ARTICLE

P.C. VAIDYA, A GANDHIAN MATHEMATICIAN-PHYSICIST AND PROPONENT OF ‘VAIDYA METRIC’: NEARLY IN OBLIVION

MANAS CHAKRABARTY*

The year 2018 marked the birth centenary of the Gandhian mathematician-cum-physicist, P.C. Vaidya who was an inspiring teacher, a dedicated populariser of mathematics and the proponent of Vaidya metric, a rare dynamic solution to the space time geometry around radiating stir. Sadly, however, this world famous expert in relativity and cosmology could not become a household name in India and has nearly gone into oblivion. There was hardly any celebration of his birth centenary across India. The life and work of this modest scientist have been presented briefly in this article.

ast year (2018) was the birth centenary of Prahalad Indeed, only a few write-ups were published and even Chunnilal Vaidya (PCV), a renowned Gujarati lesser number of seminars and symposia on the life and Lmathematician and physicist, a freedom fighter, an work of this bright Indian scientist took place last year. inspiring Gandhian teacher and a globally recognised expert Regrettably, he was not covered even in a recent article, on Einstein’s theory of relativity1,2. But despite his immense written by the present author, on the momentous incidences contribution in the field of theory of relativity, especially that rendered the year 1918 a truly remarkable year in the what is known as the ‘Vaidya metric’, PCV could not history of mankind4. The present write-up on the life and become a household name like C.V. Raman, S.N. Bose, work of PCV is an attempt to fill in this lacuna. Meghnad Saha, Homi Bhava, P.C. Mahalanobis, S. Chandrasekhar and the like, and he has almost gone into Early Life and Education oblivion. In an article entitled, ‘Centenary: P.C. Vaidya, a PCV was born on May 23, 1918 in Shahpur village Gandhian Physicist Who Laboured in India’s Shadows’ by in Junagadh District, . In 1931, when he was in the A. Ramnath and published in the WIRE on May 27, 2018, 9th standard, his father passed away. After completing his the author candidly confessed that he, although a school education first in Alfred High School, Bhavnagar professional historian of science, had never heard of Vaidya (until 1933) and then in Mumbai, he graduated from the until recently when a colleague mentioned about PCV Ismail Yusuf College, Andheri with distinction in science during the course of a public lecture on the life and work with physics and mathematics as major. Right from his of Stephen Hawking3. This statement, however shocking, school days, PCV displayed a special aptitude for bears ample testimony to the unfortunate evaluation of PCV mathematics. He, therefore, studied applied mathematics not only by the public at large but also by the scientific at the Institute of Science (formerly known as the Royal community in India. Institute of Science) and obtained his M.Sc. degree from the Bombay University where he was a topper. * Former Senior Professor of Chemistry and Emeritus Scientist (CSIR) in the Department of Chemistry, Bose Institute, Kolkata Post-M.Sc. Teaching Career 700009, West Bengal. Residence: 60/13B, Gouribari Lane, P.O. Shyambazar, Kolkata In 1940, he started his career as a Lecturer in 700004. Dharmendra Singhji College, Rajkot where he used to teach E-mail: [email protected] arithmetic and trigonometry to undergraduate students. He

254 SCIENCE AND CULTURE, JULY-AUGUST, 2019 (Source: Wiki Commons) P.C. Vaidya (23.05.1918-08.04.2010) (Source: a Documentary) was a staunch believer in Gandhian philosophy of Ahimsa, for a berth in his research group. Narlikar immediately simplicity and honesty. He took part in freedom movement, agreed, and PCV, along with his wife and six month-old but in a different way. He resigned from the lectureship in daughter Kumud, went to Banaras on the 27th June, 1942. 1941 and founded a voluntary organisation, Ahimsak But he could carry out research work at BHU for only ten Vyayam Sangh (AVS), an institute of physical education months because he did not get any scholarship and his for training youths for non-violent struggle. He was the scanty savings were almost spent by then. PCV returned Principal of AVS. In 1942, when the Quit India Movement to Gujarat with his family in the April of 1943. But even was being planned, wanted AVS to play this short period of research under the guidance of Narlikar a part in the planned movement. But Baba Prithvi Singh shaped PCV into a prolific researcher and imbibed in him Azad, the Director of the Sangh and a one-time the idea of developing a spacetime geometry of the revolutionary, did not want to oppose the British simply gravitational field around a radiating star. Justifiably, PCV because he was indeed a communist and the British were considered his research tenure with V.V. Narlikar as ‘Kashi allied with the Soviets. This ideological conflict led to the Yatra’3 and paid homage to his Teacher-mathematician in closure of the AVS sometime in 1942. an obituary5.

Entry into Research After leaving BHU, PCV taught in a number of science institutions in Surat, Rajkot and Bombay. He then This was the turning point in the life of PCV. Since spent one year (1947-’48) as a Research Associate at the the AVS was shut down, PCV had no job and his savings newly founded Tata Institute of Fundamental Research, were almost exhausted, he became somewhat aimless. Bombay where he got acquainted with Homi Bhabha. He Earlier in 1937 when PCV was an undergraduate student got his Ph.D. degree from the Bombay University in 1948. of mathematics, he attended a course of lectures on general Notably, PCV was the first holder of the Ph.D. degree in relativity at Bombay University by Professor V.V. Narlikar, mathematics in Gujarat. But long before his doctoral award, a well known physicist of Banaras Hindu University (BHU), PCV became famous for his contribution, widely known Varanasi and the father of famous Jayant V. Narlikar. These as ‘Vaidya metric’ or ‘Vaidya solution’ (vide infra). lectures had two profound influences on the course of the life of PCV. Firstly, he shifted from pure mathematics to Vaidya Metric: Major Contribution of PCV applied mathematics after the first semester in the PCV’s major interest was in the gravitational field of postgraduate course. Secondly, these lectures made PCV radiating stars. According to the general theory of relativity, aware, for the first time, of the fact that the gravitational a gravitating object can be measured by the spacetime field of a radiating star had yet to be described in terms of geometry around it. When PCV started his research work, general relativity. Inspired by these lectures, PCV became the spacetime geometry around a spherical star (with its interested to pursue research in the general field of relativity surrounding assumed to be empty) had already been worked in the school of V.V. Narlikar at BHU. out (vide the well known ‘Schwarzschild Solution’)6. But In 1939, PCV got married to Vidya Devi. In 1942, this geometry around a radiating star, like typical stars, when the AVS was wound up, PCV requested V.V. Narlikar was not known. A quarter of a century later when PCV

VOL. 85, NOS. 7–8 255 was in his early twenties, he found a solution – a metric - Sen at the University of Calcutta. The next generation of to this problem. His remarkable paper entitled ‘The influential scientists in this domain are PCV and A.K. External Field of a Radiating Star in General Relativity’ Raychaudhuri of Presidency College, Calcutta. The on this solution, called the ‘Vaidya metric’ was published contribution of PCV, mainly Vaidya metric, belongs to the in Current Science in 19437. Vaidya metric slowly acquired domain of the study of gravitational effects around local a berth in the upcoming field of relativistic astrophysics. objects while the famous ‘Raychaudhuri equation’14,15 by In his public lecture titled ‘Vaidya Metric and 100 Years late Professor A.K. Raychudhuri belongs to the domain of of Black Hole Solution’ held at on the investigation of the global structure of spacetime – the September 9, 2017, Dr. Karan Jani, a gravitational wave two domains of general relativity. The contributions of these astrophysicist and a LIGO scientist and one of the Forbes two stalwarts in their respective fields have been amply list of ‘30 Influential Scientists Under 30’ remarked that covered in a notable book entitled ‘A Random Walk in the recent applications of Vadya metric, a very rare exact Relativity and Cosmology: Essays in Honour of P.C. Vaidya dynamic solution in relativity, include probing dark energy8. and A.K. Raychaudhuri’, edited by N. Dadhich, J. Krishna A video, created by Google, deals with the work of PCV Rao, J.V. Narlikar and C.V. Vishveshwara Rao who are in the field of general theory of relativity9. experts in the field of general relativity16. A review on this A documentary on the life and work of PCV and a book highlighted the importance of this book and considers 10 recent news article in South Asia Daily have described it to be “both useful and stimulating to any interested how the idea of Vaidya metric came into being. The story reader17.” goes as follows. One day in 1942, PCV was loitering in the balcony waiting for a Hindi newspaper Aaj when the Teaching and Science Popularisation idea behind Vaidya metric flashed in his mind. He thought that, since fluids move with velocities less than that of light, After getting his Ph.D. degree, PCV moved to the maximum in nature, one must consider, not fluid, but teaching at various Colleges like Vitthalbhai Patel College, radiation moving out of the star while working on the field Vallabh Vidyanagar (later turned into Sardar Patel of a radiating star. In other words, the velocity of light, University), Gujarat College, , M.N. College, and not that of fluid, should be considered. Once the idea Visnagar, and University School of Sciences, Gujarat came to him, mathematics simply followed. Within a week, University. He became the Chairman, Gujarat Public PCV worked out the mathematical solution of his idea, and Service Commission (1971), Chairman of the Union Public thus came the Vaidya metric11. Service Commission (1977-’78), the Chancellor, Gandhi PCV’s initial research with Springer Research Vidyapeeth, Ahmedabad and also the Vice-Chancellor of Scholarship of the Bombay University resulted in a paper Gujarat University (1978-’80). ‘Nonstatic Solutions of Einstein’s Field Equations for Later in his career at Gujarat University, he once said Spheres of Fluids Radiating Energy’ with himself as the that he did not want to restrict himself to teaching at M.Sc. sole author. This work, published in Physical Review in classes since he was the highest paid teacher in mathematics 12 1951 , was highly appreciated by none other than Robert in Gujarat1. Driven by this conviction, PCV devoted himself Oppenheimer, ‘the father of the atomic bomb’. in spreading science in general and mathematics in particular amongst the students, the teachers and the public Publications of PCV alike. He founded the Gujarat Ganit Mandal (Gujarat PCV’s work was focused mainly on exact Mathematical Society) at Bhavnagar in 1964, and became solutions, supermassive objects and black holes. His its President twice (1964, 1988). He was also instrumental achievements are even more praiseworthy since he had to in founding the mathematics laboratory Vikram A. Sarabhai work with minimal infrastructural facilities. He published Community Science Centre (popularly known as CSC) in 66 research papers and 9 related articles in reputed Indian Ahmedabad in the 1960s and the Indian Association for and International journals. A complete list of his papers General Relativity and Gravitation (IAGRG) in Ahmedabad during 1942-2000 is available13. in 1969. As recalled by his nephew Arun Vaidya, PCV A Notable Tribute to P.C. Vaidya and Amal was an active organiser of sports and other activities by K. Raychaudhuri the students, and his organising ability perhaps stemmed from his past experience in founding and running Two pioneers in India in the field of general relativity the AVS3. are Professor V.V. Narlikar at BHU and Professor N. R.

256 SCIENCE AND CULTURE, JULY-AUGUST, 2019 Honours and Achievements Visiting Professor at Washington State University. In fact, PCV delivered the 11th IUCAA Foundation Day Lecture Because of his achievements in the field of theory of titled ‘Chalk and Duster’, which was reported in the relativity, he got the honour of serving various academic January, 2000 issue of KHAGOL, the bulletin of the institutions as a Visiting Professor / Visiting Scientist. Thus IUCAA18. he visited Washington State University, Pullman, Washington (USA), London University (UK), Newcastle Why PCV could not become a household University (UK), Dublin Institute of Advanced Studies, name? Dublin (Ireland) and International Centre for Theoretical Physics, Trieste (Italy) during 1964-’73. He also delivered The answer to this bewildering question is two-fold. a course of lectures at the Institute of Henrie Poincare, Firstly, during the era of PCV, the prestigious, burgeoning Paris (France) in 1971. space programmes and the atomic energy projects of the Government of India were eye-catching. In contrast, the Expectedly, PCV earned many feathers in his crown. field of general relativity, pursued by PCV, was an area In a conference in Ahmedabad in early 1969, held in that was hardly taught even in the postgraduate physics honour and felicitation of Professor V.V. Narlikar at his courses in Indian Universities. Secondly, PCV himself 60th birth anniversary, PCV proposed the formation of a “never yearned to be in the public eye3.” He was more society of Indian relativists. This led to the birth of the interested to pursue research in his field of interest, to teach IAGRG, of which PCV was a Founder Member. He was and to popularise particularly mathematics and lead a also a Fellow of the Indian Academy of Sciences, a Fellow simplistic Gandhian life far from the madding crowd. The of the Indian National Science Academy, the President net outcome was that PCV remained relatively unknown of Calcutta Mathematical Society (for 2 years; succeeded in the centres of excellence – Universities and research Sir Asutosh Mukherjee in 1924), an Honorary Fellow of the institutes in India and abroad. As a consequence, his Inter-University Centre for Astronomy and contributions in the fields of research, teaching and science Astrophysics (IUCAA), Pune, the President of the Indian popularisation, albeit invaluable, could not render him a Mathematical Society (1976, 1977), a Founder Member household name. of the Springer journal General Relativity and Gravitation (1970), a Member of Indian National Committee on Last Period Astronomy (1976-’79) and the President of the UGC Committee on Relativity and Cosmology. He also actively For the last few years, PCV’s health was deteriorating. participated in the revision of the state-level syllabi of He was mostly staying at his home at Shardanagar, mathematics textbooks. Ahmedabad. Since January, 2010, he was suffering from kidney troubles. Three months later he succumbed to death Popularisation of Mathematics and Memoirs in the morning of Friday, the 12th March, 2010 in Ahmedabad. He is survived by his four daughters Kumud, With a view to popularising particularly mathematics Ila, Smita and Hina, and their families. amongst the students, he started a mathematics magazine ‘Suganitam’ in the 1960s, wrote articles, mostly on Two important obituaries on the demise of PCV were mathematics, in the Gujarati cultural magazine ‘Kumar’ and written - one by Dr. Ajit Kembhavi, the then Director of authored several popular science books (majority in the IUCAA and the other by Dr. Pankaj S. Joshi, the then Gujarati) which include ‘Akhil Brahamandman’ (In the President of the IAGRG, and these were published in Entire Universe), ‘Dashansh Paddhati Sha Mate?’ (Why KHAGOL19. Decimal System?), ‘Dadaji Ni Vato’ (Grandpa’s Tales), ‘What is Modern Mathematics?’ and ‘Ganit Darshan’ PCV: The Astronomer (Discourses in Mathematics). Pertinently, this last named PCV considered himself as a dedicated teacher in book won the Gujarati Scientific Literature Prize (1970- mathematics. In 1997, when the Editor of the Bulletin of ’71) of the Govt. of Gujarat. Moreover, PCV published, the Astronomical Society of India invited PCV to deliver inter alia, two important memoirs – ‘Chalk ane Duster’ their Silver Jubilee Lecture, he accepted the invitation and (Chalk and Duster), Suganitam Prakashan, Ahmedabad, delivered a lecture entitled ‘Me, an Astronomer?20’ In this 2011, a memoir on his teaching life, and ‘America ane lecture, PCV elaborately explained how he was transforeded apne’ (America and Us), a memoir on his experience as a from a mathematician into an astronomer. One needs to

VOL. 85, NOS. 7–8 257 go through this article in order to be able to properly Epilogue appreciate the academic contribution of PCV in the field Quoting K.P. Jani7, “Vaidya never received any Padma of astrophysics. awards, nor any road or institute is named after him. But his legacy lives in every relativity book on earth.” He was Philosophy of PCV later remembered10 (by a journalist of South Asia Daily) Known as a ‘Gandhian mathematician’, PCV was a as “a ramrod straight man with a slight smile who exuded staunch follower of Gandhian principles. He believed in a subtle sense of authority.” Professor P.C. Vaidya aka plain living and high thinking. A remarkable trait of PCV Bachukaka will always be remembered as a remarkably is that he was simple and honest in both personal and public modest man, a lifelong Gandhian, a revered teacher, a life. He was a modest man of amicable nature. Even in his renowned physicist and a populariser of mathematics. This eighties, “he was incredibly active, both physically and humble scientist clad in ironed kurta and dhoti, wearing a intellectually.” His teaching at classes using a chalk and Gandhi cap and riding a black bicycle even in his old age blackboard used to captivate the students. He believed that certainly deserves to be retrieved from near oblivion. S it was the best means of imparting knowledge to the References students. That is why, perhaps, he named his memoir on teaching and research as ‘Chalk and Duster’21. 1. https://en.wikipedia.org/wiki/Prahalad_Chunnilal_Vaidya 2. A. Sherrif, “Remembering the Forgotten Scientist Who Fought Critical Comments on PCV For Freedom & For Science!,” The Better India, May 28, 2018. URL: https://www.thebetterindia. com/143176/ forgotten-indian- In a public lecture in Gujarat University in 2017 on scientist-who-fought-for-freedom-and-for-science/. the 98th birth anniversary of PCV, Dr. Karan Jani, referred 3. A. Ramnath, “Centenary: P.C. Vaidya, a Gandhian Physicist Who to earlier, commented on the work, lifestyle and philosophy Laboured in India’s Shadows,” The Wire, May 27, 2018. URL: of PCV. He acknowledged that PCV was the first to write https://thewire.in/the-sciences/ centenary-p-c-vaidya-a-gandhian- physicist-who-laboured-in-indias-shadows. popular science books in the Gujarat literature, he continued 4. M. Chakrabarty, “1918 – A Truly Remarkable Year in the History to teach in primary schools even when he was a Vice of Mankind,” Science and Culture, 84 (9-10), 302-309 (2018). Chancellor of the Gujarat University, he was the first 5. P.C. Vaidya, “Teacher-mathematician: An obituary of V. V. physicist to work on blackhole and he carried the legacy Narlikar,” Current Science, 60 (8), 502-503 (1991). of Einstein’s Relativity in independent India. Dr. Jani further 6. https://en.m.wikipedia.org/wiki/Schwarzschild acknowledged that it is only Vaidya’s groundbreaking work 7. P.C. Vaidya, “The External Field of a Radiating Star in General that proved the formation of blackhole from a stellar Relativity,” Current Science, 12, 183-189 (1943). collapse. 8. K. Jani, “Vaidya Metric and 100 Years of Black Hole Solution,” (P. C. Vaidya Birth Centenary Year Lecture), Gujarat University, Commemoration of PCV September 9, 2017. URL: https: //twitter.com/AstroKPJ/status/ 734761206616084480 In commemoration of P.C. Vaidya, a 120-page Special 9. http://video.google.com/videoplay?docid=4382862622658562253# Issue of Suganitam was published in 2010, and a wide 10. ‘Vaidya Metric And Bachukaka’, South Asia Daily, May 28, range of tributes appeared in it. Vigyan Prasar, Department 2018. URL: https:// southasia.typepad.com/ south_asia_daily/ of Science and Technology, Govt. of India, in collaboration 2018/05/vaidya-metric-and-bachukaka.html. with IUCAA, prepared a film ‘Professor Vaidya – a film 11. https://ipfs.io/ipfs/QmXoypizjW3Wkn on P.C. Vaidya’ (CD: Rs. 50/-) in 201722. This film, first FiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/ Vaidya_metric.html. conceived by Professors N. Dadhich and Ajit Kembhavi, 12. P.C. Vaidya, “Nonstatic Solutions of Einstein’s Field Equations not only “presents a unique and inspiring picture of a for Spheres of Fluids Radiating Energy”, Physical Review, 83, simple man with profound accomplishments”23 but also 10 (1951). reveals Dr. Vaidya’s reminiscence on how he developed 13. K. Jotania, “List of Papers Published by Prof. P.C. Vaidya,” his metric to one of Einstein’s equations. ‘Prof. P. C. Vaidya Mathematics Today, 33, 1-8 (2017). National Conference on Mathematical Sciences’ was held 14. A.K. Raychaudhuri, “Relativistic Cosmology I,” Physical Review, by St. Xavier’s College, Ahmedabad and Gujarat Ganit 98 (4), 123 (1955). DOI: 10.1103/PhysRev.98.1123. Mandal at Surat on Dec. 24-25, 201824. A write-up entitled 15. E. Poisson, ‘A Relativist’s Toolkit: The Mathematics of Black ‘Vaidya Metric and Bachukaka’ appeared in the South Asia Hole Mechanics’, Cambridge University Press, Cambridge, 2004, Chapter 2. ISBN 0-521-83091-5. Daily on May 28, 201810. PCV’s next generation of 16. N. Dadhich, J. Krishna Rao, J.V. Narlikar and C.V. Vishveshwara Gujarati acquaintances used to address him as ‘Bachukaka’. Rao, Eds., ‘A Random Walk in Relativity and Cosmology: Essays

258 SCIENCE AND CULTURE, JULY-AUGUST, 2019 in Honour of P.C. Vaidya and A.K. Raychaudhuri’, (Wiley Prakashan, Ahmedabad, 2011. Eastern Ltd., New Delhi, 1985. ISBN: 978-0470201985). 22. “Professor Vaidya - a film on Prof. P. C. Vaidya,” Vigyan Prasar, 17. http://dspace.rri.res.in/handle/2289/6624 Department of Science and Technology, Government of India, 18. ‘The Eleventh IUCAA Foundation Lecture’, KHAGOL, No. 41, New Delhi, 2017. URL: https://www.youtube.com/ watch? January, 2000. v=bvzV3RTEkF4. 19. Obituaries on PCV by A, Kembhavi (Director, IUCAA) and P.S. 23. J.V. Narlikar, “P.C. Vaidya (1918-2010),” Current Scence, 98 Joshi (President, IAGRG), KHAGOL, No. 82, p.5, April, 2010. (10), 1389 (2010). 20. P.C. Vaidya, “Me, an Astronomer?,” Bulletin of the Astronomical 24. file:///C:/Users/User/Desktop/PCV-The%20Mathematics Society of India, 25, 209-212 (1997). %20Consortium-2018.html by The Indian Mathematics Consortium. 21. P.C. Vaidya, ‘Chalk ane Duster’ (Chalk and Duster), Suganitam

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