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cluding spin networks citation needed semi classical quantum gravity main articles quantum field theory in curved spacetime and semiclassical 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 problem of time main article 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 36 in contrast general relativity treats time as a dynamical variable which relates directly with matter and moreover requires the hamiltonian constraint to vanish 37 because this variability of time has been observed macroscopically it removes any possibility of employing a fixed notion of time similar to the conception of time in quantum theory at the macroscopic level candidate theories there are a number of proposed quantum gravity theories 38 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 become available 39 40 string theory main article string theory projection of a calabi yau manifold one of the ways of compactifying the extra dimensions posited by string theory the central idea of string theory is to replace the classical concept of a point particle in quantum field with a quantum theory of one dimensional extended objects string theory 41 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 42 the theory is successful in that one mode will always correspond to a graviton the messenger particle of gravity however the price of this success is unusual features such as six extra dimensions of space in addition to the usual three for space and one for time 43 in what is called the second superstring revolution it was conjectured that both string theory and a unification of general relativity and supersymmetry known as supergravity 44 form part of a hypothesized eleven dimensional model known as m theory which would constitute a uniquely defined and consistent theory of quantum gravity 45 46 as presently understood however string theory admits a very large number 10 500 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 main article loop quantum gravity simple spin network of the type used in loop quantum gravity loop 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 that there is a granular structure of space at the planck length this is derived from the 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 spectra 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 47 48 in the quantum theory space is represented by a network structure called a spin network evolving over time in discrete steps 49 50 51 52 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 schrödinger equation is a wheeler dewitt equation which can be defined within the theory 53 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 other proposals there are a number of other approaches to quantum gravity the theories differ depending on which features of general relativity and quantum theory are accepted unchanged and which features are modified 54 55 such approaches include asymptotic safety in quantum gravity euclidean quantum gravity integral method 56 causal dynamical triangulation 57 causal fermion systems causal set theory covariant feynman path integral approach dilatonic quantum gravity double copy theory group field theory wheeler dewitt equation geometrodynamics higher spin theory hořava lifshitz gravity macdowell mansouri action noncommutative geometry path integral based models of quantum cosmology 58 quadratic gravity regge calculus shape dynamics string nets and quantum graphity supergravity twistor theory 59 canonical quantum gravity an exceptionally simple theory of everything garret lisi s e8 model 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 since the 2000s 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 60 the most widely pursued possibilities for quantum gravity phenomenology include gravitationally mediated entanglement 61 62 violations of lorentz invariance imprints of quantum gravitational effects in the cosmic microwave background in particular its polarization and decoherence induced by fluctuations 63 64 65 in the space time foam 66 the latter scenario has been searched for in light from gamma ray bursts and both astrophysical and atmospheric neutrinos placing limits on phenomenological quantum gravity parameters 67 68 69 esa s integral satellite measured polarization of photons of different wavelengths and was able to place a limit in the granularity of space that is less than 10 48 m or 13 orders of magnitude below the planck scale 70 71 better source needed 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 72 see also de sitter relativity dilaton doubly special relativity gravitational decoherence gravitomagnetism hawking radiation list of quantum gravity researchers orders of magnitude length penrose 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