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	{{Short description\|Field describing spacetime geometry in relativity and quantum-gravity discussions}}		{{Short description\|Field describing spacetime geometry in relativity and quantum-gravity discussions}}

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	A '''~~quantum~~ metric field''' refers to the spacetime metric treated as a dynamical field whose quantum behavior would be part of a theory of quantum gravity. In general relativity the metric determines distances, time intervals, curvature, and causal structure. Quantizing or replacing this field is one of the central problems in unifying quantum theory with gravitation.~~<ref>{{cite web \|title=Metric tensor \|url=https://en~~.~~wikipedia~~.org/wiki/Metric_tensor \|website=Wikipedia \|access-date=19 May 2026}}</ref><ref>{{cite book \|last=Rovelli \|first=Carlo \|title=Quantum Gravity \|publisher=Cambridge University Press \|year=2004 \|id=ISBN 978-0-521-83733-0}}</ref>		'''metric field''' is a Book II topic in the Quantum Collection. A quantum metric field refers to the spacetime metric treated as a dynamical field whose quantum behavior would be part of a theory of quantum gravity. In general relativity the metric determines distances, time intervals, curvature, and causal structure. Quantizing or replacing this field is one of the central problems in unifying quantum theory with gravitation. A quantum metric field refers to the spacetime metric treated as a dynamical field whose quantum behavior would be part of a theory of quantum gravity. In general relativity the metric determines distances, time intervals, curvature, and causal structure. Quantizing or replacing this field is one of the central problems in unifying quantum theory with gravitation.
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	== Background independence ==		== Background independence ==
	A deeper quantum-gravity theory may require the metric itself, and possibly spacetime structure, to be dynamical rather than fixed. This is why the metric field is conceptually different from ordinary matter fields defined on a fixed background.<ref>{{cite book \|last=Rovelli \|first=Carlo \|title=Quantum Gravity \|publisher=Cambridge University Press \|year=2004 \|id=ISBN 978-0-521-83733-0}}</ref>		A deeper quantum-gravity theory may require the metric itself, and possibly spacetime structure, to be dynamical rather than fixed. This is why the metric field is conceptually different from ordinary matter fields defined on a fixed background.<ref>{{cite book \|last=Rovelli \|first=Carlo \|title=Quantum Gravity \|publisher=Cambridge University Press \|year=2004 \|id=ISBN 978-0-521-83733-0}}</ref>

			== Description ==
			'''metric field''' is a matter-scale concept used to organize how quantum theory describes atoms, particles, fields, condensed matter, plasma, or spacetime-related systems. In the Quantum Collection it is placed by scale so the reader can move from materials and molecules down to subatomic degrees of freedom.

			== Quantum context ==
			At this scale, the relevant behavior is controlled by quantized states, interactions, conservation laws, and the way excitations or particles are observed. The concept is normally linked to measurable properties such as energy, momentum, charge, spin, spectra, scattering rates, or collective modes.

			== Role in the collection ==
			This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in [[Physics:Quantum mechanics\|quantum mechanics]].<ref name="matter-wiki">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>

	=See also=		=See also=

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{{Short description|Field describing spacetime geometry in relativity and quantum-gravity discussions}}

{{Quantum matter backlink|Vacuum and spacetime}}

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A '''quantum metric field''' refers to the spacetime metric treated as a dynamical field whose quantum behavior would be part of a theory of quantum gravity. In general relativity the metric determines distances, time intervals, curvature, and causal structure. Quantizing or replacing this field is one of the central problems in unifying quantum theory with gravitation.<ref>{{cite web |title=Metric tensor |url=https://en.wikipedia.org/wiki/Metric_tensor |website=Wikipedia |access-date=19 May 2026}}</ref><ref>{{cite book |last=Rovelli |first=Carlo |title=Quantum Gravity |publisher=Cambridge University Press |year=2004 |id=ISBN 978-0-521-83733-0}}</ref>
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[[File:Quantum_metric_field_yellow.png|thumb|280px|Metric field: spacetime geometry treated as a dynamical field.]]
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== Classical metric ==
The metric tensor specifies the geometry of spacetime. It determines proper time, spatial distance, light cones, geodesic motion, and the curvature that appears in Einstein's field equations.<ref>{{cite web |title=Metric tensor |url=https://en.wikipedia.org/wiki/Metric_tensor |website=Wikipedia |access-date=19 May 2026}}</ref>

== Perturbative viewpoint ==
In weak-field approaches, the metric may be expanded around a background geometry, and small fluctuations can be treated like field perturbations. This viewpoint connects gravitons with quantized metric perturbations, though it does not by itself solve full quantum gravity.<ref>{{cite book |last=Schwartz |first=Matthew D. |title=Quantum Field Theory and the Standard Model |publisher=Cambridge University Press |year=2014 |id=ISBN 978-1-107-03473-0}}</ref>

== Background independence ==
A deeper quantum-gravity theory may require the metric itself, and possibly spacetime structure, to be dynamical rather than fixed. This is why the metric field is conceptually different from ordinary matter fields defined on a fixed background.<ref>{{cite book |last=Rovelli |first=Carlo |title=Quantum Gravity |publisher=Cambridge University Press |year=2004 |id=ISBN 978-0-521-83733-0}}</ref>

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Matter}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum metric field|1}}