Written by: Jonathan Handjojo

Imagine a single framework that would be capable of explaining everything in the universe, a theory that ties together everything from the smallest quarks to the vast galaxies, bridging the laws of physics. This idea, often referred to as the “Theory of Everything” (TOE), is one of humanity’s most ambitious scientific pursuits, attempting to encompass every force, particle, and interaction. 

The search for a theory of everything has its roots in the two pillars of modern physics: general relativity and quantum mechanics. General relativity, developed by Albert Einstein, provides a framework for understanding the universe on the grandest scales, including phenomena involving massive celestial objects such as stars, planets, and galaxies. On the other hand, quantum mechanics focuses on the behavior of particles at the smallest scales, explaining interactions of atoms, subatomic particles, and the three non-gravitational fundamental forces: the strong nuclear, weak nuclear, and electromagnetic forces.

The Challenge of Unification

The incompatibility of general relativity and quantum mechanics arises from their fundamentally different descriptions of reality. General relativity portrays gravity as the curvature of spacetime caused by mass and energy, an elegant geometrical theory that excels in explaining large-scale phenomena. On the other hand, quantum mechanics describes the universe in terms of discrete particles and probabilistic wave functions governed by the Standard Model of particle physics, which describes electromagnetic, weak, and strong interactions and classifies all known elementary particles, but does not account for gravity.

At regions where the two theories overlap, like the Planck scale, where space-time becomes quantized (divided into discrete units), singularities within black holes, and the extreme early conditions of the early universe, the two theories break down. Resolving this conflict requires a new framework that would be able to merge quantum mechanics with general relativity seamlessly. Among the many attempts to achieve this goal, quantum gravity has emerged as a leading area of research. Quantum gravity seeks to describe gravity in quantum terms, bridging the gap between the macroscopic and microscopic realms. One notable approach is string theory, a candidate for the theory of everything that reimagines fundamental particles as one-dimensional vibrating strings.

Figure 1

Example of string theory; Three strings vibrating at varying frequencies along with the corresponding particle they act as

Source: Medium

String Theory and Higher Dimensions

String theory states that all particles in the universe are composed of tiny, vibrating strings, each oscillating in unique patterns. These vibrations determine the properties of particles, such as mass and charge. According to string theory, at the earliest moments of the universe (within 10^–43 seconds after the Big Bang), all four fundamental forces were unified as a single force. As the universe cooled, these forces were separated into distinct interactions.

String theory also introduces the concept of additional spatial dimensions beyond the three we are familiar with, suggesting that spacetimes comprise 10 or 11 dimensions. While these extra dimensions are compacted so small to be undetectable at ordinary scales, their presence would allow for the mathematical consistency of string theory. Despite its theoretical elegance, string theory has a lot of challenges, including a lack of testable predictions and controversies about its physical implications. 

Arguments Against 

However, all of this research could be useless, if it is impossible to make a theory of everything. Gödel’s incompleteness theorem asserts that any formal theory that can express elementary arithmetical facts and are strong enough for them to be proved will either be inconsistent or incomplete, meaning that it would have true statements that could not be proved in the system or have contradictory statements. This could mean that there could never be a theory of everything since it would be incomplete, but some scientists think that we could still prove the underlying rules of the universe and that Gödel’s incompleteness theorem is irrelevant to computable physics laws.

Another argument against a theory of everything is the accuracy and approximations we have for physical theories. Since no physical theory has been proven to be completely accurate, rather than being made through successive approximations and refining predictions, theoretical models could actually end up being more like useful tools rather than theoretical models that reflect reality. 

It also might simply be impossible to find a theory of everything since it would need to work across simple and complex scenarios, even if there is no exact solution. For example, while general relativity lacks precise solutions in all cases, its experimentally validated principles make it widely accepted. A theory of everything must work for a wide range of simple examples in a way that we could be reasonably confident will work for every solution in physics, resulting in extensive computations and an unelegant theory of everything.

Figure 2

Typical path of theories, with each unification step represented by moving one level up on the graph

Source: Wikipedia

Future Work

Currently, physicists are working on a grand unified theory (GUT) that would merge the electromagnetic, weak, and strong forces into a single “electronuclear” force, expected to emerge at extremely high energies (around 10^16 GeV), far beyond current experimental capabilities. While the simplest GUTs have been disproven, supersymmetric GUTs remain promising due to their ability to naturally explain dark matter, potential links to the force leading to the inflationary force (force expanding the universe), and theoretical elegance. However, GUTs, like the Standard Model, rely on renormalization, suggesting they are incomplete effective theories that omit crucial high-energy phenomena.

The ultimate goal is to reconcile quantum mechanics and gravity, often linked to general relativity, but no theory of quantum gravity or theory of everything has yet been validated by observational evidence. A successful theory of everything would likely address unresolved issues in GUTs and provide explanations for dark energy, the inflationary force, and dark matter, although the existence of these forces and particles remains unproven.

Conclusion

The search for a theory of everything embodies humanity’s quest to discover the universe and our place in it. While progress in frameworks like the Standard Model and quantum gravity are getting us closer to finding a possible explanation for everything in the universe, the challenge of combining quantum mechanics and general relativity, as well as limitations in testability and calculation, have prevented us from finding one so far. Despite this, each step closer to a potential theory of everything leads us closer to understanding our universe and how we came to be.

References and Sources

Fatih A. (2023, May 5). The unification of physics is a quest to find a single theory that can explain all the fundamental forces of nature, including gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. This theory is often referred to as a Theory of Everything (TOE), and it represents the ulti. Linkedin.com. https://www.linkedin.com/pulse/unification-physics-quest-theory-everything-fatih-akay/

Mann, A. (2019, August 29). What Is the Theory of Everything? Space.com. https://www.space.com/theory-of-everything-definition.html

Theory of Everything – an overview | ScienceDirect Topics. (n.d.). Www.sciencedirect.com. https://www.sciencedirect.com/topics/psychology/theory-of-everything