Editing Action (physics) (section)

{{Short description|Physical quantity of dimension energy × time}}
{{About|a property of a trajectory|the central force concept|action at a distance}}
{{Infobox physical quantity
| name = Action
| image = 
| caption = 
| unit = [[joule-second]]
| otherunits = J&sdot;Hz{{superscript|−1}}
| symbols = ''S''
| baseunits = kg&sdot;m{{superscript|2}}&sdot;s{{superscript|−1}}
| dimension = <math>\mathsf{M} \cdot \mathsf{L}^{2} \cdot \mathsf{T}^{-1}</math>
| extensive = 
| conserved = 
| derivations =
}}

In [[physics]], '''action''' is a [[Scalar (physics)|scalar quantity]] that describes how the balance of kinetic versus potential energy of a [[physical system]] changes with trajectory. Action is significant because it is an input to the [[principle of stationary action]], an approach to classical mechanics that is simpler for multiple objects.<ref name="pubs.aip.org">{{Cite journal |last1=Neuenschwander |first1=Dwight E. |last2=Taylor |first2=Edwin F. |last3=Tuleja |first3=Slavomir |date=2006-03-01 |title=Action: Forcing Energy to Predict Motion |url=https://pubs.aip.org/pte/article/44/3/146/274422/Action-Forcing-Energy-to-Predict-Motion |journal=The Physics Teacher |language=en |volume=44 |issue=3 |pages=146–152 |doi=10.1119/1.2173320 |bibcode=2006PhTea..44..146N |issn=0031-921X}}</ref> Action and the variational principle are used in [[Path integral formulation|Feynman's formulation of quantum mechanics]]<ref>{{Cite journal |last1=Ogborn |first1=Jon |last2=Taylor |first2=Edwin F |date=2005-01-01 |title=Quantum physics explains Newtons laws of motion |url=https://www.eftaylor.com/pub/QMtoNewtonsLaws.pdf |journal=Physics Education |volume=40 |issue=1 |pages=26–34 |doi=10.1088/0031-9120/40/1/001 |bibcode=2005PhyEd..40...26O |s2cid=250809103 |issn=0031-9120}}</ref> and in general relativity.<ref>{{Cite journal |last=Taylor |first=Edwin F. |date=2003-05-01 |title=A call to action |url=https://pubs.aip.org/ajp/article/71/5/423/1044678/A-call-to-action |journal=American Journal of Physics |language=en |volume=71 |issue=5 |pages=423–425 |doi=10.1119/1.1555874 |bibcode=2003AmJPh..71..423T |issn=0002-9505}}</ref> For systems with small values of action close to the [[Planck constant]], quantum effects are significant.<ref name=FeynmanII/>

In the simple case of a single particle moving with a constant velocity (thereby undergoing [[uniform linear motion]]), the action is the [[momentum]] of the particle times the distance it moves, [[integral (mathematics)|added up]] along its path; equivalently, action is the difference between the particle's [[kinetic energy]] and its [[potential energy]], times the duration for which it has that amount of energy. 

More formally, action is a [[functional (mathematics)|mathematical functional]] which takes the [[trajectory]] (also called path or history) of the system as its argument and has a [[real number]] as its result. Generally, the action takes different values for different paths.<ref name="mcgraw1">{{cite encyclopedia |last1=Goodman |first1=Bernard |title=Action |date=1993|encyclopedia=McGraw-Hill Encyclopaedia of Physics |publisher=McGraw-Hill |location=New York |editor=Parker, S. P.|isbn=0-07-051400-3|page=22 |edition=2nd |url=https://archive.org/details/mcgrawhillencycl1993park/page/22/mode/2up}}</ref> Action has [[dimensional analysis|dimensions]] of [[energy]]&nbsp;×&nbsp;[[time]] or [[momentum]]&nbsp;×&nbsp;[[length]], and its [[SI unit]] is [[joule]]-second (like the [[Planck constant]] ''h'').<ref>{{cite encyclopedia |last1=Stehle |first1=Philip M. |title=Least-action principle |date=1993|encyclopedia=McGraw-Hill Encyclopaedia of Physics |publisher=McGraw-Hill |location=New York |editor=Parker, S. P.|isbn=0-07-051400-3|page=670 |edition=2nd |url=https://archive.org/details/mcgrawhillencycl1993park/page/670/mode/2up}}</ref>