Abstract

This paper presents a brief account of contributions of Indian researchers to UFT research. It started with the famous Satyendra Nath Bose in early 1950s, and continued with Gaganbihari Bandyopadhyay, J. R. Rao, Ratna Shanker Mishra, and the USA based Jogesh Chandra Pati. Many others, either in association with them, or independently, also contributed. Indian contribution to UFT research may be termed commendable, though, similar to Einstein’s original work, it falls short of achieving a complete unification of forces, leaving the field open for future exploration.

Key Words: Unified Field Theory, Grand Unified Theory, Field Equations, Affine Connection, Mixed Geometry, Divergence Identities, Empty-Space Solutions, Linear Equations, Tensorial Objects.

Introduction

More than one hundred years have passed by since Albert Einstein (1879-1955), the initiator of the idea of ‘unified field theory (UFT)’ made the first announcements on the subject during 1920s. Following it, volumes of research have been conducted. As UFT is highly relevant to the objective of our journal, a series of short reviews on UFT were published by the present author starting with [Paramguru 2025a]. This one presents the activities of Indian scientists on the subject. The motivation for this one arose from the fact that the noteworthy historical coverage on UFT between 1930-1965 in Living Reviews in Relativity by the German theoretical physicist Hubert Goenner [2014], besides uttering ‘India’ and ‘Indian’ at various places; and quotes like, ‘(I)in the 1970s and 1980s, many papers on exact solutions of the Einstein-Schrodinger theories and alternatives were published by Indian scientists‘ [181]; assigns two pages [158 and 159] for Indians’ research on this subject. It may also be noted that in the same review a total of 723 references has been cited out of which 37, more than 5 per cent, are authored by 15 Indians. Obviously, this situation calls for a discussion on the subject.

The Indians’ contribution to UFT has also been briefly covered in the earlier publication [Paramguru 2025b]. The Indian scientists cited by Goenner [2014] start from Satyendra Nath Bose, to Ratna Shanker Mishra, Gaganbihari Bandyopadhyay and twelve others. It has been found from literature that their contributions were highly significant, and they also continued to research and publish afterwards till they were active. Therefore, the present review will discuss major parts of the UFT research conducted by these Indian scientists as reported by Goenner [2014], and will also include their contributions afterwards during the 1970s and 1980s as found in literature. In addition, the work of American-Indian physicist Jogesh Chandra Pati will also be added, since his contribution is significant.

Satyendra Nath Bose

Satyendra Nath Bose was probably the most renowned Indian scientist referred to by Goenner, and hence, he went ahead in a note: ‘This is Satyendra Nath Bose (1894-1974) of the Einstein-Bose statistics.’ Our readers also deserve a brief mention here about the Einstein-Bose statistics fame. During 1924, a thirty-year Bose submitted a four-page research paper titled ‘Planck’s law and the light quantum hypothesis’ to the journal Philosophical Magazine, which was rejected for publication; then Bose did the wisest thing possible, sent it straight to Einstein for his comment with a hand-written cover letter. Einstein liked the paper, immediately acknowledged the receipt as well as the worthiness of the same, translated it to German language and sent it to the German journal Zeitschrift fur Physik, and it was published in its 1924 August issue [Debnath 1993, 636]. It was the beginning of quantum statistics, and soon Bose’s name was reflected in the sub-atomic particle ‘boson’, and the theoretical term in physics, ‘Bose-Einstein condensate.’ Bose continued his research as well as his contact with Einstein, the fame of the later facilitated a two-year leave for research and study abroad in Europe with research fellowship and full travel expenses for Bose from his employer Dacca University during 1924; Bose got a chance to work in the laboratory of Madame Curie at Paris, and finally met Einstein at Berlin in 1925 [628]. From Berlin, getting selected for the position of professor and Head of Physics Department of Dacca University, with recommendation of Einstein, Bose came back to India during 1926 and continued working at Dacca University till 1945 when he got a chance to come back to his ‘Alma mater’ as the renowned Khaira Professor of Physics, then during 1950-56 was Head of the Department of Physics. Amongst the numerous honors received by him include Fellow of Royal Society of London, and the second highest Indian civilian award Padma Bibhushan [629].

During the 1910s and early 1920s Bose was interested in Einstein’s hot topic of the time – relativity, and along with M. N. Saha, brought out a book The Principles of Relativity in 1920. However, when he met with Einstein during 1925, he learned that Einstein had shifted his interest to unified field theory. Though Einstein spent the rest of his life researching on UFT, Bose never thought of doing any research on this subject. However, since 1948, he revived his early interest and published five papers, four of them in French, during 1953-1955 at various aspects of UFT [Bose 1953a, Bose 1953b, Bose 1953c, Bose 1954, and Bose 1955]. During 1994, S. N. Bose National Centre for Basic Sciences, Calcutta, has brought out a book, S N Bose: The Man and His Work – Part I: Collected Scientific Papers, edited by a group of editors with Santimay Chatterjee as chief editor, where all of these five papers have found place including English translation of the French papers [Chatterjee 1994]. In the first paper, Bose dealt with the divergence identities used in UFT in an easier way, whereas, in the second paper, he dealt with a complicated Lagrangian [26]. The last three papers of Bose were dealing with the field equations and their solutions [30]. Goenner [2014] has referred, not all five, but only three of Bose’s papers [Bose 1953a, Bose 1954, and Bose 1955] and has indicated that Bose rewrote the particular field equation into an inhomogeneous linear equation for tensorial objects, which was homogeneous and linear in T [Bose 1955]. He then considered the equation as a matrix equation, went ahead for its solution [Bose 1954 and Bose 1955]. It appears that many others including Einstein and Kaufman have gone in for the solutions. Goenner’s final statement on this issue is: “Although the method is more transparent than Tonnelat’s, the solution is just as implicitly given as hers [2014, 112].”

To be honest, it is really difficult to understand whether Bose had any contribution to UFT without going technically into his research. Here comes another way out to have some idea of his contribution from the Horse’s mouth, i.e., Einstein’s mouth. Like his 1924 paper, Bose also supplied his research papers to Einstein at Princeton, and Einstein wrote his own comments through two letters to Bose, one (type-written) on 4th October 1952, and the other (hand-written) on 22nd October 1953; and both are published [Chatterjee 1994, 27-29]. Chatterjee’s edited book [1994] also puts Einstein’s mind on this issue very precisely, “(T) thus to Einstein the crucial problem was: ‘Do the singularity-free solutions of the equation system have physical meaning? Are there at all singularity-free solutions which correspond to the atomistic character of matter and radiation?’ From this view point the solution of those equations is not of great help [31].” According to Debnath [1993, 643]: “Indeed Bose had a number of contributions to the unified field theory including some major changes in the field equations. He obtained the general solution of Einstein’s field equations connecting the basic field quantities and affinities in the non-symmetric field theory. —. But, according to Einstein, Bose’s work broke no new ground on the subject.” This is probably the exact gist of Einstein’s two letters to Bose. One thing can be said that Einstein knows exactly what Bose did.

Gaganbihari Bandyopadhyay

Goenner’s two pages for section 13.3 describing research by Indians starts with: “In a short note, the Indian theoretician G. Bandyopadhyay293 considered an affine theory using two variational principles such as Schrodinger [553] had suggested in 1946 [9] [158].” Here, the bracketed numbers 553 and 9 refer to the work of respectively Schrodinger and Bandyopadhyay, the superscript number 293 duly refers to the note 293 which the author considers apt to give a short introduction on Bandyopadhyay. We learn that Bandyopadhyay was associated with Government College, Darjeeling, IIT Kharagpur and then University of Calcutta from where he retired as Professor from Department of Applied mathematics.  Goenner [2014] has cited five papers of Bandyopadhyay [1951a, 1951b, 1953, 1960, and 1963]. The first paper provides particular solutions, as the title suggests, for Einstein’s then unified field theories. In fact, the symmetry of so called “1-dimensional” gravitational fields of Einstein’s general relativity, i.e., those for which the metric components depend on only a single coordinate, is high enough to try and solve for them field equations of UFT. Bandyopadhyay had found such a solution of the weak equations [1951a]. The second paper, published in the epic journal Nature, analyzed the non-symmetric tensor field variables (gµv) in Einstein’s unified field theory, specifically examining isolated singularities [Bandyopadhyay 1951b]. The third paper, the gist of which is quoted in the first line of this paragraph, considered an affine theory using two variational principles as suggested by Schrodinger earlier, generated the field equations, and also gave the solution [Bandyopadhyay 1953].

Bandopadhyay’s fourth paper started from his second paper, where one of his claims was that for the strong equations m e = 0, here m, e are the parameters for mass and charge, a discussion took place whether isolated mass-less magnetic monopoles could exist. In 1960, he came back to this question in his fourth paper and claimed that the stronger equations will not allow isolated magnetic poles with mass whereas the weaker equations will allow the existence of such entities [1960, 427]. His fifth paper is development of a theorem on spherically symmetric solutions in unified theory, which holds good for both Einstein’s and Schrodinger’s unified theories [Bandyopadhyay 1963]. He worked on para-form field equations in Schrödinger’s unified theory, focusing on static spherically symmetric fields; and showed that for certain plane-symmetric field structures, solutions in Schrödinger’s unified theory could be generated from known empty-space solutions of the general theory of relativity. His research was notable for extending solutions from empty-space conditions to those containing electromagnetic fields, providing insight into how physical situations could be generated in unified theories. As will be shown later, his work has motivated other Indian researchers and they have also extended his research further.

Goenner puts a categorical statement that – “(T) the generation of exact solutions to the Einstein-Schrodinger theory became a fashionable topic in India since the mid-1960s” [158]. Following a suggestion of G. Bandyopadhyay, R. Sarkar published two papers [Sarkar 1965 and Sarkar 1966]. In the first paper, he assumed the asymmetric metric to have the form, where, x0 is used instead of x4. Then, as a physical interpretation, he offered the analogue to a Newtonian gravitating infinite plane. The limit in the metric components led back to Bandyopadhyay’s solution [1951a] and he brought out the solution; and he could also remove some printing errors from Bandyopadhyay’s text. In his second paper [Sarkar 1966], Sarkar used the asymmetric metric again, and found that the solutions are static and with coordinate singularities. No physical interpretation was given.

Physicist N. N. Ghosh from the Department of Pure Physics of Calcutta University has published three papers [1955, 1956, and 1957] which have also been referred to by Goenner [2014, 159]. These papers deal with the general solution of field equations, specifically in the strong form, in Einstein’s unified field theory, where he has tried products of functions depending on different coordinates for the components of the asymmetric metric in his attempt at solving the strong field equations. However, Goenner comments that due to his awkward index notation and use of many ad-hoc additional assumptions, Goenner could not find out what kind of new exact solutions he has found; a clearer presentation might have helped [159].

There are some contributions from many other researchers, mostly one, or two publications by each, which are not being taken up here; however, their names are being mentioned: B. R. Rao, V. V. Narlikar, K. B. Lal and S. P. Singh, S. N. Gupta, S. Datta Mazumdar, and A. R. Roy and C. R. Datta. But one person who could make it to the ‘IIT Kharagpur Foundation (USA) Newsletter’ (volume 12.22.2024) with the article, ‘From IIT Kharagpur to Einstein’s Equations: The Story of J. R. Rao’ will have a special mention.

1. R. Rao

Goenner has referred to two papers of J. R. Rao [1959 and 1972] but has commented that “(T)there exist a number of helpful review articles covering various stages of UFT like — Rao [504], —-” [2014, 10]. This mention, in itself, should be considered as praise-worthy. However, there remains a bigger story to be told. J. R. Rao was belonging to the then Department of Mathematics of IIT Kharagpur to which Professor G. Bandyopadhyay was also once belonging before shifting to the University of Calcutta. In one of his papers, Rao expresses his deep sense of gratitude to Professor G. Bandyopadhyay for his helpful discussions and encouragement. This indicates a professional link between the two. However, what is the most significant fact in our context right now is that this mathematician as well as IITKgpean J. R. Rao successfully defended his PhD thesis ‘Some Problems in Einstein’s Unified Field Theory of 1945’ during 1962. And the story in the IIT Newsletter is based on the synopsis of this PhD thesis.

It is a well-known fact that Albert Einstein proposed the UFT in 1945 and scores of research was continuing at that time, because Einstein’s original equations contained non-symmetric tensors which raised the questions of mathematical consistency and solvability. Rao did the right thing by doing a deep review of all the issues of Einstein’s theory such as derivation of field equations, linear relations, exact solutions, and physical interpretations. He did also look into alternate approaches including works by Schrodinger and Weyl. Finally, he offered three propositions: (i) a special type of symmetry and coordinate system leading to an explicit field structure that resembled the infinite plane analogy in general relativity, (ii) a “rigorous solution”, as well as, (iii) a “restricted weaker form” solution, those were derived by simplifying certain constants. Of course, similar to Einstein’s original work, according to the story of IITKgp Foundation, Rao’s dissertation falls short of achieving a complete unification of forces, leaving the field open for future exploration.

Rao’s contribution to the UFT is not limited to his PhD thesis; rather, it is well extended to several publications mostly in association with his coauthors. Here, not all of them, but just a couple of them are cited [Rao and Tiwari 1974, Mohanty, Tiwari, and Rao 1982]. In the first one, the authors provide a theorem, which in their own words – ‘we may say that we can pass from a special empty-space solution of general theory of relativity to the solutions of unified field theory. It is indeed highly gratifying to be able to build physical solutions either in general theory of relativity or in unified theories from the empty-space solutions which form a solid base for Einstein’s gravitational theory’ [1974, 595]. Similarly, a couple of sentences are cited from the later paper, which describes, in their own words, their own contribution to UFT: ‘(Rao et al [13][14][15]) have obtained a class of solutions for cylindrically symmetric coupled zero-mass and source free electromagnetic fields described by Einstein-Rosen metric and have interpreted these solutions mainly from the view point of their singular behaviour. In a separate investigation they (Rao et al [16][17][18][19]) have extended the study to the case of Brans-Dicke theory’ [1982, 238]. There is also a mention in Rao’s coverage in the IIT Kharagpur Foundation Newsletter – The work connected Rao’s solutions to those obtained in some earlier works by Indian physicists Ghosh and Bandyopadhyay.

Here, one more Indian, Dipak Kumar Sen will be described, because he also appears as flashy as Rao. Goenner has cited four of Sen’s contributions, including one PhD thesis [1958], one book [1968], two papers with one coauthor in each [Sen and Dunn 1971, and Sen and Vanstone 1972]. The specialty of the PhD thesis is that it is in French and submitted to the faculty of science at Paris, which Goenner mentions – ‘In the thesis of D. K. Sen began [174] with G. Lyra in Goettingen and finished in Paris with M. A. Tonnelat, —’ [175]. The thesis is about a novel unified theory for a static cosmological model of the universe based on Lyra’s geometry [Sen 1958]. Of course, in later developments of the theory by Sen and his coworkers in the 1970s, it was interpreted just as an alternative theory of gravitation (scalar-tensor theory) [1971 and 1972]. The book Fields and/or particles [1968] is solely based on the PhD thesis and attracts the comment from Goenner – ‘(T)to my knowledge, the only textbook including the Einstein-Schrodinger non-symmetric theory has been written in the late 1960s by D. K. Sen [572].’ [2014, 10]. By the time the book was published, Sen had shifted to the Department of Mathematics, University of Toronto, Canada.

Ratna Shanker Mishra

Along with Gaganbihari Bandyopadhyay, Ratna Shanker Mishra (1918-1999) also appears (Ratan appears in place of Ratna) in section 13.3 where research of Indians is described. From amongst Indians, Goenner has cited the highest numbers of publications of Mishra, totaling 13, with 8 as single author [1956a, 1956b, 1958a, 1958b, 1958c, 1959a, 1959b, and 1963] and 5 with coauthors [Husain and Mishra 1956, Abrol and Mishra 1958, Kaul and Mishra 1958, Lal and Mishra 1960, and Mishra and Abrol 1960]. The note number 294 presents his credentials, of which the last but one sentence reads – ‘He has been a visiting professor in many countries, and worked and published with V. Hlavaty at Indiana University.’ [158]. And Goenner’s description of V. Hlavaty reads – ‘Hlavaty272 is the fourth of the main figures in UFT besides Einstein, Schrodinger, and Tonnelat’ [144]. This implies Mishra got the opportunity of working with the fourth main figure in the world working in UFT. One of the students of R. S. Mishra, R. B. Misra has brought out a memoir in favor of his guru as posthumously remembered by his students [2018], where it has been mentioned that – “He collaborated with Prof. V. Hlavaty at Indiana University, Bloomington (U.S.A.) twice: 1957-58 and 1961-62” [5]; and another long and big statement – “Prof. V. Hlavaty — while working on a problem of ‘Field equations’ left a note on his death bed ‘In case of my death or incapacitation, Prof. R. S. Mishra would be willing to complete this work’. It is so heartening that Prof. Mishra was able to complete the work which ran into 100 printed pages” [3].

Goenner’s mention of Mishra’s work on UFT is also wide and deep, placed at various sections. Mishra, being a mathematician, has looked into mathematical features such as ‘affine and/or mixed geometry’ [1956a, 1959a, Husain and Mishra 1956], ‘lambda transformations’ [1956b], and attempted solutions for various cases, as well as derived conditions for equations to have unique solutions [1958a, 1958b, 1959b, 1963, Lal and Mishra 1960]. According to Goenner, Mishra has also studied Einstein’s last publication with Kaufman and provided a solution for its connection [1958c]. Mishra’s joint paper with Abrol [Mishra and Abrol 1960] is also directed to Einstein-Kaufman version of Einstein’s theory, where the authors claim that ‘the equations of motion of charged particles found from the system of field equations by applying Infeld’s method of approximation, fails in this peculiar theory.’ Abrol and Mishra [1958] also re-wrote Bonner’s field equations with the help of the connections defined earlier by Bose [1953a and 1954]. In another paper [Kaul and Mishra 1958], Mishra generalized Veblen’s identities to mixed geometry with asymmetric connection, where the authors obtained 4 identities containing 8 terms each and with a mixture of ±-derivatives. It is proper, now, to reflect Goenner’s overall impression on Mishra’s work on UFT – “From my point of view as a historian of physics, R. S. Mishra’s papers are exemplary for estimable applied mathematics uncovering some of the structures of affine and/or mixed geometry without leading to further progress in the physical comprehension of unified field theory” [2014, 158]. Such a comment is certainly praise-worthy.

One can mention a bit about Mishra’s position in India. Mishra was Professor and Head of the Department of Mathematics at Gorakhpur (1958-1963) and Allahabad (1963-1968) Universities; then Head of the Department of Mathematics and Statistics at Banaras Hindu University in Varanasi from 1968 till retirement in 1978. Subsequently he was Vice-Chancellor of University of Kanpur during 1978-1980 and Lucknow University, his own alma mater, during 1982-1985. He was Visiting Professor, besides Indiana University, to Kuwait University, University of Waterloo, and University of Windsor. He was an invited participant in ‘International Conference on General Relativity and Gravitation (GR 6)’ at Copenhagen during 1971, and also (GR 7) at Tel Aviv during 1974. In India, he held various positions in academic and professional bodies. He has guided more than 50 students for PhD and DSc Degrees, published more than 300 papers and won many awards including Fellowship of almost all the established academic bodies in India. Books published by Mishra are – Structures in a Differentiable Manifold in 1978, Structures on a Differentiable Manifold and Their Applications in 1984, Almost Contact Metric Manifolds and Hyper-surfaces of Almost Hermitian Manifolds both in 1994. The Government of India has honored him with the fourth best civilian Award – Padmashree.

Jogesh Chandra Pati

This name does not appear in Goenner’s review. It may be because his research on UFT started with his paper along with the Pakistani Nobel Laureate Abdus Salam in 1974 only, much after ca. 1930 – 1965 [Pati and Salam 1974]. Actually during 1974 only, Glashow and Howard Mason Georgi III brought out what is called the Georgi-Glashow model, the first Grand Unified Theory (GUT). According to Goenner, in the beginning, GUTs were ‘unifying only the electromagnetic, weak, and strong interactions’ that is ‘with gauge group SU (5)’ [2014, 195]. They would have observable effects for energies much above 100 GeV.

Subsequently, many proposals for GUT have emerged; one of them is the Pati-Salem Model. (Jogesh) Pati (1937-), an Indian-American theoretical physicist, has contributed substantially in collaboration with Abdus Salam to formulate a GUT proposal called Pati-Salam model. John Ellis, from the Theoretical Physics Division of CERN, reports – ‘Even before the discovery of neutral currents, the restless spirit of Abdus Salam have led him and Jogesh Pati to propose the idea of grand unification of the strong and electroweak interactions –. They are the first to propose, in a motivated way, that quarks and leptons should be treated together in a common theory’ [1996, 3]. The specialty of the Pati-Salem model is its suggestions: (i) the symmetry of SU (4)-color, (ii) left-right symmetry, and (iii) the associated existence of right-handed neutrinos. They provide some of the crucial ingredients for understanding the observed masses of the neutrinos and their oscillations. After discoveries of gauge coupling unification and neutrino-oscillation, Pati himself says – ‘(I) in this context, it is remarked that with neutrino masses and coupling unification revealed, the discovery of proton decay, that remains as the missing link, should not be far behind’ [1998, 1]. Alas, after so many years, proton decay still remains eluded.

Overall, contributions of Indian researchers, as marked above, in moderate words, can be said as commendable. Goenner has once identified five major groups working on UFT in the world through his own words – ‘(T)the work done in the major “groups” lead by Einstein, Schrodinger, Lichnerowicz, Tonnelat, and Hlavaty —’ [2014, 10]. In case of Indian researchers also, it can be said that five major groups lead by Bose, Bandyopadhyay, Rao, Mishra, and Pati have contributed to UFT.

Conclusion

A brief account of contributions of Indian researchers to UFT research is given. The contribution started with Satyendra Nath Bose in the early 1950s, incidentally, he shared some of the results with Einstein himself who gladly responded with his observations. The other leading researchers were Gaganbihari Bandyopadhyay, J. R. Rao, whose own PhD thesis was on this subject and was highlighted in the IIT Kharagpur Foundation (USA) Newsletter during 2024 (after 62 years of PhD defense in 1962), Ratna Shanker Mishra, who availed the opportunity to work with Professor Hlavaty at Indiana University, and the USA based Jogesh Chandra Pati. Indian contribution to UFT research may be termed commendable, though, similar to Einstein’s original work, this research falls short of achieving a complete unification of forces, leaving the field open for future exploration.

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“Many of the advances in the Sciences that we consider today to have been made in Europe were in fact made in India, centuries ago.”

Grant Duff

British Historian

Abstract

Ancient India was a land of free-flowing ideas and thoughts in all possible directions about all possible aspects of the inner as well as the outer world making the Indian civilization as one of the unique civilizations in the world with a vibrant and comprehensive tradition of spiritual as well as natural science. The sages and seers of this land who contributed to this rich culture as great thinkers were also scholars and scientists in their capacity. Almost all the prime aspects of human knowledge apart from spirituality like mathematics, astronomy, physics, chemistry, medicine and the practical procedures in which this knowledge was put into practice like metallurgy, architecture, shipbuilding and surgery etc. were covered in great detail by this science and technology in ancient India. Intrinsic fundamental concepts and principles of modern science have been provided with a foundation by these numerous postulates and scientific methods. While some of these ground breaking contributions have been acknowledged by the world body, some are still unknown to most.

Here in this article, we would discuss the contributions to the field of Mathematics and Physics.

Key Words: Ancient Indian scientific thought, Origins of mathematics in India, Concept of zero and decimal system, Vedic and classical scientific knowledge, Contributions to astronomy and physics, Integration of philosophy and science.

Mathematics

It is now generally accepted that India is the birthplace of several mathematical concepts including ‘zero’, numerical notations, decimal system, binary numbers; Fibonacci numbers, square root, cube root of numbers, algebra, algorithms, studies of infinite series, convergence, differentiation and iterative methods of solving nonlinear equations, ideas of calculus as well as geometry etc. Will Durant, an American historian (1885-1981) said that India is the mother of a lot of our mathematical concepts and philosophy. L. Basam, the Australian Indologist writes in his book “The miracle that India was…” that the world owes most to India in the field of mathematics to a level more advanced than that achieved by any other nation of antiquity. The success of Indian mathematics was primarily due to the fact that the Indian thought system was of a very high level in abstractions to think beyond the numerical quantity of objects and conceive clearly the abstract numbers. They could conceptualize the implication and significance of the most abstract entity in mathematics such as zero and infinity in its metaphysical forms as ‘Sunya’ and ‘Ananta’, which was very unique to Indian Culture. They invented the base ten number system with zero as a number, so as to be able to introduce numbers smaller than the smallest (called in Sanskrit as ‘Anoraniyan’) as well as numbers larger than the largest (called in Sanskrit as Mahato-mahiyan) which they needed to describe Nature with all its aspects starting with particles like atoms (Anus) to celestial bodies and the universe at large. The religious texts of the Vedic period provide evidence for the use of large numbers. Yajurveda Samhita (1200-900 BCE) mentions in its sacred mantra recitation at the end of food numbers invoking powers of ten from hundred (102) to an oblation rite (Anna-homa) as well as during asvamedha, trillion (1012) and beyond. Thus, the roots of mathematics in ancient India can be traced back to the Vedic era as old as about 4000 years. Between 1000 BC to 1000 AD; a number of mathematical treatises had been written in India

One of the greatest and most important inventions of human mind is the concept of zero which owes its origin to the Indian Philosophy in connection with the idea of ‘Sunya’ which literally means void or nothingness that stands for the un-manifested unit source of all creations, the embodiment of infinite potentialities and the ground of being as depicted in the Vedic cosmology in the hymns of Nasadiya Sukta in Rig Veda. ‘Zero’ has emerged as a derivative symbol to represent this concept. The concept of ‘Sunyata’ or nothingness was also integral to Buddhist thinking according to Nagarjuna’s Sunyavada. This was an idea which no western mathematician had ever thought of. Mathematician Aryabhatta of 5th Century AD, was the first person to use this present-day symbol (0) for zero as a number and a digit, whereas a small black circular patch () was used as a symbol of zero earlier. As early as 500 BC, Indians had also developed for each number from one to nine, a system of different symbols instead of alphabetic representations. By including the symbol of zero along with these nine symbols, Indians developed the ingenious method of writing a number, no matter how large or how small, only with these ten symbols. Aryabhatta in his Aryabhattiya has stated “Sthanat Sthanam Dasa Gunam Syat” which means from place to place each digit has a value ten times that of the preceeding one. In this system, called the ‘decimal system’, each digit while having its absolute value, receives its place value according to its position as well. Due to the simplicity of this decimal notation, it facilitated mathematical operations such as addition and subtraction etc. under the efforts of Aryabhatta. One of the earliest written evidence of the decimal place value system with the use of zero can be found in the Jaina cosmological text ‘Lokavibhaga’ written by the Jaina muni Saruanandin in 458AD (Saka era 380). In this text shunya (void) has been used to refer to zero. Laplace, the French mathematician and Philosopher therefore wrote – “The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple now-a-days that its significance is no longer appreciated. Its simplicity lies in a way it facilitated calculation and placed arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of antiquity Archimedes and Apollonius.”

This decimal system made arithmetic quite useful in practical inventions much faster and easier. Therefore, Albert Einstein also once remarked with his acknowledgement that – “We owe a lot to the ancient Indians, teaching us how to count, without which most modern scientific discoveries would have been impossible.” This statement can be well appreciated if we just recollect the string of alpha-numeric Roman numbers having no zero and place value system to understand their limitations. Indian mathematicians invented negative numbers as well. Acharya Pingala; the Vedic scholar of 3rd or 2nd century BC was the author of the earliest known Sanskrit treatise on prosody (the study of poetic meters and verses) by the name ‘Chandah Sastra’. This treatise presents the first known description of the binary numerical system in connection with the systematic enumeration of meters with fixed patterns of shorts (laghu) and long (guru) syllables. In modern discussions binary numbers are usually represented by using zero (0) and one (1). Pingala’s notation was similar to Morse Code and he used the Sanskrit word ‘Sunya’ explicitly to refer to zero. This concept of binary numbers represented by ‘1’ and ‘0’ has now formed the corner stones of basic language for computer programs. Pingala is also credited with his work on Pascal’s triangle (called meruprastara) as well as materials related to Fibonacci numbers called ‘Matrameru’. Later on, the methods for the formation of these numbers in the sequence as (1, 1, 2, 3, 5, 8, 13 ……) and their implications were developed by mathematicians Virahanka, Gopala and Hemachandra, much before the Italian Mathematician Leonardo Fibonacci introduced this fascinating sequence to the western world in 13th century. Following the only method of the oral tradition of the time for the propagation of knowledge, be it spiritual or scientific, the sages, seers and scholars composed slokas in poetic styles in Sanskrit according to the rules prescribed in Sanskrit prosody described in ‘Chanda Shastra’ of Pingal. This methodology was based on natural rhythms and arrangement of tones such that the ‘Slokas’ so composed would be pleasing to the ears and easy to be remembered for a long time. Thus, mathematical concepts and formulas including various ideas were written down as meaningful syllables in verses and slokas. Indians therefore invented the ‘Katapayadi’ system, where even mathematical numbers could be transcribed as words or verses.

Indian number systems, as it is believed, probably arrived in the Arab world in 773 CE with the diplomatic mission sent by Hindu rulers of Sind to the court of Caliph Al-Mansur and subsequently through the Arabic traders. This gave rise to the famous arithmetical text written by Al-Khwarizmi in around 820 CE, which contains a detailed exposition of Indian Mathematics including usefulness of zero. Al-Khwarizmi was a Persian Mathematician who developed a technique of calculation that became known as ‘algorism’. In fact, in 7th century CE, Brahmagupta developed the ‘Chakravala Method’ to solve indeterminate quadratic equations including Pell’s equation. This method identified as a cyclic algorithm now was later generalized for a wider range of equations by Jayadeva and was further refined by Bhaskara-II in his mathematical treatise ‘Bijaganita’. Algebraic theories as well as other mathematical concepts that were prevalent in ancient India were collected and further developed by the famous Indian Mathematician Aryabhatta in 5th century CE, who lived in Pataliputra, the present-day Patna in Bihar. His treatise on Mathematics is the ‘Aryabhattiya’. Aryabhatta (466-550 CE) in his Aryabhattiya described important fundamental principles of mathematics in 332 slokas covering areas like algebra, arithmetic, trigonometry etc. He obtained the value of ‘ π’ correct upto four decimal places. The Kerala Mathematician Nilakantha at subsequent times wrote sophisticated explanations of irrationality of’ π’ before the west had heard of the concept. The classical period between 400-1600 CE is often known as the golden age of Indian Mathematics. This period saw Mathematicians such as Aryabhatta-I, Varahamihira, Brahmagupta, Bhaskar-I, Bhaskara-II, Madhava of Sangamagrama and Nilakantha Somayaji and many others. The treatise by the Persian mathematician Al-Khwarizmi which contained all these developments with due credits to these Indian sources, was translated into Latin under the title ‘Algorithm’s de numero Indorum’ meaning the system of Indian numerals. A Mathematican in Arabic is called Hindsa, which means from India. The technique of calculation developed by Al-as ‘algorism’ later became the germ for the modern computer algorithms. The ‘Bakhshali manuscripts’ of seventy birch bark leaves dating back to the early 7th centuries of the Christian era discovered in 1881 in the village Bakhshali near Peshawar (of modern-day Pakistan) reveals Indian achievements with knowledge of fractions, simultaneous equations, quadratic equations, geometric progression and even Khwarizmi, known originally calculations of profit and loss etc.

Our forefathers can also be credited for their knowledge in geometry, trigonometry and in some way calculus as well. 14th century Kerali Mathematician Madhava along with others of his Kerala School, studied infinite series, differentials and iterative methods for solving non-linear equations and examined methods and ideals relating to differential calculus. Jyesthadeva (1500-1576 AD) of the Kerala School wrote ‘Yuktibhasa’ in malayalum language comprising all these ideas. Jyesthadeva presented proofs of most mathematical theorems and infinite series discovered earlier by Madhava and other Kerala School Mathematicians. In fact the landmark in Indian Mathematics was the development of the series expansions for trigonometric functions like sine, cosine and arc-tangent etc by the mathematicians of Kerala school in 15th century CE. These remarkable works developed two centuries before the invention of calculus in Europe by Isaac Newton and Leibnitz, provided what is now considered as the first examples of power series. However, they did not formulate a systematic theory of differentiation and integration.

It would be worthwhile to mention about the Sulba Sutras, composed between 800 BC to 500 BC in Vedic Sanskrit mainly for a single theological requirement with rules for construction of sacrificial fire-altars. There are three Sulba Sutras out of which the best known is Boudhayana Sulba sutra composed by Baudhayana during 8th century BCE, which contains examples of Pythagorean triples such as: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25) and (12, 35, 37). This also contains a statement of the Pythagorean theorem for the sides of the square as “The rope which is stretched across the diagonal of a square produces an area double the size of the original square.” It also has a similar statement for the sides of a rectangle as “The rope stretched along the length of the diagonal of a rectangle makes an area which the horizontal and the vertical sides make together”. Baudhayana also gives an expression for the square root of two accurate up to five decimal places of the true value 1.41421356…. The other two Sulba Sutras are the Manava Sulba Sutra composed by Manava (750-650 BCE) and the other Apastamba Sulba Sutra, composed by Apastamba (600 BCE) with contents similar to Baudhayana Sulba Sutra. It has been found that the Babylonian cuneiform tablet ‘Plimpta – 322’ written around 1850 BCE, contains fifteen Pythagorean triples with quite large entries (13500, 12709, 18541). This indicates that there was also sophisticated understanding of the topic in Mesopotamia in 1850 BCE. Since these tablets predate the Sulba Sutras period by several centuries, taking into account this contextual appearance of some triples, it may be reasonable to expect that similar understanding would have been there in India. As the main objective of Sulba Sutras was to describe the construction of sacrificial fire-altars and the geometric principles involved in them, the subject of Pythagorean triples, even if it has been understood with its basic principles, many still not have featured in detail with the general proof in Sulba Sutras. This could have been due to the style of exposition demanded by the ancient oral tradition. Hence ‘Sutras’ adopted extreme brevity by expressing everything in a highly compressed form through multiple means. With the increasing complexity of mathematics and other branches of science like Astronomy, both writing and computation were required. Consequently, many mathematical works began to be written down in manuscripts to be copied from generation to generation.

India today has the largest body of hand-written reading materials comprising about several million manuscripts of prose commentaries and treatises. Then only derivations and proofs became favored. Thus Bhaskara-II (1114-1185 CE) in his Lilavati Bhasya, Bijaganita and Griha Ganitam that he wrote, had given a proof of the Pythagorean theorem. He had also conceived of differential calculus with concepts of derivatives, differential co-efficient. He had also stated Rolle’s theorem, a special case of mean value theorem which is one of most important theorems of calculus and analysis. Bhaskara-II had also developed the concept of infinity.

Physics

From the Vedic times around 3000 BC to 1000 BC ancient Indian sages and scholars ventured to analyze and understand the physical structure of the world. They considered that the material world of living and non-living bodies in their gross structure are constituted holistically by five basic elements called ‘Pancha Mahabhootas’ such as Khiti (earth), Apa (water), Teja (fire/energy), Marut (air), Vyoma (ether/space). They were associated with the five human sense perceptions such as earth with smell, air with feeling, fire with vision, water with taste and ether or space with sound. These ancient Indian Philosophers believed that except for ether/space, all other elements were physically palpable and hence composed of minuscule particles of matter. The last miniscule particle of matter which could not be further subdivided was termed as ‘paramanu’, the synonym for the Greek word ‘atom’. These Philosophers considered these atoms to be indestructible and hence eternal. However, in a later time the Buddhists believed atoms to be minute objects invisible to the naked eye which come into being and vanish in an instant like flares. The Vaisheshika school of Philosophers believed the atoms are mere points in space. As these concepts were based on logical analysis and abstract speculation but not on experimentation or personal observations, they are greatly abstract and enmeshed with philosophy as well. The school of Philosophy which contributed to the development of the ideas of ‘atom’ was the Vaisheshika School described earlier in chapter-4. Sage Kashyap known as Kanada Muni of 6th century BC, who composed the Vaisheshika Sutra, was the proponent of this idea. Another Indian Philosopher, a contemporary of Gautam Buddha, Pakudha Kaccayana had also propounded ideas about the atomic constitution of the material world.

Adherents of the Vaisheshika School of Philosophy founded by Kanada considered the atoms to be minute objects invisible to the naked eye and atoms of the same substance combined with each other to produce dyanuka (diatomic molecule) and tryanuka (triatomic molecules). They also believed that atoms could be combined in various ways to produce chemical changes in the presence of other factors such as heat. As an example of such a phenomenon, Kanada cited the blackening of earthen pots and ripening of fruit etc. According to Kanada, each substance is supposed to consist of four kinds of atoms out of which two kinds possess mass and the other two without mass.

Apart from the atomic postulations, Kanada also had ideas regarding the motion and rest of objects suggesting probably the same laws of motion attributed to Newton in the seventeenth century CE; more than two thousand years after him. This is because one finds in the Vaisheshika sutras, the verses regarding motion of objects as follows: –

“Vegah Nimitta Visheshat Karmano Jayate;

Vegah Nimittapekshyat Karmano Jayate,

Niyatadika kriya Prabandha Hetu,

Vegah Samayoga vishesha birodhi.”

This means action on objects generates motion. The external action being in a direction causes the motion in the same direction. An equal and opposite action can neutralize the motion.

In the fifth chapter of Vaisheshika Sutra, Kanada mentions various empirical observations on natural phenomena such as falling of objects to the ground, rising of fire and heat upwards, the growth of grass upwards, the nature of rainfall and thunderstorms, the flow of liquids, the movement towards a magnet and many other such cases and inquisitively searches why these things happen. Thus, it seems physics was central to Kanada’s assertion that all that is knowable is based on motion and therefore he attempted to integrate his observation with his ideas on atoms, molecules and their interactions in some rudimentary level.

In fact, Rig Veda asserted that gravitation is the cause that is responsible for holding the universe together. This was some twenty-four centuries before the anecdotal apple fell on Newton’s head. The notion of gravitation or gurutrakarshan is found in Siddhantas, the world’s earliest texts on astronomy and mathematics. ‘Siddhanta Siromani’ is one such text written by Bhaskara-II (1114-1185 CE) in which one can find the mention of gurutvakarshana in its Goladdhyaya-Bhubanakosha chapter as:

“Marudhalo Bhurachala Swabhabato yato

Bichitrabata-bastu Saktyah.

Aakrustisaktischa mahitaya yat khastam,

Gurutwabhimukham Swasakttya.

Akrudayate Tatpattobabhati

Samasamntat kwa patatwiyam khe.”

This means that each has the power of attraction by which it attracts material bodies towards it and so material bodies fall down on earth, when this power of attraction is uniform in all directions in the sky, then no object falls.

For this reason, the planetary systems and other stars and planets maintain their locations and motion in the sky. It has also been said that prior to Bhaskara-II, it was Varahamihira (505-587 CE), another Astronomer and mathematician of Siddhantic tradition who thought of the concept of gravity by claiming that there must be a force which might be keeping bodies stuck to earth and also keeping the heavenly bodies at specific places. Brahmagupta, another well-known mathematician of the 7th century had also commented on the concept of gravity as “Bodies fall towards the earth as it is like the earth to attract bodies, just as it is like water to flow.” Therefore Dick Teresi, the American writer of the book ‘Lost Discoveries’, a comprehensive study of the ancient non-western foundation of modern sciences, spells out clearly as:

“Two hundred years before Phythagoras,

Philosophers in northern India had

understood that gravitation held

the solar system together, and that

therefore the Sun, the most massive object,

Had to be at its centre.”

Aryabhatta, the one credited with the discovery of zero as the numeral, was also the first individual in 499 CE to explain that the daily rotation of the earth on its axis is the reason for the daily rising and setting of the Sun. Thus, he was the proponent of the helio-centric theory for the solar system. He conceived of the elliptical orbits of the planets thousand years before Kepler in the West assumed planetary orbits to be circular. Aryabhatta even came to the same conclusion. Before Kepler, Europeans estimated the value of the year as 365 days, six hours, 12 minutes and 30 seconds, only a few minutes off from the present correct value (365 days and six hours). This mathematical genius also made predictions of the solar and lunar eclipses as well as estimated the distance between the earth and the moon. The translation of Aryabhattiya into Latin in the thirteenth century taught Europeans a great deal revealing to them that Indians had known things that Europe would learn only a millennium after.

The Vedic civilization subscribed to the idea of a spherical earth at a time when everyone else, even the Greeks; assumed the earth to be flat. By the fifth century CE, Indians had calculated that the age of the earth was 4.3 billion years. But as late as the nineteenth century, English scientists believed the earth to be only a million years old. It is only in the late twentieth century that the western scientists have come to estimate it to be 4.6 billion years. This was in the aftermath of the first American Apollo mission to the moon that brought back the moon-rock to be analyzed to give this result which was highlighted in 1969 in American media comparing this outcome with ancient India’s almost accurate estimate.

There has been ample archeological evidence for ancient India’s use of ‘practical mathematics’ not only in measuring time on the basis of periodical cosmic events like earth’s rotation or orbital motion etc. but also in standardized measurements for weights as well as length. Excavations at Harappa, Mohenjo-Daro and other sites of Indus Valley Civilization have uncovered bricks whose dimensions were in proportion 4:2:1; considered favorable for the stability of brick structures. People of Indus Valley civilization used the standardized system of weights based on the ratios: 120,  110,  15,  12, 1, 2, 5, 10, 20, 50, 100, 200 and 500 with the unit weight equaling approximately 28 grams (approximately equal to one British Ounce). They mass produced weights in regular geometric shapes such as hexahedra, barrels, cones, and cylinders using their basic knowledge of geometry. They also used standardized measurement of length to a high degree of accuracy. They designed a ruler, the Mahenjodaro ruler, whose unit of length was approximately 1.32 inches or 3.4 cm which was divided into ten equal parts. The bricks manufactured at that time often had dimensions that were integral multiples of this unit of length. Hollow cylindrical objects made of shell and found at Lothal (2200 BCE) and Dholavira are demonstrated to also have the ability to also measure the angles in a plane as well as to measure the position of stars for navigation.

It is quite amazing to find that ancient Indians starting from the Vedic era had introduced various names for the units and sub-units of length or distance as well as time. As for example the Mokshya dharma parva of Shanti Parva in Mahabharat describes the units of time including Nimisha as follows. Accordingly, 1 diva Ratri (Day-Night) which is 24 hours as we know today was divided into 30 Muhurtas, I Muhurta was 30.3 kala; 1 kala was 30 kashta; 1 kasta was 15 Nimisha. 1 Nimisha is the time duration for the wink of an eye; which from the above relations can be worked out to be a recursive decimal in seconds as:

1 Nimisha = 0.2112, second.

Similarly, a unit measure of length or distance was taken as a ‘Yojana’, which has been defined in Vishnu Purana (Chapter 6 of Book 1) an ancient Vedic text in the following manner. If one starts with a standard subunit of length measure to be 1 Angula (1 finger length approximately 4 inch) then 6 Angula is 1 Pada, 2 Pada is 1 Vitasti, 2 Vitasti is 1 Hasta (cubit = 1½ feet), 4 Hastas is 1 Danda or Purusha (a man’s height = 6 ft), 2000 Dandas is 1 Gavyutis (distance to which a cow’s mowing can be heard = 12000 ft) and 4 Gavyutis is 1 Yojana which is approximately 9.09 miles. Working downwards from 1 Angula, the further sub-units are also defined in the following manners. 1 Angula which is 1.89 cm is 10 Yavas (barley grain of middle size), 1 Yava is 10 Yavodaras (heart of barely), 1 Yavodara is 10 Yukas, 1 Yuka is 10 Likhsha, 1 Likhsha is 10 Balagras (Hair’s tip), 1 Balagra is 10 Mahirajas, 1 Mahiraja (Particle of dust) is 10 Trasarenu, 1 Trasarenu is 10 Parasukshma, 1 Parasukshma is 10 Paramanu. Thus, one can find out a rough estimate of the atomic dimension to be 1.89x10cm which is rather one order of magnitude smaller than what we know today in Physics to be of the order of Angstrom units (108cm) However there is another quite interesting estimate one can arrive at regarding the speed of light on the basis of a Rigvedic hymn (50th hymn in book 1 of Rig Veda), which is:

Taranir Vishvadarshato Jyotishkradasi Surya

Vishvama bhaasirochanam

Tatha cha Smaryate yojanam

Shahasre dve dve sate dve cha yojana

Ekena niminshardhena kramamana.”

Which means;

“Swift and all beautiful art thou

O’ Surya, maker of the light;

Illuminating all the radiant realm.

It is remembered here that this light

 traverses 2202 Yojanas in half a nimisha.”

Sayanacharya, who was a minister in the court of Buka of the great Vijaya nagar empire of Karnataka in South India in early 14th century commenting on this verse in his Rigvedic commentary has pointed out its significance in estimating the speed of light. If one takes the time unit Nimisha = 0.2112 second and the distance unit Yojana = 9.09 miles as found according to the above-mentioned ancient texts; then 2202 yojana in 1½ Nimisha of travelling would mean a speed of light 2202 x 9.09 miles per 0.1056 seconds. Which means the speed of light so calculated would be:

c =  2202 x 9.09 0.1056 = miles/second

= 189547 miles / second

As per the presently known value of the speed of light, c=186000 miles/second. This is amazingly so close to the accurate value that was revealed to our ancestors several thousand years before modern science could realize it through centuries of various attempts using different experimental techniques besides the theoretical calculation based on Maxwell’s identification of light as an electromagnetic wave.

Reference

1. Basam A. L, The wonder that was India, Rupa & Co., New Delhi (1971).
2. Bose, D. M, Sen S. N, Subbarayappa B. V, A concise history of Science in India; Indian National Science Academy, New Delhi (1971).
3. Joseph G.G, Crest of the Peacock, Non-European roots of Mathematics, Princeton University Press (2000).
4. Puthaswamy T. K, Mathematical achievements of Pre-modern Indian Mathematics, Elsevier (2012).
5. Teresi Dick, Lost Discoveries: The Ancient Roots of Modern science from the Babylonians to the Maya, Simon & Schuster, New York (2002).

Factors promoting attachment of charge particles with positively charged photon in charge polarisation of light

Light particles have very-very small dimensions therefore, head-on collision among photons is rare. According to the new concept the light particles are particles of micro-micro domain carrying positive photonic charge and having nuclei and extra nuclear space structure [2] [3]. Since light particles carry photonic charge in very-very small dimension, the short-range interaction of photonic charge can be expressed in micro-micro domain scale only. Due to photonic charge interaction the collision cross-section is much larger than the dimension of the nucleus. If the density of negatively charged sub-photonic particles (pholetrons) in the medium is very low then the positively charged photon may not collide even if the collision cross-section of photon is large. If there is no collision, then there is no change in the photonic charge state of the light particle by attachment implying no polarisation of light. If all the emergent light particles take part in attachment of pholetrons, then there is 100 percent polarisation of light. The condition affecting the degree of polarisation is discussed subsequently. 

The factors affecting degree of polarisation of light are 1) density of pholetrons in the medium, which is an inherent property of the structure of material and its surface. Thus, the polarizing materials having higher density of pholetrons in free state have scope of attachment with light particles by the collision process. 2) All collisions within the collision cross-section of the light particle may not lead to attachment since the negatively charged sub-photons (pholetrons) are required to reach the proximity of the light particle for the feasibility of attachment with the light particle. This requires a minimum exposure time period for acceleration of pholetrons in reaching the proximity of light particles, which is feasible only when the velocity of a light particle is sufficiently reduced or approaches zero in its transit.

Spin polarisation of light particle

During collision of pholetrons and other space matter particles of the medium with the light particle, a turning moment is produced on the light particle and the light particle begins to spin or changes the kinematics of spin if already spinning. Hence, the emergent polarised light particles additionally acquire the spin property which may promote or foul in entering the interface and the internal structure of the solid depending on the nature of spin of the inter-atomic cavity Fig.3.

In the new concept the extra nuclear space structure of an atom is formed due to mass-space attraction. The space density of extra nuclear structure decreases outwardly due to the inverse square law of mass-space attraction. Thus, the size of the atom is a function of background space density which in turn is a function of the number density of space matter particles. Within the extra nuclear structure, a number density of space matter particles goes on increasing towards the nucleus. Thus, the size of the extra nuclear space structure of space matter particles decreases towards the nucleus. Hence, the space holding per unit of mass of a space matter particle goes on decreasing towards the atomic nucleus. In the new concept charge (electric and non-electric) is a state property of matter (mass-space integral system) characterised through the mass-space in matter relative to the mass-space ratio of matter in its background. In a given background if all matter has the same mass-space ratio (same space holding per unit of matter) then they are neutral to one another and each matter or their assembly can be considered to have zero charge potential in a relative scale. Any one space matter particle or their cluster is a neutral matter carrying zero charge in the relative charge concept. Another space matter particle with a different space holding per unit of mass entering to the neutral environment is characterised to carry charge with reference to the zero-background potential. Conventionally a mass rich particle (less space holding per unit of mass) carry positive charge and a space rich particle (more space holding per unit of mass) carry negative charge. Following the absolute scale of charge, all particles in all states and in all domains have an absolute value of charge due to its mass space ratio where the pure space without mass relates to zero absolute charge potential and the potential goes on increasing with the increase of matter content per unit of space content. Thus, the inter atomic space in solid contains mass rich space matter particles and that of space medium contains space rich space rich space matter particles. Hence, the inter atomic space potential (photonic charge potential) of solid and liquid is much higher than that of gas or space medium. Hence, the interface zone facing solid at one end and space medium at other end has a high order of potential difference. The interface is composed of mostly micro-micro domain particles (light particles) and for a di-photonic interface structure, polarization features are inevitable. One can visualize from the natural polarised electric structure of the atmosphere of the earth starting from the surface. 

Bending of light near sharp edges

The equipotential planes of the interface are parallel to the surface. A sharp edge in the form of a line is formed when two surfaces meet. But the equipotential planes of the interface don’t form such a sharp line as it takes a smooth curve at location of corners and the radius of curvature increases outwardly as shown in Fig.3. There exists a photonic charge potential gradient within the interface with high potential corresponding to charge state of photons within the inter atomic space of solid and the low potential corresponding to the charge state of photons in the space medium adjacent to the interface. The potential gradient is stronger near the solid surface and weaker towards the space medium. The degree of photonic charge polarization of the interface medium is high at the near end of the solid surface and reduces to zero at the far end from the solid surface. In order to express the polarised potential within the interface, a relative potential scale is used with a dynamic reference zero line as shown in Fig.3. With reference to the relative photonic charge potential scale the positive and negative maxima planes of the interface are shown in red and green lines respectively. 

Incident light particles passing close to the corner of a solid, though have clear access without intervention with the solid structure but are intercepted by the photonic field structure of the interface. During the transit of light particles close to the corner, the light particle is accelerated and decelerated as it crosses the decreasing potential and increasing potential zones of the polarised field respectively. Thus, the gross field effect of the interface on the light particle changes the rectilinear trajectory causing bending of light at corners (Fig.3).

Conclusion

Any realistic physical phenomenon is expected to have a realistic physical basis for understanding the phenomenon. Despite the mathematical merit of the wave theory of light, it lacks the very feasibility of the wave without a tangible medium. On the other hand, the particle concept of light though realistic but it lacks realization of mass and non-charge in finer domain, a domain below micro domain. The new perception of matter value and non-electric charge in light particles (particles of micro-micro domain) renders new scope for conventional dynamics in explaining different phenomena of light. The revised concept of the light particle and the new structure of medium have helped in understanding reflection, refraction and the constant velocity of light. This paper gives a clear picture, how the macroscopic concept successfully explains the grazing phenomena of light. If the particle concept of light is the only reality, then it can as well explain the remaining phenomena of light. If this is possible then we may not have to assume that duality is a reality of nature. 

Reference

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