In this paper, we propose a new perspective of quantum spin (angular momentum) in which the Boltzmann constant \(k_β\), Planck temperature \(T_{P}\), Planck mass \(m_{P}\) and Planck area \(l_{P}^{2}\) are the integral part of the total angular momentum \(J\). With the aid of this new perspective, we modify the equation of the area and volume operator. In the quantum geometry, for \(SO(3)\) group, the angular momentum operators \(J^{k}\) is the \(k\)th Lie group generator \(T^{k}\); hence, \(T^{k} \equiv J^{k}\). Therefore, new perspective of quantum spin can be directly applicable to quantum geometry. From data, the value of the area operator \(\hat{A}_{S}\) increases with \(n^{2}\) in discrete way that suggests discrete spectrum of the area operator similar to the actual formula of the area operator. This perspective provides an auto-correct or auto-balance mechanism within the equation of these geometrical operators. At the quantum gravity scale, it means that the mutual small change in \(T_{P}\), \(m_{P}\), and \(l_{P}^{2}\) occur in such a way that \(\hbar\), \(l_{P}\) and \(\hat{A}_{S}\) and \( \hat{V}_{S}\) remain invariant for a value of \(j_{i}\). The constancy of the reduced Planck constant \(\hbar\) in the geometrical operators can provide a way through which smooth transition of the Planck scale to the nuclear or the atomic scale can be understood.
Loop quantum gravity (LQG) quantizes gravity through the quantization of the space-time. It begins with general relativity (GR) and brings some concepts from quantum field theory to quantize the space-time. The conceptual background of GR is necessary to comprehend the LQG framework. Therefore, in this paper, prerequisite concepts such as special relativity, general relativity, covariant electromagnetism, tensor analysis, Lagrangian formulation, Hamiltonian formulation and basics of quantum mechanics are briefly introduced; that, are needed to study loop quantum gravity(LQG).
New quantum spin perspective redefines notion of quantum spin and reduced Planck c onstant h. Other consequences of this perspective are well-known. Here I propose smooth scale transition of quantum domain using auto-correct orauto-balance mechanism of this perspective. Equilibrium governs nature. All universal constants and equations work just to contribute to maintain equilibrium of cosmos. Relation between elementary quantum of action (¯h) and new quantum spin perspective is also established. why matter wave works the way it works? and why simultaneous measurement of two main pair of canonical conjugates ( x and p and E and t) are not possible in nature? are also explained via this perspective. Cause of uncertainty principle of quantum physics is also comprehended. De Broglie hypothesis and uncertainty principle emerge out of novel formula of h.
Consequences of new quantum spin perspective in quantum gravity are far-reaching. Results of this novel perspective in loop quantum gravity, i.e., the modification of the equation of geometrical operators such as the area and the volume operator are known. Using newly proposed formula from this perspective, the magnitude of fundamental constants such as the reduced Planck constant ℏ, the gravitational constant G, the speed of light c, the Boltzmann constant kβ , the fine structure constant α, can be validated. With the aid of this perspective, we find new formulas for the fundamental Planckian quantities and the derived Planckian quantities. We also propose novel formulas for the Planck star such as the size, the curvature, the surface area and the size of black hole (for the Planck star) without modifying its significance. The relation of the quantum spin with the Planck temperature TP (TP ∝ n2 ), the Planck mass mP (mP ∝ n2 ), the Planck length l P (l P ∝ n) are also proposed using this novel perspective.
In this article, Planck star and remnant scenario i.e., solution of black hole information paradox in loop quantum gravity (LQG) are elaborated. Since, Black hole is the final fate of collapse scenario in general relativity; firstly, gravitational collapse with two possible final outcomes i.e., black hole and naked singularity, is outlined. Thereafter, black hole thermodynamics along with four laws of black hole thermodynamics, Hawking radiation, brief introduction to information theory and cause of information paradox are given. Then, solution of black hole information paradox outside the LQG are briefly explained. Thereafter, basic concepts of LQG along with loop quantum cosmology (LQC) are described. LQG can solve information paradox by its natural cut off on the value of quantum volume operator. In LQG, a star namely, Planck star is also proposed that is formed at Planck density and resides at so-called singularity point. Since, LQG removes singularity through big bounce and proposes Planck star which provides enough room for information to escape; hence, it can solve information paradox. LQG predicts remnant of black hole of the order of \(10^{-14} m\); which, is under current technological regime. In the remnant scenario, black hole makes quantum transition into white hole and this white hole behaves as a long lived remnants that can solve information paradox. In this quantum transition, a black hole tunnels into a white hole at the end of evaporation.
The Barbero–Immirzi parameter, (γ), is introduced in loop quantum gravity (LQG), whose physical significance is still the biggest open question because of its profound traits. In some cases, it is real valued, while it is complex valued in other cases. This parameter emerges in the process of denoting a Lorentz connection with a non-compact group SO(3,1) in the form of a complex connection with values in a compact group of rotations, either SO(3) or SU(2). Initially, it appeared in the Ashtekar variables. Fernando Barbero proposed its possibility for inclusion within formalism. Its present value is fixed by counting micro states in loop quantum gravity and matching with the semi-classical black hole entropy computed by Stephen Hawking. This parameter is used to count the size of the quantum of area in Planck units. Until the discovery of the spectrum of the area operator in LQG, its significance remained unknown. However, its complete physical significance is yet to be explored. In the present paper, an introduction to the Barbero–Immirzi parameter in LQG, a timeline of this research area, and various proposals regarding its physical significance are given.
The fundamental building block of the loop quantum gravity (LQG) is the spin network which is used to quantize the physical space-time in the LQG. Recently, the novel quantum spin is proposed using the basic concepts of the spin network. This perspective redefines the notion of the quantum spin and also introduces the novel definition of the reduced Planck constant. Implications of this perspective are not only limited to the quantum gravity, but also found in the quantum mechanics. Using this perspective, we propose the quantization of the space-time of the mind-stuff. Similarity between the physical space-time and the space-time of the mind-stuff provides novel notions to study the space-time scientifically as well philosophically. The comparative study between the physical-space-time and the space-time of the mind-stuff is also given.
An attempt is made to demystify loop quantum gravity (LQG) in a concise and lucid way. LQG is a background-independent as well as non-perturbative approach of the theory of quantum gravity. Since LQG is one of the supposed candidates of a theory of quantum gravity, firstly, prerequisite concepts that are needed for LQG are outlined. Since LQG belongs to the canonical quantization approach, the ADM formalism along with the metric formulation is introduced. Thereafter, other associated concepts regarding the connection formulation are given, such as tetrads, spin connection, and the Palatini action. Afterwards, a modification of the connection formulation, i.e., the Ashtekar formulation, a basis for the current framework of LQG, is presented. Thereafter, the kinematic and dynamical framework, i.e., spin network and spin foam, respectively, are explained; here, the geometrical observables such as area and volume are quantized. Applications of LQG, such as the black hole entropy problem and loop quantum cosmology, are also briefly introduced. This article targets on beginners and novice who wants to enter this research field.
The Barbero-Immirzi parameter ($γ$) is introduced in loop quantum gravity (LQG) whose physical significance is still a biggest open question; because of its profound traits. In some cases, it is real-valued; while, it is complex-valued in other cases. This parameter emerges out in the process of denoting a Lorentz connection with non compact group $SO(3,1)$ in the form of a complex connection with values in a compact group of rotations, either $SO(3)$ or $SU(2)$. Initially, it was appeared in the Ashtekar variables. Fernando Barbero proposed its possibility to include within formalism. Its present value is fixed by counting of micro states in loop quantum gravity and matching with the semi classical black hole entropy computed by Stephen Hawking. This parameter is used to count the size of the quantum of area in Planck units. Until, the discovery of the spectrum of the area operator in LQG; its significance remains unknown. However, its complete physical significance is yet to be explored. In the present article, an introduction to the Barbero-Immirzi parameter in LQG, time line of this research area, various proposals regarding its physical significance are given.
