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

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

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“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

• 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. 
• Capra, Fritjof. 1975. The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism. Boulder: Shambhala.
• van Dongen, Jeroen. 2002. “Einstein and the Kaluza-Klein Particle.” Studies in History and Philosophy of Modern Physics 33 (2002): 185-210.
• Einstein, Albert. 1921. “Ueber eine naheliegende Ergaenzung des Fundamentes derallgemeinen Relativitaetstheorie.” Preussische Akademie der Wissenschaften, Phys.-math. Klasse, Sitzungsberichte : 261-264. c.f. Sauer 2007.
• Einstein, Albert. 1925. “Einheitliche Feldtheorie von Gravitation und Elektrizitaet.” Preussische Akademie der Wissenschaften, Phys.-math. Klasse, Sitzungsberichte : 414-419. c.f. Sauer 2007.
• Einstein, Albert. 1941. “Demonstration of the Non-Existence of Gravitational Fields with A Non-Vanishing Total Mass Free of Singularities.” Tucuman Universidad Nacional, Revista A2, 11-15.
• Einstein, Albert. 1943. “Bivector Fields, II.” Annals of Mathematics 45, 15-23.
• Einstein, Albert. 1945. “Generalization of the Relativistic Theory of Gravitation.” Annals of Mathematics 46, 578-584.
• Einstein, Albert, and Bargmann, Valentin. 1943. “Bivector Fields, I.” Annals of Mathematics 45, 1-14.
• Einstein, Albert, Bargmann, Valentin, and Bergmann, Peter. 1941. “Five-Dimensional Representation of Gravitation and Electricity.” In: Theodore von Karman Anniversary Volume, Pasadena: California Institute of Technology.
• Einstein, Albert, and Bergmann, Peter. 1938. “Generalization of Kaluza’s Theory of Electricity.” Annals of Mathematics 39, 683-701.
• Einstein, Albert, and Pauli, Wolfgang. 1943. “Non-Existence of Regular Solutions of Relativistic Field Equations.” Annals of Mathematics 44, 131-137.
• Felker, Laurence G. October 2005. The Evans Equations of Unified Field Theory. https://www.upitec.org/documents/uft/Evans_Equations_Rev3.pdf.
• Janssen, Michel and Christoph Lehner. Eds. 2014. The Cambridge Companion to Einstein. Cambridge University Press.
• Kaufmann, Bruria. 1956. “Mathematical structure of the non-symmetric field theory.” In: Fuenfzig Jahre Relativitaetstheorie. Cinquantenaire de la Theorie de la Relativite.
• Jubilee of Relativity Theory. Mercier, A. and Kervaire, M. (eds), Basel: Birkhaeuser, 1956 (Helvetica Physica Acta Supplementum IV), 227-238. c.f. Sauer 2007.
• Maxwell. J. Clerk. 1865. “A Dynamical Theory of the Electromagnetic Field.” Phil. Trans.
• R. Soc. Lond. 155: 459-512. doi: 10.1098/rstl.1865.0008.    
• Paramguru, Raja Kishore. 2025. “Statue of Nataraja at CERN: The cosmic dance of subatomic particles.” Towards Unification of Sciences 2 (4): 232-243.
• Sauer, Tilman. (April 11) 2007. “Einstein’s Unified Field Theory Program.” Einstein Papers Project. California Institute of Technology 20-7, Pasadena, CA 91125, USA. https://philsci-archive.pitt.edu/3293/1/uft.pdf 
• Sauer, Tilman and Tobias Schuetz. (August 25) 2020. “Einstein’s Washington Manuscript on Unified Field Theory.” https://arxiv.org/pdf/2008.10005

Abstract

The European Organization of Nuclear Research (CERN) is having a statue of Nataraja at its headquarters. This paper analyses the scientific, mystic, as well as the historic meaning of this occurrence, that is, why such a spiritual symbol is placed at a place where deep rooted research involving subatomic particles takes place. For doing so, some literature pertaining to art-history and modern physics involving subatomic particles was consulted. It was observed that there exist a number of parallels between the observations of modern physics and Eastern mysticism. Finally, it turned out that for the modern physicists, Shiva’s dance is the dance of subatomic matter. The metaphor of the cosmic dance thus unifies ancient mythology, religious art, and modern physics. 

Keywords: Statue of Lord Shiva, CERN, Cosmic Dance, Subatomic Particles, Eastern Mysticism, Scientific Exploration, Creation and Destruction, Hadron Collider, Bubble Chamber, Rhythmic Pulse

Introduction

Twentieth century has seen some epoch-making developments in modern physics, specifically penetrating deep into the atomic structures of materials, identifying numbers of subatomic particles, and exploring their exotic world. During this period, precisely on 29 September 1954, ‘The European Organization for Nuclear Research’, (in French Conseil Européen pour la Recherche Nucléaire – CERN), was established. An intergovernmental (European Governments) organization, it stands at Meyrin, a western suburb of Geneva on the France – Switzerland border, and operates the largest particle physics laboratory in the world. CERN boasts of possessing the world’s largest and most complex scientific instruments, mostly particle accelerators and detectors, tailor-made to study subatomic particles in minute detail. Using these excellent facilities, the physicists and engineers of CERN have made, and are making, wonderful contributions to the field of the subatomic particle world, providing insights into the fundamental laws of nature. 

Here, it is worth mentioning another event that occurred at CERN approximately fifty years after its inception. On 8th June, 2004, a six feet tall Lord Nataraja idol was unveiled at its headquarters, just in front of the Director General’s office. We know that Lord Shiva is worshipped in India as one of the Trinity deities of Hinduism, and Lord Nataraja is his depiction as the divine cosmic dancer. Accordingly, on the base of this idol, “Adi Sankara’s sloka (56th sloka of Sivananda Lahari) is engraved in Sanskrit with English translation” (Raja 2017, 63). A special plaque is also placed next to the idol and explains the significance of the metaphor of Nataraja’s cosmic dance with several quotations from the book “The Tao of Physics” written by “Fritjof Capra, an Austrian born American Physicist” (63). Is it, then, a reality that modern advanced science has found its visual three-dimensional expression in Nataraja’s dance? Is it that science and spirituality meet here? And, is it that spirituality gives completeness and wholeness to science, and vice-versa? This paper makes an honest attempt to find answers to these questions. For this purpose, it makes an effort to analyze what the physicists like Capra have observed through their experimentations, and what the spiritualists have realized through their meditative experience.

The starting point has been chosen from the plaque placed near the Nataraja idol at CERN, where, Fritjof Capra explained that “Modern physics has shown that the rhythm of creation and destruction is not only manifest in the turn of the seasons and in the birth and death of all living creatures, but is also the very essence of inorganic matter,” and that “For the modern physicists, then, Shiva’s dance is the dance of subatomic particles.” Thus, there are three aspects that need a discussion here; one, elements of Nataraja’s dance; two, properties of subatomic particles of inorganic matter; and finally the relationship between the two. Obviously, the focal literature chosen here is the book The Tao of Physics (Capra 1975), and of course, supported by some other relevant literature.

Dance of Nataraja

Lord Nataraja, as mentioned above, is the depiction of Lord Shiva as the divine cosmic dancer; and has place of worship in India and the neighboring countries from time immemorial. The Natyashastra of Bharatmuni (2003), which was believed to be written approximately some 2000 years ago, mentions two Hindu deities to be “closely associated with the science of dance. Lord Siva is the primordial Nataraja (king of dancers) and Brahma is the author of Natya Veda” (10). Fritjof Capra, in his deliberations with the dance of Nataraja, has referred to two scholars, namely, Ananda Kentish Coomaraswamy (1877-1947) and Heinrich Robert Zimmer (1890-1943). The former was a Ceylonese metaphysician, historian and a philosopher of Indian art who was largely responsible for introducing ancient Indian art and culture to the West; and his essay The Dance of Shiva (1918) is on focal plane. In this essay, for interpretation, out of many dances of Shiva, Coomaraswamy has selected three dances; the first, the evening dance he performed in Himalayas with divine chorus; the second, his usual well-known dance of tandava; and the third, the Nadanta dance he performed before the assembly (sabha) in the golden hall of Chidambaram or Tillai, usually called the center of the Universe. Again, out of the three, in his own words, “only one of them alone forming the main subject of interpretation,” there is no doubt that it is the last one (56). Further, he cites – “—without reliance upon literary references, the interpretation of this dance would not be difficult. Fortunately, however, we have the assistance of a copious contemporary literature, which enables us to fully explain not only the general significance of the dance, but equally, the details of its concrete symbolism” (59). The later scholar, Heinrich Zimmer, was a German Indologist, linguist, and a historian of South Asian art, mostly known for his book, Myths and Symbols in Indian Art and Civilization (1990), which is also relevant here. ‘The Dance of Shiva’ forms one of seven sections of a chapter in the book, thoroughly analyzed on the basis of numbers of historical statues found at various places, and relevant literature including those of Coomaraswamy. 

Both these authors have dealt in detail about the dance of Nataraja, and Fritjof Capra has cited some statements from their work. To start with, it may be mentioned that, while Coomaraswamy refers to Nataraja as “Lord of Dancers, or, King of Actors” (1918, 56), Zimmer addresses him as “King of Dancers” (1990, 151). Zimmer mentions, “On a universal scale Shiva is the Cosmic Dancer in his Dancing Manifestation (nritya murti) he embodies in himself and simultaneously gives manifestation to Eternal Energy” (1990, 152); whereas, Coomaraswamy states, “How many various dances of Siva are known to his worshippers I cannot say. No doubt the root idea behind all of these dances is more or less one and the same, the manifestation of primal rhythmic energy” (1918, 56). 

Five Activities of Nataraja’s Dance

Zimmer states that “Shiva as the Cosmic Dancer is the embodiment and manifestation of eternal energy in its five activities (pancha kriya)” (1990, 154). Coomaraswamy, on the other hand, refers to the Saivas’ understanding of Nadanta dance – “Our Lord is the Dancer, who, like the heat latent in firewood, diffuses His power in mind and matter, and make them dance in their turn”, and then states that – “The dance, in fact, represents His five activities (Panchakritya)” (59). Of course, the five activities are the same, viz: (1) Shrishti (creation, evolution, pouring forth, or, unfolding), (2) Sthiti (preservation, maintenance, support), (3) Samhara (destruction, taking back, or, reabsorption), (4) Tirobhava (Concealment, veiling of, or, masking, illusion, or, display of Maya, and also, giving rest), (5) Anugraha (Favor, release, salvation, grace) (Coomaraswamy 1918, 59; Zimmer 1990, 154). In fact, these five activities are believed to be separately and respectively performed by deities Brahma, Vishnu, Rudra, Mahesvara, and Sadasiva. Coomaraswamy goes further to explain that “Creation arises from the drum: protection proceeds from the hand of hope: from fire proceeds destruction: the foot held aloft gives release” (1918, 59-60). All the five activities are “made manifest simultaneously with the pulse of every moment and in sequence through change of time” (Zimmer 1990, 155).

Coomaraswamy summarizes the whole interpretation of Siva’s dance to have three-fold essential significance: “First, it is the image of his Rhythmic Play as the Source of all movement within the Cosmos, which is Represented by the Arch: Secondly, the Purpose of his Dance is to Release the countless souls of men from the Snare of Illusion: Thirdly the Place of the Dance, Chidambaram, the Centre of the Universe, is within the Heart” (1918, 65). 

Modern Physics

At the beginning of the twentieth century, the physicists had two theories, namely, Newtonian mechanics and Maxwell’s electrodynamics, applied successfully to different physical phenomena. However, the first few decades of the twentieth century, specifically the two separate developments – that of relativity theory and of atomic physics – totally shattered the Newtonian world view. The main Newtonian concepts, such as, the notion of absolute space and time, the elementary solid particles, the strictly causal nature of physical phenomena, and the ideal of an objective description of nature, had limitations to be extended to the new domains of atomic physics. By then, we were already aware that the Newtonian model is valid only for objects consisting of a large number of atoms, and only for velocities which are small compared to the speed of light. When the first condition is not satisfied, then Newtonian mechanics is to be replaced by quantum theory; and when the second condition is not met, relativity theory is to be applied. Basically, these two replacements, so to speak, have come from the revolutionary thoughts of Albert Einstein, a scientist-par-excellence. In 1905, he published two papers, one his special theory of relativity, and the other was a novel way of looking at electromagnetic radiation which practically led the way to formulate the quantum theory, may be called the theory of atomic phenomena.

Beginning in the 1930s two further developments, one experimental and the other theoretical, took modern physics to altogether a different domain. The experimental techniques were refined to detect more and more subatomic particles, such that, by 1935, the number increased to six from three; by 1955, it became eighteen; and by 1975, it had been more than two hundred. This increase in number has strengthened one point that – none of these particles can be termed either ‘elementary’, or, ‘building block’. Further, the theoretical developments, on one side supported this view, and on the other brought out new ideas regarding the subatomic matters. By this time, the very strange dual property of matter and also of light, that each one is simultaneously matter as well as wave, have been accepted. The light quanta, which has given quantum theory its name, is already accepted as bona fide particles called photons, which are particles of a very special kind – mass-less, yet travel with the speed of light. Study of particles at this speed means relativity theory must be applied, and was applied. High-energy collisions of subatomic particles, affected in large sized particle accelerators, not only produced subatomic particles, but also helped study their properties, even taking pictures in the bubble chambers. It was observed that most of these subatomic particles created in these collisions, live for a very short time, and disintegrate again to protons, neutrons, and electrons. Relativity theory showed that – mass of a substance is nothing but energy, and energy is a dynamic quantity associated with activity and processes. Existence of anti-particle of every particle was observed, and also observed symmetry between these pairs. With availability of energy, pairs of such particles can be created; and they can also be reverted to energy by the reverse process of annihilation. Matter has appeared in these high-energy experiments as completely mutable. All particles can be transmuted into other particles; can be created from energy and can vanish into energy. 

Thus, in modern physics, the universe is experienced as a dynamic inseparable whole; the observer too is included within. In this experience, the traditional concepts of isolated objects, space and time, cause and effect are meaningless. “Such an experience, however, is very similar to Eastern mystics” – says Capra; and continues further to add that the theories, quantum and relativity, “combine to produce the most striking parallels to Eastern mysticism” (81). He clarifies that Eastern mysticism, here, means “the various schools in the religious philosophies of Hinduism, Buddhism, and Taoism” (81). We will present some of these parallels in the following lines.  

A basic oneness of the universe

The spiritual tradition and the practice of getting experience may be different in the various schools of thought; however, the basic elements of the world view developed in all these traditions are the same. The most important characteristic of the Eastern world view is that – all things and events are seen as inter-connected, interdependent, and inseparable parts of this cosmic whole; as different manifestations of the same ultimate reality. Now, Fritjof Capra states that – “The basic oneness of the universe is not only the central characteristic of the mystical experience, but is also one of the most important revelations of modern physics” (131). We can see what these revelations of modern physics are, and how they formulate the basic oneness of the universe. Basically, the interconnectedness of nature arises in quantum theory. Let us start with any ‘observed system’ which may consist of ‘observed particles’, and ‘observed phenomena’; the ‘observing system’ will include ‘experimental apparatus’, and ‘human observers’. The first point in quantum theory is that the observed systems are described in terms of probabilities. Then, since the subatomic particles are not stable, they disintegrate (or decay), and again, the same term ‘probability’ applies to the decay ‘time’, and decay ‘mode’. Thus, what quantum theory brings out are not ‘definite’ characters of the particles, rather, ‘probabilistic relations’ between the ‘particle(s)’ and ‘phenomena’, mostly available in terms of probabilistic dynamic patterns. Further, the ‘experimental setup, or measuring technique’ and the ‘human observers’ get merged into this ‘probabilistic relation’, as participators. Therefore, finally, quantum theory “has come to see the universe as an interconnected web of physical and mental relations whose parts are only defined through their connections to the whole” (141). Thus, ‘the unity of all things and events’ forms the first most significant parallel between Eastern mysticism and modern physics.

The universe is intrinsically dynamic 

This is the second most significant world view of Eastern mysticism. All the Indian philosophical texts, starting from Vedas, Upanishads to Bhagavad Gita, give an organic, growing and rhythmically moving picture of the universe where everything is fluid and ever-changing. The picture is similar with the other Eastern philosophies such as Buddhism and Taoism. Each of these philosophies views the universe as an inseparable web whose interconnections are dynamic and not static. Thus, the cosmic web is alive; it moves, grows, and changes continually. Modern physics, too, has come to conceive the universe as such a web of relations and has recognized that this web is intrinsically dynamic. In fact, both quantum and relativity theories have established that the properties of subatomic particles can only be understood in a dynamic context; in terms of movement, interaction and transformation. Not only with the smaller dimensions of subatomic particles, modern physics have also recognized the larger dimensions of stars and galaxies to be dynamic. They are continuously spinning, contracting, expanding, and even exploding. Actually, in this world, we deal with large, atomic, and nuclear dimensions; and in the case of the later, the particles move very fast. At this stage, once the relativity theory told us that mass is nothing but a form of energy, we had to change our view. Material is no more understood as consisting of some basic ‘stuff’; rather, it is a ‘bundle of energy,’ a part of a ‘dynamic pattern’ within the framework of space and time fused into a four-dimensional continuum. When we observe them, we don’t find any mater; we only observe dynamic patterns continually changing into one another. Thus, ‘the universe is intrinsically dynamic’ forms the second most significant parallel between Eastern mysticism and modern physics.

The unity of opposites

Usually, opposites are abstract concepts of our thought process, but well entrenched into our regular life such as, ‘good and bad’, ‘pleasure and pain’, ‘life and death’, ‘light and darkness’, ‘winning and losing’, ‘virtue and vice’, ‘male and female’ etc. We also realize that these are not absolute experiences, but are merely two sides of the same reality; extreme parts of a single whole. However, the awareness that all opposites are polars and, thus have unity, is seen by the Eastern spiritual tradition as one of the highest aims of man. Instead of trying to eliminate the bad ones, rather, an attempt made to maintain a dynamic balance between the good and bad ones is preferred. 

Now, we will have to see how modern physics views this. The examples of opposite concepts in atomic physics are: ‘force and matter’, ‘particles and waves’, ‘motion and rest’, ‘existence and non-existence’ etc. Probably the best example of unification of contradicting concepts is ‘particles and waves’ in atomic physics. This dual behavior is already discussed above. It may be mentioned that the waves associated with particles are not ‘real’ three-dimensional waves like ‘water waves’, or, ‘sound waves’, but are only ‘probability waves’; which are abstract mathematical quantities related to the probabilities of finding the particles at various places and with various properties. Here, ‘probability wave’ may apparently show unity of ‘particle and wave’, however, it throws out another pair of fundamental opposite concepts of ‘existence and non-existence’ of atomic reality. We cannot say that an atomic particle exists at a certain place, nor can we say that it does not exist. To show this parallel between atomic physics and Eastern mysticism, Capra brings out this statement – “In the words of Robert Oppenheimer, if we ask, for instance: Whether the electron’s position remains the same? Our answer is– ‘No’. Whether the electron’s position changes with time? Our answer is – ‘No’. Whether the electron is at rest? Our answer is – ‘No’. Whether it is in motion? Our answer is – ‘No’.” “Oppenheimer’s words thus seem to echo the words of the Upanishads: It moves. It moves not. It is far, and it is near. It is within all this, and it is outside of all this” (1975, 154). Probably, this example provides the best possible parallel.

All spatial and temporal specifications are relative 

The notion of space and time figure prominently, not only in our everyday life, but also in our understandings of nature, philosophy, and science. For example, formulation of each of the laws of physics requires the concepts of space and time. We know that our classical physics is based on a concept of space and time as absolute, separate, and independent of the material world. On the other hand, Eastern philosophy has always maintained that space and time are constructs of mind, and are like all other intellectual concepts; as relative, limited, and illusory. Then where is the parallelism? True, there is no parallelism here. However, the modern physicists believe that the modification in the concept of space and time brought out by relativity theory is one of the greatest evolutions in the history of modern physics, and it provides the parallelism. What, then, is the new concept of space and time in relativity theory? “It is based on the discovery that all space and time measurements are relative”(Capra 1975, 164). This, in fact, is the starting point of formulation of relativity theory. Then relativity theory showed that space is not three-dimensional and time is not a separate entity; both are intimately and inseparably connected to form a “four-dimensional continuum which is called ‘space-time’” (168). This unification of space and time may also be viewed as the unification of other basic concepts in the previous section of the unity of opposites; the only difference here is that space and time are not opposites, but kept unrelated so far in classical physics. Of course, the notions of space-time are based on experience; on scientific experiments in the case of the modern physicists, and on meditative experience of the Eastern mystics. Thus, the full meaning of space-time in relativistic physics turns out to be – “space and time are fully equivalent; they are unified into a four-dimensional continuum in which the particle interactions can stretch in any direction” (185). In conclusion, we can say that – “Eastern mysticism is liberation from time, in a way; the same may be said of relativistic physics” (187).

The void and form 

In the Eastern mystical view, the reality underlying all phenomena is beyond all forms and defies all description and specifications; therefore, often said to be formless, empty or void. The term Brahman used by Hindus in India, Sunyata used by Buddhists everywhere, and Tao used by Taoists in China; all represent void or emptiness. However, this emptiness should not be taken to be mere nothingness; rather, on the contrary, this void has an infinite creative potential. Now, the modern physicists have come up with a statement that “the void of Eastern mystics can easily be compared to the quantum field of subatomic physics”(Capra 1975, 212). Originally, the classical, mechanistic world view had the notion of solid as indestructible materials moving in the void. But, when quantum theory and relativity theory were combined to describe the force fields of subatomic particles through the ‘quantum field theories,’ the distinction between particles and the space (void) surrounding them lost its original sharpness and the ‘void’ is recognized as a dynamic quantity of paramount significance. It could be shown through numbers of experimental evidence that virtual particles can come into being spontaneously out of the void, and vanish again into the void, without any nucleon being present. According to field theory, events of that kind happen all the time. The vacuum is far from empty. On the contrary, it contains an unlimited number of particles which come into being and vanish without end. “Here then, is the closest parallel to the void of Eastern mysticism in modern physics. Like the Eastern void, the ‘physical vacuum’ – as it is called in field theory – is not a state of mere nothingness, but contains the potentiality for all forms of the particle world. These forms, in turn, are not independent physical entities but merely transient manifestations of the underlying void”(222-223). 

There are more parallels between the Eastern mystical experiences and experimental observations of modern physics, such as symmetries, patterns of change, and interpenetration; however, we stop here describing them and make a shift to the cosmic dance, which is our main theme and it is also another strong parallel. 

The Cosmic Dance Nataraja

Even before describing the cosmic dance of Nataraja in a specific chapter, Capra has mentioned that – “Through his dance, Shiva sustains the manifold phenomena in the world, unifying all things by immersing them in his rhythm and making them participate in the dance – a magnificent image of the dynamic unity of the universe” (1975, 191). The chapter The Cosmic Dance starts with what the modern physicists have gathered through the exploration of the subatomic world in the twentieth century. It has already shown that the subatomic particles are dynamic patterns, not isolated entities, but are integral parts of an inseparable network of interactions. These interactions involve a ceaseless flow of energy manifesting itself as the exchange of particles; a dynamic interplay in which particles are created and destroyed without end in a continual variation of energy patterns. “The whole universe is thus engaged in endless motion and activity; in a continual cosmic dance of energy”(225). 

These phenomena are observed, not only in the collision experiments of high-energy physics, but also occur naturally, yet more intensely all the time in the Earth’s atmosphere. A continual flow of energy is going through a great variety of particle patterns in a rhythmic dance of creation and destruction all the time. Capra cites many examples obtained from the high-energy collision experiments, and refers to the American physicist Kenneth William Ford who has constructed a complicated example of such a network involving the creation and destruction of eleven virtual particles in his book The World of Elementary Particles. He has also cited Ford’s comment – “Every proton occasionally goes through exactly this dance of creation and destruction” (1975, 240). Capra goes further – “Ford is not the only physicist to have used phrases like ‘dance of creation and destruction’ and ‘energy dance’. The ideas of rhythm and dance naturally come to mind —”(240). Again, modern physics has not only shown us that all matter, whether here on Earth or in outer space, is involved in a continual cosmic dance, but also has shown through field theory that, “each particle does indeed ‘perpetually sing its song’, producing rhythmic patterns of energy (the virtual particles) in ‘dense and subtle forms’”(242).

Now, Capra makes the comment that – “the metaphor of the cosmic dance has found it’s most profound and beautiful expression in Hinduism in the image of the dancing god Shiva. —. According to Hindu belief, all life is part of a great rhythmic process of creation and destruction, of death and rebirth, and Shiva’s dance symbolizes this eternal life-death rhythm which goes on in endless cycles” (242). To take the metaphor deeper, he has cited a long passage from Coomaraswamy – “In the night of Brahman, nature is inert, and cannot dance till Shiva wills it: He rises from his rapture, and dancing sends through inert matter pulsing waves of awakening sound, and lo! Matter also dances, appearing as a glory round about him. Dancing, He sustains its manifold phenomena. In the fullness of time, still dancing, He destroys all forms and names by fire and gives new rest. This is poetry, but nonetheless science”(242). This passage has all features and phenomena what Capra looks for – the creation starts with his dance, which means that he creates, he sends pulsing waves through inert matter that awakens sound, the matters also dance, through dancing he sustains all the phenomena, through dancing he also destroys all the forms, and gives new rest. To have the parallel, he shows that modern physics has also revealed that every sub-atomic particle not only performs an energy dance, but also is an energy dance; a pulsating process of creation and destruction. The patterns of this dance are an essential aspect of each particle’s nature and determine many of its properties. Further, not only matter, but also the void, participates in the cosmic dance, creating and destroying energy patterns without end. 

At the same time, Shiva reminds us that the manifold forms in the world are maya – not fundamental, but illusory and ever-changing – as he keeps creating and dissolving them in the ceaseless flow of his dance. This has relevance to the creation and destruction of virtual particles in subatomic physics. Capra is not just content with this reference to maya, he further quotes – “As Heinrich Zimmer has put it: ‘His gestures wild and full of grace, precipitate the cosmic illusion; his flying arms and legs and his swaying of torso produced – indeed, they are – the continuous creation-destruction of the universe, death exactly balancing birth, annihilation the end of every coming-forth’” (243). 

Capra’s conclusion of the chapter is – “For the modern physicists, then, Shiva’s dance is the dance of subatomic matter. –. The bubble-chamber photographs of interacting particles, which bear testimony to the continual rhythm of creation and destruction in the universe, are visual images of the dance of Shiva equaling those of the Indian artists’ beauty and profound significance. The metaphor of the cosmic dance thus unifies ancient mythology, religious art, and modern physics. It is indeed, as Coomaraswamy has said, ‘poetry, but nonetheless science’” (245).

Conclusion

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. Capra makes a statement – “The Brahman of the Hindus, like the Dharmakaya of the Buddhists and the Tao of the Taoists, can be seen, perhaps, as the ultimate unified field from which spring not only the phenomena studied in physics, but all other phenomena as well”(211).

The other one is that, like a few questions are raised in the introduction, Capra has also raised some questions. Those are: is modern science merely rediscovering what the Eastern sagas discovered thousands of years ago? Should physicists abandon their scientific exploration and meditate? Can there be a mutual influence between science and mysticism, or, even a collaboration or synthesis? While answering these questions in negative, Capra has concluded that – “Neither is comprehended in the other, nor can either of them be reduced to the other, but both of them are necessary, supplementing one another for a fuller understanding of the world” (306).    

Reference

1. Bharatmuni. 2003. The Natya Sastra. (Translated into English by A Board of Scholars). Reprinted. Delhi: Sri Satguru Publications.
2. Capra, Fritjof. 1975. The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism. Boulder: Shambhala.
3. Coomaraswamy, Ananda. 1918. The Dance of Siva: Fourteen Indian Essays. New York: The Sunwise Turn, Inc.
4. Raja, M. L., 2017. Swami Vivekananda and Modern Science. Kochi: Kurukshetra Prakasan.
5. Zimmer, Heinrich. 1990. Myths and Symbols in Indian Art and Civilization. Ed: Joseph Campbell. Delhi: Motilal Banarsidass Publishers Private Limited.