The Theory of Everything: are we almost there?
Rathan Subramanian
The Theory of Everything 1 is a hypothesized framework consisting of the fundamental laws of the universe from which all laws can be derived and is generally considered the holy grail of physics. Since the advent of relativity and quantum mechanics in the early 20 th century, the objective of many theoretical physicists has been finding a theory of everything by uniting the four fundamental interactions (namely the weak, strong, electromagnetic, and gravitational interactions). Today, the weak, strong, and electromagnetic forces have been explained quantum mechanically in electroweak theory, quantum chromodynamics and quantum electrodynamics (QED) respectively. However, the leading framework to describe the gravitational force is general relativity. Therefore, many believe that a unification between general relativity and quantum mechanics and hence a unification all four interactions is the last step toward a theory of everything.
This proposed unified theory of general relativity and quantum mechanics is known as quantum gravity. 2 However, there are clearly incompatible ideas in the two constituent theories that make quantum gravity as a simple combination of general relativity and quantum mechanics impossible.
8𝜋𝐺 𝑐 4
𝐺 𝜇𝜈 +𝑔 𝜇𝜈 Λ=
𝑇 𝜇𝜈
The above equations are Einstein’s field equations 3 which are the central equations describing the predictions of general relativity. 4 In general relativity, Einstein united the initially separate concepts of space and time into a singular 4-dimensional mutable space-time and proposed that the presence of matter 5 will distort the geometry of space-time which is what we observe as a gravitational field. In this equation, 𝑇 𝜇𝜈 , known as the stress-energy tensor, is the mathematical description of energy and momentum present in a point in space time and 𝐺 𝜇𝜈 is the Einstein tensor which describes the curvature of space-time at a point. Therefore, this equation predicted that when there is energy and momentum at a point in space, the local space-time must be distorted. In this interpretation we ignore the 𝑔 𝜇𝜈 Λ term as this term accounts for dark matter and the expansion of the universe and is negligible the majority of the time. When this space-time curvature is accounted for at all points in space-time, it results in a continuous gravitational field. On the other hand, one of the key ideas in quantum mechanics is that energy can be quantized into discrete indivisible packets known as quanta. Based upon this notion, the standard model was created in which all forms of known matter can be subdivided into a series of quarks and leptons, with forces being mediated by virtual particles known as gauge bosons and mass being a property of the Higgs 1 See Mann 2019. 2 See Wood 2019. 3 See Einstein Field Equations (General Relativity) (2019) 4 This is plural as the equation shown above is the contracted form of 10 equations. 5 Space-time can be curved by mass or energy as they are proven to be equivalent for bodies at rest by E=mc 2 .
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