proposed the parton model -- a quantum model that included certain aspects of general relativity). For his contributions to the development of quantum electrodynamics, Feynman, jointly with Julian Schwinger and Sin-Itiro Tomaonaga, received the Nobel Prize in Physics in 1965. 

He invented a widely used pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. (Again, see the figure at the beginning of this article for an example. Time is the Y axis and space is the X axis. Much more complicated diagrams were developed by Feynman to visualize many quantum interactions.) 

During his lifetime, Feynman became one of the best-known scientists in the world. In a 1999 poll of 130 leading physicists worldwide by the British journal Physics World he was ranked as one of the ten greatest physicists of all time.

Fresh out of college, he assisted in the development of the atomic bomb. One of his last contributions was as a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his work in theoretical physics, Feynman has been credited with pioneering the field of quantum computing, and introducing the concept of nanotechnology. He held the Richard Chace Tolman professorship in theoretical physics at the California Institute of Technology.

Feynman was a keen popularizer of physics through both books and lectures, notably a 1959 talk on top-down nanotechnology called, “There’s Plenty of Room at the Bottom,” and the three volume publication of his undergraduate lectures, “The Feynman Lectures on Physics.” Feynman also became known through his semi-autobiographical books, “Surely You’re Joking, Mr. Feynman!” and “What Do You Care What Other People Think?” and books written about him, such as “Tuva or Bust!”

I’ve always considered Richard Feynman as my special mentor. I’ve read every one of his books and studied his lectures. His light-hearted focus on what was really going on in physics and complete absence of pretense, even though he was one of the smartest physicists since Albert Einstein, made him a very special man and something of a hero to me.

Plus, he wasn’t a bad bongo drummer. I’ll have to write about that later. Heck, I even have a collection of Tuva throat music CDs. Although I am now studying at a university in California, it is Stanford, not Cal Tech. There are plenty of people at Stanford who knew Feynman personally. I look forward to meeting them and discussing the brilliant scientist. It is one of the reasons that I am attending Stanford.

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