Study of Some Aspects of Quantum Gravity and Its Some Implications

The thesis entitled, “Study of Some Aspects of Quantum Gravity and Its Some Implications”, representing an elaborated report of the author’s research work will be covering in the following seven chapters. Chapter:1- loop quantum gravity: a demystified view There are many theories of quantum gravity in theoretical physics. Among all quantum gravity theories, the loop quantum gravity (LQG) is one of the supposed candidate of quantum gravity theory. In this thesis, more emphasis is put on LQG to study the quan tum gravity. In the first chapter, prerequisites for LQG (necessary introduction of special and general theories of relativity, a brief introduction to mathematical theories for LQG, Lagrangian and Hamiltonian formulations, covariant electromagnetism, a brief introduc tion to quantum mechanics and quantum field theories), basic concepts of LQG, viz. (ADM formalism, metric formulation, Palatini action, connection formulation, Ashtekar’s variable, geometrical operators, spin network, spin foam and application of LQG), are discussed. Chapter:2- the Barbero Immirzi parameter: an enig matic parameter of loop quantum gravity The Barbero- Immirzi parameter γ is one free parameter that appears in the mathematical framework of LQG which appears in Ashtekar’s variable, black hole entropy calculation in LQG and in geometrical operators of LQG. The γ can be real as well as complex valued in LQG. The exact physical significance of γ is still unknown. In the second chapter, the origin, history and various proposals on the physical significance of the Barbero- Immirzi parameter (γ) are discussed. Chapter:3- solution of black hole information paradox in loop quantum gravity Black hole information paradox is one of the frontier topic of modern theoretical physics. Each quantum gravity theory attempts to solve this paradox. Hence, the third chapter is about solution of black hole information paradox in LQG. In essence, in the third chapter, the basics of black hole physics, which includes brief introduction to gravitational collapse, naked singularity, laws of black hole thermodynamics, Hawking radiation and Bekenstein Hawking black hole entropy calculation. In the information theory, the topics covered are brief introduction to information, quantum framework of information theory and cause of information paradox. Finally, the solution of black hole information in LQG covering Planck star and remnant scenario are discussed. Chapter:4- new quantum spin perspective and geomet rical operators of quantum geometry In the fourth chapter, firstly, new quantum spin perspective is proposed by using the framework of thermodynamics out of formula of temperature leading to new definition the total angular momentum J and reduced Planck constant ℏ . Thereafter, the equation of geometrical operators such as the area and volume operator are modified using this proposal. In the equation of operators of area and volume, by putting the new formula of reduced Planck constant ℏ, one can have modified formula of these geometrical operators. From this proposal, one can also explain smooth transition of quantum geometry from Planck scale to nuclear scale. Chapter: 5- implications of new quantum spin perspec tive in quantum gravity Fifth chapter covers implications of new quantum spin perspective in quantum gravity. In essence, in the fifth chapter, the new formulas of fundamental constants such as gravitational constant G, Boltzmann constant kβ, speed of light c, fine structure constant α, the fundamental Planckian quantities such as Planck temperature TP, Planck mass mP, Planck length lP, Planck time tP, Planck temperature TP, the derived Planckian quantities such as Planck density ρP, Planck momentum PP, Planck acceleration aP, Planck force FP, Planck energy EP, Planck frequency fP, and Planck charge QP and the new formulas regarding some quantities of the Planck star are proposed using new quantum spin perspective. At last, relationship of quantum spin with Planck temperature, Planck mass, and Planck length is established using new quantum spin perspective. Chapter:6- new quantum spin perspective and space time of mind-stuff In the sixth chapter, the relation between new quantum spin perspective and space-time of the mind-stuff is established. In Yogic philosophy, there are three sort of space-time: (1) physical space-time, (2) space-time of mind-stuff and (3) space-time of consciousness. Using the basic concepts of spin network of LQG and the new quantum spin perspective, here, the quantization of the space-time of mind-stuff is proposed. This proposal will create new branch of physics, i.e., Physics of Yoga or Yogic Physics (It will provide a quantum theory of Yoga). At last, discrepancies between physical space-time and space time of mind-stuff are given. Chapter:7- summary and future scopes The seventh chapter is about summary and the future of scope of this work.