Noether's theorem
E29375
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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Noether's theorem canonical | 6 |
| Noether’s theorem | 4 |
| first Noether theorem | 2 |
| second Noether theorem | 2 |
| Noether current | 1 |
| Noether symmetry | 1 |
| Noether theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T228991 — 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: Noether's theorem Context triple: [Emmy Noether, notableWork, Noether's theorem]
-
A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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B.
Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
-
C.
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.
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D.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
E.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
- 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: Noether's theorem Target entity description: 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.
-
A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
B.
Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
-
C.
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.
-
D.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
E.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
result in mathematics
ⓘ
result in theoretical physics ⓘ theorem ⓘ |
| appliesIn |
Hamiltonian and Lagrangian formulations of mechanics
ⓘ
gauge theories ⓘ general relativity ⓘ particle physics ⓘ |
| appliesTo |
Lagrangian mechanics
ⓘ
surface form:
Lagrangian systems
classical mechanical systems ⓘ field theories ⓘ systems described by an action principle ⓘ |
| basedOn |
Euler–Lagrange equation
ⓘ
surface form:
Euler–Lagrange equations
calculus of variations ⓘ |
| concerns |
invariance of the action under continuous transformations
ⓘ
symmetry groups of the action ⓘ |
| field |
Lagrangian mechanics
ⓘ
classical field theory ⓘ differential geometry ⓘ mathematical physics ⓘ quantum field theory ⓘ symplectic geometry ⓘ theoretical physics ⓘ variational calculus ⓘ |
| hasConsequence |
deep link between symmetry and conservation
ⓘ
systematic derivation of conservation laws ⓘ |
| hasDomain |
continuous symmetries
ⓘ
differentiable manifolds ⓘ |
| hasVersion |
Noether's theorem
self-linksurface differs
ⓘ
surface form:
first Noether theorem
Noether's theorem self-linksurface differs ⓘ
surface form:
second Noether theorem
|
| implies |
conservation of angular momentum from rotational symmetry
ⓘ
conservation of electric charge from global gauge symmetry ⓘ conservation of energy from time-translation symmetry ⓘ conservation of linear momentum from spatial-translation symmetry ⓘ existence of a conserved current for each continuous symmetry ⓘ existence of a conserved quantity for each one-parameter Lie group of symmetries ⓘ |
| introducedIn | 1918 ⓘ |
| isConsidered | fundamental principle of modern theoretical physics ⓘ |
| isFoundationFor |
modern gauge theory
ⓘ
standard model of particle physics ⓘ |
| languageOfOriginalPublication | German ⓘ |
| namedAfter | Emmy Noether ⓘ |
| publishedIn | "Invariante Variationsprobleme" ⓘ |
| relates |
conservation laws
ⓘ
continuous symmetries ⓘ |
| usesConcept |
Lie group
ⓘ
surface form:
Lie groups
Noether charge ⓘ Noether's theorem self-linksurface differs ⓘ
surface form:
Noether current
infinitesimal transformations ⓘ |
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: Noether's theorem Description of subject: 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.
Referenced by (17)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
first Noether theorem
this entity surface form:
second Noether theorem
this entity surface form:
Noether current
subject surface form:
Amalie Noether
this entity surface form:
Noether’s theorem
subject surface form:
Invariante Variationsprobleme
this entity surface form:
first Noether theorem
subject surface form:
Invariante Variationsprobleme
this entity surface form:
second Noether theorem
subject surface form:
Invariante Variationsprobleme
this entity surface form:
Noether symmetry
subject surface form:
Geometrical Methods of Mathematical Physics
this entity surface form:
Noether’s theorem
this entity surface form:
Noether’s theorem
this entity surface form:
Noether’s theorem
this entity surface form:
Noether theorem