الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
Quantum Mechanics was proposed after Max Planck’s solution in 1900 to the black- body radiation problem, which could not be explained by classical physics, with Planck’s hypothesis of quanta of energy of the radiation. Besides Planck, many other physicists like Dirac, Heisenberg, Schrödinger, Bohr, and Pauli contributed to the formulation of Quantum Mechanics.
In Quantum Physics, in contrast to Classical Physics, there are accuracy limits in predicting the values of physical quantities of a particle, such as position x and momentum p, given some initial conditions. This is what is known as the Heisenberg Uncertainty Principle. Proposed by the German physicist Werner Heisenberg in 1927, the Heisenberg Uncertainty Principle states that measuring the position of a particle with high accuracy implies lower precision in predicting its momentum from initial conditions, and vice versa. Representing the uncertainty in position and momentum by ∆x and ∆p, respectively, the
HUP can be formulated as
∆x∆p ≥ ℏ ,
where ℏ = h is the reduced Planck constant. Quantum Mechanics has achieved several
successes in describing different physical phenomena. Three of the four fundamental Interactions (electromagnetic, weak, and strong interactions) in Nature are described within the framework of Quantum Mechanics under what is well-known as the Standard Model of Particle Physics which received various experimental confirmations. The most recent success was the discovery of the Higgs boson in 2012 at the Large Hadron Collider.
Despite the fact that the Standard Model is believed to be theoretically self-consistent and considered a milestone toward the success of Quantum Mechanics with many experimental observations, it fails to describe the fourth most familiar fundamental interaction, i.e., gravity, due to the inconsistency that arises when one tries to combine Quantum Mechanics with General Relativity.
The general theory of gravity was proposed by Albert Einstein in 1915. General Relativity is the current description of the fourth fundamental interaction, i.e., gravity, as a geometric property (curvature) of four-dimensional spacetime due to the presence of matter and radiation. General Relativity is the generalization of Newton’s law of universal gravitation, which describes the classical gravity for flat spacetime geometry.
Einstein formulated different thought experiments to understand the consequences of two fundamental principles: the general principle of relativity which states that the laws of physics are the same for all observers (frames of reference), and the Einstein’s equivalence principle which states that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames.
The mathematical framework on which Einstein developed General Relativity is called Riemannian Geometry. He formulated a relativistic and geometric description of the effects of gravity without solving the question of what is the gravity’s source. In Newtonian Gravity, the source is mass. In Special Relativity, mass turns out to be part of a more general quantity called the energy–momentum tensor (Tµν), which includes both energy and momentum densities as well as stress (that is, pressure and shear). As an analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor (Rµν), which is a geometric object that measures the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space.
With the evidence of many experimental observations, General Relativity was able to predict and describe successfully different astrophysical and cosmological phenomena. However, it suffers when one tries to apply it at a very large scale or in the presence of very strong gravitational forces.
Despite the significant achievements of Quantum Mechanics and General Relativity which have been tested by different experiments, describing Nature in the context of both
theories is not exempt from problems. When one tries to reconcile General Relativity with the laws of Quantum Mechanics, infinities start to emerge in what is known as the non-renormalizability problem. The field of theoretical physics that seeks to unify all fundamental laws of physics by describing gravity according to the principles of Quantum Mechanics is called Quantum Gravity. Many theoretical physics models in the literature nowadays are trying to resolve the inconsistencies between both theories which will enable the physicists to achieve the main goal of getting a complete self-consistent theory of Quantum Gravity. It is not yet known how gravity can be unified with the three non- gravitational forces: strong, weak, and electromagnetic. Developing a quantum theory of gravitation and integrating it with the other three fundamental forces of nature are two of the most fundamental and unresolved issues in the domain of theoretical physics.
In Chapter 1, we shall outline the nature of Quantum Mechanics and General Relativity, and discuss some of the unsolved problems that emerge when one tries to incorporate Quantum Mechanics into General Relativity. Moreover, we shall provide a brief review of the main Quantum Gravity theories such as String theory, Black Hole Physics, Doubly Special Relativity, and Loop Quantum Gravity in Chapter 2. These theories are among the most promising theoretical frameworks that have demonstrated notable progress toward addressing the aforementioned challenges. Despite the progress made by these theoretical frameworks, they have yielded predictions that cannot currently be experimentally tested in laboratories. This is a crucial requirement for any scientific theory, as empirical verification is necessary for proving its validity and accuracy.
The primary goal of my thesis is to try to impose a testable approach through some experimental signatures. Within the context of this research, most of the Quantum Gravity theories predict some sort of modification of the Heisenberg Uncertainty Principle near the Planck scale which is now known as the Generalized Uncertainty Principle. We shall discuss and formulate the Generalized Uncertainty Principle form which is consistent with String Theory, Black Hole Physics, Doubly Special Relativity, and Loop Quantum Gravity
in Chapter 3. We shall start with a brief review of the Heisenberg Uncertainty Principle, and then we discuss the different forms of the Generalized Uncertainty Principle (Linear Generalized Uncertainty Principle and Quadratic Generalized Uncertainty Principle) which were proposed in the different approaches of Quantum Gravity. Then, at the end of the chapter, we shall discuss the main Generalized Uncertainty Principle form in my thesis which combines the two aforementioned forms in a single form which is collectively known as Linear and Quadratic Generalized Uncertainty Principle (LQGUP).
∆x∆p ≥ ℏ 11 − 2α∆p + 4α2∆p22 .
The equivalence principles are foundational concepts in General Relativity that describe the relationship between gravity, acceleration, and the laws of physics. There are two forms of the equivalence principle: the weak equivalence principle and the strong equivalence principle. The weak equivalence principle states that the motion of a particle under the influence of gravity is indistinguishable from the motion of the same particle in an accelerated reference frame in the absence of gravity. In other words, the effects of gravity are locally indistinguishable from the effects of acceleration. This principle applies to small, local regions of spacetime and implies that the trajectory and behavior of a freely falling object are independent of its mass or composition. On the other hand, the strong equivalence principle extends the idea of the weak equivalence principle and applies to all freely falling reference frames, regardless of their size or location. It states that the laws of physics, including gravitational interactions, are the same in any freely falling reference frame. This principle goes beyond local effects and asserts that the effects of gravity can be completely “turned off” locally. It implies the equivalence of gravitational and inertial mass and leads to concepts such as gravitational time dilation.
The weak equivalence principle is not violated by Quantum Mechanics, as can be demonstrated through an analysis of the Heisenberg equations of motion. However, these
findings may appear to contradict the results of a neutron interferometry experiment which suggests that the weak equivalence principle is violated at small length scales. In Chapter 4, we suggest that LQGUP can explain these experimental results based on what we found in Ref. [1]. Moreover, we demonstrate how the equations of motion are affected by LQGUP and present an analogue of the Liouville theorem that applies in the presence of LQGUP. Furthermore, we shall discuss whether the number of states inside a volume of phase space does not change with time in the presence of LQGUP and its implications for some physical phenomena like the cosmological constant problem, the black body radiation in curved spacetime, as well as the concurrent energy and the consequential no Brick Wall entropy.
The existence of massless charged particles and a naked singularity in a massless Reissner-Nordström-de Sitter-like (RNdS) spacetime in the context of LQGUP has been proposed in a series of papers [1–3]. In Ref. [4], our study establishes not only the confinement of energy density for massless charged particles, including both fermions and bosons, but also their capability to tunnel through the cosmological horizon. These massless particles could potentially interact with the Dirac Sea, leading to their emergence outside the cosmological horizon within the framework of dS/CFT holography. This finding presents a fundamental explanation for the expansion of the Dirac Sea and, consequently, suggests the possibility of a spacetime Big Crunch. We provide a detailed study of this endeavor in Chapter 5.
We shall study the effect of the corresponding weight factor on the de Broglie wavelength
of tunneling fields. Then, we comment on how the LQGUP introduces an effective gravitational field strength in the Colella, Overhauser, and Werner experiments. Moreover, we calculate the tidal force corresponding to the massless RNdS spacetime in order to obtain the
characteristic momentum related to the effective Newton’s gravitational constant. Furthermore, we propose a general methodology for calculating the tunneling through the cosmological horizon of the massless RNdS spacetime within the framework of LQGUP. Finally, we
consider studying the effect of the LQGUP, in the massless RNdS spacetime, on the tunneling of spin fields.
In our recent paper [5], we investigate the modification of the temperature of Schwarzschild black hole in the context of LQGUP and compare it with the same obtained in a quantum context. We shall study six different gravitational observations to test Quantum Gravity in the laboratory in Chapter 6, named: light deflection, perihelion precession, pulsar periastron shift, Shapiro time delay, gravitational redshift, and geodetic precession. We find tighter bounds in the context of LQGUP compared to those obtained from GUP with only linear or only quadratic terms in momentum.
The last chapter serves to provide a comprehensive summary of the entire research endeavor, including a discussion of the central concepts presented and a recapitulation of the findings obtained. We shall discuss the important ideas of the thesis, summarize the results, and discuss future plans.