Quantum Physics & General Relativity are the two great leaps in modernization of Theoritical Physics during 20th century. While General Relativity gives us the idea of the large-scale expansion of the Universe. It also gives small corrections to Newtonian Theory, deflection of light rays, and also predicts the existence of gravitational radiation and black holes. It describes the gravitational force in terms of the curvature of spacetime has fundamentally changed our view of space and time: they are now viewed as dynamical.
Quantum mechanics, on the other hand, is the essential tool for understanding microscopic physics. It explores the basic nature of particles. Certainly, its exact validity is a basic assumption in all string theory research.
The understanding of the fundamental laws of Nature is surely incomplete until general relativity and quantum mechanics are successfully reconciled and unified. That this is very challenging can be seen from many different viewpoints. The concepts, observables and types of calculations that characterize the two subjects are strikingly different. Moreover, until about 1980 the two fields developed almost independently of one another. Very few physicists were experts in both. With the goal of unifying both subjects, string theory has dramatically altered the sociology as well as the science. In relativistic quantum mechanics, called quantum field theory, one requires that two fields that are defined at space-time points with a space-like separation should commute (or anticommute if they are fermionic).
In the gravitational context one doesn’t know whether or not two space-time points have a space-like separation until the metric has been computed, which is part of the dynamical problem. Worse yet, the metric is subject to quantum fluctuations just like other quantum fields. Clearly, these are rather challenging issues. Another set of challenges is associated with the quantum description of black holes and the description of the Universe in the very early stages of its history.
The most straightforward attempts to combine quantum mechanics and general relativity, in the framework of perturbative quantum field theory, run into problems due to uncontrollable infinities. Ultraviolet divergences are a characteristic feature of radiative corrections to gravitational processes, and they become worse at each order in perturbation theory. Because Newton’s constant is proportional to square of length in four dimensions, simple powercounting arguments show that it is not possible to remove these infinities by the conventional renormalization methods of quantum field theory.
Detailed calculations demonstrate that there is no miracle that invalidates this simple dimensional analysis. String theorists are trying to overcome these difficulties and to provide a consistent quantum theory of gravity.
However, the theory is not yet understood fully by scientists. As we have learned time and time again, string theory contains many deep truths that are there to be discovered. Gradually a consistent picture is emerging of how this remarkable and fascinating theory deals with the many challenges that need to be addressed for a successful unification of quantum mechanics and general relativity.
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