Loop Quantum Research Articles

On two body gravitational scattering within perturbative gravity

We study the gravitational scattering of two scalar particles up to the one-loop order. We calculate off-shell amplitudes and operators with the recently developed package FeynGrav. We obtained the tree-level amplitude and found it consistent with classical results in relativistic and non-relativistic cases. We obtained explicit expressions for the vertex operator and the scattering amplitude at the one-loop level off-shell. They are consistent with the previous results obtained in the low energy limit. Analysis of the scattering amplitudes and operators is given. We outline the further development achievable with the FeynGrav and other computational packages.

Microscopic interpretation of generalized entropy

Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the Rényi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single umbrella. However, the microscopic origin of such generalized entropy as well as its relation to thermodynamic system(s) is not clear. In the present work, we will provide a microscopic thermodynamic explanation of generalized entropy(ies) from canonical and grand-canonical ensembles. It turns out that in both the canonical and grand-canonical descriptions, the generalized entropies can be interpreted as the statistical ensemble average of a series of microscopic quantity(ies) given by various powers of (−kln⁡ρ)n (with n being a positive integer and ρ symbolizes the phase space density of the respective ensemble), along with a term representing the fluctuation of Hamiltonian and number of particles of the system under consideration (in case of canonical ensemble, the fluctuation on the particle number vanishes).

Realization of Dirac quantization in loop quantum gravity

The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to two versions of well-defined operators in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian can become some symmetric operators. By the deparametrized form, a general expression of the solutions to either of the quantum scalar constraints is obtained, and the observables on the space of solutions can be constructed. Thus, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system.

Strong gravitational lensing by loop quantum gravity motivated rotating black holes and EHT observations

We investigate gravitational lensing in the strong deflection regime by loop quantum gravity (LQG)-motivated rotating black hole (LMRBH) metrics with an additional parameter l besides mass M and rotation a. The LMRBH spacetimes are regular everywhere, asymptotically encompassing the Kerr black hole as a particular case and, depending on the parameters, describe black holes with one horizon only (BH-I), black holes with an event horizon and a Cauchy horizon (BH-II), black holes with three horizons (BH-III), or black holes with no horizons (NH) spacetime. It turns out that as the LQG parameter l increases, the unstable photon orbit radius xps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_{ps}$$\\end{document}, the critical impact parameter ups\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{ps}$$\\end{document}, the deflection angle αD(θ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D(\ heta )$$\\end{document} and angular position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document} also increases. Meanwhile, the angular separation s decreases, and relative magnitude rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document} increases with increasing l for prograde motion but they show opposite behaviour for the retrograde motion. Using supermassive black holes (SMBH) Sgr A* and M87* as lenses, we compare the observable signatures of LMRBH with those of Kerr black holes. For Sgr A*, the angular position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document}∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (16.4, 39.8) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as, while for M87* ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (12.33, 29.9) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as. The angular separation s, for SMBHs Sgr A* and M87*, differs significantly, with values ranging ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.008–0.376) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as for Sgr A* and ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.006–0.282) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as for M87*. The deviations of the lensing observables Δθ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \ heta _{\\infty }$$\\end{document} and Δs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta s$$\\end{document} for LMRBH (a=0.80,l=2.0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a=0.80,l=2.0$$\\end{document}) from Kerr black holes can reach up to 10.22μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10.22\\,\\upmu $$\\end{document}as and 0.241μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.241~\\upmu $$\\end{document}as for Sgr A*, and 7.683μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.683~\\upmu $$\\end{document}as and 0.181μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.181~\\upmu $$\\end{document}as for M87*. The relative magnitude rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document}∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.047, 1.54). We estimate the time delay between the first and second relativistic images using twenty supermassive galactic centre black holes as lenses to find, for example, the time delay for Sgr A* and M87* can reach approximately 23.26 min and 33,261.8 min, respectively. Our analysis concludes that, within the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\sigma $$\\end{document} region, a significant portion of the BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. The possibility of LMRBH being a BH-III with three horizons has been almost ruled out, except for a small portion of parameter space, by θsh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{sh}$$\\end{document} bounds of Sgr A* and M87* measured by EHT. In contrast, NH without a horizon is completely ruled out. We discover that the EHT results of Sgr A* place more stringent limits on the parameter space of LMRBH black holes than those established by the EHT results of M87*.

Gambini-Pullin electrodynamics as a scenario for Cherenkov radiation in QED vacuum

We examine the electromagnetic radiation produced by a moving charge in the QED vacuum that behaves as a dispersive medium characterized by a geometrical structure (discreteness/granularity) that emerges from loop quantum gravity. It is shown that the radiation is driven by the refractive vacuum the charged particle travels through reproducing the profile of the Cherenkov effect.

Different Aspects of Spin in Quantum Mechanics and General Relativity

In this paper, different aspects of the concept of spin are studied. The most well-established one is, of course, the quantum mechanical aspect: spin is a broken symmetry in the sense that the solutions of the Dirac equation tend to have directional properties that cannot be seen in the equation itself. It has been clear since the early days of quantum mechanics that this has something to do with the indefinite metric in Lorentz geometry, but the mechanism behind this connection is elusive. Although spin is not the same as rotation in the usual sense, there must certainly be a close relationship between these concepts. And, a possible way to investigate this connection is to instead start from the underlying geometry in general relativity. Is there a reason why rotating motion in Lorentz geometry should be more natural than non-rotating motion? In a certain sense, the answer turns out to be yes. But, it is by no means easy to see what this should correspond to in the usual quantum mechanical picture. On the other hand, it seems very unlikely that the similarities should be just coincidental. The interpretation of the author is that this can be a golden opportunity to investigate the interplay between these two theories.

Constraints on the rotating self-dual black hole with quasi-periodic oscillations

An impressive feature of loop quantum gravity (LQG) is that it can elegantly resolve both the big bang and black hole singularities. By using the Newman-Janis algorithm, a regular and effective rotating self-dual black hole (SDBH) metric could be constructed, which alters the Kerr geometry with a polymeric function P from the quantum effects of LQG geometry. In this paper, we investigate its impact on the frequency characteristics of the X-ray quasi-periodic oscillations (QPOs) from 5 X-ray binaries and contrast it with the existing results of the orbital, periastron precession and nodal precession frequencies within the relativistic precession model. We apply a Monte Carlo Markov Chain (MCMC) simulation to examine the possible LQG effects on the X-ray QPOs. We found that the best constraint result for the rotating self-dual geometry from LQG came from the QPOs of X-ray binary GRO J1655-40, which establish an upper bound on the polymeric function P less than 6.15 × 10-3 at 95% confidence level. This bound leads to a restriction on the polymeric parameter δ of LQG to be 0.66.

Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity

Multi-messenger astronomy provides us with the possibility of discovering phenomenological signatures of quantum-gravity effects. This should be of paramount importance in the pursuit of an elusive quantum theory for the gravitational interactions. Here we discuss feasible explorations within the effective field theory (EFT) treatment of general relativity. By exploring current techniques borrowed from modern amplitude methods, we calculate leading quantum corrections to the classical radiated momentum and spectral waveforms. The lessons drawn from these low-energy results are that phenomenological applications in gravitational-wave physics can be discussed in line with the EFT approach. In turn, we also examine possible phenomenological surveys from the perspective of a UV completion for quantum gravity which employs the metric as the fundamental dynamical variable, namely quadratic gravity. Being more specific, by resorting to the eikonal approximation, we compute the leading-order time delay/advance in the scattering of light by a heavy object and find a possible significant deviation from the standard general-relativity prediction. This allows us to probe causal uncertainty due to quantum fluctuations of the gravitational field as a genuine prediction from Planck-scale physics.

Discreteness Unravels the Black Hole Information Puzzle: Insights from a Quantum Gravity Toy Model.

The black hole information puzzle can be resolved if two conditions are met. The first is that the information about what falls inside a black hole remains encoded in degrees of freedom that persist after the black hole completely evaporates. These degrees of freedom should be capable of purifying the information. The second is if these purifying degrees of freedom do not significantly contribute to the system's energy, as the macroscopic mass of the initial black hole has been radiated away as Hawking radiation to infinity. The presence of microscopic degrees of freedom at the Planck scale provides a natural mechanism for achieving these two conditions without running into the problem of the large pair-creation probabilities of standard remnant scenarios. In the context of Hawking radiation, the first condition implies that correlations between the in and out Hawking partner particles need to be transferred to correlations between the microscopic degrees of freedom and the out partners in the radiation. This transfer occurs dynamically when the in partners reach the singularity inside the black hole, entering the UV regime of quantum gravity where the interaction with the microscopic degrees of freedom becomes strong. The second condition suggests that the conventional notion of the vacuum's uniqueness in quantum field theory should fail when considering the full quantum gravity degrees of freedom. In this paper, we demonstrate both key aspects of this mechanism using a solvable toy model of a quantum black hole inspired by loop quantum gravity.

Shadow, quasinormal modes, greybody bounds, and Hawking sparsity of loop quantum gravity motivated non-rotating black hole

We consider loop quantum gravity (LQG) motivated 4D polymerized black hole and study shadow, quasinormal modes, and Hawking radiation. We obtain analytical expressions of photonsphere radius and shadow radius and study their qualitative and quantitative nature of variation with respect to the LQG parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. We also show shadows of the black hole for various values of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Our study reveals that both radii increase with an increase in the parameter value. We, then, study quasinormal modes for scalar and electromagnetic perturbations using the 6th order WKB method. Our study reveals that the LQG parameter impacts quasinormal modes. We observe that the oscillation of gravitational wave (GW) and decay rate decrease as α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} increases. At the same time, the error associated with the 6th order WKB method increases with an increase in α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. The ringdown waveform for electromagnetic and scalar perturbations is shown. We also study greybody bounds, power spectrum, and sparsity of Hawking radiation. Greybody bounds for electromagnetic perturbations do not depend on α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. For scalar perturbation, greybody bounds increase as the LQG parameter increases, but the variation with α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is very small. The peak of the power spectrum as well as total power emitted decrease as we increase the value of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Also, the sparsity of Hawking radiation gets significantly impacted by quantum correction. Finally, we obtain the area spectrum of the black hole. It is found to be significantly different than that for the Schwarzschild black hole.

A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications

Loop quantum gravity (LQG) is a quantization program for gravity based on the principles of QFT and general covariance of general relativity. Quantum states of LQG describe gravitational excitations based on graphs embedded in a spatial slice of spacetime. We show that, under certain assumptions on the class of diffeomorphisms, the space of diffeomorphism invariant states carries a Fock space structure. The role of one-particle excitations for this structure is played by the diffeomorphism invariant states based on graphs with a single (linked) component. This means, however, that a lot of the structure of the diffeomorphism invariant Hilbert space remains unresolved by this structure. We show how the Fock structure allows to write at least some condensate states of group field theory as diffeomorphism invariant coherent states of LQG in a precise sense. We also show how to construct other interesting states using this Fock structure. We finally explore the quantum geometry of single- and multi-particle states and tentatively observe some resemblance to geometries with a single or multiple components, respectively.

Semi-classical rotating black hole in loop quantum gravity

In the research paper [1], the analytical solution of semi-classical rotating black holes (BH) in loop quantum gravity theory (LQG) is obtained, but an unknown function H is still preserved. In this note, we obtain an expression for the unknown function H, which makes the space-time line element of the semi-classical rotating BH in the LQG theory sufficiently well-expressed and thus provides a basis for the study of such rotating BHs.

Quantum entanglement dynamics of spacetime and matter

It was known long ago that quantum theory and general relativity are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in physics. Here we propose an information-complete quantum field theory (ICQFT), which describes elementary fermions, their gauge fields, and gravity (together, called the trinary fields) as an elementary trinity without any conceptual inconsistency of existing theories. The ICQFT unifies matter and spacetime (gravity) as information via spacetime-matter entanglement, which encodes complete physical predictions of the theory and leads to a compelling solution to the problem of time. We consider two particular forms of spacetime-matter entangled states and their physical consequences. One of them results in a universal relation between entanglement entropy and geometry (area and volume), allowing us to determine the cosmological constant term in the classical Einstein equation. Based on a quantum-information definition of dark energy, our Universe is not strictly holographic. We predict the interior quantum state of a Schwarzschild black hole to be maximally information-complete. As a concrete quantum formulation of gravity coupled with matter, the ICQFT is quantum entanglement dynamics for spacetime and matter and eliminates the conceptual obstacles of existing quantum gravity theory.

The Magical “Born Rule” and Quantum “Measurement”: Implications for Physics

I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real physical world—is the classical four-dimensional physical spacetime. III. The “Born rule” is the random process “magically” transforming I into II. Wavefunctions are superposed and entangled only in the abstract space I, never in spacetime II. Attempted formulations of quantum theory directly in real physical spacetime actually constitute examples of “locally real” theories, as defined by Clauser and Horne, and are therefore already empirically refuted by the numerous tests of Bell’s theorem in real, controlled experiments in laboratories here on Earth. Observed quantum entities (i.e., events) are never superposed or entangled as they: (1) exclusively “live” (manifest) in real physical spacetime and (2) are not described by entangled wavefunctions after “measurement” effectuated by III. When separated and treated correctly in this way, a number of fundamental problems and “paradoxes” of quantum theory vs. relativity (i.e., spacetime) simply vanish, such as the black hole information paradox, the infinite zero-point energy of quantum field theory and the quantization of general relativity.

Fermions in loop quantum gravity and resolution of doubling problem

The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity (LQG). As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the background geometry given by a coherent state resembling the classical Minkowski spacetime. Moreover, as a critical feature of LQG, the superposition over graphs is employed to define the vacuum state. It turns out that the graph superposition leads to the propagator being the average of the propagators of the lattice field theory over various graphs so that all fermion doubler modes are suppressed in the propagator. This resolves the doubling problem in LQG. Our result suggests that the superposition nature of quantum geometry should, on the one hand, resolve the tension between fermion and the fundamental discreteness and, on the other hand, relate to the continuum limit of quantum gravity.

Bouncing Universe in loop quantum gravity: full theory calculation

In loop quantum gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we will study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to massless scalar field. In our previous research we introduced a method to reduce the model to homogeneous-isotropic sector at the quantum level. In this paper we propose a method to restrict our homogeneous-isotropic model to the spatially flat sector. After this restriction the number of degrees of freedom gets substantially reduced. This allows us to make numerical and analytical calculations. Remarkably, the resulting model shares some structural similarities with the loop quantum cosmological models and therefore sheds some new light on the relation between loop quantum gravity and loop quantum cosmology. According to our model the evolution of the Universe is periodic. The quantum gravity effects resolve the Big Bang singularity leading to a Big Bounce and cause the Universe to contract after a classical expansion phase.

Quantum reference frames for an indefinite metric

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence of mass configurations in superposition, and hence an indefinite spacetime metric, using quantum reference frame (QRF) transformations. Specifically, we show that, as long as the mass configurations in the different branches are related via relative-distance-preserving transformations, one can use an extension of the current framework of QRFs to change to a frame in which the mass configuration becomes definite. Assuming covariance of dynamical laws under quantum coordinate transformations, this allows to use known physics to determine the dynamics. We apply this procedure to find the motion of a probe particle and the behavior of clocks near the mass configuration, and thus find the time dilation caused by a gravitating object in superposition. Comparison with other models shows that semi-classical gravity and gravitational collapse models do not obey the covariance of dynamical laws under quantum coordinate transformations.

Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity

A fine tuned rainbow gravity describes both relativistic quantum particles and anti-particles alike. That is, the ratio y=E/EP in the rainbow functions g0(y) and g1(y) should be fine tuned into 0≤y=E/EP≤1⇒y=|E|/EP, otherwise rainbow gravity will only secure Planck's energy scale Ep as the maximal energy for relativistic particles and the anti-particles are left unfortunate (in the sense that their energies will be indefinitely unbounded). Using this fine tuning we discuss the rainbow gravity effect on Klein-Gordon (KG) oscillators in Som-Raychaudhuri cosmic string rainbow gravity spacetime background. We use the rainbow functions: (i) g0(y)=1, g1(y)=1−ϵyn,n=1,2, loop quantum gravity motivated pairs, (ii) g0(y)=g1(y)=(1−ϵy)−1, a horizon problem motivated pair, and (iii) g0(y)=(eϵy−1)/ϵy, g1(y)=1, a gamma-ray bursts motivated pair. We show that the energies obtained using the first two rainbow functions in (i) completely comply with the rainbow gravity model and secure Planck's energy Ep as the maximal energy for both particles and anti-particles. The rainbow function pair in (ii) has no effect on massless KG-oscillators. Whereas, the one in (iii) does not show any eminent tendency towards the Planck's energy as the maximal energy.

Classicality of single quantum particles in curved spacetime through the hydrodynamical reformulation of quantum mechanics

Single-particle physics focuses on the behavior and properties of individual particles, providing insight into the building blocks of quantum mechanics. The theory of quantum particles in curved spacetime has been getting attention in recent years for gaining a deeper understanding of the relationship between quantum mechanics and general relativity, the two pillars of modern physics. In this note, we show how single quantum particles can obtain classical behavior. In particular, for a quantum particle that follows the Klein–Gordon equation in curved spacetime in the presence of external potential, we show that when the amplitude of its wavefunction follows the Klein–Gordon equation with an arbitrary effective mass, empty curved spacetime, but with the same curved geometry appearing in the original Klein–Gordon equation of the wavefunction, the quantum force of the particle vanishes, providing a classical description of the quantum particle using a system of coupled classical equations. The result relies on the Madelung hydrodynamical reformulation of quantum mechanics. Understanding how quantum systems transition to a classical behavior is a long-standing challenge in mesoscopic physics, with important implications for a wide range of applications, from quantum computing to condensed matter physics. The result provides a fresh perspective on the relations between quantum and classical effects in curved spacetime.

Particle in a Box with Generalized Uncertainty Principle

in ordinary quantum mechanics for the position uncertainty since the minimum value for the uncertainty can be tend to zero. Different theories of quantum gravity, such as string theory, loop quantum gravity, and black hole physics, confirm a minimal observable length. Kempf et al have formulated The minimal length is a fundamental length for position measurement, although there is no lower bound a generalized uncertainty principle (GUP) by modifying the Heisenberg uncertainty principle to include an appearance of the length in quantum mechanics. In this study, we have found out the influence of the GUP on the particle for its confinement in a 1D potential box and calculated energy eigenvalues. The modified Schrödinger equation for the particle is factorized to be of second order to obtain the eigenvalues in a handy way. The obtained energy levels are modified from the usual result with GUP parameter dependency. The modification in the energy spectrum due to the GUP characterized by the presence of the minimal length has been also explored graphically.