principle of least action
E145354
The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Hamilton's principle | 2 |
| Hamilton’s principle | 2 |
| principle of least action canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1266110 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: principle of least action Context triple: [Pierre-Louis Moreau de Maupertuis, knownFor, principle of least action]
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A.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
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B.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
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C.
Fermat’s principle of least time
Fermat’s principle of least time is a fundamental variational principle in optics stating that light follows the path that takes the least time, from which many laws of geometrical optics can be derived.
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D.
Mach principle
Mach principle is a philosophical and physical concept proposing that local inertial properties of matter are determined by the large-scale distribution of mass and energy in the universe.
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E.
equivalence principle
The equivalence principle is the foundational idea in relativity that locally, the effects of gravity are indistinguishable from those of acceleration, unifying gravitational and inertial mass.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: principle of least action Target entity description: The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
-
A.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
-
B.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
C.
Fermat’s principle of least time
Fermat’s principle of least time is a fundamental variational principle in optics stating that light follows the path that takes the least time, from which many laws of geometrical optics can be derived.
-
D.
Mach principle
Mach principle is a philosophical and physical concept proposing that local inertial properties of matter are determined by the large-scale distribution of mass and energy in the universe.
-
E.
equivalence principle
The equivalence principle is the foundational idea in relativity that locally, the effects of gravity are indistinguishable from those of acceleration, unifying gravitational and inertial mass.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
concept in theoretical physics
ⓘ
physical principle ⓘ variational principle ⓘ |
| actionDefinedAs | time integral of the Lagrangian ⓘ |
| allows | derivation of Euler–Lagrange equations ⓘ |
| appliesTo |
classical field theories
ⓘ
conservative systems ⓘ electromagnetic field ⓘ gravitational field ⓘ nonrelativistic mechanics ⓘ relativistic mechanics ⓘ |
| associatedWithScientist |
Carl Gustav Jacob Jacobi
ⓘ
surface form:
Carl Gustav Jacobi
Joseph-Louis Lagrange ⓘ Leonhard Euler ⓘ Pierre-Louis Moreau de Maupertuis ⓘ
surface form:
Pierre Louis Maupertuis
Richard Feynman ⓘ William Rowan Hamilton ⓘ |
| basedOn | action functional ⓘ |
| canYield |
maxima of action
ⓘ
minima of action ⓘ saddle points of action ⓘ |
| conceptualFeature | global description of motion between boundary conditions ⓘ |
| coreConceptOf |
Hamiltonian mechanics
ⓘ
Lagrangian mechanics ⓘ path integral formulation of quantum mechanics ⓘ |
| defines | dynamical evolution of physical systems ⓘ |
| equivalentTo | Newton's laws for many mechanical systems ⓘ |
| field |
classical mechanics
ⓘ
field theory ⓘ general relativity ⓘ quantum mechanics ⓘ |
| generalizes | Newtonian mechanics ⓘ |
| historicalPrecursor | Fermat's principle of least time ⓘ |
| implies | conservation laws via Noether's theorem ⓘ |
| mathematicalFormulationUses | calculus of variations ⓘ |
| modernInterpretation | compact mathematical encoding of dynamics ⓘ |
| oftenMisstatedAs | physical trajectory minimizes the action ⓘ |
| philosophicalAspect | teleological interpretations historically discussed ⓘ |
| relatedConcept |
principle of least action
self-linksurface differs
ⓘ
surface form:
Hamilton's principle
stationary action principle ⓘ |
| relatedQuantity | Hamiltonian ⓘ |
| requires | boundary conditions at initial and final times ⓘ |
| statedAs | physical trajectory makes the action stationary ⓘ |
| usedFor |
deriving Einstein field equations in general relativity
ⓘ
deriving Maxwell's equations ⓘ deriving equations of motion ⓘ formulating gauge theories ⓘ formulating relativistic particle dynamics ⓘ |
| usesQuantity | Lagrangian ⓘ |
| variationCondition | first variation of action vanishes on true path ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: principle of least action Description of subject: The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hamilton’s principle
this entity surface form:
Hamilton's principle
this entity surface form:
Hamilton's principle
this entity surface form:
Hamilton’s principle