Born rule in quantum mechanics
E75605
The Born rule in quantum mechanics is the fundamental postulate that connects a system’s wavefunction to experimentally observed probabilities by stating that measurement outcomes occur with probabilities given by the squared magnitude of the wavefunction’s amplitudes.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Born rule | 4 |
| Born rule for outcome probabilities | 1 |
| Born rule for probabilities | 1 |
| Born rule for transition probabilities | 1 |
| Born rule in quantum mechanics canonical | 1 |
| Born's probabilistic interpretation | 1 |
| Born’s rule | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T605533 — 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: Born rule in quantum mechanics Context triple: [Max Born, knownFor, Born rule in quantum mechanics]
-
A.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
-
B.
Super-many-time theory of quantum mechanics
The Super-many-time theory of quantum mechanics is a relativistic generalization of quantum mechanics that introduces multiple time variables to consistently describe interacting quantum fields in different reference frames.
-
C.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
D.
Revised Extended Standard Theory
Revised Extended Standard Theory is a later development in generative grammar that expanded and refined Chomsky’s Standard Theory by incorporating more sophisticated treatments of syntax–semantics interfaces and constraints on transformations.
-
E.
Logical Foundations of Probability
Logical Foundations of Probability is a seminal philosophical work by Rudolf Carnap that develops a rigorous logical and formal account of probability and inductive reasoning.
- 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: Born rule in quantum mechanics Target entity description: The Born rule in quantum mechanics is the fundamental postulate that connects a system’s wavefunction to experimentally observed probabilities by stating that measurement outcomes occur with probabilities given by the squared magnitude of the wavefunction’s amplitudes.
-
A.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
-
B.
Super-many-time theory of quantum mechanics
The Super-many-time theory of quantum mechanics is a relativistic generalization of quantum mechanics that introduces multiple time variables to consistently describe interacting quantum fields in different reference frames.
-
C.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
D.
Revised Extended Standard Theory
Revised Extended Standard Theory is a later development in generative grammar that expanded and refined Chomsky’s Standard Theory by incorporating more sophisticated treatments of syntax–semantics interfaces and constraints on transformations.
-
E.
Logical Foundations of Probability
Logical Foundations of Probability is a seminal philosophical work by Rudolf Carnap that develops a rigorous logical and formal account of probability and inductive reasoning.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
postulate of quantum mechanics
ⓘ
probability rule ⓘ |
| alsoKnownAs |
Born statistical interpretation
ⓘ
Born rule in quantum mechanics ⓘ
surface form:
Born’s rule
|
| appliesTo |
positive operator-valued measures
ⓘ
projective measurements ⓘ quantum measurement outcomes ⓘ |
| assumes | normalized wavefunction ⓘ |
| concerns | outcome statistics of repeated measurements ⓘ |
| connects | Hilbert space formalism to experimental statistics ⓘ |
| domain | Hilbert space of quantum states ⓘ |
| field | quantum mechanics ⓘ |
| formalExpression |
P(a) = ⟨ψ|Π_a|ψ⟩ where Π_a is the projector onto the eigenspace of outcome a
ⓘ
P(i) = |c_i|^2 for a state |ψ⟩ = Σ_i c_i |i⟩ ⓘ |
| implies |
interference patterns in double-slit experiments
ⓘ
probabilities depend on relative phases of amplitudes ⓘ total probability equals one ⓘ |
| isAssumedIn | standard quantum theory ⓘ |
| isAssumedRatherThanDerivedIn | standard textbook formulations ⓘ |
| isCompatibleWith | unitary time evolution between measurements ⓘ |
| isDebatedIn | interpretations of quantum mechanics ⓘ |
| isDerivedInSomeApproachesFrom |
decision-theoretic axioms
ⓘ
envariance arguments ⓘ symmetry principles ⓘ typicality arguments ⓘ |
| isEssentialFor | empirical predictions of quantum mechanics ⓘ |
| isFoundationFor |
Bayesian approaches to quantum probabilities
ⓘ
Born measure on projective Hilbert space ⓘ frequentist interpretation of quantum probabilities ⓘ quantum decision theory ⓘ |
| isPostulateIn | Copenhagen interpretation of quantum mechanics ⓘ |
| isUsedIn |
Born approximation in scattering
ⓘ
particle physics experiments ⓘ quantum computing ⓘ quantum information theory ⓘ quantum optics ⓘ quantum state tomography ⓘ quantum statistical mechanics ⓘ scattering theory ⓘ spectroscopy ⓘ |
| namedAfter | Max Born ⓘ |
| relates |
measurement probabilities
ⓘ
wavefunction ⓘ |
| requires | complex-valued wavefunction or state vector ⓘ |
| role |
gives operational meaning to the wavefunction
ⓘ
links quantum states to observable probabilities ⓘ |
| statesThat | the probability of obtaining a measurement outcome is given by the squared modulus of the corresponding amplitude in the wavefunction ⓘ |
| usesQuantity |
probability amplitude
ⓘ
squared magnitude of the wavefunction ⓘ |
| yearProposed | 1926 ⓘ |
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: Born rule in quantum mechanics Description of subject: The Born rule in quantum mechanics is the fundamental postulate that connects a system’s wavefunction to experimentally observed probabilities by stating that measurement outcomes occur with probabilities given by the squared magnitude of the wavefunction’s amplitudes.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Born rule
this entity surface form:
Born's probabilistic interpretation
subject surface form:
Born rule
this entity surface form:
Born’s rule
this entity surface form:
Born rule for outcome probabilities
this entity surface form:
Born rule for transition probabilities
this entity surface form:
Born rule for probabilities
this entity surface form:
Born rule
this entity surface form:
Born rule
this entity surface form:
Born rule