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Dec 09, 2022

Quantum Gravity

We have all read about gravity in school and heard about it as a general force of attraction between two particles according to classical mechanics which causes the earth to revolve around the sun and of course it’s what keeps our feet on the ground. But if you have read about general relativity we get to know that actually gravity is nothing but a curvature in spacetime a curve in a higher dimension that we can’t perceive in 3d space, general relativity has explained many things about gravity but it also breaks at extreme gravitational conditions like what happens at the center of a black hole. What exactly happened before the initial singularity? These questions have been puzzling physicists for decades since no one right now can predict what happens when such a high amount of mass is compressed in such a small volume, here we are dealing with unimaginable gravitational force coming from a single point at the quantum level which brings us to the question what is quantum mechanics + gravity? Well, it is quantum gravity.


Why is it so important?

Well, quantum gravity is where quantum mechanics and gravity along with the other 3 fundamental forces come into play which has been really difficult to combine, and if we can solve this will also complete the theory of everything which has been the biggest puzzle in physics.

Quantum Mechanics & General Relativity


Some of you might be familiar with Higgs Boson also regarded as a god particle associated with the Higgs field the particle which provides mass to elementary particles like electrons quarks etc. Just like that graviton is a particle that is responsible for the gravitational force. But so far this hasn’t been found yet. Unlike general relativity, it’s trying to explain gravity at the quantum level which has been a matter of headache among physicists, discovery of this particle might as well combine the standard model and general relativity. But so far, no luck. 


Quantum Gravity as an Effective Field Theory:

In an effective field theory, not all but the first few of the infinite set of parameters in a nonrenormalizable theory are suppressed by huge energy scales and hence can be neglected when computing low-energy effects. Thus, at least in the low-energy regime, the model is a predictive quantum field theory. Furthermore, many theorists argue that the Standard Model should be regarded as an effective field theory itself, with "nonrenormalizable" interactions suppressed by large energy scales and whose effects have consequently not been observed experimentally. Works pioneered by Barvinsky and Vilkovisky suggest as a starting point up to the second order in curvature the following action, consisting of local and non-local terms:




is an energy scale. The exact values of the coefficients c1,c2,c3 are unknown, as they depend on the nature of the ultra-violet theory of quantum gravity.


is an operator with the integral representation


By treating general relativity as an effective field theory, one can actually make legitimate predictions for quantum gravity, at least for low-energy phenomena. An example is the well-known calculation of the tiny first-order quantum-mechanical correction to the classical Newtonian gravitational potential between two masses. Moreover, one can compute the quantum gravitational corrections to classical thermodynamic properties of black holes, most importantly the entropy. A rigorous derivation of the quantum gravitational corrections to the entropy of Schwarzschild black holes was provided by Calmet and Kuipers. A generalization for charged (Reissner-Nordstrom) black holes was subsequently carried out by Campos Delgado.

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