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pacetime with a fixed metric bosonic fermionic operator fields supercommute for spacelike separated points this is a way of imposing a principle of locality however in quantum gravity the metric is dynamical so that whether two points are spacelike separated depends on the state in fact they can be in a quantum superposition of being spacelike and not spacelike separated citation needed quantum mechanics and general relativity graviton main article graviton 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 for gravity this hypothetical particle is known as the graviton these particles act as a force particle similar to the photon of the electromagnetic interaction under mild assumptions the structure of general relativity requires them to follow the quantum mechanical description of interacting theoretical spin 2 massless particles 19 20 21 22 23 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 the weinberg witten theorem places some constraints on theories in which the graviton is a composite particle 24 25 while gravitons are an important theoretical step in a quantum mechanical description of gravity they are generally believed to be undetectable because they interact too weakly 26 nonrenormalizability of gravity further information renormalization and asymptotic safety in quantum gravity 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 27 28 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 29 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 ultraviolet fixed point for gravity since this is a question of non perturbative quantum field theory finding a reliable answer is difficult pursued in the asymptotic safety program 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 30 better source needed quantum gravity as an effective field theory main article 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 31 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 32 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 31 another example is the calculation of the corrections to the bekenstein hawking entropy formula 33 34 spacetime background dependence main article background independence 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 simple to grasp in principle this is a complex 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 35 in which the only physically relevant information is the relationship between different events in spacetime 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 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 dynamic 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 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 experimen...
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