Raja Kishore Paramguru, Author at Institute of Philosophy of Nature

Unified Field Theory: Indians Part of Research

Raja Kishore Paramguru — Sat, 02 May 2026 04:24:07 +0000

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.

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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Unified Field Theory: Chinese Vision Through Yin-Yang Philosophy

Raja Kishore Paramguru — Sun, 25 Jan 2026 05:25:05 +0000

Abstract

This paper presents a brief review of the universal archetypal opposites yin and yang, the ancient Chinese philosophy, in relation to unified field theory. The researchers have given detailed account of the origin, history, application, and practice of the yin-yang philosophy in Chinese tradition. Its application and worthiness in unified field theory have been examined through yangton and yington hypothetical theory, use of yin-yang philosophy as virtual and physical duality, as bipolar dynamic logic, as complex mechanics etc. It remained to be examined by the theoretical physicists.

Key Words: Unified Field Theory, Chinese Vision, Yin-Yang Philosophy, Virtumanity, Dialectical nature, Virtual and physical duality, Yangton and yington hypothetical theory, Complex-valued mechanics, Bipolar dynamic logic.

Introduction

This paper starts from where the last paper [Paramguru 2025] ended. The particular portion may be cited here – “As regards the incompatibility between GR and QM is concerned, Beichler provides an interesting observation; he writes – ‘Relativity is first and foremost about form (structure) and the quantum is primarily all about function, which come together as one of the most fundamental dualities (known as non-commuting quantities in physics) in nature, but there is always a bit of each in other. However, these two ideas, form and function, are not necessarily incompatible since there is always a little of one in the other at a higher level of understanding’ [95]. Here, most interestingly, the author puts a picture of the ancient Chinese symbol called ‘T‘ai-chi T’u’, or ‘Diagram of the Supreme Ultimate’, meaning – GR and QM can combine the same way as ‘yin and yang’, the universal archetypal opposite poles of nature combine” [232]. Thus, the subject matter of this paper is combining the dualities of form and function utilizing the universal archetypal opposites of yin and yang, the ancient Chinese philosophy.

Incidentally, significant amount of literature on this subject by a number of Chinese scholars are available. A resourceful software engineer cum entrepreneur Wei Xu has successfully combined philosophy of nature, universal field theory (UFT), natural cosmology and ontological evolution by using yin-yang philosophy to understand the virtual and physical dualities which exist in nature. Many of his publications are through his own theoretical framework Virtumanity Inc which means sciences in dialectical nature of virtual and physical duality [Xu 2016, Xu 2017, Xu 2019a, Xu 2019b]. Another scholar Edward Tao Hung Wu (1952-), born in Taiwan, graduate from Tsing Hua University, PhD from UCLA, living in California, USA; besides his software and piezoelectric entrepreneurship interests, during last years, has developed yangton and yington hypothetical theory [Wu 2015a, Wu 2015b, Wu 2016a, Wu 2016b, Wu 2018, Wu 2024]. While, Wen-Ren Zhang, a PhD in electrical and computer engineering and a Professor teaching quantum computing has published on bipolar features of yin-yang philosophy [Zhang 2009, Zhang 2012]; Ciann-Dong Yang, a Distinguished Professor in the Department of Aeronautics and Astronautics at National Cheng Kung University, Taiwan, and a specialist in complex mechanics and quantum mechanics has thrown significant light on realization and verification of yin-yang theory [Yang 2010].

Literature on this subject continues to pour in. Luo Shan, working as a pharmacist in a staff hospital in China, keeps interest in the traditional Chinese yin and yang theory and its application to scientific understanding of matter and systems [Shan 2019]. Qiu-zi Cong, Xiang Yu and De-yang Yu, all of them Professors in China, have integrated theory of physical particles and yi field [Cong etal 2021]. Wutong T. Song and Hongxin Cao, Chinese researchers in the area of Traditional Chinese Medicine (TCM) with specific interest in concepts of yin-yang, consciousness, and psychosomatic health have published their work on reality and application of yin and yang [Song and Cao 2022]. Based on this treasury of literature, this paper aims at giving a brief account of this Chinese vision of yin-yang philosophy in relation to UFT.

What is Yin-Yang philosophy

The book, The Tao of Physics, written by the Austrian born American physicist Fritjof Capra [1975] has already been discussed by the present author in the pages of this journal. The origin of yin-yang philosophy is Taoism, in the words of Capra – ‘The Tao is the cosmic process in which all things are involved; the world is seen as a continuous flow and change’ [104]. He goes on further – ‘The principal characteristic of the Tao is the cyclic nature of its ceaseless motion and change’ [105]. Here comes the polar opposite yin and yang which give a definite structure and meaning to the cyclic patterns of the motion of the Tao, the nature. The Chinese believe that all manifestations of the Tao are the results of the dynamic interplay of yin and yang. This symbolism of the archetypal pair yin and yang is pretty old, might have been derived more than two thousand years ago, and afterwards generations of people built it up through their thought process into a fundamental Chinese concept. These two archetypal poles of nature represent not only bright and darkness, but also male and female, firm and yielding, above and below, and many more. Yang is believed to be the strong, male, creative power associated with heaven; whereas, yin is taken as the dark, receptive, female representing the earth. In this symbol of yin and yang, the former is always denoted by black and the later by white; however, it is believed that there is always some black within the white and vice-versa. The Chinese people also believe that all things have yin and yang, which are universal and opposites, yet they complement and supplement each other with interdependence forming unity and harmony. In the course of this article, as will be seen, various authors will bring out various other essential characteristics of yin-yang.

The Yangton and Yington Hypothesis

As indicated above, this hypothesis has been built by the entrepreneur-thinker Edward Tao Hung Wu. The basis of this hypothetical theory is a circulating pair named as ‘Yangton and Yington’ with an inter-attractive force termed as ‘Force of Creation’. When this pair, made up of some-sort-of superfine magic-like particles, moves in space is termed as ‘Photon’; and when it sits in still is called as ‘Wu’s Particles’ or ‘Still Photon’. This particle named according to the name of the author is apparently imagined as the real ‘Photon’, and the circulating pair is given the apparent impression of yin-yang, though the author has never spelt out in this manner anywhere in his publications. He starts with the paper “Yangton and Yington – A Hypothetical Theory of Everything” [Wu 2015a] where, after defining the basic terms, he spells out that this pair can be spontaneously created at anywhere and anytime in the universe, and he proposes this to be the mode of creation of our universe. Then, he goes on explaining skillfully – how his proposition worked during the creation of our universe according to the Big Bang theory; how the free photon travelling at the speed of light combines Particle Physics and Quantum Mechanics explaining all the properties of light; how the Still Photon becomes the building block of all matters and the Force of Creation becomes the base for four forces. Finally, he explains Einstein’s relativity equation and existence of dark matter according to his hypothetical Yangton and Yington theory.

In his subsequent papers he has expanded his hypothetical vision of Yangton and Yington theory to explain subatomic particle structures in relation to the unified field theory [Wu 2015b]; to interpret gravitational waves, Newton’s Law and Coulomb’s Law by particle radiation and interaction theory [Wu 2016a]; to define the meanings and inter-relations between mass, momentum, force and energy of photons and subatomic particles [Wu 2016b]; and finally brings out his book My Universe: A Theory of Yangton and Yington Pairs [Wu 2018], with a summary [Wu 2024]. Between 2015 and 2024, a total of 71 papers and a book have been published by the author highlighting all details about his hypothetical theory [Wu 2024]. In the words of the author himself, his theory is: ‘As a result, Wu’s Pairs is an excellent model in study of the universe. Even without direct proves of the existence by physical experiments, Wu’s Pairs and Yangton and Yington Theory can be considered as the foundations of a binary universe. Just like the binary system to the decimal system in mathematics, many theories and principles developed in the binary universe can be used effectively in the real universe’ [2024, 13].

The Yin-Yang Theory

Unlike the entrepreneur-thinker Edward Wu whose work formed the previous section, the present section discusses three publications, the first by a specialized pharmacist working in a Chinese hospital, the second by three Chinese Professors, and the third by Chinese researchers in the area of TCM, all with specific interest in concepts of yin-yang and straightaway talk about applications of yin-yang theory. The pharmacist, Luo Shan’s paper reads “The Law and Applications of the Theory of Yin and Yang” [Shan 2019]. Here, the author starts with the conventional nature of yin and yang which is according to him – ‘the substance that constitutes the phenomena of matter system’, where ‘the scientific connotation of “Yin and Yang” is that “Yang” is the macro-structure of the quality system of matter phenomena, and “Yin” is the energy flow potential field matching with “Yang”’ [27]. Then he goes on deducing the laws and elaborating their meaning and interpretation. He points out that, during matching of yin and yang, since the latter represents the matter formation with mass M, it is easy to observe and measure it, and because the former represents the energy flow, it is difficult to observe and measure it. Then he presents the matching methods and finally concludes that ‘To sum up, the law of Yin-Yang balance explains that the phenomena of the matter system are the projection of mass-energy interaction. The maintenance of phenomena must maintain the integration of the mass-energy state, and the change of phenomena is accompanied by the direction of state change, which can be judged by the change of state parameters’ [31].

The second publication is the book The Theory of Physical Particles and Yi Field [Cong et al 2021] also deals with similar philosophy. The authors also term this theory as Li-Yi field theory, or, simply Liyi; and here, they combine the traditional Yi concept and the five-element theory of Li Yin and Yang, which integrates, with it, the analytical results of Western natural science. The authors claim that it also forms the LiYi time-space concept, and particularly add that these four fundamental principles are based on the Li Yin-Yang/mass-energy-time-space four-image principle of nature. Further, the conservation of field momentum, the Li Yin-Yang principle of interaction, and complex energy conservation are also supplemented with it.

The third title reads “The Reality and Application of Yin and Yang” [Song and Cao 2022], where the authors illustrate the origin, history, and characteristic of Yin and Yang philosophy in Chinese tradition, then explain how it functions, and finally demonstrate their application. ‘Yin and Yang originated in Chinese civilization more than 2000 years ago. In the first stage, ancient philosophers discovered yin and yang and their laws of motion —. In the second stage, yin and yang and the laws of yin and yang movement are used to explore methods and techniques’ [25]. Then the authors show that ‘Yin and Yang reveal the nature and state of matter’ [25], they also reveal ‘the laws of physical motion’ and ‘transfer of energy conversion’ [26]. Then they have shown their practical applications in the field of agriculture, heat transfer in different aquifer media, solar thermoelectric conversion, Chinese traditional medicine, and discovery of binary numbers for use in computation etc. ‘In conclusion’, they mention that ‘yin-yang is a key to unlocking the treasures of traditional Chinese civilization, which can help to bring into play its original values, and continue to provide new insights and directions for the development of modern science and the advancement of humanities’ [23].

Virtumanity – Yin Yang Physics – UFT

Wei Xu, originally a theoretical physicist from China, then an electrical and computer engineer from the United States of America, working in America as a resourceful entrepreneur, simultaneously delivered comprehensive innovations in information technologies as well as scientific principles and philosophies in natural cosmology and UFT. We are interested in the later. It seems that he ‘received a set of the divine books in the old classic manuscripts: worlds in universe’, during the period 2009 – 2019, from where the ground-breaking philosophies of theoretical physics, starting from constitution of elementary particles to inception of ontology of nature emerged’ [Xu 2019b, ix]. Based on which he straightaway jumped to the statements – ‘The year 2015 bids farewell to an intellectual age defined by classical physics, from Newton’s mechanics of 1687, to General Relativity of 1915, to Quantum Theory of 1920s, and to mathematical physics of today.– The vagueness of mathematized physics has been gone awry and pushed to extreme for a forty-year search on a “Theory of Everything”, followed by another sixty-year period wasted on String or Superstring Theory, M-Theory, and other fairy-tale physics’ [Xu 2019a, x]. From here he moves on to the solution – ‘our ancestors discovered that duality orchestrated and harmonized their reality: sun-moon, warm-cold, materialization-consciousness, body-mind, male-female, thought-action, and more. — What promise hides in the dualities of physics: space-time, wave-particle, energy-mass, spin-charge, positive-negative, symmetry-asymmetry? — These dualities are balanced, interdependent, and inexorable. They are manifest in each particular action and movement, the outcome of a dialectical struggle for superiority. — It is essential to believe that the true framework of our universe is a topological hierarchy of virtual and physical duality, flourishing everywhere among the great streams of life, inspiration, and enlightenment. — Yinyang duality is rooted in the philosophy of seven millennia past, when our ancestors built a profound metaphysics. — Now is the time to realize the duality of metaphysics and physics, and to unite these disciplines in a greater whole’ [xi].

Then he created ‘Virtumanity Inc’, a platform to deal with the sciences in the dialectical nature of virtual and physical duality, where he put up all his thoughts as well as research work which he names ‘yin-yang physics’. The basis of yin-yang is ‘the supernatural principles in an environment of virtual space’, that the ‘Chinese tradition has developed the profound metaphysics and established scientifically the natural laws of Xing or YinYang duality: the reciprocal interaction of the opposite Matter and States is to cause all universal phenomena. — The Yin or Yang, or simply – and +, are the states of or the operation on an element or object, which form a coherent fabric of our nature, as exhibited in all physical existence.’ [Xu 2019b, 4]. From this basic principle, he proceeds with explaining the ‘duality of nature’; ‘energy and mass’, where he shows these two to be one duality of yin-yang nature of universe; ‘universal topology’; ‘quantum fields’; ‘symmetric and asymmetric fields’; ‘principles of ontology’; with generation of essential equations at each stage. His last conclusion is – ‘Finally, quantum ontology integrates general relativity, quantum curvature, gravitational fields seamlessly together’ [180].

The following two sections deal with specific scientific issues, one, bipolar dynamic logic; and the other, complex-valued mechanics, linked with yin-yang theory.

Yin-Yang Theory and Bipolar Dynamic Logic

Wen-Ran Zhang, a computer engineer, alone or along with his co-authors, published many papers using the bipolar dynamic logic to link Yin-Yang to various phenomena such as, quantum cellular automation, quantum computing, equilibrium-based bio-system simulation, bipolar fuzzy logic etc. Here, just two of his publications have been picked for a brief discussion, one, where he uses ‘bipolar Yin-Yang relativity’ as ‘a unifying theory of nature, agents, and life science’ [2009]; and the other, how a ‘Yin-Yang bipolar atom’ can lead ‘an eastern road toward quantum gravity’ [2012]. In these two publications, the author has cited some significant references of Yin-Yang philosophy being used by prominent people in the past such as: ‘the legendary German mathematician Leibniz invented binary numeral system in the 17th century and attributed his invention to YinYang trigrams’ and ‘now binary numeral system is a basis for all digital technologies’ and ‘according to the Daoist cosmology YinYang stands for “everything has two sides or two poles”’, in the former [2009, 382]; and ‘legendary Danish physicist Niels Bohr, a father figure of quantum mechanics, brought YinYang into quantum theory for his particle-wave complementarity principle’ in the later [2012, 1261]. Even, later, Bohr designed his own coat having the Yin-Yang logo with the Latin statement “contraria sunt complementa” which means “opposites are complementary” [1262]. The two publications are based on this particular philosophy.

In the former publication, the author has introduced ‘Yin Yang bipolar relativity and a real-world bipolar string theory as a unification of nature, agents, and life science.’ He has based his argument on the facts that, ‘bipolarity as an integral and inherent part of equilibrium is inseparable from equilibrium-based holistic truth’; that, action-reaction forces, particle-antiparticle pairs, negative-positive energies, input and output, or Yin and Yang in general are the most fundamental opposites of nature; and that, ‘the Yin-Yang bipolar sub-atomic particles discovered at the Fermi National Accelerator Laboratory show typical bipolar equilibrium/non-equilibrium properties’. Then, by introducing string theory and using ‘nine axioms and 16 conjectures for microscopic and macroscopic agent interaction, regulation, coordination, and exploratory scientific discovery in physical and social sciences’, he has proved that ‘bipolar relativity constitutes an equilibrium-based axiomatization of physics – a partial but most general solution Hilbert’s problem 6’ [2009,377]. In conclusion, he mentions that ‘the significance of this work lies in its equilibrium-based open-world open-ended unification of nature, life science, and socioeconomics as well as general relativity, electromagnetism, quantum mechanics, causality, and agent interaction’ [382].

In the later publication, the author starts with the facts that ‘Yin-Yang bipolar equilibrium-based approach to physics and science provides a fundamental super symmetrical alternative for scientific unification’ and ‘atom as a basic unit of matter should follow equilibrium or non-equilibrium conditions’ [2012, 1261]. Then he introduces a causal theory of Yin-Yang bipolar atom based on bipolar dynamic logic and bipolar quantum linear algebra which ‘provides a springboard to an equilibrium-based logical unification of particle and wave, matter and antimatter, relativity and quantum theory, strings and reality as well as big bang and black hole’ [1262]. Finally, the author brings out five postulates: (1) ‘Bipolar quantum entanglement is the most fundamental entanglement in quantum gravity’, (2) ‘YinYang bipolarity is the most fundamental property of the universe’, (3) ‘YinYang bipolar atom is a bipolar set of quantum entangled particle and antiparticle pairs’, (4) ‘Gravity is fundamentally large or small scale bipolar quantum entanglement’, and (5) ‘The speed of gravity is limited by the speed of quantum entanglement and not by that of light’ [1269]. The final lines of his conclusion read – ‘— the equilibrium-based approach to quantum gravity is fundamentally different from other approaches in philosophical basis. Since all beings must exist in a certain equilibrium or non-equilibrium, a scientific reincarnation of philosophy is predicted’ [1270].

Yin-Yang Theory and Complex Mechanics

One very important publication here is “A scientific realization and verification of Yin-Yang theory: complex-valued mechanics” [Yang 2010] by an author who is a super-specialist in the real scientific domain of complex and quantum mechanics. He starts with the fact that the philosophy of Tai Chi believes that the Tao, meaning nature, contains two parts, one is yang which is the observable (real) part, and the other is yin that is the unobservable (imaginary) part. Mathematically, it means that the nature is a complex-valued world and what we sense and measure is only the real physical world we experience in our daily life. The author compares it to be similar as the complex-valued mechanics, also known as quantum Hamilton mechanics with which he works in his laboratory, which is based on the same philosophy that the actual scenario of dynamic motion happens in complex space and the physical reality is merely its projection into the real space. Then he makes the statement – ‘Complex-valued mechanics (complex mechanics in short) is a rigorous physical realization of Yin-Yang theory, providing a unified approach to classical mechanics, quantum mechanics and relativistic mechanics under complex space.’ [136].

The author mentions that the symbol of Tai Chi is a combination of yin and yang, the former is marked with black and the later with white; although it is believed that always there is some white in the black and vice-versa. The author also believes that the Yin-Yang theory has remained an issue of pure-philosophy for a long time and this complex mechanics study of his is the first scientific realization of this theory through the mathematical language of complex variables and points out strong evidence of Yin-Yang duality in quantum mechanics. To prove his point, the author proceeds to first define a motion in complex space according to the Yin-Yang philosophy, then derives its equations of motion from the quantum Hamilton equations, and subsequently verifies ‘the Yin-Yang duality in quantum mechanics by showing how complex motions and their related real/imaginary interactions give rise to various quantum phenomena as observed from the real space’ [137]. All these quantum phenomena include tunnelling, spin, quantization, uncertainty principle, multiple paths and wave-particle duality, all originate from the Yin-Yang entanglement, i.e., the interaction between real and imaginary motions in complex space. Finally, he concludes – ‘— just as the interaction between Yin and Yang creates the universe, the interaction between real and imaginary motions produces all the observed quantum phenomena. The couplet shown in Fig. 11 highlights the role of the complex mechanics as a bridge between the Yin-Yang duality in Tai Chi and the wave-particle duality in quantum mechanics.’ [154].

Conclusion

In the introduction, the objective of this paper was fixed to combine the dualities of form and function utilizing the universal archetypal opposites of yin and yang, the ancient Chinese philosophy. To what extent this objective is fulfilled? Obviously, many of the studies presented above have used the yin-yang philosophy as a combination of virtual and physical dualities, whether in hypothesis, in reality, as bipolar dynamic logic, or, as complex-valued mechanics. One citation demands a place here – ‘Therefore, yin and yang are created to describe the properties of natural substances, and the movement of yin and yang is to illustrate the change patterns of the natural substances. Form and field are inseparable and can be transformed into each other under certain conditions. The properties of yin and yang are not absolutely fixed’ [Song and Cao 2022, 25]. At least form and field find special mention. How all these studies will influence the theoretical physicists remains to be seen.

References

Beichler, James E. April 2015. “The Einstein unified field theory completed.” Preliminary Paper. https://de173.com/wp content/uploads/2019/04/Einstein_Unified_Field_Theory_Completed.pdf
Capra, Fritjof. 1975. The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism. Boulder: Shambhala.
Cong, Qiu-zi, Yu, Xiang, and Yu, De-yang. The Theory of Physical Particles and Yi Field. Cambridge Scholars Publishing, UK, 2021.
Paramguru, Raja Kishore. 2025. “Unified Field Theory: Post-Einstein-Journey So Far.” Towards Unification of Sciences 3 (4): 225-234.
Shan, Luo. “The Law and Applications of the Theory of Yin and Yang.” 2019 3rd International Workshop on Arts, Culture, Literature and Language (IWACLL 2019), Francis Academic Press, UK: pp. 27-31. doi:10.25236/iwacll.2019.007 https://webofproceedings.org/proceedings_series/ART2L/IWACLL%202019/IWACLL19007.pdf
Song, Wutong, T. and Cao, Hongxin, X. “The Reality and Application of Yin and Yang.” Chinese Medcine 13 (2022): 23-31. https://doi.org/10.4236/cm.2022.132003
Wu, Edward T. H. 2015a. “Yangton and Yington – A Hypothetical Theory of Everything.” Science Journal of Physics Volume 2015, Article ID sjp-242, 6 pages. doi: 10.7237/sjp/242.
Wu, Edward T. H. 2015b. “Subatomic Particle Structures and Unified Field Theory Based on Yangton and Yington Hypothetical Theory.” American Journal of Modern Physics 4 (4) 2015: 189-195. doi: 10.11648/j.ajmp.20150404.15.
Wu, Edward T. H. 2016a. “Gravitational Waves, Newton’s Law of Universal Gravitation and Coulomb’s Law of Electrical Forces Interpreted by Particle Radiation and Interaction Theory Based on Yangton & Yington Theory.” American Journal of Modern Physics 5 (2) 2016: 20-24. doi: 10.11648/j.ajmp.20160502.11.
Wu, Edward T. H. 2016b. “Mass, Momentum, Force and Energy of Photon and Subatomic Particles, and Mechanism of Constant Light Speed Based on Yangton & Yington Theory.” American Journal of Modern Physics 5 (4) 2016: 45-50. doi: 10.11648/j.ajmp.20160504.11.
Wu, Edward T. H. 2018. My Universe – A Theory of Yangton and Yington Pairs. Independently published.
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Xu, Wei. 2016. Unified Physics: Horizon Fields. Universal and Unified Field Theory. 4. General Asymmetric Fields of Ontology and Cosmology. Virtumanity Inc., August 1st, 2016. USA.
Xu, Wei. 2017. “Unified Field Theory – 1. Universal Topology and First Horizon of Quantum Fields.” International Journal of Physics 5 (1) 2017: 16-20. Available online: http://pubs.sciepub.com/ijp/5/1/3. doi: 10.12691/ijp-5-1-3.
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Yang, Ciann-Dong. 2010. “A Scientific Realization and Verification of Yin-Yang Theory: Complex-Valued Mechanics.” International Journal of Nonlinear Science, and Numerical Simulation 11 (2) 2010: 135-156. https://www.researchgate.net/publication/287178962
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Unified Field Theory: Post-Einstein-Journey So Far

Raja Kishore Paramguru — Sat, 25 Oct 2025 12:02:14 +0000

Abstract

Following Einstein’s vision of Unified Field Theory (UFT) in the last issue of this journal, this paper is a brief narrative of the efforts towards achieving a consistent UFT during the post Einstein era extending till today. After Einstein, a limited effort has gone in towards UFT based on classical methods. Major efforts have been made in the direction of developing Grand Unified Theories (GUTs) and Theory of Everything (TOEs), the last one trying to combine general relativity and quantum mechanics. In spite of lots of efforts, the theoretical physicists are yet to approve a consistent TOE, which is the modern equivalent of UFT.

Keywords: Unified Field Theory, Post Einstein era, Grand Unified Theory, Theory of Everything.

Introduction

Seventy years have passed by after the legendary world-famous scientist Albert Einstein left for his heavenly abode in 1955. By this time, volumes of knowledge have entered into the ocean of theoretical physics which was his domain of research, with scores of people researching in the area of unified field theory (UFT), one of his dream subjects which was already well-founded by him as discussed in the last issue of this journal [Paramguru 2025]. This research have also been widely covered in a number of research papers [Beichler 2015, de la Cuesta and Grok 2025, Cao et al 2015, Ellis 1996, Ho 1995-1 and -2, Moffat 1979, Pati and Salam 1974, Bergmann, 1979, Popli 2003, Tiwary 2011] and books [Hlavaty 1957, Felker 2005, van Dongen 2010, Eckardt 2022]; besides one noteworthy historical coverage in Living Reviews in Relativity by the German theoretical physicist Hubert Goenner [2014] and two books by the French counterpart Marie-Antoinette Tonnelat [1966 and 2014]. Goenner has rightly summed-up through the statement that ‘(T)the idea of unifying all fundamental physical interactions in one common representation is as alive today as it was in Einstein’s times’ [2014, 195]. This research position with such a vast literature base calls for a review which is being aimed here.

After Einstein’s ground-breaking special relativity theory in 1905, general relativity theory in 1915 and his utterances about UFT during 1920s, many theoretical physicists and mathematicians enthusiastically jumped into research to unify the then-known fundamental physical interactions. Tonnelat’s book [1966] and Goenner’s review [2014] purposefully describe the state of research on UFT till mid-1960s. Interestingly, Goenner states that ‘(I)in total, about 150-170 scientists did take part in research in UFT between 1930 and 1965’ [183], and as regards the knowledge production in UFT during this period is concerned, ‘a yearly average of 18 papers’ (630 papers during 35 years) have been reported [183]. This period is supposedly the most productive period of research on UFT. From mid-1960s started the modern era of UFT with advent of quantum field theory, electroweak interaction, Higgs mechanism, spontaneous symmetry breaking, and many more, which make the UFT research still attractive. The present review will make an honest attempt to briefly discuss the UFT research subsequent to mid-1960s in lines of UFT in classical direction, UFT and quantum theory, Grand Unified Theories (GUTs), and Theory of Everything (TOE).

UFT in classical path

Practically speaking, the classical path of UFT, for all purpose, has ended with the demise of its creator Albert Einstein without producing a concrete result. In the original words of his former assistant P. G. Bergmann ‘Einstein spent the last five years of his life investigating this theory (the ‘asymmetric’ theory) without arriving at clear-cut answers’ [Goenner 2014, 195]. Of course, by that time, Einstein was already isolated from the main stream physicists, and Goenner himself has stated, referring to his last years at Princeton, USA, that ‘(N)nevertheless, while highly respected, Einstein and his theories lived there in splendid scientific isolation’ [2014, 178]. Even then, Einstein had his followings and many researchers kept working on his theories during the subsequent years; one quite often finds a title ‘The Einstein unified field theory completed’ [Beichler 2015]. Also, each of Goenner and Bergmann, had similar opinion in their statements; the former: ‘(I)in the 1970s and 1980s, many papers on exact solutions of the Einstein-Schrodinger theories and alternatives were published by Indian scientists‘ [Goenner 2014, 181]; the later: ‘—the theories concerning the unavoidability of singularities in the standard theory were all discovered long after Einstein’s death –‘ [Bergmann 1979, 15]. This section is scheduled to present some of these stories.

Though Goenner has termed ‘Indian scientists’ as mentioned above, he has actually done so in a context of geographical expansion of research on UFT with researchers involved from ‘all continents’ spreading over ‘more than twenty different countries’ including England, France, Italy, Australia, Japan, India and others [2014, 181]. American physicist James E Beichler (1931-2025), interested in physics of consciousness, has given a comprehensive overview of unified field theory from beginning till now [2015]. He has given a total pictorial view ’unification tree’ [101]; also details about ‘the evolution of classical unified field theories’ separately [20 and 36]. A couple of contributions, one from the Danish-Canadian physicist John William Moffat [1979 and 1995] and another from the Vietnam born Australian physicist Vu B Ho [1995-1 and -2] are mentioned here. In the first one, the author proposes ‘a new theory of gravity’ ‘in which the geometry of space-time is determined by a nonsymmetric field structure’ [Moffat 1979]. One of the claims of the author is ‘the theory agrees with all the classical (weak gravitational field) tests of Einstein’s general relativity’ [3554]. Later on, the author presented ‘a new version of nonsymmetrical gravitational theory – which has physically consistent perturbative expansion for weak fields, and does not have singularities and black holes’ [1995]. In the other one, the author Ho provided ‘a geometric formulation of strong interaction which is assumed to be described by the Yukawa potential’ [1995-1]. He has also shown that ‘by defining a suitable energy momentum tensor, the field equations of general relativity admit a line element of Yukawa potential as an exact solution [1995-2]. Beichler has duly referred these contributions [20]. There are some other researches which have associated Einstein’s name such as ‘Einstein-Cartan-Evans unified field theory’ [Felker 2005 and Eckardt 2022] which, in fact, fall under the purview of other sections, and hence, will be discussed there.

As regards the contribution of Indian scientists to UFT, Goenner [2014] has covered well about publications during 1950s and early 1960s by Satyendra Nath Bose (1894-1974) of ‘Bose-Einstein statistics’ and ‘Boson’ fame, Ratan Shanker Mishra (1918-1999), worked and published with V. Hlavaty at Indiana University on UFT, Gaganbihari Bandyopadhyay and others. Their contributions were significant, and they also continued to research and publish afterwards till they were active. Further, in case of stalwarts like Bose and Mishra, even after their demise, their students and followers highlighted their research through memoirs or similar volumes. For example, in these two categories one can list the followings: 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; memoirs such as: Padmashri Prof. Dr. R. S. Mishra in 2018, S N Bose: The Man and His Work – Part I: Collected Scientific Papers in 1994, and ‘S. N. Bose (1894-1974) and the Bose quantum statistics a centennial tribute’ by Lokenath Debnath in International Journal of Mathematics and Mathematical Sciences 16 (4) 1993: 625-644. All these volumes have certainly enriched the subject area covered by them. Besides, these scholars and their work have motivated other Indian workers to research and write in these fields. Just two examples are cited in this direction: one, Indian nuclear physicist Rakesh Popli (1952-2007) has come up with a book A Stroll Through Space-Time: A Leisurely discourse on Einstein’s Relativity Theory [2003], where he has described all the details about Einstein’s theory for, not scientific discourse, but public consumption and fittingly ended with the famous Princeton anecdote ‘Yes, I will recognize you’; two, Dhananjay Tiwari, an associate professor in Maths education, comes up with ‘fundamental particles, their classifications on the basis of Bose – Einstein statistics, Fermi – Dirac statistics and quark theory along with four types of existing fundamental forces’ to finally explain how they reflect in unified field theory [211, 16]. Another case may be mentioned – that of the American Indian Jagdish Mehra (1931-2008), prominent historian of modern physics and the author of The Historical Development of Quantum Theory in six volumes during 1982 to 2000, though has not worked directly on UFT, Einstein was his childhood idol and he has penned down important books: Einstein, Hilbert, and The Theory of Gravitation: Historical Origins of General Relativity Theory in 1974 and Einstein, Physics And Reality in 1999, the former has found place in the references of Beichler [2015, 2].

UFT and quantum theory

The first issue in a discussion connecting quantum theory with UFT would be the stand of Einstein on this issue, rather than the issue itself. Goenner, in his discourse, first of all, brings out a section on ‘UFT and quantum theory’, that too just before the section on ‘A glimpse of today’s status of unification’; further, most importantly, mentions in the first line ‘Einstein’s position with regard to quantum mechanics, particularly his resistance to the statistical interpretation of it is well known’ [2014, 191]. Though ‘Einstein’, along with ‘Planck’, originally founded the quantum theory and others namely, ‘Bohr, Born, Schrodinger, Heisenberg, Hilbert, Dirac, Compton, Pauli and de Broglie’ continued to develop it further; even he attempted few times to include this theory in his effort of developing UFT; yet, he was never in favour of this theory be part of UFT [Felker 2005, 56, note 14]. Probably, he was looking for a day when quantum mechanics will develop into a complete deterministic theory, instead of an incomplete probabilistic one; he would accept it whole-heartedly, because he was well aware of this theory’s relevance to UFT.

Now, let us come to its relevance to UFT. Felker reports that ‘Among the things which up until now relativity has not been able to describe while quantum mechanics has, are the quantum packets of energy, the particle-wave duality of existence, and the angular momentum (spin) of particles’ [2005, 56]. Basically, quantum mechanics describes the basic particles such as photons, electrons etc which are also parts to be unified into UFT along with the fundamental forces. As regards the particles present in the complicated structure of all matter we see, Indian physicist Professor Niranjan Barik provides a clear picture in his article published in the last issue of this journal [2025]. Primarily ‘two kinds of fundamental particles’ called ‘fermions and bosons’ constitute all matter; ‘quarks and electrons belong to this class of fermions which provide the material content’, and the bosons include another class of ‘force-carrying particles called gauge bosons’ ‘which provide all types of bindings to these material contents necessary for various structure formations’ [132]. Further, he goes ahead – ‘(B)besides these fundamental fermions and bosons, science has discovered a zoo of subatomic particles and their mirror world of antiparticles revealing a far greater structure – these subatomic particles display contradictory dual behaviour as waves and particles – the location of such a particle is only probabilistic –. These quantum particles do not have any definite property of their own including any definite location or motion at any instant of time before observation – these constituent parts are in a constant state of flux and the propeller of this flux is energy – they are nothing but discrete packets of energy’ [132]. Then he brings in the abstract notion of field ‘where the matter fields of fermions and the force fields of bosons seem to be more primary than matter itself, since these fields behave as the breeding ground for the so-called elementary particles’ [133]. Very soon, Prof. Barik nears his conclusion – ‘Thus, science seems to have found the most crucial elements of existence in quantum vacuum by comprehending this intrinsic fundamental reality of our cosmos in support of the concept of the ‘one source’ – the nothingness or sunyata of Buddhism or the ‘Brahman’ of the Vedantic tradition [134]. He is not the only physicist to have this view.

Where does quantum mechanics stand today? According to Felker [2005], quantum mechanics is the foundation incorporating into it ‘quantum electrodynamics which includes electromagnetic phenomena and quantum chromo-dynamics which adds the quark color theory’ [56]. Utilizing Planck’s parameters, it has developed full-fledged ‘mathematical ability to make most precise predictions of the results of experiments concerning the mutual interaction between particles,’ and even polarization of the ‘vacuum’ [57]. Starting from the development of particle physics from its foundations till the discovery of Higgs boson, bringing in phenomena like scattering matrix or S-matrix and spontaneous symmetry breaking, quantum field theory and Standard Model have arrived to take care of present-day complexities [Mulders 2008 and Schwartz 2014]. In this context, Goenner’s statement – ‘—already at the time suggestions for a ‘unitary’ field theory in the framework of quantum (field) theory were made’ [2014, 192]; and Beichler’s mention – ‘During the 1970s the tables started to turn and quantum theorists became interested in unifying physics’ [2015, 1] bears a lot of significance. Specifically, Beichler stresses on two points regarding the quantum theorists’ claim that ‘quantum theory was more fundamental than relativity’ and ‘the quantum and relativity are mutually incompatible’; then, he says, that is the reason why they are set to replace relativity completely by quantum once and for all [1].

Grand Unified Theory (GUT)

The period beyond mid-1960s can be counted as the period of modern UFT. In 1963, American theoretical physicist Sheldon Lee Glashow (1932- ), for the first time, proposed that the weak nuclear force, electricity and magnetism could arise from a partially unified electroweak theory. Within four years, in 1967, Pakisthani theoretical physicist Abdus Salam (1926-1996) and American theoretical physicist Steven Weinberg (1933-2021), ‘working independently’, revised Glashow’s theory to hypothetically unify ‘the weak and electrical forces into a single entity ‘the electroweak force’’ [Tiwary 2011, 19]. This model (unified theory) ‘given by Glashow, Salam and Weinberg is commonly known as ‘Standard Model’’, and ‘according to this model, all the leptons and quarks are also mass-less and below the symmetry breaking scale they have their masses. – The standard model predicts the existence of new particles like w+ w+, w- w-, z and Higgs bosons’ [19]. This theory got the first experimental support when discovery of weak neutral currents was made in 1973, then in 1983, Italian particle physicist Carlo Rubbia (1934- ) came up with the discovery of w and z bosons at CERN by using the reactor erected based on stochastic cooling by Dutch physical engineer Simon van der Meer (1925-2011). All these five people received Nobel Prize for their discoveries, the first three, Glashow, Salam and Weinberg in 1979, and the later two, Rubbia and Meer in 1984. Later in 2012, two theoretical physicists Francois Englert (1932- ) from Belgium and Peter Higgs (1929-2024) from Great Britain discovered Higgs boson in the ATLAS and CMS experiments at CERN’s Large Hadron Collider; and both of them received Nobel prize in 2013. Further, Dutch theoretical physicist and Nobel Laureate (1999) Gerardus’t Hooft (1946- ) showed that this theory is mathematically consistent; thus, this theory was thoroughly established.

In the meanwhile, in 1974, Glashow with American theoretical physicist Howard Mason Georgi III (1947- ) brought out what is called Georgi-Glashow model, the first Grand Unified Theory (GUT). According to Goenner, at first, 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 above100 GeV. Subsequently, many proposals for GUT have emerged; one of them is Pati-Salem Model. (Jogesh) Pati (1937- ), an Indian-American theoretical physicist, has contributed in collaboration with Pakisthani Nobel Laureate 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 Pati-Salem model is its suggestions such as the symmetry of SU(4)-color, left-right symmetry, and 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.

Another GUT, the authors call it Grand Unified Field Theory, GUFT, that is Einstein-Cartan-Evans (ECE) Unified Field Theory will be briefly discussed here. This theory has been developed by the Welsh chemist and physicist Myron Wyn Evans (1950-2019), and being with him for almost 30 years and moving the theory ahead after him is the noted physicist and computer engineer of Germany Horst Eckardt (1954- ). Laurence George Felker (1946–) in his book The Evans Equations of Unified Field Theory [2005] tells us – ‘The combination of general relativity and quantum theory into one unified theory was Einstein’s goal for the last 30 years of his life. —. This has been achieved by Professor Myron Wyn Evans using Einstein’s general relativity as the foundation, Cartan’s differential geometry to define the space-time, and his own wave equation to describe both relativity and quantum mechanics’ [4]. Then follow a series of claims such as – ‘Evans does not reject quantum theory, he shows that it emerges from general relativity and with a few paradigm changes, unification occurs’ [57] – ‘The Evans principle of least curvature indicates that there is a calculable minimum volume for every particle’ [67] – ‘This is a wonderful example of how general relativity and quantum electrodynamics can work together’ with the mathematical methods coming ‘from quantum theory and the minimum volume is defined in general relativity’ [67] – ‘The term Grand Unified Field Theory (GUFT) describes the combined theories – The Evans equations are equations of GUFT’ [68] – ‘Quantum gravity is any of a variety of research areas that have attempted to combine gravitational and quantum phenomena’ [68] – ‘The Evans equations show that the 3-dimensional quantum descriptions emanate from Einstein’s general relativity’ [69] – ‘Only four dimensions are needed’ [69] – ‘The Evans Wave Equation mathematically combine the two theories rigorously’ [69] – ‘The Evans equations indicate that R = -kT applies to all radiated and matter fields, not just gravitation. This was Einstein’s unfinished goal’ [126] – ‘The development of the Evans Wave Equation in Chapter 7 unites general relativity and quantum theory, completing unification’ [145] – ‘The Evans metric of spacetime has both curvature and torsion – gravitation and spin’ [154] – ‘Einstein shows the gravitational field is space-time curving. Evans shows the electromagnetic field is space-time spinning’ [155] – ‘The Evans Wave Equation of unified field theory: (equation 2). It is the link between general relativity and quantum mechanics and is the unification equation’ [157], and finally – ‘The Evans equations complete Einstein’s unification goal’ [266]. Apparently, Felker’s claims have not yet been accepted by mainstream physics community.

Theory of everything

Besides the major problems faced by GUTs such as, the experimental verification of predictions at extremely high temperatures, as well as, proton decay; even if GUTs become successful in these ventures, they still cannot include gravity. Therefore, there was an attempt by some physicists to unify the quantum mechanics, that describes the very small, with general relativity, which describes the very large, into one constituent theory named ‘Theory of Everything (TOE)’; which is, in the words of Goenner ‘as the modern equivalent to UFT’ [2014, 196]. The first candidate of this attempt was string theory which attempts to unify all gauge interactions with gravity following string phenomenology, that is, search for the standard model of elementary particles in super-symmetric string theory. The other candidates for TOE are superstring theory, M-Theory, Loop Quantum Gravity (LQG) brane-world scenarios, and many more. In fact, there are vast literatures; however, only two of them will be briefly discussed below.

The first one is a paper ‘Theory of Everything’ by Cao et al [2015], where the authors mention – ‘The Torque Grid is the fundamental unit of universe. It is driven from gravity forces as result of space-time-energy-force unification. –. UFT unifies four major forces by resonance conditions with help of an arbitrary 3D prime wave model in which the twist/stretch ratio is 137. The resonance condition (distortion equals original size) of the gravity force decides the size of universe and UFT concludes that the Grand universe is hierarchical’ [31]. The authors claim this UFT theory as Theory of Everything (TOE), the final theory of the Physics. In the second paper, the authors Javier Munoj de la Cuesta and Grok [2025] present an UFT ‘that integrates gravity, electroweak, and strong interactions, alongside cosmological phenomena into a single coherent framework’. They claim – through use of ‘layered structure of interacting fields and resonance mechanism’, the UFT ‘bridges General Relativity (GR) and Quantum Mechanics (QM), unifying all fundamental forces – at the Grand Unification Theory (GUT) scale.’ – ‘Through 200 trials involving mathematical analysis, 3D simulations, and real-data-validation’, they ‘refined the theory to achieve an error margin below 0.0001%’ [1]. They conclude that – by ‘addressing the incompatibilities between GR and QM and offering a novel mechanism for force unification, the UFT positions itself as a robust candidate for a Theory of Everything’ [17].

In spite of vast literature, claims and criticisms, theoretical physicists have not yet accepted a consistent TOE; besides the still unexplained elementary particle mass-spectrum, they cite combining the graviton with the strong and electroweak interactions, and incompatibility between GR and QM as major reasons. As regards the incompatibility between GR and QM is concerned, Beichler provides an interesting observation; he writes – ‘Relativity is first and foremost about form (structure) and the quantum is primarily all about function, which come together as one of the most fundamental dualities (known as non-commuting quantities in physics) in nature, but there is always a bit of each in other. However, these two ideas, form and function, are not necessarily incompatible since there is always a little of one in the other at a higher level of understanding’ [95]. Here, most interestingly, the author puts a picture of the ancient Chinese symbol called ‘T‘ai-chi T’u’, or ‘Diagram of the Supreme Ultimate’, meaning – GR and QM can combine the same way as ‘yin and yang’, the universal archetypal opposite poles of nature combine.

Conclusion

At the outset of the conclusion, an honest submission may be made that in spite of availability of vast literature on the selected topic; only a very brief paper is presented using arbitrarily chosen limited literature. The reason for this approach is to put up the facts in a clear and concise manner; against the background that no concrete final result has yet emerged. There have been efforts after efforts to advance UFT following Grand Unified Theory, as well as, Theory of Everything path. Volumes of results are already generated, though the theoretical physicist fraternity is yet to approve one theory as consistent and accepted theory. Here, it is apt to conclude the way Beichler has concluded – ‘The unified field theory is now a done deal. If it is not taken seriously now, it will be in the future’ [2015, 100].

References

Barik, Niranjan. 2025. “Nature of Truth and Reality.” Towards Unification of Sciences 3 (3): 129-163.
Beichler, James E. April 2015. “The Einstein unified field theory completed.” Preliminary Paper.https://de173.com/wp-content/uploads/2019/04/Einstein_Unified_Field_Theory_Completed.pdf.
Bergmann, Peter G. 1979. “The Quest for Unity: General Relativity and Unitary Field Theories.” Syracuse Scholar (1979-1991): Vol.1, Iss. 1, Article 4. Pages 8-18. https://surface.syr.edu/suscholar.
Cao, Zhiliang, Cao, Henry Gu, and Qiang, Wenan. 2015. “Theory of Everything.” Frontiers of Astronomy, Astrophysics and Cosmology1(1): 31-36.doi: 10.12691/faac-1-1-4.
de la Cuesta, Javier Munoj and Grok. 2025. “A Unified Field Theory: Comprehensive Unification of General Relativity, Quantum Mechanics, and Fundamental Forces Through Resonance and Layered Dynamics.” https://www.researchgate.net/publication/391526716.
van Dongen, Jeroen. 2010. Einstein’s Unification. Cambridge University Press, New York.
Eckardt, Horst. 2022. Einstein–Cartan–Evans Unified Field Theory: The Geometrical Basis of Physics. Volume 1: Classical Physics. Published by the Author.
Ellis, John. 1996. “Abdus Salam: A pioneer in Physics.” CERN Libraries, Geneva. CM- P00058518. December 1995, Archives.
Felker, Laurence G. October 2005. The Evans Equations of Unified Field Theory.

https://www.upitec.org/documents/uft/Evans_Equations_Rev3.pdf.

Goenner, Hubert F. M. 2014. “On the History of United Field Theories. Part II. (ca. 1930-ca. 1965)” Living Rev. Relativity17: 5- 241. http://www.livingreviews.org/1rr-2014-5. doi: 10.12942/1rr-2014-5.
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Ho, Vu B. 1995-2. “A metric of Yukawa potential as an exact solution to the field equation of general relativity.” Available online at airXiv.org/abs/hep-th/9506154v3.
Moffat, John W. 1979. “New theory of gravitation.” Phys. Rev. D 19: 3554-3558.
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Mulders, P. J. 2008. Quantum Field Theory. Vrije Universiteit Amsterdam.
Paramguru, Raja Kishore. 2025. “Unified Field Theory: Envisioned by Einstein.” Towards Unification of Sciences 3 (3): 153-163.
Pati, Jogesh C. and Salam, Abdus. 1974. “Lepton number as the fourth color.” Phys. Rev.D10: 275-289.
Pati, Jogesh C. 1998. “With neutrino masses revealed, proton decay is the missing link.” UMD-PP99-052.https://arxiv.org/pdf/hep-ph/9811442.
Popli, Rakesh K. 2003. A Stroll Through Space-Time: A Leisurely Discourse on Einstein’s Relativity Theory. Vigyan Prasar, New Delhi.
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Tiwari, Dhananjay K. 2011. “Fundamental Forces and Unified Field Theory.” Academic Voices 1 (1): 16-19.
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The post Unified Field Theory: Post-Einstein-Journey So Far appeared first on Institute of Philosophy of Nature.

Unified Field Theory: Envisioned by Einstein

Raja Kishore Paramguru — Sat, 30 Aug 2025 05:51:39 +0000

“All of science is nothing more than the refinement of everyday thinking.”

– Albert Einstein on science.

Abstract

This paper is a small review of Einstein’s Unified Field Theory program. Here, the presentation covers the initiation, his visualization, attributes and postulates of the program, his successful contributions of the special relativity theory unifying space and time, general theory of relativity and the relativistic field theory of gravitation resolving the conceptual contradictions between classical gravitation theory and the Maxwellian theory of the electromagnetic field. The paper also discusses Einstein’s attempts at various other concepts of five-dimension, affine connection, distant parallelism, co-vectors, and asymmetric theory, either proposed by other researchers, or generated by his own original ideas, till the last day of his life.

Key Words: Unified Field Theory, Einstein’s attributes, Special relativity theory, General theory of relativity, Relativistic field theory of gravitation, Asymmetric theory, Five-dimensional approach, Affine connection.

Introduction

This paper starts from the conclusion of my last paper published in this journal on the subject of placement of the statue of Nataraja at CERN [Paramguru 2025, 232]. In order to start in a clear note, I cite that portion of the text here:

‘In conclusion, two issues can be put forth. The first one is that – “The conception of physical things and phenomena as transient manifestations of an underlying fundamental entity is not only a basic element of quantum field theory, but also a basic element of the Eastern world view” [Capra 1975, 211]. Scientists of high standing such as Einstein, as well as the Eastern mystics, are of the view that – this underlying entity is the only reality; all its phenomenal manifestations are transitory or illusory. The scientists are attempting to unify the various fields into a single fundamental field, called ‘unified field’ which would incorporate all physical phenomena…’ [242].

From the above statement, I developed interest in the specific part represented by the last line, and looked to the available literature on ‘unified field theory’. I could find a good number of interesting papers and books; and felt that, probably, since the unified field theory is also a domain of unification of sciences, my readers will also be interested in reading them, if I can provide in a suitable format. What can be a better format than as paper(s) in this particular journal? Hence, I decided to write a series of (very brief) review papers, for our journal, on ‘unified field theory’; and this is the first one, naturally scheduled to present how Albert Einstein (1879-1955), the German-born theoretical physicist, arguably the initiator of the idea of ‘unified field theory’, visualized this idea and pursued it during the last few decades of his life. Of course, this will be based on the available literature.

The beginning of the vision

Historically, the credit for publishing the first paper related to classical unified field theory goes to the Scottish physicist and mathematician, James Clerk Maxwell, for his paper “A Dynamic Theory of the Electromagnetic Field” [1865], where he showed that electricity and magnetism were not separate phenomena but rather different aspects of the same force, and, in the same paper, he provided the mathematical description of electromagnetic field through equations. However, Albert Einstein is credited to have coined the term ‘unified field theory’ for the first time [Sauer 2007]. Tilman Sauer (1963- ), a German theoretical physicist and historian of natural sciences with specific expertise on the history of the development of general relativity theory, besides many publications on the subject, have published specific papers related to Einstein’s unified field theory program [2007], Einstein’s Washington Manuscript on unified field theory [2020], and also a chapter in the book The Cambridge Companion to Einstein [2014]. He straightaway reports that “Einstein explicitly used the term ‘unified field theory’ in the title of a publication for the first time in 1925.” [2007, 1]. This paper, published in the journal of Prussian Academy, was in German language, and hence, the title mentions ‘Einheitliche Feldtheorie …’, the English translation of which is ‘Unified Field theory …’ [Einstein, 1925]. Sauer [2007] goes on to provide further details that Einstein, though used the term in the title for some ten more papers immediately after that first paper, had dealt with the subject already in about “half a dozen” publications before 1925 without using the term in the title. This is in print, on the other hand, Jeroen van Dongen has also told about Einstein’s first positive public utterance about the unification program in 1920 [2002, 186]. In any case, Sauer reports that Einstein wrote, in total, “more than forty technical papers on the subject” [2007, 1].

The basic concept of a unified field theory is to describe all fundamental forces and particles within a single framework that is a single type of field. In terms of modern physics, the forces, instead of being transmitted directly between interacting objects, are described and interpreted by intermediary entities called fields. Thus, there are various fields in physics, such as, vector fields (electromagnetic field), spinor fields (fermionic particles like electrons), and tensor fields (the metric tensor field that describes the shape of space-time and also gravitation in general relativity). Further, according to quantum field theory, particles are treated themselves as quanta of fields. Unified field theory attempts to organize these fields, namely four fundamental forces (strong interaction, weak interaction, electromagnetic interaction, and gravitational interaction), and matter (electrons, quarks, neutrinos etc.) including Higgs bosons, into a single mathematical structure.

Against the basic objective of ‘unified field theory’ as depicted above, it is highly significant to identify the specific features; we may call it attributes of Einstein’s visualization of the same theory. Of course, the very first attribute of his vision must take into account his naming of such a theory with this very specific title which speaks volumes with width and depth. The second attribute of Einstein’s work on a unified field theory was what Sauer termed as “dimensions”, such as “conceptual, representational, biographical, and philosophical dimensions.” [2007, 1]. As usual, the first one refers to the problems and solutions within the knowledge of physics, the second one describes mathematical representations of physical phenomena, the third one from a historical perspective of various approaches made to work out the theory on a historical time frame, and the last one is the philosophical outlook of Einstein. In the words of Sauer “(T)he space spanned by these four dimensions constitutes Einstein’s unified field theory program.” [1]. When we come to identify the third attribute, Einstein’s philosophical outlook comes into picture, because it is very specific. It is true that the theories usually constitute some/many general laws which would explain various phenomena; however, Einstein being Einstein, his basic philosophical outlook is significantly different. When we would express, in general terms, our own understanding of the theories, and their explanations; Einstein would include ‘human reasoning’ within the understanding. Sauer terms “Einstein’s unification program was a program of reflection”, and Einstein’s motivation for such a program of reflection was in Sauer’s own words: “a conception of the task of human reasoning that would be adequate to a holistic understanding of a nature in which human beings live their lives.” [2]. This philosophical outlook of Einstein, as Sauer argues, holds well, not just for this work, but for the entire carrier’s work of Einstein. The fourth attribute, may also be taken as a corollary of this philosophical outlook, because Einstein always used to have strong confidence in all his programs, similarly, he had a strong “insistence” that such a unified field theory is very much “possible” and “desirable” for mankind and would bring in successful result [1]. The last and, also the fifth attribute is, for Einstein, “unification efforts had to start from a theory of the gravitational field and hence be general relativistic” [8]. Sauer has further linked “historical continuity” to this attribute, because, scientific developments have always followed this path in the time-frame of historical perspective; and according to him, it is that historical continuity that has “placed the endeavor of finding a unified field theory above the theory of gravitation implied by general relativity”, and “it was this conviction that separated Einstein from the majority of contemporaries” [26].

Einstein’s special relativity theory

As stated earlier, the journey of classical unified field theory started with the unification of electricity and magnetism within the dynamic theory framework of the electromagnetic field published by Maxwell during 1865. Hardly forty years hence, in 1905, Einstein brought out two ground-breaking theories in physics. The first one was his explanation of the photoelectric effect by using Planck’s constant h which paved the way for the development of quantum theory. Of course, for some reasons, Einstein was not much interested to use this concept for unification of field theory, nor we intend to follow on this, rather, our interest is his second theory of that time, namely, special theory of relativity. According to Peter Gabriel Bergmann (1915-2002), a German – American physicist and also an assistant to Einstein, most of physics around that time was dominated by Newtonian mechanics which quantitatively explained the working of the solar system [1979, 9]. As regards the absolute properties of space and time, Newton’s laws required states of uniform rectilinear motion usually satisfied by inertial frames of reference. However, the electromagnetic field formulated by Faraday, Maxwell and Lorentz involved a dynamic state where electromagnetic waves move at a velocity equal to the speed of light. These two situations contradict each other, and at this stage, the brilliance of Einstein solved the issue through his notion of special theory of relativity. The basic postulates of special relativity are [Bergmann 1979, 10; Felker 2005, 16-33; Sauer 2007, 3]: (i) the notion of space and time changed into a single entity space-time, later known as Minkowski’s four-dimensional space-time model; (ii) the concept of simultaneity in moving frames of reference was redefined; (iii) the constancy of the velocity of light (also constancy of the basic existences such as mass and charge including the laws of conservation), whatever may be the reference frame, was explained; and (iv) this constancy of speed of light was used to provide a conceptual justification for Maxwell’s theory as well as Lorentz transformations. Through this theory, Einstein could unify not only space and time into space-time, but also, classical principle of relativity of mechanics and the laws of electrodynamics, two major fields of physics.

Einstein’s general relativity theory

While using Minkowski’s four-dimensional space-time concepts, unification of two major fields of physics could be obtained, however, a new contradiction was surfaced. Special relativity requires an inertial reference frame and the existence of an absolute and finite limit to the speed of any signal transmission; this later one was violated by Newtonian gravitation theory. Along with this conceptual conflict, another inherent difference, as discussed earlier between the Newtonian gravitational interaction with static inter-particle processes and Maxwellian electromagnetism dealing with dynamic waves, also persisted. A possible solution to resolve this conceptual contradiction needed a relativistic gravitational field, and Einstein once again brought out another of his brilliant discoveries that acceleration and gravitation are almost the same thing, and it must also be remembered that gravitation is not a force, though it appears so. With this analogy he could explain that the local gravitational acceleration for all bodies is uniform, and hence, the frames of reference are precluded by local means. Thus, Einstein’s general theory of relativity, also known as, theory of the gravitational field was born. In essence, his special relativity theory is expanded to a description of gravity; the gravitational interaction was conceptualized as a dynamic field; accelerating reference frames were incorporated; and the flat space-time of Minkowski was replaced with the curving geometry of Riemannian space-time [Bergmann 1979, 11; Sauer 2007, 4; Felker 2005, 34-35]. This theory came into effect during 1915 and is considered as the third ground-breaking theory of Einstein in theoretical physics.

After Einstein’s general theory of relativity as discussed above, Bergmann’s statement: “The quest for unity had apparently reached its objective” [1979, 13], should indicate that Einstein’s unification program reached its successful end. “However, it is not so.” He further states that: “But there are several hairs in the ointment” [13], and Sauer also states that the most desirable cases of unified description “has never been achieved” [2007, 5]. Such statements indicate that there remains some ‘desirable cases’ to be satisfied in Einstein’s unified theory program. According to Sauer, although there was no compelling reason, Einstein himself felt that “the new understanding of gravitation demanded further unification with classical Maxwellian theory of the electromagnetic field” [4]. Also, there was apparently a need for the unification to predict new physical effects arising out of unification, and there was always a necessity to take care of the representation of matter within unification. Therefore, Sauer has given a list of possible postulates to be included within Einstein’s unified field theory program [2007]. Those are: (i) “a unified description that would both yield the known laws of gravitation and electromagnetism and would also predict new effects, arising from a combination of the fields inherent in the unified description, that would also be compatible with known empirical facts” [5], (ii) “to account for the existence of only a proton and an electron, —, i.e. proton mass and electron mass, and one elementary charge” [7], and (iii) “(t)he explanation of quantum mechanics within a unified field theory remained a programmatic desideratum in Einstein’s work” [8]. Einstein, though was involved in bringing out the quantum theory, was never in favor of this theory since it is not deterministic, but statistical mechanics. However, the last postulate was included because in presence of elementary material mass and charge, this may help in bringing continuous conceptualization of matter; and after all, Einstein did not ignore this possibility [7].

Einstein’s UFT pursuit beyond 1915: response to others’ approaches

After successful demonstration of general theory of relativity, Einstein continued to pursue his dream of UFT because that would address the above mentioned postulates; and further, many other physicists were also motivated to conduct research on UFT, and hence, as the pioneer, he would react to their results. That way, he continued in spite of his ill-health during 1928, and the events; such as Nazis’ rise to power, cruel persecution of Jews, 2nd World War, the holocaust, and use of 1st atom bombs; due to which he resigned from Prussian Academy, left Germany and lived in United States of America since late 1933; yet, he never stopped research, and maintained developing ever-new approaches for his dream UFT till his death [Bergmann 1979 and Sauer 2007]. Of course, his research engagements have also produced significant results in the area of general relativity, besides in UFT. This section intends to present some of his UFT endeavors during this period, mostly his reactions to other’s approaches.

The first reaction of Einstein was to the proposition of Hermann Weyl during 1918, which was generally concerned to Riemannian geometrization, specifically to parallel vector transport. Basically, his approach was to introduce a vector “length connection” to the Riemannian geometry structure keeping the four-dimensionality of space-time intact. Though Einstein was initially attracted towards the idea, very quickly he could find out the setbacks. He had specific objections to the existence of parallel transportable measuring lengths as a fundamental assumption of general relativity [Einstein 1921]. Then onwards he did not consider Weyl’s approach having any value for UFT.

His second reaction was to Theodor Kaluza’s ‘five-dimensional theory’ proposed in 1919. Though, like his previous reaction to Weyl’s approach, he could quickly find set-backs in this theory also; yet, he has examined/re-examined this five-dimensional approach a number of times: first in 1919-23, then in 1927, 1931-32, and last in 1938-41. Sauer [2007], Sauer and Schuetz [2020], and van Dongen [2002] have given a detailed description of Einstein’s reactions to this theory. The reaction started when Kaluza sent him a manuscript where he introduced the fifth dimension to the Riemannian space-time manifold of general relativity. Einstein could locate several difficulties at different levels of the theory, and their initial correspondence ended in May 1919 [Sauer 2007, 13]. However, after some rethinking, Einstein invited Kaluza after around two years to resubmit his manuscript, and this time, not only he helped him publish the paper; but also, himself co-authored by Grommer published another paper investigating the problem of solutions to Kaluza’s theory. After another stint in 1927 on this approach with two publications, he visited again in 1931-32, by this time it has become Kaluza-Klein theory, when, after his experience with distant parallelism, he could visualize a possibility with the application of tetrad formalism here. In association with Walther Mayer, he constructed a five-dimensional vector space at each point of four-dimensional space-time and explored the functioning of the tetrad formalism. However, this approach also ran into difficulties due to problems in accounting for the structure of matter [19]. Then in 1938, Einstein and Bergmann published the penultimate paper on reconsideration of Kaluza-Klein’s five-dimensional approach [1938]; and three years later came up with the final paper [Einstein, Bargmann, and Bergmann 1941], where the authors have addressed all the problems including impossibility to describe particles by non-singular solutions [Sauer 2007, 21; van Dongen 2002, 193]. Even one of the authors of the last paper, Peter Bergmann, while describing their idea concludes: “Alas, the idea did not work out” [1979, 16].

Einstein reacted to a third approach towards UFT called affine connection proposed by Arthur Eddington, who started with a manifold equipped with a linear affine connection that allowed a Riemann curvature tensor and of a, supposedly anti-symmetric, Ricci tensor; then, he continued to treat the anti-symmetric and symmetric parts of the Ricci tensor, respectively, as the electromagnetic field tensor and usual metric tensor field. However, he did not provide field equations to determine the affine connections, which Einstein provided; yet, he experienced problems including the theory not accounting for the electron-proton mass symmetry [Sauer 2007, 14].

Einstein’s UFT pursuit beyond 1915: own approaches

Thus, all the above responses of Einstein to the external propositions ended in no fruitful result; and this section will present some of his original approaches. During 1923, Einstein published an original paper, interestingly searching for a possible solution for UFT in quantum theory. Though he was expecting to account for quantum phenomena by means of differential equations, he admitted that he was still unable to solve the quantum problem. However, according to Sauer [2007, 15], he was contemplating the quantum issue as early as 1920; later on, during the early 1930s, he came out to investigate UFT where the problem of quantum theory had the most direct involvement. This happened when he came across his old professional friend Paul Ehrenfest, who brought to him the investigations of a relativistic quantum theory by Wolfgang Pauli and Paul Dirac. Einstein jumped into the investigation, worked with his coauthor Mayer using ‘semi-vectors’ in place of ‘spinors’ used earlier and published four papers during 1932 – 1934. However, fruitful results still eluded them; quantum problems remained unsolved [19].

During 1928 Einstein fell sick and was ordered strict bed rest, while taking rest, his fertile brain cooked up some interesting research idea which, after some time, he published two notes in Prussian Academy on a mathematical structure which he called Riemannian geometry, maintaining the concept of distant parallelism, where, he investigated if a UFT can be formulated within this geometric framework. Soon, he learned that the mathematical concept of distant parallelism had already been developed by mathematicians Roland Weitzenboch and Elie Cartan; he acknowledged their mathematics, and hopefully went ahead formulating a UFT within this structure. However, finally, the distant parallelism approach ended in an attempt only [17-18].

Accounting for matter in a UFT was posing a problem, hence, Einstein attempted to investigate this aspect in a note published during 1941 [Einstein 1941]; which was reinvestigated after two years in a joint paper with Pauli [Einstein and Pauli 1943]. Here, they could prove the non-existence of regular solutions to the vacuum field equations that would asymptotically behave like the Newtonian gravitational potential, whatever be the symmetry conditions of the field in finite field strength regions; also, this result was valid for both four- and five- dimensional theories. This means, under general conditions, a UFT on Riemann tensor would always involve singularities in particle-like solutions; and he should look for new approaches, which he did [Einstein 1943], and another with his coauthor Valentin Bargmann [Einstein and Bargmann 1943]. Here, the authors attempted at a new kind of a non-local relativistic theory of gravitation which they called ‘bi-vector approach’. Apparently, the ‘bi-vector approach’, judging by the published record, is Einstein’s penultimate distinct approach in the sequence of UFT approaches, also ran into difficulties to end in a failure [Sauer 2007, 21-22].

Now, we enter into Einstein’s last approach, rather, the approach where he devoted the last ten years of his life. Incidentally and interestingly, this approach was started by him in 1925, where he used the term ‘Unified Field Theory’ in the title of the paper for the first time. It was also based on a local Riemannian metric but an asymmetric one. In the first paper published in 1925 [Einstein 1925], he took both a metric tensor field and a linear affine connection, both assumed asymmetric, at the same time as fundamental variables. He defined the field equations, tried to associate the gravitational and electromagnetic fields, respectively, with the symmetric and anti-symmetric parts of the metric field, and attempted to recover the known cases. Though he could get satisfactory results with respect to the gravitational case, the results with Maxwell’s equations were not entirely satisfactory; he could not know how to move on from here [Sauer 2007, 15-16]. He, now, returned to investigate this problem in 1945 [Einstein 1945], and went ahead with the investigation publishing a series of papers between 1946 and 1955, most of them with himself as single author, only one with Straus, and another two with Kaufmann as his co-authors. In these papers, tentative field equations were tested for their mathematical properties, satisfactions of the criteria for a physical interpretation were checked, and as usual, his deep interests of compatibility were examined. Since the mathematics of a framework based on an asymmetric metric tensor is highly complex, he spent the rest of his life elaborating the asymmetric theory. His very last considerations in his final approach were presented by his last assistant, Bruria Kaufmann [Kaufmann 1956], at the 50th anniversary of the relativity theory in Bern in July 1955 a few weeks after Einstein’s death [Sauer 2007, 22-23]. Thus, the efforts and contributions of a genius ended here, to be taken up further by other researchers in future.

Conclusion

In conclusion, one point can be clearly stressed upon that details on an account of Einstein’s work on UFT would be beyond the scope of this paper. However, an honest attempt has been made to present, very briefly, the initiation of his UFT program, his attributes and postulates of the program, his successful journey through the special relativity and general relativity theories, and his genuine attempts at various approaches proposed by other researchers and also generated in his brilliant thought process, most importantly maintaining his high intellectual heritage till the last moment of his life. He is not with us since 1955, long seventy years have passed by, how his followers have followed up his ideas, will expectedly be the subject matter of next papers in this column.

References

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