Physics - The Power Of Mathematics : A Persuasive View

Chabungbam Amuba Singh *

A popular joke among physicists goes like this : In a Chicago meat shop, a customer was shown an array of brain-packs with price tags which ran somewhat like this-- Physicist-$ 10, Mathematician-.........., Educationist-$100, Politician-$100. The customer who was a budding politician was elated. But intrigued, he asked why the Physicist's brain is so much cheaper than the Politician's. The shop keeper replied, "The brain stuff is so rare in a politician, that's why". The customer took some time to understand. (Personally, I now understand my 'promotion' from 'Physicist' to 'Educationist'!). Remember, way back in 1937, Albert Einstein politely declined the offer of the Vice -Chancellorship of the University of Travancore (later renamed as Kerala University) at a princely salary of Rs.6,000/- per month (The Telegraph, Kolkata, 3 January 2012).

Why do physicists rate themselves so high? Because they can drain up any amount of public money for their purpose! [For example, US $ 4.5 billion for the LHC (Large Hadron Collider) at CERN, Geneva.] But ponder over the following questions:- where mankind would have been today had not
(i) Newton found the answer to his own question why the apple falls;
(ii) Newton formulated his laws of motion analytically by developing his version of infinitesimal calculus;
(iii) Einstein discovered his mass energy equivalence formula,
(iv) Maxwell discovered his equations of electrodynamics;
(v) Dirac discovered his equation and found the negative energy solutions; so on and so forth.
I have taken the names of a few giants whose laboratories in their heads did not require a penny of the public money to function.

For what purpose have the scientists constructed the LHC, a huge underground structure, at a huge cost where some 2000 odd physicists from around the world would work ? Well, they are looking for the 'God' particle, a name for the Higgs boson coined by the media after Leon Lederman, a Nobel laureate, once dubbed it the 'goddamn' particle because it proved so hard to find even as the Standard Model needs its existence so crucially.

Higgs boson is a mathematical construct introduced by the British physicist Peter Higgs in 1964 to explain the intrigue of the electroweak symmetry breaking, that is, the breaking of the symmetry between the electromagnetic force and the weak nuclear force. This was an important ingredient in the formulation of the Standard Model by Steven Weinberg, Abdus Salam, Sheldon Glashow and others.

Those days (or years!), the High Energy physicists were so much preoccupied with the Standard Model - shaping up and testing - that it took some time for them to realise that it is through interactions with the all pervasive Higgs field that the fundamental particles acquire mass. And lo! they have the answer to the fundamental question - Where do the mass come from?

Discovery of the Higgs boson will also provide a clue to the resolution of the mystery of the 'dark matter' in the universe which has puzzled the physicists/astronomers since they observed that the galaxies are rotating too fast for their gravity to keep them intact. They had postulated the existence of dark matter which would provide the necessary gravity but which would not be 'visible' to the distant observers on the earth.

Historically, it was the American astronomer Fritz Zwicky in 1934 who postulated the existence of dark matter to remedy the apparent violation of the virial theorem in the rotation of the galaxies. The presence of dark matter is also essential, it seems, for proper accounting of the observed gravitational lensing effect of the galaxies. Presently, it is estimated that 83 p.c. of all the matter in the universe is dark matter; that leaves only 17 p.c. for the ordinary matter.

The bottom line of this small narrative here is that nature, more often than not, speaks to the physicist through the language of mathematics. We can augment this line of view by plugging in Richard Feynman--a Nobel laureate of Feynman diagram fame--who developed the path integral formulation of Quantum Mechanics, pioneered the field of Quantum Computing and introduced the concept of nano-technology 52 years ago.

Pursuing Physics through its natural language of Mathematics is always profitable, because it only requires investment of the mind at little cost to the public ex-chequer. Coupled with the high dividend it yields, we have a high-dividend low-cost system for pursuit of knowledge. It deserves warm encouragement at the Indian Universities.

The advent of the electronic computer and digital technology has added another dimension to the physicists' exploration of nature through the language of mathematics--nature unravelling its secrets of the dynamics of complex systems. Complex systems are not confined to the arena of physics. In fact, the trendsetting bench-mark in the development of this field is the Lorenz's butterfly, a mapping computer-generated by Edward Lorenz in 1961 while working for weather prediction. This pioneering piece of work has led to the development of the Chaos Theory as a tool for the study of the dynamics of complex systems.

Complex systems offer a challenging field of research. However, if you take it for an easy path to a research degree you are mistaken. In hard science, there is no soft path.

I am, by no means, arguing for undue indulgence in theoretical physics. The world is moving ahead of the golden age of Einstein, Bohr, Schrodinger, Heisenberg, Dirac, Pauli, Fermi, Wigner etc. I am only emphasising the value and power of Mathematics as the language of Physics and as a tool of pursuing Physics.

Finally, for the Indian scientists, there is no wisdom in lamenting that 'China (is) way ahead in research race' (The Times of India, January 9, 2012). Look at it The Hindu way ('India ahead of China in quality of scientific papers', January 7, 2012). There is nothing to be elated about in both the articles. A point of concern for everyone, especially for the science policy managers, is the trend of reversal in the discipline-wise classification of the areas of competence/global leadership between Indian science and Chinese science.

In China, areas of leadership in research fell mostly in the disciplines of computer science, medical specialities, mathematics, physics and health sciences: in India these very disciplines form the lowest rungs. The sequence for India is : chemistry- 38%, engineering-15%, biology and biotechnology-14%, mathematics and physics-10%, computer science-5%, medical science-4%.

And for the nation, there is a matter of grave concern in the Sunday Times' head line news, "Indian schoolkids rank 2nd last in global test." (January 15, 2012). This is about the result of testing the skills and the knowledge of 15-year-old students in Reading, Mathematics and Science conducted worldwide by the Organisation for Economic Co-operation and Development under its Programme for International Students Assessment - an international educational benchmarking system. Once again China comes at the top.

The worst shocker in the details is that the test found an Indian eighth-grader is only as good as a Korean third-grader in mathematics abilities. Something wrong with the design of our voluminous school education system! We cannot build a sound structure of higher education on a weak foundation of school education.