Editing Quantum mechanics (section)

=== Special relativity and electrodynamics ===

Early attempts to merge quantum mechanics with [[special relativity]] involved the replacement of the Schrödinger equation with a covariant equation such as the [[Klein–Gordon equation]] or the [[Dirac equation]]. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, [[quantum electrodynamics]], provides a fully quantum description of the [[electromagnetic interaction]]. Quantum electrodynamics is, along with [[general relativity]], one of the most accurate physical theories ever devised.<ref>{{cite book |url=https://books.google.com/books?id=6a-agBFWuyQC&pg=PA61 |title=The Nature of Space and Time |date=2010 |isbn=978-1-4008-3474-7 |last1=Hawking |first1=Stephen |last2=Penrose |first2=Roger |publisher=Princeton University Press}}</ref><ref>{{cite journal |last1=Aoyama |first1=Tatsumi |last2=Hayakawa |first2=Masashi |last3=Kinoshita |first3=Toichiro |last4=Nio |first4=Makiko |year=2012 |title=Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant |journal=[[Physical Review Letters]] |volume=109 |issue=11 |page=111807 |arxiv=1205.5368 |bibcode=2012PhRvL.109k1807A |doi=10.1103/PhysRevLett.109.111807 |pmid=23005618 |s2cid=14712017}}</ref>

The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been used since the inception of quantum mechanics, is to treat [[electric charge|charged]] particles as quantum mechanical objects being acted on by a classical [[electromagnetic field]]. For example, the elementary quantum model of the [[hydrogen atom]] describes the [[electric field]] of the hydrogen atom using a classical <math>\textstyle -e^2/(4 \pi\epsilon_{_0}r)</math> [[Electric potential|Coulomb potential]].<ref name="Zwiebach2022" />{{rp|285}} Likewise, in a [[Stern–Gerlach experiment]], a charged particle is modeled as a quantum system, while the background magnetic field is described classically.<ref name="Peres1993" />{{rp|26}} This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by [[charged particle]]s.

[[Field (physics)|Quantum field]] theories for the [[strong nuclear force]] and the [[weak nuclear force]] have also been developed. The quantum field theory of the strong nuclear force is called [[quantum chromodynamics]], and describes the interactions of subnuclear particles such as [[quark]]s and [[gluon]]s. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as [[electroweak theory]]), by the physicists [[Abdus Salam]], [[Sheldon Glashow]] and [[Steven Weinberg]].<ref>{{cite web |url=http://nobelprize.org/nobel_prizes/physics/laureates/1979/index.html |title=The Nobel Prize in Physics 1979 |publisher=Nobel Foundation |access-date=16 December 2020}}</ref>