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quantum gravity

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**Quantum gravity**(

**QG**) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored,JOURNAL, Rovelli, Carlo, Carlo Rovelli, 2008, Quantum gravity,weblink Scholarpedia, 3, 5, 7117, 10.4249/scholarpedia.7117, 2008SchpJ...3.7117R, such as near compact astrophysical objects where the effects of gravity are strong.The current understanding of gravity is based on Albert Einstein's general theory of relativity, which is formulated within the framework of classical physics. On the other hand, the other three fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory, radically different formalisms for describing physical phenomena.BOOK, Griffiths, David J., Introduction to Quantum Mechanics, 2004, Pearson Prentice Hall, 803860989, It is sometimes argued that a quantum mechanical description of gravity is necessary on the grounds that one cannot consistently couple a classical system to a quantum one.BOOK, Wald, Robert M., General Relativity, 1984, University of Chicago Press, 471881415, 382, BOOK,weblink Feynman Lectures on Gravitation, Feynman, Richard P., Morinigo, Fernando B., Wagner, William G., Addison-Wesley, 1995, 0201627345, Reading, Mass., 32509962, Richard Feynman, {{rp|11–12}}While a quantum theory of gravity may be needed to reconcile general relativity with the principles of quantum mechanics, difficulties arise when applying the usual prescriptions of quantum field theory to the force of gravity via graviton bosons. The problem is that the theory one gets in this way is not renormalizable and therefore cannot be used to make meaningful physical predictions. As a result, theorists have taken up more radical approaches to the problem of quantum gravity, the most popular approaches being string theory and loop quantum gravity.BOOK, Penrose, Roger, The road to reality : a complete guide to the laws of the universe, 2007, Vintage, 716437154, 1017, Although some quantum gravity theories, such as string theory, try to unify gravity with the other fundamental forces, others, such as loop quantum gravity, make no such attempt; instead, they make an effort to quantize the gravitational field while it is kept separate from the other forces.Strictly speaking, the aim of quantum gravity is only to describe the quantum behavior of the gravitational field and should not be confused with the objective of unifying all fundamental interactions into a single mathematical framework. A theory of quantum gravity that is also a grand unification of all known interactions is sometimes referred to as The Theory of Everything (TOE). While any substantial improvement into the present understanding of gravity would aid further work towards unification, the study of quantum gravity is a field in its own right with various branches having different approaches to unification.One of the difficulties of formulating a quantum gravity theory is that quantum gravitational effects only appear at length scales near the Planck scale, around 10âˆ’35 meter, a scale far smaller, and equivalently far larger in energy, than those currently accessible by high energy particle accelerators. Therefore physicists lack experimental data which could distinguish between the competing theories which have been proposed.Quantum effects in the early universe might have an observable effect on the structure of the present universe, for example, or gravity might play a role in the unification of the other forces. Cf. the text by Wald cited above.On the quantization of the geometry of spacetime, see also in the article Planck length, in the examples.

## Overview

{{unsolved|physics|How can the theory of quantum mechanics be merged with the theory of general relativity / gravitational force and remain correct at microscopic length scales? What verifiable predictions does any theory of quantum gravity make?}}(File:Quantum gravity.svg|right|thumb|480px|Diagram showing where quantum gravity sits in the hierarchy of physics theories)Much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. General relativity models gravity as curvature of spacetime: in the slogan of John Archibald Wheeler, "Spacetime tells matter how to move; matter tells spacetime how to curve."BOOK, John Archibald, Wheeler, Geons, Black Holes, and Quantum Foam: A Life in Physics, 2010, W. W. Norton & Company, 9780393079487, 235, On the other hand, quantum field theory is typically formulated in the*flat*spacetime used in special relativity. No theory has yet proven successful in describing the general situation where the dynamics of matter, modeled with quantum mechanics, affect the curvature of spacetime. If one attempts to treat gravity as simply another quantum field, the resulting theory is not renormalizable.BOOK, Quantum Field Theory in a Nutshell, Zee, Anthony, Princeton University Press, 2010, 978-0-691-14034-6, second, 172,434–435, 659549695, Anthony Zee, Even in the simpler case where the curvature of spacetime is fixed

*a priori,*developing quantum field theory becomes more mathematically challenging, and many ideas physicists use in quantum field theory on flat spacetime are no longer applicable.BOOK, Wald, Robert M., Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, 1994, University of Chicago Press, 0-226-87027-8, It is widely hoped that a theory of quantum gravity would allow us to understand problems of very high energy and very small dimensions of space, such as the behavior of black holes, and the origin of the universe.

## Quantum mechanics and general relativity

File:Gravity Probe B.jpg|thumb|right|150px|Gravity Probe BGravity Probe B### Graviton

Popularly harmonizing the theory of general relativity that describes gravitation, and applications to large-scale structures like stars, planets, and galaxies with quantum mechanics, that describes the other three fundamental forces acting on the atomic scale, quantum mechanics and general relativity can seem fundamentally incompatible. Also, demonstrations of the structure of general relativity essentially follows inevitably from the quantum mechanics of interacting theoretical spin-2 massless particles called gravitons.JOURNAL, Kraichnan, R. H., Robert Kraichnan, Special-Relativistic Derivation of Generally Covariant Gravitation Theory, 1955, Physical Review, 98, 4, 1118â€“1122, 10.1103/PhysRev.98.1118, harv, 1955PhRv...98.1118K, JOURNAL, Gupta, S. N., Suraj N. Gupta, Gravitation and Electromagnetism, 1954, Physical Review, 96, 6, 1683â€“1685, 10.1103/PhysRev.96.1683, harv, 1954PhRv...96.1683G, JOURNAL, Gupta, S. N., Suraj N. Gupta, Einstein's and Other Theories of Gravitation, 1957, Reviews of Modern Physics, 29, 3, 334â€“336, 10.1103/RevModPhys.29.334, harv, 1957RvMP...29..334G, BOOK, S. N., Gupta, Suraj N. Gupta, Recent Developments in General Relativity, Quantum Theory of Gravitation, 1962, 251â€“258, Pergamon Press, JOURNAL, Deser, S., Stanley Deser, Self-Interaction and Gauge Invariance, 1970, General Relativity and Gravitation, 1, 9â€“18, 10.1007/BF00759198, harv, 1970GReGr...1....9D, gr-qc/0411023, No concrete proof of gravitons exists, but quantized theories of matter may necessitate their existence.WEB, Charles Ginenthal,weblink Newton, Einstein, and Velikovsky, The observation that all fundamental forces except gravity have one or more known messenger particles leads researchers to believe that at least one must exist. This hypothetical particle is known as the*graviton*. The predicted find would result in the classification of the graviton as a force particle similar to the photon of the electromagnetic interaction. Many of the accepted notions of a unified theory of physics since the 1970s assume, and to some degree depend upon, the existence of the graviton. These include string theory, superstring theory, and M-theory. Detection of gravitons would validate these various lines of research to unify quantum mechanics and relativity theory.The Weinbergâ€“Witten theorem places some constraints on theories in which the graviton is a composite particle.JOURNAL, Steven, Weinberg, Edward, Witten, Steven Weinberg, Edward Witten, Limits on massless particles, Physics Letters B, 96, 1980, 59–62, 10.1016/0370-2693(80)90212-9, 1980PhLB...96...59W, BOOK, Gary T., Horowitz, Joseph, Polchinski, Joseph Polchinski, Gauge/gravity duality, Approaches to Quantum Gravity, Cambridge University Press, Oriti, Daniele, 9780511575549, 873715753, gr-qc/0602037, 2006gr.qc.....2037H,

### Dilaton

The dilaton made its first appearance in Kaluzaâ€“Klein theory, a five-dimensional theory that combined gravitation and electromagnetism. It appears in string theory. However, it's become central to the lower-dimensional many-bodied gravity problemJOURNAL, Ohta, Tadayuki, Mann, Robert, Canonical reduction of two-dimensional gravity for particle dynamics, Classical and Quantum Gravity, 13, 9, 2585â€“2602, 1996, 10.1088/0264-9381/13/9/022, gr-qc/9605004, harv, 1996CQGra..13.2585O, based on the field theoretic approach of Roman Jackiw. The impetus arose from the fact that complete analytical solutions for the metric of a covariant*N*-body system have proven elusive in general relativity. To simplify the problem, the number of dimensions was lowered to

*1+1*- one spatial dimension and one temporal dimension. This model problem, known as

*R=T*theory,JOURNAL, Sikkema, A E, Mann, R B, Gravitation and cosmology in (1+1) dimensions, Classical and Quantum Gravity, 8, 219â€“235, 1991, 10.1088/0264-9381/8/1/022, harv, 1991CQGra...8..219S, as opposed to the general

*G=T*theory, was amenable to exact solutions in terms of a generalization of the Lambert W function. Also, the field equation governing the dilaton, derived from differential geometry, as the SchrÃ¶dinger equation could be amenable to quantization.JOURNAL, Farrugia, Mann, Scott, 10.1088/0264-9381/24/18/006, Classical and Quantum Gravity, 24, N-body Gravity and the Schroedinger Equation, 18, 4647â€“4659, 2007, gr-qc/0611144, 2007CQGra..24.4647F, This combines gravity, quantization, and even the electromagnetic interaction, promising ingredients of a fundamental physical theory. This outcome revealed a previously unknown and already existing natural link between general relativity and quantum mechanics. There lacks clarity in the generalization of this theory to

*3+1*dimensions. However, a recent derivation in

*3+1*dimensions under the right coordinate conditions yields a formulation similar to the earlier

*1+1*, a dilaton field governed by the logarithmic SchrÃ¶dinger equationJOURNAL, Scott, T.C., Zhang, Xiangdong, Mann, Robert, Fee, G.J., Canonical reduction for dilatonic gravity in 3 + 1 dimensions, Physical Review D, 93, 8, 084017, 2016, 10.1103/PhysRevD.93.084017, 2016PhRvD..93h4017S, 1605.03431, that is seen in condensed matter physics and superfluids. The field equations are amenable to such a generalization, as shown with the inclusion of a one-graviton process,JOURNAL, Mann, R B, Ohta, T, Exact solution for the metric and the motion of two bodies in (1+1)-dimensional gravity, Physical Review, Phys. Rev. D, 55, 8, 4723â€“4747, 1997, 10.1103/PhysRevD.55.4723, gr-qc/9611008, harv, 1997PhRvD..55.4723M, and yield the correct Newtonian limit in

*d*dimensions, but only with a dilaton. Furthermore, some speculate on the view of the apparent resemblance between the dilaton and the Higgs boson.JOURNAL, Bellazzini, B., Csaki, C., Hubisz, J., Serra, J., Terning, J., A higgs-like dilaton, Eur. Phys. J. C., 73, 2, 2333, 2013, 10.1140/epjc/s10052-013-2333-x, 2013EPJC...73.2333B, 1209.3299, However, there needs more experimentation to resolve the relationship between these two particles. Finally, since this theory can combine gravitational, electromagnetic, and quantum effects, their coupling could potentially lead to a means of testing the theory through cosmology and experimentation.

### Nonrenormalizability of gravity

{{Further|Renormalization}}General relativity, like electromagnetism, is a classical field theory. One might expect that, as with electromagnetism, the gravitational force should also have a corresponding quantum field theory.However, gravity is perturbatively nonrenormalizable.{{rp|xxxvi–xxxviii;211–212}} For a quantum field theory to be well-defined according to this understanding of the subject, it must be asymptotically free or asymptotically safe. The theory must be characterized by a choice of*finitely many*parameters, which could, in principle, be set by experiment. For example, in quantum electrodynamics these parameters are the charge and mass of the electron, as measured at a particular energy scale.On the other hand, in quantizing gravity there are, in perturbation theory,

*infinitely many independent parameters*(counterterm coefficients) needed to define the theory. For a given choice of those parameters, one could make sense of the theory, but since it is impossible to conduct infinite experiments to fix the values of every parameter, it has been argued that one does not, in perturbation theory, have a meaningful physical theory. At low energies, the logic of the renormalization group tells us that, despite the unknown choices of these infinitely many parameters, quantum gravity will reduce to the usual Einstein theory of general relativity. On the other hand, if we could probe very high energies where quantum effects take over, then

*every one*of the infinitely many unknown parameters would begin to matter, and we could make no predictions at all.It is conceivable that, in the correct theory of quantum gravity, the infinitely many unknown parameters will reduce to a finite number that can then be measured. One possibility is that normal perturbation theory is not a reliable guide to the renormalizability of the theory, and that there really

*is*a UV fixed point for gravity. Since this is a question of non-perturbative quantum field theory, it is difficult to find a reliable answer, but some people still pursue this option. Another possibility is that there are new, undiscovered symmetry principles that constrain the parameters and reduce them to a finite set. This is the route taken by string theory, where all of the excitations of the string essentially manifest themselves as new symmetries.WEB,weblink Motivation, Distler, Jacques, Jacques Distler, 2005-09-01, golem.ph.utexas.edu, en, 2018-02-24,

### Quantum gravity as an effective field theory

In an effective field theory, all but the first few of the infinite set of parameters in a nonrenormalizable theory are suppressed by huge energy scales and hence can be neglected when computing low-energy effects. Thus, at least in the low-energy regime, the model is a predictive quantum field theory. Furthermore, many theorists argue that the Standard Model should be regarded as an effective field theory itself, with "nonrenormalizable" interactions suppressed by large energy scales and whose effects have consequently not been observed experimentally.BOOK,weblink Phase transitions and renormalization group, Zinn-Justin, Jean, 2007, Oxford University Press, 9780199665167, Oxford, 255563633, Jean Zinn-Justin, By treating general relativity as an effective field theory, one can actually make legitimate predictions for quantum gravity, at least for low-energy phenomena. An example is the well-known calculation of the tiny first-order quantum-mechanical correction to the classical Newtonian gravitational potential between two masses.### Spacetime background dependence

A fundamental lesson of general relativity is that there is no fixed spacetime background, as found in Newtonian mechanics and special relativity; the spacetime geometry is dynamic. While easy to grasp in principle, this is the hardest idea to understand about general relativity, and its consequences are profound and not fully explored, even at the classical level. To a certain extent, general relativity can be seen to be a relational theory,BOOK, Smolin, Lee, Lee Smolin, Three Roads to Quantum Gravity, Basic Books, 2001, 20â€“25, 0-465-07835-4, Pages 220â€“226 are annotated references and guide for further reading. in which the only physically relevant information is the relationship between different events in space-time.On the other hand, quantum mechanics has depended since its inception on a fixed background (non-dynamic) structure. In the case of quantum mechanics, it is time that is given and not dynamic, just as in Newtonian classical mechanics. In relativistic quantum field theory, just as in classical field theory, Minkowski spacetime is the fixed background of the theory.#### String theory

File:Point&string.png|right|thumb|Interaction in the subatomic world: world lines of point-like particles in the Standard Model or a world sheet swept up by closed strings in string theory]]String theory can be seen as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background, although the interactions among closed strings give rise to space-time in a dynamical way.Although string theory had its origins in the study of quark confinement and not of quantum gravity, it was soon discovered that the string spectrum contains the graviton, and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background. In this sense, string perturbation theory exhibits exactly the features one would expect of a perturbation theory that may exhibit a strong dependence on asymptotics (as seen, for example, in the AdS/CFT correspondence) which is a weak form of background dependence.#### Background independent theories

Loop quantum gravity is the fruit of an effort to formulate a background-independent quantum theory.Topological quantum field theory provided an example of background-independent quantum theory, but with no local degrees of freedom, and only finitely many degrees of freedom globally. This is inadequate to describe gravity in 3+1 dimensions, which has local degrees of freedom according to general relativity. In 2+1 dimensions, however, gravity is a topological field theory, and it has been successfully quantized in several different ways, including spin networks.### Semi-classical quantum gravity

Quantum field theory on curved (non-Minkowskian) backgrounds, while not a full quantum theory of gravity, has shown many promising early results. In an analogous way to the development of quantum electrodynamics in the early part of the 20th century (when physicists considered quantum mechanics in classical electromagnetic fields), the consideration of quantum field theory on a curved background has led to predictions such as black hole radiation.Phenomena such as the Unruh effect, in which particles exist in certain accelerating frames but not in stationary ones, do not pose any difficulty when considered on a curved background (the Unruh effect occurs even in flat Minkowskian backgrounds). The vacuum state is the state with the least energy (and may or may not contain particles).See Quantum field theory in curved spacetime for a more complete discussion.### Problem of Time

A conceptual difficulty in combining quantum mechanics with general relativity arises from the contrasting role of time within these two frameworks. In quantum theories time acts as an independent background through which states evolve, with the Hamiltonian operator acting as the generator of infinitesimal translations of quantum states through time.BOOK, Modern Quantum Mechanics, Sakurai, J. J., Napolitano, Jim J., 2010-07-14, Pearson, 978-0-8053-8291-4, 2, 68, English, In contrast, general relativity treats time as a dynamical variable which interacts directly with matter and moreover requires the Hamiltonian constraint to vanish,BOOK,weblink Cosmology and Gravitation: Xth Brazilian School of Cosmology and Gravitation; 25th Anniversary (1977â€“2002), Mangaratiba, Rio de Janeiro, Brazil,, Novello, Mario, Bergliaffa, Santiago E., 2003-06-11, Springer Science & Business Media, 978-0-7354-0131-0, 95, en, removing any possibility of employing a notion of time similar to that in quantum theory.## Candidate theories

There are a number of proposed quantum gravity theories.A timeline and overview can be found in ARXIV, Rovelli, Carlo, Carlo Rovelli, 2000, Notes for a brief history of quantum gravity, gr-qc/0006061, harv, (verify against {{ISBN|9789812777386}}) Currently, there is still no complete and consistent quantum theory of gravity, and the candidate models still need to overcome major formal and conceptual problems. They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests, although there is hope for this to change as future data from cosmological observations and particle physics experiments becomes available."MEMBERWIDE">FIRST=ABHAY, Abhay Ashtekar, 2007, Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions, 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, 126, 0705.2222, 10.1142/9789812834300_0008, 2008mgm..conf..126A, harv, JOURNAL, Schwarz, John H., String Theory: Progress and Problems, Progress of Theoretical Physics Supplement, 170, 214â€“226, 2007, hep-th/0702219, 10.1143/PTPS.170.214, 2007PThPS.170..214S, harv,### String theory

File:Calabi-Yau.png|thumb|Projection of a Calabiâ€“Yau manifold, one of the ways of compactifying the extra dimensions posited by string theory]]One suggested starting point is ordinary quantum field theories which are successful in describing the other three basic fundamental forces in the context of the standard model of elementary particle physics. However, while this leads to an acceptable effective (quantum) field theory of gravity at low energies,BOOK, Donoghue, John F. (editor), Introduction to the Effective Field Theory Description of Gravity, 1995, gr-qc/9512024, Cornet, Fernando, Effective Theories: Proceedings of the Advanced School, Almunecar, Spain, 26 Juneâ€“1 July 1995, 981-02-2908-9, World Scientific, Singapore, 1995gr.qc....12024D, gravity turns out to be much more problematic at higher energies. For ordinary field theories such as quantum electrodynamics, a technique known as renormalization is an integral part of deriving predictions which take into account higher-energy contributions,BOOK, Weinbergchapter=Chapters 17â€“18, Steven Weinberg, The Quantum Theory of Fields II: Modern Applications, Cambridge University Press, 1996, 0-521-55002-5, but gravity turns out to be nonrenormalizable: at high energies, applying the recipes of ordinary quantum field theory yields models that are devoid of all predictive power.JOURNAL, 10.1016/0370-2693(85)91470-4first=Marc H.first2=Augustofirst3=Augusto, Quantum gravity at two loops, 1985, Physics Letters B, 160, 81â€“86, harv, 1985PhLB..160...81G, One attempt to overcome these limitations is to replace ordinary quantum field theory, which is based on the classical concept of a point particle, with a quantum theory of one-dimensional extended objects: string theory.An accessible introduction at the undergraduate level can be found in BOOK, Zwiebach, Barton, Barton Zwiebach, A First Course in String Theory, Cambridge University Press, 2004, 0-521-83143-1, harv, , and more complete overviews in BOOK, Polchinski, Joseph, Joseph Polchinski, 1998, String Theory Vol. I: An Introduction to the Bosonic String, Cambridge University Press, 0-521-63303-6, and BOOK, Polchinski, Joseph, Joseph Polchinski, 1998b, String Theory Vol. II: Superstring Theory and Beyond, Cambridge University Press, 0-521-63304-4, At the energies reached in current experiments, these strings are indistinguishable from point-like particles, but, crucially, different modes of oscillation of one and the same type of fundamental string appear as particles with different (electric and other) charges. In this way, string theory promises to be a unified description of all particles and interactions.JOURNAL, Ibanez, L. E., The second string (phenomenology) revolution, Classical and Quantum Gravity, 17, 5, 2000, 1117â€“1128, hep-ph/9911499, 10.1088/0264-9381/17/5/321, harvgraviton, the messenger particle of gravity; however, the price of this success are unusual features such as six extra dimensions of space in addition to the usual three for space and one for time.For the graviton as part of the string spectrum, e.g. {{Harvnb>GreenWittenloc=sec. 2.3 and 5.3}}; for the extra dimensions, ibid sec. 4.2.In what is called the (History of string theory#1984â€“1989: first superstring revolution|second superstring revolution), it was conjectured that both string theory and a unification of general relativity and supersymmetry known as supergravityBOOK, Weinbergchapter=Chapter 31, Steven Weinberg, The Quantum Theory of Fields II: Modern Applications, Cambridge University Pressurl=https://books.google.com/books?id=aYDDRKqODpUC&printsec=frontcover, 0-521-55002-5, form part of a hypothesized eleven-dimensional model known as M-theory, which would constitute a uniquely defined and consistent theory of quantum gravity.BOOK, Townsend, Paul K., Four Lectures on M-Theory, 1996 Summer School in High Energy Physics and Cosmology, ICTP Series in Theoretical Physics, 385, 1996, hep-th/9612121, 1997hepcbconf..385T, harv, JOURNAL, Duff, Michael, Michael Duff (physicist), M-Theory (the Theory Formerly Known as Strings), International Journal of Modern Physics Aissue=32, 1996, 5623â€“5642, 10.1142/S0217751X96002583, hep-th/9608117, 1996IJMPA..11.5623D, harv, As presently understood, however, string theory admits a very large number (10500 by some estimates) of consistent vacua, comprising the so-called "string landscape". Sorting through this large family of solutions remains a major challenge.### Loop quantum gravity

File:Spin network.svg|right|thumb|200px|Simple spin networkspin networkLoop quantum gravity seriously considers general relativity's insight that spacetime is a dynamical field and is therefore a quantum object. Its second idea is that the quantum discreteness that determines the particle-like behavior of other field theories (for instance, the photons of the electromagnetic field) also affects the structure of space.The main result of loop quantum gravity is the derivation of a granular structure of space at the Planck length. This is derived from following considerations: In the case of electromagnetism, the quantum operator representing the energy of each frequency of the field has a discrete spectrum. Thus the energy of each frequency is quantized, and the quanta are the photons. In the case of gravity, the operators representing the area and the volume of each surface or space region likewise have discrete spectrum. Thus area and volume of any portion of space are also quantized, where the quanta are elementary quanta of space. It follows, then, that spacetime has an elementary quantum granular structure at the Planck scale, which cuts off the ultraviolet infinities of quantum field theory.The quantum state of spacetime is described in the theory by means of a mathematical structure called spin networks. Spin networks were initially introduced by Roger Penrose in abstract form, and later shown by Carlo Rovelli and Lee Smolin to derive naturally from a non-perturbative quantization of general relativity. Spin networks do not represent quantum states of a field in spacetime: they represent directly quantum states of spacetime.The theory is based on the reformulation of general relativity known as Ashtekar variables, which represent geometric gravity using mathematical analogues of electric and magnetic fields.JOURNAL, Ashtekar, Abhay, Abhay Ashtekar, New variables for classical and quantum gravity, Physical Review Letters, 57, 2244â€“2247, 1986, 10.1103/PhysRevLett.57.2244, 10033673, 18, harv, 1986PhRvL..57.2244A, JOURNAL, Ashtekar, Abhay, Abhay Ashtekar, New Hamiltonian formulation of general relativity, Physical Review Dissue=6, 1587â€“1602, 1987, 10.1103/PhysRevD.36.1587bibcode = 1987PhRvD..36.1587A, In the quantum theory, space is represented by a network structure called a spin network, evolving over time in discrete steps.JOURNAL, Thiemann, Thomas, Loop Quantum Gravity: An Inside View, Approaches to Fundamental Physics, 721, 185â€“263, 2006, hep-th/0608210, 2007LNP...721..185T, harv, 10.1007/978-3-540-71117-9_10, Lecture Notes in Physics, 978-3-540-71115-5, JOURNAL, Rovelli, Carlo, Carlo Rovelli, Loop Quantum Gravity, Living Reviews in Relativity, 1, 1998,weblink 2008-03-13, harv, JOURNAL, Ashtekar

, Abhay

, Abhay Ashtekar

, Jerzy

, Lewandowski

, Background Independent Quantum Gravity: A Status Report

, Classical and Quantum Gravity

, 21

, 2004

, 15

, R53â€“R152

, gr-qc/0404018

, 10.1088/0264-9381/21/15/R01

, 2004CQGra..21R..53A, JOURNAL, Thiemann, Thomas, Lectures on Loop Quantum Gravity, 2003, Lecture Notes in Physics, 631, 41â€“135, harv, gr-qc/0210094, 2003LNP...631...41T

series=Lecture Notes in Physics, 978-3-540-40810-9, The dynamics of the theory is today constructed in several versions. One version starts with the canonical quantization of general relativity. The analogue of the SchrÃ¶dinger equation is a Wheelerâ€“DeWitt equation, which can be defined within the theory.BOOK, Rovelli, Carlo, Quantum Gravity, 2004, Cambridge University Press, 0-521-71596-2, In the covariant, or spinfoam formulation of the theory, the quantum dynamics is obtained via a sum over discrete versions of spacetime, called spinfoams. These represent histories of spin networks., Abhay

, Abhay Ashtekar

, Jerzy

, Lewandowski

, Background Independent Quantum Gravity: A Status Report

, Classical and Quantum Gravity

, 21

, 2004

, 15

, R53â€“R152

, gr-qc/0404018

, 10.1088/0264-9381/21/15/R01

, 2004CQGra..21R..53A, JOURNAL, Thiemann, Thomas, Lectures on Loop Quantum Gravity, 2003, Lecture Notes in Physics, 631, 41â€“135, harv, gr-qc/0210094, 2003LNP...631...41T

### Other approaches

There are a number of other approaches to quantum gravity. The approaches differ depending on which features of general relativity and quantum theory are accepted unchanged, and which features are modified.BOOK, Isham, Christopher J., Christopher Isham, Prima facie questions in quantum gravity, Ehlers, JÃ¼rgen, Friedrich, Helmut, Canonical Gravity: From Classical to Quantum, 1994, Springer, gr-qc/9310031, 3-540-58339-4, 1994LNP...434....1I, 10.1007/3-540-58339-4_13, JOURNAL, Sorkin, Rafael D., Rafael Sorkin, Forks in the Road, on the Way to Quantum Gravity, gr-qc/9706002, International Journal of Theoretical Physics, 36, 1997, 12, 2759â€“2781, 10.1007/BF02435709bibcode = 1997IJTP...36.2759S, Examples include:- Asymptotic safety in quantum gravity
- Euclidean quantum gravity
- Causal dynamical triangulationJOURNAL, Loll, Renate, Discrete Approaches to Quantum Gravity in Four Dimensions, Living Reviews in Relativity, 1, 13, 1998,weblink 1998LRR.....1...13L, 2008-03-09, harv

- Causal fermion systems
- Causal Set Theory
- Covariant Feynman path integral approach
- Group field theory
- Wheelerâ€“DeWitt equation
- Geometrodynamics
- HoÅ™avaâ€“Lifshitz gravity
- MacDowellâ€“Mansouri action
- Noncommutative geometry
- Path-integral based models of quantum cosmologyBOOK, Hawking, Stephen W., Stephen Hawking, Quantum cosmology, 631â€“651, Israel, Werner, Hawking, Stephen W., 300 Years of Gravitation, Cambridge University Press, 1987, 0-521-37976-8

- Regge calculus
- Scale relativity
- Shape Dynamics
- String-nets and quantum graphity
- Superfluid vacuum theory a.k.a. theory of BEC vacuum
- Supergravity
- Twistor theorySee ch. 33 in {{Harvnb|Penrose|2004}} and references therein.
- Canonical quantum gravity
- E8 Theory
- Quantum holonomy theoryJOURNAL, Quantum Holonomy Theory, Fortschritte der Physik, 64, 10, 783, Aastrup, J., Grimstrup, J. M., 27 Apr 2015, 1504.07100, 10.1002/prop.201600073, 2016ForPh..64..783A,

## Experimental tests

As was emphasized above, quantum gravitational effects are extremely weak and therefore difficult to test. For this reason, the possibility of experimentally testing quantum gravity had not received much attention prior to the late 1990s. However, in the past decade, physicists have realized that evidence for quantum gravitational effects can guide the development of the theory. Since theoretical development has been slow, the field of phenomenological quantum gravity, which studies the possibility of experimental tests, has obtained increased attention.BOOK, Hossenfelder, Sabine, Classical and Quantum Gravity: Theory, Analysis and Applications, 2011, Nova Publishers, Chapter 5, 978-1-61122-957-8,weblink Experimental Search for Quantum Gravity, V. R. Frignanni, The most widely pursued possibilities for quantum gravity phenomenology include violations of Lorentz invariance, imprints of quantum gravitational effects in the cosmic microwave background (in particular its polarization), and decoherence induced by fluctuations in the space-time foam.The BICEP2 experiment detected what was initially thought to be primordial B-mode polarization caused by gravitational waves in the early universe. Had the signal in fact been primordial in origin, it could have been an indication of quantum gravitational effects, but it soon transpired that the polarization was due to interstellar dust interference.JOURNAL, Cowen, Ron

, 30 January 2015

, Gravitational waves discovery now officially dead

, Nature (journal), Nature

, 10.1038/nature.2015.16830

, , 30 January 2015

, Gravitational waves discovery now officially dead

, Nature (journal), Nature

, 10.1038/nature.2015.16830

## See also

{{div col|colwidth=22em}}- Abrahamâ€“Lorentz force
- Beyond black holes
- Black hole electron
- Centauro event
- De Sitter relativity
- Doubly special relativity
- Event symmetry
- Fockâ€“Lorentz symmetry
- Gravitomagnetism
- Hawking radiation
- List of quantum gravity researchers
- Macrocosm and microcosm
- Orders of magnitude (length)
- Penrose interpretation
- Planck epoch
- Planck units
- Quantum realm
- Weak Gravity Conjecture

## References

{{Reflist|30em}}## Further reading

- JOURNAL, Ahluwalia, D. V., Interface of Gravitational and Quantum Realms, gr-qc/0205121, 2002, Modern Physics Letters A, 10.1142/S021773230200765X, 17, 15â€“17, 2002MPLA...17.1135A, 1135â€“1145, harv, .

- JOURNAL, Ashtekar, Abhay, Abhay Ashtekar, The winding road to quantum gravity,weblink Current Science, 89, 2064â€“2074, 2005

- JOURNAL, Carlip, Steven, Steve Carlip, Quantum Gravity: a Progress Report, Reports on Progress in Physics, 64, 8, 2001, 885â€“942, gr-qc/0108040

, 10.1088/0034-4885/64/8/301, harv, ., 2001RPPh...64..885C,

- BOOK, Herbert W. Hamber, Quantum Gravitation, Springer Publishing, 2009, 10.1007/978-3-540-85293-3, 978-3-540-85292-6,weblink
- BOOK, Kiefer, Claus, Quantum Gravity, 2007, Oxford University Press, 0-19-921252-X, harv,
- JOURNAL, Kiefer, Claus, Quantum Gravity: General Introduction and Recent Developments, 2005, Annalen der Physik, 15, gr-qc/0508120, 10.1002/andp.200510175, 129â€“148, harv, 2006AnP...518..129K,
- BOOK, LÃ¤mmerzahl, Claus, Quantum Gravity: From Theory to Experimental Search, Lecture Notes in Physics, 2003, Springer, 3-540-40810-X, harv,
- BOOK, Rovelli, Carlo, Carlo Rovelli, Quantum Gravity, 2004, Cambridge University Press, 0-521-83733-2, harv,
- JOURNAL, Trifonov, Vladimir, GR-friendly description of quantum systems, 2008, International Journal of Theoretical Physics

## External links

- "Planck Era" and "Planck Time" (up to 10âˆ’43 seconds after birth of Universe) (University of Oregon).
- "Quantum Gravity", BBC Radio 4 discussion with John Gribbin, Lee Smolin and Janna Levin (
*In Our Time*, Feb. 22, 2001)

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