Theory Of Everything As A Fundamental Power That Govern The Universe

We experience gravity continually in our everyday lives; it is the reason our feet stay on the floor, why leaves fall, and why the Earth orbits the sun. While typically described by Newton’s law of universal gravitation, gravity is most precisely described by Einstein’s theory of general relativity, which describes gravity not as a force, but as a consequence of the curvature of spacetime resulting from the irregular distribution of mass and energy. In addition to gravity, there are three other fundamental forces: electromagnetism, the strong force and the weak force. These three fundamental forces (interactions) of physics are described within the framework of quantum field theory, a radically different formalism for describing physical phenomena. Stitching these three quantum descriptions together gives us the Standard Model of Particle Physics.

However, there are questions that the Standard Model and general relativity leave unanswered. Gravity is by far the weakest of the four fundamental forces, dozens of orders of magnitude weaker than the other three fundamental forces. This is an enormous discrepancy and neither general relativity nor the Standard Model offer an explanation for this hierarchy problem. Another problem with the Standard Model is that there are at least nineteen free parameters. Free parameters are numerical constants whose values are unrelated and arbitrary, determined only by experiment; consequently, a mathematical model is less likely to be a product of wishful thinking and is more likely to be correct if it utilizes as few free parameters as possible. This fine tuning is highly unnatural and results in an inelegant Chimera as a theoretical model.

Furthermore, some argue that the Standard Model should contain a term that breaks charge conjugation parity (CP) symmetry, which would relate matter to antimatter, in the strong interaction domain; however, no such violation has been found in experiments, which suggests that this term is extremely close to zero, which requires a high degree of fine tuning. The Standard Model also doesn’t offer an explanation for dark matter, dark energy, neutrino masses, or the matter-antimatter asymmetry in the universe.Worse still, we run into another problem. We have two theories which describe the four fundamental forces that govern the universe; however, when we try to amalgamate the theory of general relativity together with quantum field theory, we get untenable infinities. To settle this issue, we need a theoretical framework that unifyies gravity with the other three fundamental forces in order to elegantly combine general relativity and quantum field theory into a single theory that is capable of entirely describing all physics. To this end, Theories of Everything have become an active area of research.

String theory is one such theoretical framework that endeavors to unify general relativity and quantum mechanics. In string theory, one-dimensional extended objects called strings replace the zero-dimensional particles of the Standard Model. String theory describes how strings propagate through spacetime and interact with one another. In any given version of string theory, there is only one type of string, which may appear as a closed loop, called a closed string, or as a segment of string with free ends, called an open string, and it can vibrate in variegated ways. On distance scales much larger than the string scale, which is approximately 10-34 meters, a string will look like an ordinary particle, with its properties such as mass, electric charge, etc. determined by the vibrational state of the string. In this fashion, all the elementary particles may be viewed as vibrating strings; moreover, one of these vibrational states of a string gives rise to the graviton, a long-theorized quantum particle that mediates the gravitational interaction.

Accordingly, string theory seems to be one of the most promising candidates for a Theory of Everything. The introduction of supersymmetry, a symmetry required in string theory that relates bosons, which have an integer-valued spin, and fermions, which have a half-integer spin, automatically ameliorates the hierarchy problem [2] and provides a candidate for dark matter. Moreover, string theory has almost no free parameters and has the potential to resolve the strong CP problem [3]. Most promising of all, gravity naturally arises in string theory, unifying the four fundamental forces. It is my belief that string theory is the key to unlocking the secrets of the universe. I wish to work on string theory for my Ph.D. research.

With my Ph.D. research, I aim the further bridge the gap between quantum field theory and general relativity. A critical question that I wish to pursue is nonperturbative formulations of string theory. Perturbation theory is a mathematical method for finding an approximate solution to a problem by starting from the exact solution of a related, simpler problem. Perturbation theory is applied when a problem cannot be solved exactly but can be approximated by adding a minute term to the mathematical description of the exactly solvable problem. Perturbation theory yields an expression for the solution in terms of a (usually infinite) power series expanded in terms of the small parameter. Historically, string theory has been formulated entirely perturbatively, but recent work has attempted to construct nonperturbative formulations [4].

Nonperturbative formulations of string theory have to potential to yield closed-form solutions that are more easily interpreted. I plan to further explore this topic and deepen our understanding of string theory. In addition to tackling fundamental science harmoniously through theoretical considerations, this project contains broader impacts. One of the major outstanding questions of astrophysics is the nature of dark matter. String theory provides a natural candidate for dark matter in the form of supersymmetric particles [6], which are needed to make the theory work, but which scientists have not yet observed. Furthermore, by revealing physics beyond the Standard Model, we may be able to describe or even construct new matter from elementary particles like gluons and quarks − one such highlight in recent years is the strong evidence for the tetraquark found at CERN [7]. This new matter might impact our searches for additional stable elements that may assist in creating new materials and efforts in high energy plasma physics which has immediate applications for fusion.

There are some who see string theory as nothing more than an interesting aside, but the possibilities that lie in further research into string theory hold much more than just an intriguing story. When the theory of gravity was first discovered by Newton, it was an extraordinary revelation; but it was just that. While it was revolutionary, the immediate applications of Newton’s discovery were nothing compared to what they are today. From Newton to Einstein, this ever-evolving theory has allowed scientists to continue to innovate, invent, and progress. Without this advancement and knowledge, flight, space exploration, and even modern medicine would not exist as we know them. Analogously, with string theory, if the boundaries of theoretical physics continue to be pushed, then it will one day be possible to use such invaluable information to once again shape our scientific viewpoints.

References:

1. Mannel, Thomas. “Theory and Phenomenology of CP Violation”. Nuclear Physics B, vol. 167 pp. 170–174 (2006).
2. Kawamura. “Gauge hierarchy problem, supersymmetry and fermionic symmetry”. Int. J. Mod. Phys. A 30, 1550153 (2015) arXiv:1311.2365
3. Acharya, Bobkov, Kumar. “An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse”. JHEP 1011:105 (2010). arXiv:1004.5138
4. Motl. “Nonperturbative Formulations of Superstring Theory”. (2001) arXiv:hep-th/0109149
5. Sato. “String Geometry and Non-perturbative Formulation of String Theory”. (2017) arXiv:1709.03506
6. Ellis, Olive. “Supersymmetric Dark Matter Candidates”. From `Particle Dark Matter: Observations, Models and Searches' edited by Gianfranco Bertone. Chapter 8, pp. 142-163 Hardback ISBN 9780521763684. (2010) arXiv:1001.3651