Quantum gravity Totally Explained

Everything about Quantum Gravity totally explained

Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature (electromagnetism, weak interaction, and strong interaction), with general relativity, the theory of the fourth fundamental force: gravity. One ultimate goal hoped to emerge as a result of this is a unified framework for all fundamental forces— called a "theory of everything" (TOE).

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. General relativity models gravity as a curvature within space-time that changes as a gravitational mass moves. Historically, the most obvious way of combining the two (such as treating gravity as simply another particle field) ran quickly into what is known as the renormalization problem. In the old-fashioned understanding of renormalization, gravity particles would attract each other and adding together all of the interactions results in many infinite values which can't easily be cancelled out mathematically to yield sensible, finite results. This is in contrast with quantum electrodynamics where, while the series still don't converge, the interactions sometimes evaluate to infinite results, but those are few enough in number to be removable via renormalization.

Effective field theories

In recent decades, however, this antiquated understanding of renormalization has given way to the modern idea of effective field theory. All quantum field theories come with some high-energy cutoff, beyond which we don't expect that the theory provides a good description of nature. The "infinities" then become large but finite quantities proportional to this finite cutoff scale, and correspond to processes that involve very high energies near the fundamental cutoff. These quantities can then be absorbed into an infinite collection of coupling constants, and at energies well below the fundamental cutoff of the theory, to any desired precision only a finite number of these coupling constants need to be measured in order to make legitimate quantum-mechanical predictions.This same logic works just as well for the highly successful theory of low-energy pions as for quantum gravity. Indeed, the first quantum-mechanical corrections to graviton-graviton scattering and Newton's law of gravitation have been explicitly computed (although they're so astronomically small that we may never be able to measure them), and any more fundamental theory of nature would need to replicate these results in order to be taken seriously. 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 start to break down above its cutoff at the much smaller scale of around 1000 GeV.)
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. That is, in the modern way of thinking, the problem of combining quantum mechanics and gravity becomes an issue only at very high energies, and may well require a totally new kind of model.

Quantum gravity theory for the highest energy scales

The general approach taken in deriving a theory of quantum gravity that's 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 isn't known if quantum gravity will be a simple and elegant theory (that resolves the conundrum of special and general relativity with regard to the uniformity of acceleration and gravity, in the former case and spacetime curvature in the latter case).
Such a theory is required in order to understand those problems involving the combination of very large mass or 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

The graviton

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 atomic scale. This problem must be put in the proper context, however. 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 theoretical spin-2 massless particles (called gravitons).
While there's no concrete proof of the existence of gravitons, all quantized theories of matter necessitate their existence. Supporting this theory is the observation that all other fundamental forces have one or more messenger particles, except gravity, leading researchers to believe that at least one most likely does exist; they've dubbed these hypothetical particles gravitons. Many of the accepted notions of a unified theory of physics since the 1970s, including string theory, superstring theory, M-theory, loop quantum gravity, all assume, and to some degree depend upon the existence of the graviton. Many researchers view the detection of the graviton as vital to validating their work. CERN plans to dedicate a large timeshare to search for the graviton using the Large Hadron Collider.

Nonrenormalizability of gravity

Historically, many believed that general relativity was in fact fundamentally inconsistent with quantum mechanics. General relativity, like electromagnetism, is a classical field theory. One might expect that, as with electromagnetism, there should be a corresponding quantum field theory.
However, gravity is nonrenormalizable. 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 infinitely many independent parameters needed to define the theory. 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 don't 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. As explained below, there's a way around this problem by treating QG as an effective field theory.

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 isn't 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's difficult to find a reliable answer, but some people still pursue this option.

Another possibility is that there are new 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.

QG 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 indeed a predictive quantum field theory. (A very similar situation occurs for the very similar effective field theory of low-energy pions.) Furthermore, many 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.
Recent work.

Candidate theories

There are a number of proposed quantum gravity theories. Currently, there's 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's no way to put quantum gravity predictions to experimental tests, although there's hope for this to change as future data from cosmological observations and particle physics experiments becomes available.

String theory

standard model of elementary particle physics. However, while this leads to an acceptable effective (quantum) field theory of gravity at low energies, gravity turns out to be much more problematic at higher energies. Where, 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, 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.
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. 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. The theory is successful in that one mode will always correspond to a graviton, the messenger particle of gravity; however, the price to pay are unusual features such as six extra dimensions of space in addition to the usual three. 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 form part of a hypothesized eleven-dimensional model known as M-theory, which would constitute a uniquely defined and consistent theory of quantum gravity.

Loop quantum gravity

canonical quantization procedures of quantum theory. Starting with the initial-value-formulation of general relativity (cf. the section on evolution equations, above), the result is an analogue of the Schrödinger equation: the Wheeler-deWitt equation which, regrettably, turns out to be ill-defined. A major break-through came with the introduction of what are now known as Ashtekar variables, which represent geometric gravity using mathematical analogues of electric and magnetic fields. The resulting candidate for a theory of quantum gravity is Loop quantum gravity, in which space is represented by a network structure called a spin network, evolving over time in discrete steps.

Other candidates

Depending on which features of general relativity and quantum theory are accepted unchanged, and on what level changes are introduced, there are numerous other attempts to arrive at a viable theory of quantum gravity, some example being dynamical triangulations, causal sets, twistor models or the path-integral based models of quantum cosmology. Further candidates include:

Supergravity

Regge calculus

Acoustic metric and other analog models of gravity

Process physics

Causal Dynamical Triangulation

An Exceptionally Simple Theory of Everything

The Omega Point and the quantum gravity Theory of Everything

Weinberg-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.

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.

Quantum gravity is said to be the reason behind the dual realities in the anime film The Place Promised in Our Early Days.

Hard science fiction author Greg Egan proposed in his short story The Planck Dive a concept of quantum gravity in which spacetime itself is a function of networks of all possible world lines and gravity is merely the alteration of probabilities associated with individual worldlines according the increased or decreased incidences of quantum phase shift due to time dilation which is a result of interactions with virtual particles.Further Information

Get more info on 'Quantum Gravity'.

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