Loop Quantum Gravity Is Based, at a Rather Gravitational field Is Still Open
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Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
universe Review Loop Quantum Cosmology, Modified Gravity and Extra Dimensions Xiangdong Zhang Department of Physics, South China University of Technology, Guangzhou 510641, China; [email protected] Academic Editor: Jaume Haro Received: 24 May 2016; Accepted: 2 August 2016; Published: 10 August 2016 Abstract: Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed. Keywords: loop quantum cosmology; singularity resolution; effective equation 1. Introduction Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1–4]. Many issues of LQG have been carried out in the past thirty years. In particular, among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5–9]. It is well known that GR suffers singularity problems and this, in turn, implies that our universe also has an infinitely dense singularity point that is highly unphysical. -
Quantum Vacuum Energy Density and Unifying Perspectives Between Gravity and Quantum Behaviour of Matter
Annales de la Fondation Louis de Broglie, Volume 42, numéro 2, 2017 251 Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter Davide Fiscalettia, Amrit Sorlib aSpaceLife Institute, S. Lorenzo in Campo (PU), Italy corresponding author, email: [email protected] bSpaceLife Institute, S. Lorenzo in Campo (PU), Italy Foundations of Physics Institute, Idrija, Slovenia email: [email protected] ABSTRACT. A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. This model introduces the possibility to interpret gravity and the quantum behaviour of matter as two different aspects of the same origin. The change of the quantum vacuum energy density can be considered as the fundamental medium which determines a bridge between gravity and the quantum behaviour, leading to new interest- ing perspectives about the problem of unifying gravity with quantum theory. PACS numbers: 04. ; 04.20-q ; 04.50.Kd ; 04.60.-m. Key words: general relativity, three-dimensional space, quantum vac- uum energy density, quantum mechanics, generalized Klein-Gordon equation for the quantum vacuum energy density, generalized Dirac equation for the quantum vacuum energy density. 1 Introduction The standard interpretation of phenomena in gravitational fields is in terms of a fundamentally curved space-time. However, this approach leads to well known problems if one aims to find a unifying picture which takes into account some basic aspects of the quantum theory. For this reason, several authors advocated different ways in order to treat gravitational interaction, in which the space-time manifold can be considered as an emergence of the deepest processes situated at the fundamental level of quantum gravity. -
Aspects of Loop Quantum Gravity
Aspects of loop quantum gravity Alexander Nagen 23 September 2020 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 1 Contents 1 Introduction 4 2 Classical theory 12 2.1 The ADM / initial-value formulation of GR . 12 2.2 Hamiltonian GR . 14 2.3 Ashtekar variables . 18 2.4 Reality conditions . 22 3 Quantisation 23 3.1 Holonomies . 23 3.2 The connection representation . 25 3.3 The loop representation . 25 3.4 Constraints and Hilbert spaces in canonical quantisation . 27 3.4.1 The kinematical Hilbert space . 27 3.4.2 Imposing the Gauss constraint . 29 3.4.3 Imposing the diffeomorphism constraint . 29 3.4.4 Imposing the Hamiltonian constraint . 31 3.4.5 The master constraint . 32 4 Aspects of canonical loop quantum gravity 35 4.1 Properties of spin networks . 35 4.2 The area operator . 36 4.3 The volume operator . 43 2 4.4 Geometry in loop quantum gravity . 46 5 Spin foams 48 5.1 The nature and origin of spin foams . 48 5.2 Spin foam models . 49 5.3 The BF model . 50 5.4 The Barrett-Crane model . 53 5.5 The EPRL model . 57 5.6 The spin foam - GFT correspondence . 59 6 Applications to black holes 61 6.1 Black hole entropy . 61 6.2 Hawking radiation . 65 7 Current topics 69 7.1 Fractal horizons . 69 7.2 Quantum-corrected black hole . 70 7.3 A model for Hawking radiation . 73 7.4 Effective spin-foam models . -
Introduction to Loop Quantum Gravity
Introduction to Loop Quantum Gravity Abhay Ashtekar Institute for Gravitation and the Cosmos, Penn State A broad perspective on the challenges, structure and successes of loop quantum gravity. Addressed to Young Researchers: From Beginning Students to Senior Post-docs. Organization: 1. Historical & Conceptual Setting 2. Structure of Loop Quantum Gravity 3. Outlook: Challenges and Opportunities – p. 1. Historical and Conceptual Setting Einstein’s resistance to accept quantum mechanics as a fundamental theory is well known. However, he had a deep respect for quantum mechanics and was the first to raise the problem of unifying general relativity with quantum theory. “Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.” (Albert Einstein, Preussische Akademie Sitzungsberichte, 1916) – p. • Physics has advanced tremendously in the last 90 years but the the problem of unification of general relativity and quantum physics still open. Why? ⋆ No experimental data with direct ramifications on the quantum nature of Gravity. – p. • Physics has advanced tremendously in the last nine decades but the the problem of unification of general relativity and quantum physics is still open. Why? ⋆ No experimental data with direct ramifications on the quantum nature of Gravity. ⋆ But then this should be a theorist’s haven! Why isn’t there a plethora of theories? – p. ⋆ No experimental data with direct ramifications on quantum Gravity. -
BEYOND SPACE and TIME the Secret Network of the Universe: How Quantum Geometry Might Complete Einstein’S Dream
BEYOND SPACE AND TIME The secret network of the universe: How quantum geometry might complete Einstein’s dream By Rüdiger Vaas With the help of a few innocuous - albeit subtle and potent - equations, Abhay Ashtekar can escape the realm of ordinary space and time. The mathematics developed specifically for this purpose makes it possible to look behind the scenes of the apparent stage of all events - or better yet: to shed light on the very foundation of reality. What sounds like black magic, is actually incredibly hard physics. Were Albert Einstein alive today, it would have given him great pleasure. For the goal is to fulfil the big dream of a unified theory of gravity and the quantum world. With the new branch of science of quantum geometry, also called loop quantum gravity, Ashtekar has come close to fulfilling this dream - and tries thereby, in addition, to answer the ultimate questions of physics: the mysteries of the big bang and black holes. "On the Planck scale there is a precise, rich, and discrete structure,” says Ashtekar, professor of physics and Director of the Center for Gravitational Physics and Geometry at Pennsylvania State University. The Planck scale is the smallest possible length scale with units of the order of 10-33 centimeters. That is 20 orders of magnitude smaller than what the world’s best particle accelerators can detect. At this scale, Einstein’s theory of general relativity fails. Its subject is the connection between space, time, matter and energy. But on the Planck scale it gives unreasonable values - absurd infinities and singularities. -
Physics Needs Philosophy. Philosophy Needs Physics. Carlo Rovelli
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilSci Archive Physics needs philosophy. Philosophy needs physics. Carlo Rovelli Extended version of a keynote talk at the XVIII UK-European Conference on the Foundation of Physics, given at the London School of Economics the 16 July 2016 Published on Foundations of Physics, 48, 481-491, 2018 Abstract Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had damaging effects on the fertility of science. I also suggest that recent important empirical results, such as the detection of the Higgs particle and gravitational waves, and the failure to detect supersymmetry where many expected to find it, question the validity of certain philosophical assumptions common among theoretical physicists, inviting us to engage in a clearer philosophical reflection on scientific method. 1. Against Philosophy is the title of a chapter of a book by one of the great physicists of the last generation: Steven Weinberg, Nobel Prize winner and one of the architects of the Standard Model of elementary particle physicsi. Weinberg argues eloquently that philosophy is more damaging than helpful for physics—although it might provide some good ideas at times, it is often a straightjacket that physicists have to free themselves from. More radically, Stephen Hawking famously wrote that “philosophy is dead” because the big questions that used to be discussed by philosophers are now in the hands of physicistsii. -
Loop Quantum Gravity Alejandro Perez, Centre De Physique Théorique and Université Aix-Marseille II • Campus De Luminy, Case 907 • 13288 Marseille • France
features Loop quantum gravity Alejandro Perez, Centre de Physique Théorique and Université Aix-Marseille II • Campus de Luminy, case 907 • 13288 Marseille • France. he revolution brought by Einstein’s theory of gravity lies more the notion of particle, Fourier modes, vacuum, Poincaré invariance Tin the discovery of the principle of general covariance than in are essential tools that can only be constructed on a given space- the form of the dynamical equations of general relativity. General time geometry.This is a strong limitation when it comes to quantum covariance brings the relational character of nature into our descrip- gravity since the very notion of space-time geometry is most likely tion of physics as an essential ingredient for the understanding of not defined in the deep quantum regime. Secondly, quantum field the gravitational force. In general relativity the gravitational field is theory is plagued by singularities too (UV divergences) coming encoded in the dynamical geometry of space-time, implying a from the contribution of arbitrary high energy quantum processes. strong form of universality that precludes the existence of any non- This limitation of standard QFT’s is expected to disappear once the dynamical reference system—or non-dynamical background—on quantum fluctuations of the gravitational field, involving the dynam- top of which things occur. This leaves no room for the old view ical treatment of spacetime geometry, are appropriately taken into where fields evolve on a rigid preestablished space-time geometry account. But because of its intrinsically background dependent (e.g. Minkowski space-time): to understand gravity one must definition, standard QFT cannot be used to shed light on this issue. -
Loop Quantum Gravity: the First 25 Years Carlo Rovelli
Loop quantum gravity: the first 25 years Carlo Rovelli To cite this version: Carlo Rovelli. Loop quantum gravity: the first 25 years. Classical and Quantum Gravity, IOP Publishing, 2011, 28 (15), pp.153002. 10.1088/0264-9381/28/15/153002. hal-00723006 HAL Id: hal-00723006 https://hal.archives-ouvertes.fr/hal-00723006 Submitted on 7 Aug 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Loop quantum gravity: the first twenty five years Carlo Rovelli Centre de Physique Th´eorique de Luminy∗, Case 907, F-13288 Marseille, EU (Dated: January 27, 2011) I give a synthetic presentation of loop quantum gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits. I. INTRODUCTION The history of quantum gravity is full of great hopes later disappointed. I remember as a young student sitting in a major conference where a world-renowned physicists Loop gravity is not quite twenty-five years old, but announced that the final theory of quantum gravity and is getting close to such a venerable age: several basic everything had finally been found. -
An Introduction to Loop Quantum Gravity with Application to Cosmology
DEPARTMENT OF PHYSICS IMPERIAL COLLEGE LONDON MSC DISSERTATION An Introduction to Loop Quantum Gravity with Application to Cosmology Author: Supervisor: Wan Mohamad Husni Wan Mokhtar Prof. Jo~ao Magueijo September 2014 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London Abstract The development of a quantum theory of gravity has been ongoing in the theoretical physics community for about 80 years, yet it remains unsolved. In this dissertation, we review the loop quantum gravity approach and its application to cosmology, better known as loop quantum cosmology. In particular, we present the background formalism of the full theory together with its main result, namely the discreteness of space on the Planck scale. For its application to cosmology, we focus on the homogeneous isotropic universe with free massless scalar field. We present the kinematical structure and the features it shares with the full theory. Also, we review the way in which classical Big Bang singularity is avoided in this model. Specifically, the spectrum of the operator corresponding to the classical inverse scale factor is bounded from above, the quantum evolution is governed by a difference rather than a differential equation and the Big Bang is replaced by a Big Bounce. i Acknowledgement In the name of Allah, the Most Gracious, the Most Merciful. All praise be to Allah for giving me the opportunity to pursue my study of the fundamentals of nature. In particular, I am very grateful for the opportunity to explore loop quantum gravity and its application to cosmology for my MSc dissertation. -
Emergence of Time in Loop Quantum Gravity∗
Emergence of time in Loop Quantum Gravity∗ Suddhasattwa Brahma,1y 1 Center for Field Theory and Particle Physics, Fudan University, 200433 Shanghai, China Abstract Loop quantum gravity has formalized a robust scheme in resolving classical singu- larities in a variety of symmetry-reduced models of gravity. In this essay, we demon- strate that the same quantum correction which is crucial for singularity resolution is also responsible for the phenomenon of signature change in these models, whereby one effectively transitions from a `fuzzy' Euclidean space to a Lorentzian space-time in deep quantum regimes. As long as one uses a quantization scheme which re- spects covariance, holonomy corrections from loop quantum gravity generically leads to non-singular signature change, thereby giving an emergent notion of time in the theory. Robustness of this mechanism is established by comparison across large class of midisuperspace models and allowing for diverse quantization ambiguities. Con- ceptual and mathematical consequences of such an underlying quantum-deformed space-time are briefly discussed. 1 Introduction It is not difficult to imagine a mind to which the sequence of things happens not in space but only in time like the sequence of notes in music. For such a mind such conception of reality is akin to the musical reality in which Pythagorean geometry can have no meaning. | Tagore to Einstein, 1920. We are yet to come up with a formal theory of quantum gravity which is mathematically consistent and allows us to draw phenomenological predictions from it. Yet, there are widespread beliefs among physicists working in fundamental theory regarding some aspects of such a theory, once realized. -
2 Cosmic Rays and Atmospheric Neutrinos 4
PDF hosted at the Radboud Repository of the Radboud University Nijmegen The following full text is a preprint version which may differ from the publisher's version. For additional information about this publication click this link. http://hdl.handle.net/2066/75873 Please be advised that this information was generated on 2021-10-05 and may be subject to change. S e a r c h in g f o r Q u a n t u m G r a v it y w it h H ig h - e n e r g y A t m o s p h e r ic N e u t r in o s a n d A M A N D A - I I by J o h n L a w r e n c e K e l l e y A dissertation submitted in partial fulfillment of the requirements for the degree of D o c t o r o f P h il o s o p h y (P h y s ic s ) at the U n iv e r s it y o f W is c o n s in - M a d is o n 2008 © 2008 John Lawrence Kelley All Rights Reserved S e a r c h i n g f o r Q u a n t u m G r a v it y w i t h H i g h - e n e r g y A t m o s p h e r i c N e u t r i n o s a n d AMANDA-II John Lawrence Kelley Under the supervision of Professor Albrecht Karle At the University of Wisconsin - Madison The AMANDA-II detector, operating since 2000 in the deep ice at the geographic South Pole, has accumulated a large sample of atmospheric muon neutrinos in the 100 GeV to 10 TeV energy range. -
No-Go Result for Covariance in Models of Loop Quantum Gravity
PHYSICAL REVIEW D 102, 046006 (2020) No-go result for covariance in models of loop quantum gravity Martin Bojowald Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, USA (Received 3 July 2020; accepted 30 July 2020; published 10 August 2020) Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by symmetry-reduced models of quantum cosmology can be used to derive corresponding modified spherically symmetric equations. Generally covariant theories are much more restricted in spherical symmetry compared with homogeneous slicings, given by 1 þ 1-dimensional dilaton models if they are local. As shown here, modifications used in loop quantum cosmology do not have a corresponding covariant spherically symmetric theory. Models of loop quantum cosmology therefore violate general covariance in the form of slicing independence. Only a generalized form of covariance with a non-Riemannian geometry could consistently describe space-time in models of loop quantum gravity. DOI: 10.1103/PhysRevD.102.046006 I. INTRODUCTION space-time structure in models of loop quantum gravity [9]. Here, we elaborate on this application and use it to Models of black holes in quantum gravity are valuable demonstrate a no-go result that implies the noncovariance not only because their strong-field effects draw consider- of any model of loop quantum gravity, if covariance is able physical interest, but also because they are understood understood in the classical way related to slicing inde- as a consequence of nontrivial dynamical properties of pendence in Riemannian geometry.