Editing Quantum gravity (section)

== Overview ==
{{unsolved|physics|How can the theory of quantum mechanics be merged with the theory of [[general relativity]] / [[gravitation]]al force and remain correct at microscopic length scales? What verifiable predictions does any theory of quantum gravity make?}}

[[File:Quantum gravity.svg|thumb|upright=1.4|Diagram showing the place of quantum gravity in the hierarchy of physics theories]]

Much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. General relativity models gravity as curvature of [[spacetime]]: in the slogan of [[John Archibald Wheeler]], "Spacetime tells matter how to move; matter tells spacetime how to curve."<ref>{{cite book|first=John Archibald|last=Wheeler|title=Geons, Black Holes, and Quantum Foam: A Life in Physics|year=2010|publisher=[[W. W. Norton & Company]]|isbn=9780393079487|pages=235}}</ref> On the other hand, quantum field theory is typically formulated in the ''flat'' spacetime used in [[special relativity]]. No theory has yet proven successful in describing the general situation where the dynamics of matter, modeled with quantum mechanics, affect the curvature of spacetime. If one attempts to treat gravity as simply another quantum field, the resulting theory is not [[renormalization|renormalizable]].<ref name=":1">{{cite book|title=Quantum Field Theory in a Nutshell|last=Zee|first=Anthony|publisher=[[Princeton University Press]]|year=2010|isbn=978-0-691-14034-6|edition=second|pages=[https://archive.org/details/isbn_9780691140346/page/172 172,434&ndash;435]|oclc=659549695|author-link=Anthony Zee|title-link=Quantum Field Theory in a Nutshell}}</ref> Even in the simpler case where the curvature of spacetime is fixed ''a priori'', developing quantum field theory becomes more mathematically challenging, and many ideas physicists use in quantum field theory on flat spacetime are no longer applicable.<ref name="Wald 1994">{{cite book |last=Wald |first=Robert M. |title= Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics |date=1994 |publisher=University of Chicago Press |isbn=978-0-226-87027-4}}</ref>

It is widely hoped that a theory of quantum gravity would allow us to understand problems of very high energy and very small dimensions of space, such as the behavior of [[black hole]]s, and the [[Big Bang|origin of the universe]].<ref name="scholarpedia"/>

One major obstacle is that for [[quantum field theory in curved spacetime]] with a fixed metric, [[Boson|bosonic]]/[[Fermion|fermionic]] operator fields [[Lie superalgebra|supercommute]] for [[Causal structure|spacelike separated points]]. (This is a way of imposing a [[principle of locality#Relativistic quantum mechanics|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.{{cn|date=June 2024}}