Editing Quantum mechanics (section)

== Relation to other scientific theories ==
{{Modern physics}}

=== Classical mechanics ===

The rules of quantum mechanics assert that the state space of a system is a Hilbert space and that observables of the system are Hermitian operators acting on vectors in that space&nbsp;– although they do not tell us which Hilbert space or which operators. These can be chosen appropriately in order to obtain a quantitative description of a quantum system, a necessary step in making physical predictions. An important guide for making these choices is the [[correspondence principle]], a heuristic which states that the predictions of quantum mechanics reduce to those of [[classical mechanics]] in the regime of large [[quantum number]]s.<ref name="Tipler">{{cite book |last1=Tipler |first1=Paul |last2=Llewellyn |first2=Ralph |title=Modern Physics |edition=5th |year=2008 |publisher=W. H. Freeman and Company |isbn=978-0-7167-7550-8 |pages=160–161}}</ref> One can also start from an established classical model of a particular system, and then try to guess the underlying quantum model that would give rise to the classical model in the correspondence limit. This approach is known as [[Canonical quantization|quantization]].<ref name="Peres1993">{{cite book |last=Peres |first=Asher |author-link=Asher Peres |title=Quantum Theory: Concepts and Methods |title-link=Quantum Theory: Concepts and Methods |publisher=Kluwer |year=1993 |isbn=0-7923-2549-4}}</ref>{{rp|299}}<ref>{{cite magazine |first=John C. |last=Baez |author-link=John C. Baez |url=https://nautil.us/the-math-that-takes-newton-into-the-quantum-world-237339/ |title=The Math That Takes Newton Into the Quantum World |magazine=[[Nautilus Quarterly]] |date=2019-02-26 |access-date=2024-03-23}}</ref>

When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was [[theory of relativity|non-relativistic]] classical mechanics. For instance, the well-known model of the [[quantum harmonic oscillator]] uses an explicitly non-relativistic expression for the [[kinetic energy]] of the oscillator, and is thus a quantum version of the [[harmonic oscillator|classical harmonic oscillator]].<ref name="Zwiebach2022" />{{rp|234}}

Complications arise with [[chaotic systems]], which do not have good quantum numbers, and [[quantum chaos]] studies the relationship between classical and quantum descriptions in these systems.<ref name="Peres1993" />{{rp|353}}

[[Quantum decoherence]] is a mechanism through which quantum systems lose [[quantum coherence|coherence]], and thus become incapable of displaying many typically quantum effects: [[quantum superposition]]s become simply probabilistic mixtures, and quantum entanglement becomes simply classical correlations.<ref name="Zwiebach2022" />{{rp|687-730}} Quantum coherence is not typically evident at macroscopic scales, though at temperatures approaching [[absolute zero]] quantum behavior may manifest macroscopically.{{refn|group=note|See ''[[Macroscopic quantum phenomena]]'', ''[[Bose–Einstein condensate]]'', and ''[[Quantum machine]]''}}

Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of bulk matter (consisting of atoms and [[molecule]]s which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of [[electric charge]]s under the rules of quantum mechanics.<ref>{{cite web |url=http://academic.brooklyn.cuny.edu/physics/sobel/Nucphys/atomprop.html |title=Atomic Properties |publisher=Academic.brooklyn.cuny.edu |access-date=18 August 2012}}</ref>

=== 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>

=== Relation to general relativity ===
Even though the predictions of both quantum theory and general relativity have been supported by rigorous and repeated [[empirical evidence]], their abstract formalisms contradict each other and they have proven extremely difficult to incorporate into one consistent, cohesive model. Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those particular applications. However, the lack of a correct theory of [[quantum gravity]] is an important issue in [[physical cosmology]] and the search by physicists for an elegant "[[Theory of Everything]]" (TOE). Consequently, resolving the inconsistencies between both theories has been a major goal of 20th- and 21st-century physics. This TOE would combine not only the models of subatomic physics but also derive the four fundamental forces of nature from a single force or phenomenon.<ref name="NYT-20221010">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Black Holes May Hide a Mind-Bending Secret About Our Universe – Take gravity, add quantum mechanics, stir. What do you get? Just maybe, a holographic cosmos |url=https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html |date=10 October 2022 |work=[[The New York Times]] |access-date=10 October 2022}}</ref>
[[File:String Vibrations.gif|thumb|upright=0.8|In [[string theory]], particles are re-conceived of as strings, with properties such as mass and charge determined by the string's vibrational state.]]
One proposal for doing so is [[string theory]], which posits that the [[Point particle|point-like particles]] of [[particle physics]] are replaced by [[Dimension (mathematics and physics)|one-dimensional]] objects called [[String (physics)|strings]]. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its [[mass]], [[charge (physics)|charge]], and other properties determined by the [[vibration]]al state of the string. In string theory, one of the many vibrational states of the string corresponds to the [[graviton]], a quantum mechanical particle that carries gravitational force.<ref>{{cite book |last1=Becker |first1=Katrin |last2=Becker |first2=Melanie |author-link2=Melanie Becker |last3=Schwarz |first3=John |title=String theory and M-theory: A modern introduction |date=2007 |publisher=Cambridge University Press |isbn=978-0-521-86069-7}}</ref><ref>{{cite book |last1=Zwiebach |first1=Barton |title=A First Course in String Theory |date=2009 |publisher=Cambridge University Press |isbn=978-0-521-88032-9 |author-link=Barton Zwiebach}}</ref>

Another popular theory is [[loop quantum gravity]] (LQG), which describes quantum properties of gravity and is thus a theory of [[quantum spacetime]]. LQG is an attempt to merge and adapt standard quantum mechanics and standard general relativity. This theory describes space as an extremely fine fabric "woven" of finite loops called [[spin network]]s. The evolution of a spin network over time is called a [[spin foam]]. The characteristic length scale of a spin foam is the [[Planck length]], approximately 1.616×10<sup>−35</sup> m, and so lengths shorter than the Planck length are not physically meaningful in LQG.<ref>{{Cite book |last1=Rovelli |first1=Carlo |url=https://books.google.com/books?id=w6z0BQAAQBAJ |title=Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory |last2=Vidotto |first2=Francesca |year=2014 |publisher=Cambridge University Press |isbn=978-1-316-14811-2}}</ref>