Toward a Quantum theory of Gravity and a Resolution of the Time paradox
One of the major issues confronting theoretical physics is finding a quantum theory of gravity and a resolution to the cosmological constant problem. It is believed that a true quantum theory of gravity will lead to a solution to the this problem. Finding a quantum theory of gravity has been a difficult issue mainly because of the high energy scale required for testing quantum gravity which is far the reach of current accelerators. Also general relativity does not possess a natural time variable thus the nature of time is not clear in quantum gravity, a problem called the time paradox. The two main approaches are string theory and loop quantum gravity. String theory unifies all interaction but provides a perturbative background dependent formulation which violates general covariance. Loop quantum gravity provides a non-perturbative approach but does not provide a unified theory of interactions, which most physicist believe should be the case at Planck scale energies. It doesn't also seem to connect with low energy phenomena. In this note I look at how quantum cosmology provides useful inference toward a quantum gravity theory by merging inputs from the perturbative and the non-perturbative approaches, and resolving the time paradox issue.