{{short description|Type of approximation to an underlying physical theory}} In science, an '''effective theory''' is a deliberately limited scientific theory applicable under specific circumstances. In practice, all theories are effective theories, with the name "effective theory" being used to signal that the limitations are built in by design.<ref name=Wells-2012>{{Cite book |last=Wells |first=James D. |url=https://link.springer.com/book/10.1007/978-3-642-34892-1 |title=Effective Theories in Physics |date=2012 |language=en |doi=10.1007/978-3-642-34892-1 |issn=2191-5423}}</ref>{{rp|1}}
== Examples == An early example<ref name="Wells-2012" />{{rp|2}} is Galileo Galilei's theory of falling bodies. Using observed values, Galileo deduced that the height of a falling body can be accounted for by constant acceleration, written here in modern notation: <math display="block">\frac{d^2z}{dt^2} = -g,</math>where ''t'' is the time, ''z'' is the vertical position of an object and ''g'' is gravitational acceleration near the surface of Earth.
Within the scope of objects falling on Earth, this theory works well. However, as Isaac Newton discovered in his Newton's law of universal gravitation, a more elaborate but still effective theory, has more scope at the expense of additional complications. The next layer was Albert Einstein's general relativity, with more scope but even more complications.<ref name="Wells-2012" />{{rp|5}}
== Effective field theory == {{Main|Effective field theory}} Effective field theory is a method used to describe physical theories when there is a hierarchy of scales. Effective field theories in physics can include quantum field theories in which the fields are treated as fundamental, and effective theories describing phenomena in solid-state physics. For instance, the BCS theory of superconduction treats vibrations of the solid-state lattice as a "field" (i.e. without claiming that there is really a field), with its own field quanta, known as phonons. Such "effective particles" derived from effective fields are also known as quasiparticles.{{Cn|date=November 2024}} The standard Big Bang cosmological theory, Lambda-CDM is an effective theory for some as yet undiscovered underlying physical theory.<ref>{{Cite journal |last=Di Valentino |first=Eleonora |last2=Mena |first2=Olga |last3=Pan |first3=Supriya |last4=Visinelli |first4=Luca |last5=Yang |first5=Weiqiang |author6-link=Alessandro Melchiorri |last6=Melchiorri |first6=Alessandro |last7=Mota |first7=David F |last8=Riess |first8=Adam G |last9=Silk |first9=Joseph |date=July 2021 |title=In the realm of the Hubble tension—a review of solutions* |url=https://dx.doi.org/10.1088/1361-6382/ac086d |journal=Classical and Quantum Gravity |language=en |volume=38 |issue=15 |pages=153001 |doi=10.1088/1361-6382/ac086d |issn=0264-9381|arxiv=2103.01183 }}</ref>
In a certain sense, quantum field theory, and any other currently known physical theory, could be described as "effective", as in being the "low energy limit" of an as-yet unknown theory of everything.<ref>cf. {{cite book |first1=Ion-Olimpiu |last1=Stamatescu |first2=Erhard |last2=Seiler |title=Approaches to Fundamental Physics: An Assessment of Current Theoretical Ideas |series=Lecture Notes in Physics |volume=721 |publisher=Springer |year=2007 |isbn=978-3-540-71115-5 |page=47 }}</ref>
==See also== {{Div col|colwidth=20em}} *Effective mass (solid-state physics) *Emergence *Empirism *Epistemology *Heuristics *Hypotheses non fingo *Phenomenological model *Phenomenology (physics) *Scientific method *Turing test {{Div col end}}
==References== {{reflist}}
Category:Scientific theories