Sachi Sri Kantha - Professor Christie Jeyaratnam Eliezer

Selected Writings by Sachi Sri Kantha

Professor Christie Jeyaratnam Eliezer

March 2001

Professor Eliezer, the pride of Eelam, excelled in numbers. Thus it is apt to cite what the chapter named 'Numbers' in the Holy Bible says:

"And Eleazar the son of Aaron the priest was to be chief over the leaders of the Levites, and to have oversight of those who had charge of the sanctuary." [Old Testament, Numbers - 3:32]

Like what is said in the holy book, our Eliezer of Eelam, born on June 12, 1918 at Navatkuli, Jaffna, also became the chief of the Tamil diaspora at a critical period. Here is another passage.

"After the plague the LORD said to Moses and to Eleazar the son of Aaron, the priest, 'Take a census of all the congregtion of the people of Israel, from twenty years old and upward, by their fathers' houses, all in Israel who are able to go forth to war." [Old Testament, Numbers - 26: 1-2]

Like what the holy book says, our Eliezer, the son of Jacob Richard Eliezer and Elizabeth Ponnamah, also took a census of all the congregation of Tamil diaspora and polished them for the pre-eminent campaign of their lives.

While Eelam Tamils bid farewell to Professor Eliezer's mortal remains today, his accomplishments in the academic arena and human rights activism will continue to glitter for a long time to come. In the 21st century and hence, excellence and elegance among Tamil intellectuals and scientists will be measured by the now established 'Eliezer yardstick'. How one stands up in comparison with Eliezer? - this will be the ultimate measure of achievement for any Tamil kid growing up in this newly-minted century.

Professor Eliezer's mentor in Cambridge University was Paul Adrien Maurice Dirac (1902-1984), one of the giants of 20th century physics. Dirac established his reputation among his illustrious contemporaries such as Einstein, Bohr, Raman, Rutherford, Curies and Pauling by being awarded the Nobel prize in physics at the age of 31 for the discovery of new productive forms of atomic theory.

Dirac was also renowned as an unpretentious gem of a man with minimal words. There is a humorous anecdote about an American journalist who visited Dirac and found out that his initial words of greetings 'Come in' was the longest sentence Dirac uttered in the entire interview. Precision of thoughts and words was Paul Dirac's forte, and presumably Professor Eliezer also absorbed this talent under Dirac's tutelage.

An example of this is evident in the transcript of the now-infamous SBS Television (October 4, 2000) program shown in Australia. Excerpts follow:

"Reporter: Are you an agent for the LTTE?
Prof. C.J.Eliezer: Certainly not.
Reporter: How would you describe, then, your relationship with the LTTE?
Prof.C.J.Eliezer: As an admirer, as an emotional admirer of the LTTE.
Reporter: A sympathizer?
Prof.C.J.Eliezer: Sympathiser, yes.
Reporter: Somebody who gives the LTTE advice?
Prof.C.J.Eliezer: I have not given them any advice.
Reporter: Somebody who provides the LTTE with support when asked?
Prof.C.J.Eliezer: Well, they haven't asked me for anything, but irrespective of that, they'll find my pronouncements at meetings and things, they'll find them useful.
Reporter: Useful in terms of furthering their cause?
Prof.C.J.Eliezer: Yes, because they're all committed to the idea of liberation, and as they are, I am, and we do it in different ways."

In this exchange of opinion, I found Dirac's influence on Prof. Eliezer: just stating specifically and precisely where he stood in his relationship with LTTE. To savor, I provide Prof. Eliezer's reminiscences of his Cambridge days in 1940s, about how he came to write his first scientific paper. This first appeared in the book, Tributes to Paul Dirac, edited by J.G.Taylor [Adam Hilger, Bristol, 1987, pp.58-60].

Excerpts are given below.

"My supervision by Professor Dirac

It was by a chance circumstance that Professor Dirac agreed to supervise me for the PhD. He usually did not take on students. In June 1941, after completing Part III of the Tripos, I was intending to stay on for research, and Dr.A.H.Wilson had agreed to supervise me. During that long vacation, however Dr.Wilson was called away on war work. In early October I had a letter from Professor Dirac, in his very neat handwriting, which went something like this: 'As I am appointed your supervisor, come up and see me sometime. I lecture Tuesdays, Thursday, Saturdays at 10, and the best time to catch me is after a lecture.'

I saw him at the earliest opportunity, and showed him some papers I had been reading about mesons, which were new particles then. Dirac looked at them carefully and said: 'These are interesting particles - our theories for all particles have some serious difficulties when we consider how they interact with each other. It is better to try to solve the difficulty for the simplest of all particles - the electron - before dealing with some complicated ones'. He said he had recently completed a theory of radiating electrons. He gave me a thick reprint and suggested that if I read it and found it of interest, we could then think of a specific problem.

My first paper

After months of my preliminary reading, Dirac suggested that I look into the hydrogen atom problem, with radiation taken into account. From the family of mathematical solutions, one had to select a physically acceptable solution.

I first tried the three-dimensional case, then the two-dimensional and finally the straight line case where an electron is projected towards a stationary proton. I had expected (and so had Dirac) that one would get different solutions with the electron hitting the proton in different ways.....

Methods of solving non-linear differential equations were not well known in those days. I was foolish enough to think that an exact solution could exist, but I could not find one. I wrote off to Miss.M.L.Cartwright and Professor J.E.Littlewood for advice. Both of them very kindly helped. It turned out that the electron got stopped before it could reach the proton.

I told this to Dirac, and he seemed surprised. Then he asked the obvious question which foolishly I had not asked myself. What does the electron do after it gets stopped? At the spur of the moment, I said: 'The electron would start moving outwards, then come to a halt, and move back towards the proton and get stopped, probably closer to the proton, and continue this oscillating motion till it falls into the proton'. Dirac's face lit up with pleasure. That is a very beautiful solution, he said.

I left the room in high spirits. But my elation was short lived. When I worked out the equation, I found that the electron, after its first stop, would move away from the proton in a run-away type solution. At the earliest opportunity, I met Dirac again and told him. He said he too had worked it out and come to the same conclusion. Write up what you have in a paper, he said. That paper was published in the Proceedings of the Cambridge Philosophical Society (1943".

When Prof. Eliezer published this paper, he was 25. Until last year, even after reaching 80, he continued to publish research papers in physics and mathematics solely or in collaboration with other colleagues. For record, here is a select list of Prof. Eliezer's technical papers which had appeared in the international journals. For journal papers, annotations are in the order of year, volume number and page numbers.

A Personal Note

On a personal note, I like to add that I have been unlucky in not meeting Prof. Eliezer in person. But his was the first name of scientist I heard when I was 10 and learning the first steps in science. My father, who is 5 years younger than Prof. Eliezer [and a junior contemporary to him at Hartley College, Point Pedro] used to talk about him quite often at home, to inspire me.

During my Colombo University days in the 1970s, one of Prof. Eliezer's nephews, Dr. Kumar Eliezer (who was senior to me by five years) became a friend of mine, when we jointly traversed the Eelam zone of the island in a van to conduct science quiz contests in Tamil for the Sri Lankan Association for the Advancement of Science between 1978 and 1980.

My link to immediate Eliezer household was through gracious Mrs. Ranee Eliezer, with whom I have exchanged annual New Year-Easter greeting letters during the past 10 years. When I read in her last year's letter where she had quipped humorously and cryptically, "We have become doctor's pets", I had a premonition that the illustrious life of Prof. Eliezer is nearing its end. It did end on March 10, 2001. What a wonderful life it has been, spanning three generations and influencing minds in Ceylon, Britain, Malaysia and lastly Australia.

Prof. Eliezer's scientific publications (select list)

1. The hydrogen atom and the classical theory of radiation. Proceedings of Cambridge Philosophical Society, 1943; 39: 173-180.

2. On the classical theory of radiating electrons. Proceedings of Cambridge Philosophical Society, 1945; 41: 184-186 (with A.W.Mailvaganam)

3. A discussion on the exactness of the Lorentz-Dirac classical equations. Bulletin of Calcutta Mathematical Society, 1945; 37: 125-130.

4. On Dirac's theory of quantum electrodynamics: the interaction of an electron and radiation field. Proceedings of Royal Society London, 1946; A187: 197-210.

5. The application of quantum electrodynamics to multiple processes. Proceedings of Royal Society London, 1946; 187: 210-219.

6. Radiating electron in a magnetic field. Proceedings of Cambridge Philosophical Society, 1946; 42: 40-44.

7. The classical equations of motion of an electron. Proceedings of Cambridge Philosophical Society, 1946; 42: 278-286.

8. The hydrogen atom in a generalized classical electrodynamics. Physical Review, 1947; 71(2): 49-53.

9. Quantum electrodynamics and the interaction of the hydrogen-like atoms with a radiation field. Bulletin of Calcutta Mathematical Society, 1946; 38: 145-160.

10. The interaction of electrons and an electromagnetic field. Reviews of Modern Physics, 1947; 19: 147-184.

11. Quantum electrodynamics and low energy photons. Proceedings of Royal Society London, 1947; A191: 133-136.

12. Relativistic wave equations. Nature, 1947; 159: 60.

13. On the classical theory of particles. Proceedings of Royal Society London, 1948; A194: 543-555.

14. Generalizations of the A.M. and G.M. inequality. Mathematical Magazine, 1967; 40: 247-250 (with D.E.Daykin)

15. Generalizations and applications of Cauchy-Schwarz inequalities. Quarterly Journal of Mathematics, Oxford Series, 1967; 18(2): 357-360 (with D.E.Daykin)

16. On some convex functions and related inequalities. Symposia on Theoretical Physics and Mathematics, vol.8 (Symposium, Madras, 1967), Plenum Press, New York, 1968, pp.129-132.

17. Generalization of Holder's and Minkowski's inequalities. Proceedings of Cambridge Philosophical Society, 1968; 64: 1023-1027 (with D.E.Daykin)

18. Elementary inequalities for integrals. Mathematical Magazine, 1972; 45: 89-91.

19. Generalizations of the Cauchy-Schwarz and Holder inequalities. Inequalities, III (Proceedings of Third Symposium, University of California, Los Angeles, 1969; dedicated to the memory of Theodore S.Motzkin), Academy Press, New York, 1972, pp.97-101 (with B.Mond)

20. A note on time-dependent harmonic-oscillator. Siam Journal of Applied Mathematics, 1976; 30(3): 464-468 (with A.Gray)

21. Equivalence principle and quantum mechanics - note. American Journal of Physics, 1977; 45(12): 1218-1221 (with P.G.Leach)

22. Symmetries and first integrals of some differential equations of dynamics. Hadronic Journal, 1979; 2(5): 1067-1109.

23. The Lie and Lie-admissible symmetries of dynamical systems. Hadronic Journal, 1979/80; 3(1): 390-439 (with G.E.Prince, P.G.L.Leach, T.M.Kalotas and R.M.Santilli)

24. Symmetries of the time-independent N-dimensional oscillator. Journal of Physics, A 1980; 13(3): 815-823 (with G.E.Prince)

25. On the Lie symmetries of the classical Kepler problem. Journal of Physics, A 1981; 14(3): 587-596 (with G.E.Prince)

26. The equivalence principle and quantum mechanics. In: Proceedings of the Conference on Particle Interactions and Astrophysics, Mysore 1981 Feb.4-8, edited by T.S.Santhanam, R.Parthasarathy, Math Science Report 108, Institute of Mathematical Sciences, Madras, 1982, pp.22-27.

27. Introduction to selected topics of Lie symmetries. Math Science Report 109, Institute of Mathematical Sciences, Madras, 1982, 78 pp. [a set of lecture notes]

28. Some reminiscences of Prof.P.A.M.Dirac. In: Tributes to Paul Dirac, Memorial Meeting held at the Cambridge University, 1985 April 19; edited by J.G.Taylor, Hilger, Bristol, 1987, pp.58-60.

29. On pursuit curves. Journal of Australian Mathematical Society, B 2000; 41: 358-371 (with J.C.Barton).