Two theories encapsulate the known and tested aspects of Physics - General Relativity (GR) and Quantum Field Theory (QFT). The former models gravitation as the geometry of spacetime, while the latter captures non-gravitational physics including the Standard Model. GR has shown success in modeling planetary motion, black hole formation, black hole mergers, time dilation, pulsar precession and gravitational waves among others. Likewise, Quantum Theory deals in entirety particle interactions through fundamental forces except gravity explaining forces, particle production/annihilation, atomic effects like Lamb Shift and Compton scattering, and Entanglement. A departure from Newtonian physics to Quantum Mechanics is relevant when energies are of the order of the Planck’s constant, while Relativity is relevant when speeds approach the speed of light or matter density is of Planckian orders.
A natural question that to ask is how does physics behave at the intersection of these regimes. Approximate and effective theories have been formulated and tested in some scenarios. For instance, QFT has been studied in curved space time background and has proved accurate in cosmology with precise predictions of the CMB power spectrum. In such as theory, the general relativistic solution for curvature is treated as a background, while the perturbations are treated as quantum objects. In other words, the matter fields and gravitational interaction are treated quantum mechanically, while gravity itself is treated classically. But such description falls short when the true quantum nature of gravity is relevant– such as in resolving spacetime “singularities” in big bang and blackholes as predicted by classical GR. Present research into a unified theory of gravitation and quantum mechanics [1, 2, 3, 4] include String Theory, Loop Quantum Gravity and AdS/CFT, all of which are mathematical constructions with the requirement of consistency with QFT and GR in the respective regimes.

In the history of Physics, two approaches exist to constructing theories. First is an experiment driven approach where a theory was built to explain certain observations and made mathematically consistent and elegant iteratively. This includes early pre-Newtonian physics, Newtonian physics and arguably the development of Quantum Mechanics. Wave particle duality had been established in experiments like Compton scattering, Double slit experiment with particles and Photoelectric effect before the development of Quantum Mechanics. Likewise, Quantum Field Theory was developed to explain effects like Lamb Shift and Particle Production where a Quantum treatment of the Electromagnetic field

was warranted.

The second is unification of theories, potentially supported by thought experiments. While special relativity was formulated with a similar motivation, to explain the constancy of speed of light as witnessed by Michelson-Morley’s experiment, General Relativity was born out of Einstein’s work towards building a relativistic theory of gravity. GR’s ability to explain Mercury’s precession was a verification of the theory rather than the motivation for its construction. Since then GR has stood several observational tests which came almost of century later. In this approach, the predictions even after a theory is constructed could be hard to verify, as is likely why they weren’t observed earlier in the first place. Thus, it is important to seek ways to validate, at least indirectly, some of the key postulates. One such example is Bell’s inequality which categorically precludes local-realist descriptions.

The present quest for quantum theory of gravity is driven by mathematical constructions and asymptotic consistency with QFT and GR, owing to the lack of experimental signatures. The observations that distinguish these theories from

either classical GR or Quantum Field Theory in their respective regimes remain elusive, given that probing physics at the Planck scale (∼ 1028 eV) is necessary for QG effects to become relevant. Such observations appear impossible to be verified with foreseeable technology and resources through man-made experiments. For instance, if we were to obtain such conditions in a collider, the size of the collider must at least be of order 1010 m, dictated by the Schwinger Limit on electromagnetic acceleration [5]. This is larger than the distance between the moon and the earth. Given this circumstance, it is valuable to consider the postulates. There is not much debate surrounding many aspects of quantum gravity including that it should provide a “quantum” description of particles and of fields such as electromagnetic field which we know has quantum degrees of freedom. It is also acceptable that gravity should admit quantum sources, as we can verify from the success of QFT in curved space time.

The unaddressed postulate would deal with the quantum nature of the gravitational free field. Though unnatural, it is possible to imagine a theory where gravity is driven by quantum sources but is classical. Whether gravity has quantum degrees of freedom and if it does what can we understand about its nature is a key postulate in any QG construction. Answering this question is the focus of this thesis. Drawing insights from Quantum Information theory we construct probes into the “quantumness” of gravity.