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Compatibilising the Incompatible: A Brief History of String Theory and its Limitations 

Written by Kat Jivkova. How has String Theory in physiscs developed since the 1970s? Kat Jivkova examines the twists and turns in this controversial yet enduring 'theory of everything'.

General relativity and quantum mechanics, named ‘the two pillars of twentieth-century physics’ by Rovelli, are incompatible in their current forms. The quantum description concerned the sub-atomic world and emerged in the 1920s after a quarter of a century of experimental success and theoretical deliberations of several great minds. General relativity, in contrast, was a culmination of previous theories of gravity, space and time, conceived by a single mind over approximately 15 years. The predictions of both theories inside their application domains – the very small and the very large – have been demonstrated to be in remarkable agreement with experimental observations for nearly a century now. Yet, the two theories clash in many aspects, one being that general relativity results in rather divergent quantum corrections. The task of reconciling quantum mechanics and general relativity created a new impetus for theoretical physicists to find a “theory of everything”, and string theory was one candidate for offering a solution. But while it has been born out of ‘down-to-earth high energy physics’ it is now being described by many physicists as an idea detached from reality, no longer resembling the spirit of Einstein’s work. And still, string theory continues to attract enormous funding, and young physicists into its field – is its popularity still justifiable?  

Though the history of string theory has not warranted the attention of many historians of science, much can be inferred from its development, particularly in relation to how it is viewed in the present. String theory was stumbled upon by accident in the late 1960s, specifically in the understanding of the hadronic S-matrix. At this time, string theory was actually known as The Dual Resonance Model (DRM). String theories were generally coming into fashion as a way of explaining strong interactions, but it was soon realised that such theories were not suitable for this purpose and were eclipsed by Quantum Chromodynamics, despite the fact that hadronic physics exhibited a number of string-like features. Notably, CERN theorist Gabriel Veneziano was able to write an expression for the S-matrix, and his insight was amplified by Nambu, who suggested this model was equivalent to a theory of strings. Thus, string theory was consolidated as a concept in which subatomic particles are “stringlike” as opposed to zero-dimensional “points”.  

While most researchers concluded in the mid-1970s that string theory could no longer be considered of relevance to the physical universe, the theory’s appeal did not falter. Instead, physicists began to explore string theories in the 1970s and 1980s as possible theories of quantum gravity and noticed that the non-anomalous versions came close to unifying particle physics. What was called a relativistic quantum string theory was outlined in the form of three defining properties: (1) a theory of general relativity, i.e. a quantum field theory; (2) a theory with gauge interactions; and (3) a theory of finitism. The reason why string theory attracted so much attention in this period (apart from its obvious potential to unify quantum physics) was due to point (3): string theory was free of ultraviolet divergences that created problems within ordinary field theories (this refers to a situation in which an integral diverges due to the contributions of objects with high energy, or because of physical phenomena at short distances). Hence, physicists including Scherk, Schwartz and Yoneya made the bold proposal that string theories could well be viable theories of quantum gravity.  

The announcements of these theorists were initially ignored. String theory had failed to describe the strong force, so how could it provide a solution to Einstein’s entire unifying theory? Furthermore, some string theories were seriously limited within their own theoretical frameworks: some displayed inconsistent equations, while others required the universe to have six dimensions in addition to our three spatial ones. As a result, many physicists dropped out of the pursuit of a unifying theory following this approach. However, Schwarz and theorist Michael Green continued for over a decade, finally achieving a breakthrough in 1984. During their investigation of several string theories, they discovered that the equations of two known string theories were consistent after all. Their work triggered a renewal in string theory research, with hundreds of physicists re-joining the hunt for a unified framework. Different analogies were developed to explain the phenomenon of “stringlike” particles: just as how different vibrations of a violin string can produce different musical notes, the vibrations of the strands in string theory that make up our universe were suggested to produce different particles. There were also great efforts (and still are) to explain the extra six spatial dimensions (later revised to seven by Edward Witten) that coincide with string theory – using Einstein’s logic that space can expand, contract and bend, a dimension could potentially contract to become smaller than an atom, hence why we cannot see it. While there is no real way to test for extra dimensions, particle accelerators at CERN could find evidence of particles that can only exist if extra dimensions were real, though this has not happened yet.  

From the late 1990s, physicists made great progress in understanding the deeper structures of string theories, which were described as different limits of a larger structure. The first string theories only consisted of bosons, but this was later expanded to fermions which led to the discovery of a new property of string theory: supersymmetry. Referred to as an extension of the Standard Model of Particle Physics, supersymmetry predicts that each particle in the Standard Model has a partner, but also links together fermions and bosons. This seems unlikely since bosons are sometimes described as “clannish” in comparison to the “standoffish” fermions, however supersymmetry brings them together with a spin differing by about half a unit. So far, there has been no evidence for the existence of supersymmetry particles, which may be due to their heaviness. However, if they are found, this is not enough evidence to verify string theory; there are other theories which also require supersymmetry. Thus, this discovery would have to be accompanied by the discovery of extra dimensions to completely rule out other quantum field theories. The development of a new particle accelerator at CERN did indeed create some doubts about string theory among physicists. The majority of those who supported string theory expected supersymmetric particles to immediately become evident, and when they were not observed, they were undoubtedly disappointed. While this can be explained by the mass of these particles as mentioned before, this discovery, or lack thereof, places in favour the other most studied alternative theory: loop quantum gravity.  

Loop quantum gravity is a quantisation of general relativity which postulates that the structure of what Einstein calls ‘spacetime’ is in the form of finite loops woven within networks called spin networks. These spin networks evolve, which is referred to as spin foam since these networks are made of surfaces that meet on lines, and then meet on vertices resembling soap-like foam bubbles. This is a theory of determinacy, proven to be finite more definitively than string theory. It also does not require supersymmetry particles in order to be a viable theory – perhaps a major victory over string theory? Indeed, this direction for the discovery of a quantum theory of gravity seems the more promising since the main concern of string theory seems to be more the unification of all known fields rather than the study of quantum properties of space and time. This is too ambitious of an endeavour considering our given knowledge of the universe.  

Nonetheless, the prospect of uniting the theoretical structures of the twentieth century has captivated theorists in an outstanding way, seen by the undying loyalty of Schwarz and Green during the short decline of string theory in the early 1980s. While it may be the case that string theory in whichever form will always remain a speculation, there is still a hope that the LHC (Large Hadron Collider) will produce results of supersymmetry and multiple dimensions to at least give string theorists a foothold over loop theorists. Or perhaps CERN will develop an even more powerful particle accelerator to accommodate the heavier masses of supersymmetry particles that have not been previously observed. In any case, string theory will remain an important contender in the search for a unified theory of everything.  

Written by Kat Jivkova 

Bibliography:

Blum, Alexander. “Dean Rickles. A Brief History of String Theory: From Dual Models to M-Theory. (The Frontiers Collection.) Xix + 251 Pp., Figs., Tables, Index. Berlin: Springer, 2014. Isis 106, no. 4 (2015): 990–991. 

Cappelli, Andrea, Elena Castellani, F. Colomo, and P. Di Vecchia. The Birth of String Theory / Edited by Andrea Cappelli, INFN, Florence, Elena Castellani, Department of Philosophy, University of Florence, Filippo Colomo, INFN, Florence, Paolo Di Vecchia, Nordita, Stockholm and Niels Bohr Institute, Copenhagen. Cambridge: Cambridge University Press, 2012.

CERN. ‘Extra Dimensions, Gravitons, and Tiny Black Holes.’ [Online]. [Accessed on 15 November]. 

https://home.cern/science/physics/extra-dimensions-gravitons-and-tiny-black-holes

CERN. ‘Supersymmetry.’ [Online]. [Accessed on 15 November 2021]. 

https://home.cern/science/physics/supersymmetry

Dine, Michael. Supersymmetry and String Theory: Beyond the Standard Model. Vol. 9780521858410. Cambridge: Cambridge University Press, 2007. 

Ibáñez, Luis E., and A. Uranga. String Theory and Particle Physics : an Introduction to String Phenomenology / Luis E. Ibáñez, Angel M. Uranga. Cambridge: Cambridge University Press, 2012. 

Rovelli, Carlo. “Loop Quantum Gravity.” Living reviews in relativity 11, no. 1 (2008): 1–69. 

Rovelli, Carlo. Reality Is Not What It Seems. St Ives: Clays Ltd, 2016.  

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