Editing Quantum gravity (section)

=== Loop quantum gravity ===
{{Main|Loop quantum gravity}}
[[File:Spin network.svg|thumb|upright=1|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 network]]s. 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 field|electric]] and [[magnetic field]]s.<ref>{{Cite journal
|last=Ashtekar
|first=Abhay
|author-link=Abhay Ashtekar
|title=New variables for classical and quantum gravity
|journal=[[Physical Review Letters]]
|volume=57
|pages=2244–2247
|date=1986
|doi=10.1103/PhysRevLett.57.2244
|pmid=10033673
|issue=18
|bibcode=1986PhRvL..57.2244A
}}</ref><ref>{{Cite journal
|last=Ashtekar
|first=Abhay
|author-link=Abhay Ashtekar
|title=New Hamiltonian formulation of general relativity
|journal=[[Physical Review D]]
|volume=36|issue=6|pages=1587–1602
|date=1987
|doi=10.1103/PhysRevD.36.1587
|pmid=9958340
|bibcode = 1987PhRvD..36.1587A }}</ref> In the quantum theory, space is represented by a network structure called a spin network, evolving over time in discrete steps.<ref>{{Cite book|last=Thiemann|first=Thomas|title=Approaches to Fundamental Physics|year=2007|isbn=978-3-540-71115-5|series=Lecture Notes in Physics|volume=721|pages=185–263|chapter=Loop Quantum Gravity: An Inside View|bibcode=2007LNP...721..185T|doi=10.1007/978-3-540-71117-9_10|arxiv=hep-th/0608210|s2cid=119572847}}</ref><ref>{{cite journal
|last=Rovelli
|first=Carlo
|author-link=Carlo Rovelli
|title=Loop Quantum Gravity
|journal=[[Living Reviews in Relativity]]
|volume=1
|date=1998
|issue=1
|page=1
|doi=10.12942/lrr-1998-1
|doi-access=free
|pmid=28937180
|pmc=5567241
|arxiv=gr-qc/9710008
|bibcode=1998LRR.....1....1R
}}</ref><ref>{{cite journal
 | last1=Ashtekar
 | first1=Abhay
 | author-link=Abhay Ashtekar
 | first2=Jerzy
 | last2=Lewandowski
 | title=Background Independent Quantum Gravity: A Status Report
 | journal=[[Classical and Quantum Gravity]]
 | volume=21
 | date=2004
 | issue=15
 | pages=R53–R152
 | arxiv=gr-qc/0404018
 | doi=10.1088/0264-9381/21/15/R01
 |bibcode = 2004CQGra..21R..53A | s2cid=119175535
 }}</ref><ref>{{Cite book
|last=Thiemann
|first=Thomas
|chapter=Lectures on Loop Quantum Gravity
|date=2003
|volume=631
|pages=41–135
|arxiv=gr-qc/0210094
|bibcode=2003LNP...631...41T
|doi = 10.1007/978-3-540-45230-0_3 |series=Lecture Notes in Physics
|isbn=978-3-540-40810-9
|title=Quantum Gravity
|s2cid=119151491
}}</ref>

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.<ref>{{Cite book
|last=Rovelli
|first=Carlo
|title=Quantum Gravity
|date=2004
|publisher=Cambridge University Press
|isbn=978-0-521-71596-6
}}</ref> 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.