Theory of Everything
𝛿 2 𝛿 𝛾𝑖𝑗 𝛿 𝛾𝑘𝑙
− 𝑅 3 (𝛾)𝛾 1/2 +2Λ𝛾 1/2 ]Ψ[𝛾
[−𝐺 𝑖𝑗𝑘𝑙
𝑖𝑗 ]=0
The equation shown above is known as the Wheeler-DeWitt equation which mathematically describes this idea. However, this equation is unsolvable using our normal metrics of space-time curvature but only using mathematical objects known as Ashketar variables. Ashketar variables are quanta of angular momentum which will change orientation depending on the curvature of space-time and the path of the quanta and therefore acts as a representation of the curvature of space-time itself. When these variables are used to solve the Wheeler-DeWitt equation, the result is a quantum field of gravity which is resemblant of other quantum fields in quantum field theory. Although, in order to do so, these Ashketar variable needed to be evaluated over closed loops and hence the name, loop quantum gravity. Therefore, any geometry of 3d space can be represented as a formation of these loops known as spin networks. An implication of the quantization of space-time is that there is a smallest length and minimum time, namely the Planck time and Planck time respectively, that are indivisible. The theory of loop quantum gravity has many merits such as its merger of quantum mechanics and general relativity without the need for inductive leaps like other theories of quantum gravity. Moreover, loop quantum gravity is consistent with Hawking and Beckenstein’s equations for black hole entropy. However, as a result of the quantization of space, another prediction of loop quantum gravity is the speed of light is slightly slower for higher frequencies of light compared to lower frequencies due to higher frequencies’ faster oscillations being impeded by the ‘ granular ’ space-time it travels through. However, this was tested using a gamma ray burst and measuring at which points in time different frequencies of light reach us and during this test there was no clear difference between the arrival times of different frequencies of light. (However, this could be due to being unable to measure the difference in time at high enough precision.) A second theory of quantum gravity is known as M theory 9 which is the successor to super string theory. It postulates that all particles are, in reality, a series of open and closed strings with varying modes of oscillation rather than the point particles that we currently conceptualize them as. These strings can describe the properties of all fundamental particles in the standard model and how they evolve in time, however, it also predicts the existence of the graviton and the axion which in theory would solve both quantum gravity as well as our uncertainty on dark matter. However, in order for this theory to be mathematically viable, these strings must be oscillating in 11 dimensions which is contrary to the 3 spatial and 1 temporal dimensions we observe. Therefore, theoretical physicists suggests that these unseen dimensions are actually entwined among one another on the Planck scale and that we are just currently unable to observe them. This assumption can explain certain phenomena that we observe such as the relative weak strength of the gravitational force when compared to the other fundamental forces which is due to the graviton being able to move through more dimensions that the other gauge bosons and therefore having a lesser effect on the dimensions we can observe. Moreover, in 1997 Juan Maldacena published a paper which addressed AdS/CFT conformality. 10 AdS, referring to anti-de Sitter
9 See String Theory. 10 See AdS/CFT correspondence.
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