# Gravity: Renormalization

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## Introduction

By the late 1960's, the Canonical Quantum Gravity or 'Superspace Quantization' approach quickly bogged down in an ever-growing mathematical formalism inwhich the equations defining the quantum states of spacetime became too difficult to solve in general.

Covariant Quantum Gravity, on the other hand, with its reliance on concepts refined in the study of particle physics received several infusions of fresh blood during the 60's. Richard Feynman and Bryce DeWitt worked on systematically applying the techniquesof QED — the so-called perturbation series approach to gravity.This simply meant that they started with a very simple Feynmann diagram for, say, a photon emitting a single graviton, then two gravitons, then three etc. The contributions at each stage were added up to give the total strength of the process that involved a single photon interactingwith a cloud of virtual gravitons.

From this mathematical approach, they were able to prove that whatever quantum gravity theory may look like, it was at least a unitary theory, meaning that for every new term added to the series, probabilities would continue to sum to 1.000. This was at least true for weak gravitational fields. For strong fields it was quickly discovered that gravity continued to be non-renormalizable. A complete calculation of some process in this limit would spawn more and more quantities that needed to be 'renormalized'.At least in QED the renormalization approach only led to the redefinition of two quantities, the electron mass and charge.

There were some similarities between gravity and the weak force that also suggested a new approach might be warranted. Fermi's original theory of the weakinteraction was also not cureable of its infinities until electroweak unification showed that at high energies, new processes become important in the sums. These new processes, when added to the calculations, would make the weak interaction a renormalizable theory. Could it be that the non-renormalizability of Canonical Quantum Gravity just meant that, like Fermi's theory, something had to be added to gravity to make it a finite theory? This belief ushered-in many new attempts at creating a new family of renormalizable quantum gravity theories by adding new terms to Einstein's original equation for gravity. Einstein had already added the cosmological constant term to stabalize the universe. Similar terms were added to stabalize gravitational calculations against the scourge of infinity. This work was, however, overtaken by developments in the search for GUTs and the unification of GUTs with gravity.

## Related EoC Articles

- Gravity: Canonical Quantization
- Gravity: Covariant Quantization
- Gravity: Dimensionally-Extended
- Gravity: Gauge Field
- Gravity: Graviton
- Gravity: Kaluza-Kline Theory
- Gravity: Quantization ca. 1990
- Gravity: Quantum
- Gravity: Renormalization
- Gravity: String Theory
- Gravity: Superspace Quantization
- Gravity: Supersymmetry
- Gravity: What is Gravity?

## Image Preview

Gravitational waves are propagating gravitational fields, "ripples" in the curvature of space-time, generated by the motion of massive particles, such as two stars or two black holes orbiting each other. Gravitational waves cause a variable strain of space-time, which result in changes in the distance between points, with the size of the changes proportional to the distance between the points. Gravitational waves can be detected by devices which measure the induced length changes. Waves of different frequencies are caused by different motions of mass, and difference in the phases of the waves allow us to perceive the direction to the source and the shape of the matter that generated them. (Source: NASA-The Laser Interferometer Space Antenna (LISA).)

Citation

Odenwald, Sten, Ph.D. (Contributing Author); Bernard Haisch (Topic Editor). 2008. "Gravity: Renormalization." In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published February 13, 2008].

<http://www.cosmosportal.org/articles/view/135654/>

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