On Paul Dirac’s Theory of Electrons and Positrons | Quantum Science Philippines
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On Paul Dirac’s Theory of Electrons and Positrons

Hananish Joy G. Odarve

Paul Adrien Maurice Dirac was born on 8th August, 1902, at Bristol, England. He was educated at the Merchant Venturer’s Secondary School, Bristol, and then went on to Bristol University where he studied and obtained B.Sc. in Electrical Engineering degree. He also studied mathematics for two years at Bristol University, later going on to St. John’s College, Cambridge, as a research student in mathematics. He received his Ph.D. degree in 1926. He became a Fellow of St. John’s College and also held the position Lucasian Professor of Mathematics at Cambridge. Dirac was given The Nobel Prize in Physics 1933 together with Erwin Schrödinger for their discovery of new productive forms of atomic theory. He then gave a lecture regarding matter and antimatter specifically on electrons and protons on the Nobel Lecture he delivered on December 12, 1933.

In his lecture, Dirac emphasizes that the procedure he came up with is successful in the case of electrons and positrons and that he hoped that in the future some such procedure will be found for the case of the other particles. He considered the electron and positron because in their case, the theory has been developed further. He outline the method for electrons and positrons, showing how one can deduce the spin properties of the electron, and then how one can infer the existence of positrons with similar spin properties and with the possibility of being annihilated in collisions with electrons.

The general quantum mechanics at Dirac’s time describe the motion of any kind of particle, no matter what their properties are. However, it is only valid when the particles have small velocities and fail when the effect of relativity comes in. Basically, Dirac started with an equation connecting the kinetic energy [eq]W[/eq] and momentum [eq]p_r[/eq] and let this act on a wave function [eq]\Psi[/eq] since we can view [eq]W[/eq] and [eq]p_r[/eq] as operators. The equation is not linear in the kinetic energy and momentum. Now, according to the general requirement of quantum mechanics, the wave equation should be linear in the operator [eq]W[/eq] and in order that the equation may have relativistic invariance, it must also be linear in [eq]p_r[/eq]. Thus, new variables where introduced which give rise to the spin of the electron and give rise to some rather unexpected phenomena concerning the motion of the electron. In practice, the kinetic energy of a particle is always positive however the equation allows two kinds of motion. Only one motion is familiar. The other corresponds to electrons with a very peculiar motion. The faster they move, the less energy they have, and one must put energy into them to bring them to rest called the positron which corresponds to the motion of an electron with a positive charge instead of the usual negative one. We can then look at the process of annihilation where an ordinary electron, with positive energy, drops into a hole, fill up this hole and electromagnetic radiation is liberated. On the other hand, creation of an electron and a positron from electromagnetic radiation should also be observed.

Also, he added that if we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we can also get negative protons. However, the process will be more rigorous since protons are more complicated and the theory would require reliable basis which was not yet discovered at that time.

One Response to “On Paul Dirac’s Theory of Electrons and Positrons”

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