Gravitation acting at submicroscopic length scales where quantum effects are important. Theories of quantum gravity seek to combine features of quantum mechanics and general relativity. In quantum gravity, gravitational interaction would occur via the exchange of gravitons, the proposed quantum of gravitation. However, the view has no experimental support, and as yet no consistent theory has been developed.
Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity.
Unsolved problems in 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?‹The template Unsolved has been proposed for deletion here.›
Overview
Much of the difficulty in merging these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. Quantum field theory depends on particle fields embedded in the flat space-time of special relativity. All quantum field theories come with some high-energy cutoff, beyond which we do not expect that the theory provides a good description of nature. This same logic works just as well for the highly successful theory of low-energy pions as for quantum gravity. In fact, gravity is in many ways a much better quantum field theory than the Standard Model, since it appears to be valid all the way up to its cutoff at the Planck scale. (By comparison, the Standard Model is expected to break down above its cutoff at the much smaller TeV scale.)
While confirming that quantum mechanics and gravity are indeed consistent at reasonable energies (in fact, the complete structure of gravity can be shown to arise automatically from the quantum mechanics of spin-2 massless particles), this way of thinking makes clear that near or above the fundamental cutoff of our effective quantum theory of gravity (the cutoff is generally assumed to be of order the Planck scale), a new model of nature will be needed.
The general approach taken in deriving a theory of quantum gravity that is valid at even the highest energy scales is to assume that the underlying theory will be simple and elegant and then to look at current theories for symmetries and hints for how to combine them elegantly into an overarching theory. One problem with this approach is that it is not known if quantum gravity will be a simple and elegant theory.
Historical perspective
Historically, there have been many reactions to the apparent inconsistency of quantum theories with general relativity.
Others believe that understanding a quantum theory of gravity will lead to a radically new view of space and time, and that geometry will only emerge in a semi-classical limit.
While various approaches are currently considered, the two major theories are String theory and loop quantum gravity. String theory is a background-dependent, perturbative theory of gravity, normally formulated on a flat (Minkowski) spacetime. In the time since its conception, string theory has become a major hope towards a "theory of everything" since, within its many limits, it appears to include the symmetry groups of the Standard Model of particle physics. In stark contrast, loop quantum gravity is an attempt merely to directly quantise General Relativity and makes no claims towards being a "theory of everything". In loop quantum gravity, spacetime is redefined in new Ashtekar variables that facilitate the removal of the infinities that plague a more traditional approach to a quantum theory of general relativity. In essence, while string theory is an ambitious attempt to generate a theory of everything from (unsubstantiated) fundamental principles, loop quantum gravity merely seeks to pursue well-established quantisation procedures within the context of curved-spacetimes. Despite this intrinsic (and fundamental) disparity in philosophy, it has been suggested that string theory and loop quantum gravity, to some extents, embody effects of an underlying unity. For all this, proponents of loop quantum gravity will point out that while a free (Imirzi) parameter in LQG can be fixed with reference to the entropy of black holes, there are few -- if any -- possible observational constraints on string theory.
The "incompatibility" of quantum mechanics and general relativity
At present, one of the deepest problems in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, planets, galaxies), with quantum mechanics, which describes the other three fundamental forces acting on the microscopic scale. In particular, contrary to the popular but erroneous claim that quantum mechanics and general relativity are fundamentally incompatible, one can in fact demonstrate that the structure of general relativity essentially follows inevitably from the quantum mechanics of interacting spin-2 massless particles (called gravitons). Furthermore, recent work has shown that by treating general relativity as an effective field theory, one can actually make legitimate predictions for quantum gravity, at least for low-energy phenomenology. Such predictions would need to be replicated by any candidate theory of high-energy quantum gravity. Naively one expects that, as with electromagnetism, there should be a corresponding quantum field theory. For a quantum field theory to be well-defined, according to this now-outdated understanding of the subject, it must be asymptotically free or asymptotically safe. For a given choice of those parameters, one could make sense of the theory, but since we can never do infinitely many experiments to fix the values of every parameter, we do not 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.
However, from the perspective of effective field theory, one sees that all but the first few such parameters 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 indeed a predictive quantum field theory. (A very similar situation occurs for the very similar effective field theory of low-energy pions.) Furthermore, most theorists agree that even the Standard Model should really be regarded as an effective field theory as well, with "nonrenormalizable" interactions suppressed by large energy scales and whose effects have consequently not been observed experimentally.
However, any meaningful theory of quantum gravity that makes sense and is predictive at all energy scales must have some deep principle that reduces the infinitely many unknown parameters 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 nonperturbative quantum field theory, it is difficult to find a reliable answer, but some people still pursue this option. In relativistic quantum field theory, just as in classical field theory, Minkowski spacetime is the fixed background of the theory. Finally, string theory started out as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background. 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.
Quantum field theory on curved (non-Minkowskian) backgrounds, while not a quantum theory of gravity, has shown that some of the assumptions of quantum field theory cannot be carried over to curved spacetime, let alone to full-blown quantum gravity.
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. In 2+1 dimensions, however, gravity is a topological field theory, and it has been successfully quantized in several different ways, including spin networks. First, general relativity predicts its own breakdown at singularities, and quantum mechanics becomes inconsistent with general relativity in a neighborhood of singularities (however, no one is certain that classical general relativity should necessarily be trusted near singularities in the first place).
Theories
There are a number of proposed quantum gravity theories:
String theory/superstring theory/M-theory Supergravity AdS/CFT Wheeler-deWitt equation Loop quantum gravity Euclidean quantum gravity Noncommutative geometry Twistor theory Discrete Lorentzian quantum gravity Sakharov induced gravity Regge calculus acoustic metric and other analog models of gravity Process physics Calogero hypothesisWeinberg-Witten theorem
There is a theorem in quantum field theory called the Weinberg-Witten theorem which places some constraints on theories of composite gravity/emergent gravity.
Quantum gravity theorists
See list of quantum gravity researchers
In popular culture
The famous spoof of postmodernism by Alan Sokal (see Sokal Affair) was entitled Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity.
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