Dirac and his equation
In Theoretical Physics, Paul Adrien Maurice Dirac is comparable to Isaac Newton and Albert Einstein. He discovered his famous equation that combined the two revolutions that shook the twentieth century world of Physics, namely quantum mechanics and relativity.
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Birth and early years
Paul Dirac's father, Charles Dirac had immigrated from Switzerland to England at a young age. In 1896, he became the Head of the Department of Languages in a school at Bristol. He married Florence Holden. Paul was born in 1902. He had a brother one year older and a sister four years younger.
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Education was arranged at home itself. Dirac's father had ordered that everybody must speak only in French. Mother will speak in English only. Paul did not know French well. So nobody spoke at home! Later Paul has written that his childhood was not happy.
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In the Dirac family, they did not take meals together. Paul and his father used to take food in one room while others ate in another room. Dirac said: "Nobody liked another. Only in story books people loved each other." This family environment might be the cause for Paul Dirac's strange social habits in later life.
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Dirac joined in the same school where his father taught. He was academically far superior to other students. His Physics teacher sent him to the library
with the names of a few books. He completed his college education also in Bristol and in his 16th age, got the engineering degree.
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Higher education
In the beginning, Paul followed the footsteps of his brother and studied engineering. But his mind was in mathematics and physics. So there too, he went to the library and completed reading his favourite books. After two years of study, he liked Einstein's Theory of Relativity more than electrical engineering.
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Dirac wanted to go to Cambridge University and pursue research in mathematics or physics. Although he got a scholarship for that, the economic situation of
his family did not allow that. Fortunately, his teacher Ronald Hasle arranged for his free mathematics education in Bristol University. Two years were spent
on that. For Dirac, mathematics lessons were not that hard. So he learnt physics also simultaneously. He was attracted by Quantum Theory.
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After that, with the help of Hasle, Dirac joined Cambridge and learnt Relativity under the supervision of Ralph Fowler. In 1923, he left Bristol and moved to the
majestic St John's College.
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He did not have the habit of talking with anybody. Once somebody near him asked him "It seems to be raining. Is it not?". This was done just for conversation. But Dirac went out and looked. Returning he said: "It is not raining now."
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Just as in Bristol, in Cambridge too, Dirac did not move around with anybody. When others were drinking beer in the pub, he spent his time in the library. On sunday mornings he used to walk in the rural areas and return on monday with renewed enthusiasm.
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Quantum Mechanics
Many ideas were born in his brain. He learnt Niels Bohr's quantum model of the atom. Although his mind was thinking along the mathematical routes, he heard many physics lectures in the Cavendish Laboratory. At that time Rutherford was the Director of Cavendish laboratory. It is here that he met two of his very few friends, Patrick Blacket and Peter Kapitza.
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He wrote many good research papers. For some time he went into mental depression because of his brother's suicide. Nevertheless, he continued his work. He got the Exhibition Scholarship for three years. His interest in Quantum Mechanics continued to increase. Fowler encouraged him. Dirac listened to the lectures of Bohr and Werner Heisenberg. When Heisenberg's paper came for refereeing to Fowler, he gave that to Dirac for his opinion.
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Heisenberg's paper was on Matrix Mechanics. Heisenberg removed concepts like the electron's orbit in the atom and created his theory only using the observable
properties of the atom such as the frequencies of spectral lines emitted by the atom. In this new theory, the position of the electron and its momentum were specified as matrices. A matrix is formed by numbers written in the form of arrays of rows and columns. An important property of matrices is that the product of two matrices A x B will be different from B x A. The dynamics of the electron cannot be visualized in the mind; only matrix mathematics can describe it.
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Dirac was attracted by this matrix mathematics, in particular, by the fact that A X B is different from B x A. Dirac found an important connection between quantum mechanics and classical mechanics. He discovered that the difference between A x B and B x A in quantum mechanics is intimately related to the Poisson Bracket of the two dynamical quantities A and B in classical mechanics.
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There is an interesting story about this discovery of Dirac. He discovered this during one of his walks during the weekend. But he wanted to check his memory of the formula for Poisson Bracket. Since the Library will open only on Monday, he experienced quite a bit of anxiety until he could check the formula.
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In a few months after Heisenberg discovered Matrix Mechanics, Erwin Schrodinger discovered Wave Mechanics. Matrix Mechanics was in the form of mathematics that was hard for most physicists to understand. Wave Mechanics was about waves familiar to physicists and so it was easy for them to understand.
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But Matrix Mechanics and Wave Mechanics described the behaviour of the same electrons. How can both be correct? Schrodinger himself showed how they are both connected, but Dirac gave the more general answer. He showed that Matrix Mechanics and Wave Mechanics are just two avatars of quantum mechanics and there are many avatars. Not only that, he discovered the basic principle underlying Quantum Mechanics and showed that this basic idea can be expressed in many forms or representations.
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Dirac brought out all his discoveries in the form of a book which is regarded as the Bible of Quantum Mechanics. He wrote this in his characteristic style, without a single unnecessary word or sentence. He stated emphatically that no mental picture will help to understand Quantum Mechanics.
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Let us next come to Dirac's most important discovery.
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Dirac Equation
In 1928, Dirac discovered the relativistic quantum mechanical equation for the electron. This is an important discovery, for it succeeded in combining the two great revolutions in Physics, Relativity and Quantum Mechanics.
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Through this equation, the existence of positron as the antiparticle of the electron was revealed. After that, it became clear that the existence of antiparticle for every particle is an important law of relativistic quantum mechanics.
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Dirac discovered truths about the physical world from Mathematics. Before him Mathematics was used as the language to express the Laws of Physics. Dirac brought out the Laws of Physics from Mathematics.
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He said "I used to play with mathematical equations." From such play was born the equation that combined relativity and quantum mechanics. It is Dirac equation that controls the dynamics of the electron. Apart from the prediction of the positron, Dirac equation showed that electron has an intrinsic spin. Electron spin was empirically discovered earlier from atomic spectroscopy.
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About his equation, Dirac said that this equation is the basis for all chemistry and almost all physics. This is a little exaggerated statement. But as far as chemistry is concerned it is a completely correct statement. For, chemistry is about atoms and molecules. Electrons control the behaviour of atoms and molecules and Dirac equation controls electrons.
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Although Dirac equation required the existence of the antiparticle to the electron, such a particle had not been discovered until then. So Heisenberg and Pauli were prepared to throw Dirac equation into the sea!
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But, finally, Nature came to the rescue of Dirac. Carl Anderson of CATECH in USA discovered the track of the positron in Cosmic Ray research.
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Dirac Monopole
A few years before Anderson experimentally discovered the positron were a testing time for Dirac. He was prepared to reject his equation as wrong.
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Instead, he created a new concept. It was about magnetic monopole. The paper which he published on this is a wonderful essay. At the beginning of this essay, he describes his deep notions about Mathematics. He says that in future, new concepts in Physics will be born from Mathematics.
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What he discovered about monopole also is beautiful. He showed that if the monopole has to be consistent with quantum mechanics, the magnetic charge of the monopole and the electric charge of particles like the electron must be related by a condition. This is called Dirac's quantum
condition.
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Quantum Field Theory
Dirac equation led to the relativistic quantum mechanics of the electron interacting with the electromagnetic field. This evolved into Quantum Electrodynamics (QED). But that is a big story.
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QED also is a creation of Dirac. Although Heisenberg and Schrodinger had created the quantum mechanics of particles, electromagnetic field still remained classical. Planck and Einstein had brought the photon, but Dirac showed in 1927 how photon changes the electromagnetic field. This was QED. In 1947-1950, Feynman, Schwinger, Tomonoga and Dyson brought QED to its final complete form. After another 20 years, in 1967-1973, QED was enlarged into Standard
Model that became the theory of electromagnetic, weak and strong interactions.
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Thus Dirac's 1927 discovery became the basis of quantum Field Theory which describes all the Forces of Nature except gravitational force.
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Other discoveries
We said Heisenberg and Schrodinger created two forms of Quantum Mechanics. Dirac created the seed for a third form. Later, Feynman developed this into the full theory. If we throw an object or particle, in classical mechanics, it travels in a specific trajectory. In the third form of quantum mechanics, it travels in all trajectories.
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Satyendranath Bose discovered quantum statistics of photons while trying to derive Planck's frequency distribution of black body radiation by treating photons as a collection of particles. Einstein generalized this. This is called Bose-Einstein Statistics. Electrons follow another form of statistics that was discovered by Enrico Fermi and generalized by Dirac. This is called Fermi-Dirac Statistics.
All particles with integral spin number 0,1,2... are called Bosons and all particles with half-integral spin numbers 1/2,3/2... are called Fermions. Photon with spin 1 is a boson while electron with spin 1/2 is a fermion.
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From 1932 to 1969, Dirac was the Lucasian Professor of Mathematics at Cambridge. In 1933, Dirac and Schrodinger got the Nobel Prize, In 1937, Dirac married Margit,the sister of Eugene Wigner who is a famous physicist. Dirac used to introduce her as Wigner's sister.
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Dirac visited India accepting the invitation of Homi Bhabha. He stayed in Bombay for many months and gave a series of lectures on Quantum Mechanics in Tata Institute of Fundamental This came out as a book.
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An interesting episode during his lecture: Somebody in the audience said that he did not understand something that Dirac had mentioned. Dirac simply continued his lecture. The other person asked why he did not answer his question, to which Dirac replied that was not a question, but a comment!
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In 1971, Dirac joined Florida State University in USA and passed away in 1984 when he was 82.
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Later, a memorial stone with his name and his equation inscribed was installed in Westminster Abbey where Isaac newton was buried.