Robertson–Schrödinger uncertainty relation
E450152
generalization of Heisenberg uncertainty principle
quantum mechanical inequality
uncertainty relation
The Robertson–Schrödinger uncertainty relation is a generalized quantum mechanical inequality that extends Heisenberg’s uncertainty principle to arbitrary pairs of observables, incorporating both their commutator and statistical correlations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Robertson–Schrödinger uncertainty relation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4537354 — 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: Robertson–Schrödinger uncertainty relation Context triple: [uncertainty principle, hasGeneralFormulation, Robertson–Schrödinger uncertainty relation]
-
A.
uncertainty principle
The uncertainty principle is a fundamental concept in quantum mechanics stating that certain pairs of physical properties, such as position and momentum, cannot both be known to arbitrary precision simultaneously.
-
B.
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.
-
C.
Heisenberg operator formulation of quantum mechanics
The Heisenberg operator formulation of quantum mechanics is a foundational approach in which observables evolve in time as operators while states remain fixed, providing a mathematically equivalent description to other formulations such as Schrödinger’s and the path integral.
-
D.
Einstein’s photon box
Einstein’s photon box is a famous thought experiment proposed by Albert Einstein to challenge the foundations of quantum mechanics by questioning the limits of energy-time uncertainty.
-
E.
Frauchiger–Renner paradox
The Frauchiger–Renner paradox is a thought experiment in quantum foundations that extends Wigner’s friend scenario to argue that standard quantum theory cannot consistently describe its own use by multiple observers.
- 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: Robertson–Schrödinger uncertainty relation Target entity description: The Robertson–Schrödinger uncertainty relation is a generalized quantum mechanical inequality that extends Heisenberg’s uncertainty principle to arbitrary pairs of observables, incorporating both their commutator and statistical correlations.
-
A.
uncertainty principle
The uncertainty principle is a fundamental concept in quantum mechanics stating that certain pairs of physical properties, such as position and momentum, cannot both be known to arbitrary precision simultaneously.
-
B.
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.
-
C.
Heisenberg operator formulation of quantum mechanics
The Heisenberg operator formulation of quantum mechanics is a foundational approach in which observables evolve in time as operators while states remain fixed, providing a mathematically equivalent description to other formulations such as Schrödinger’s and the path integral.
-
D.
Einstein’s photon box
Einstein’s photon box is a famous thought experiment proposed by Albert Einstein to challenge the foundations of quantum mechanics by questioning the limits of energy-time uncertainty.
-
E.
Frauchiger–Renner paradox
The Frauchiger–Renner paradox is a thought experiment in quantum foundations that extends Wigner’s friend scenario to argue that standard quantum theory cannot consistently describe its own use by multiple observers.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
generalization of Heisenberg uncertainty principle
ⓘ
quantum mechanical inequality ⓘ uncertainty relation ⓘ |
| appliesIn |
Hilbert space formalism
ⓘ
linked to:
Hilbert spaces
density operators ⓘ state vectors ⓘ |
| appliesTo |
non-commuting observables
ⓘ
pairs of observables ⓘ |
| assumes | normalized quantum state ⓘ |
| concerns |
measurement uncertainty
ⓘ
preparation uncertainty ⓘ |
| expresses |
lower bound on product of standard deviations
ⓘ
trade-off between measurement precisions ⓘ |
| field | quantum mechanics ⓘ |
| generalizes |
Heisenberg uncertainty principle
ⓘ
linked to:
uncertainty principle
|
| hasConsequence |
correlated observables obey tighter constraints than uncorrelated ones
ⓘ
no quantum state can have arbitrarily sharp values for all observables ⓘ |
| hasDomain | theoretical physics ⓘ |
| hasForm | ΔA² ΔB² ≥ |⟨[A,B]⟩|²/4 + |cov(A,B)|² ⓘ |
| hasStrongerFormThan |
Heisenberg–Kennard uncertainty relation
ⓘ
linked to:
uncertainty principle
|
| holdsFor | any pair of self-adjoint operators with finite variances ⓘ |
| implies |
correlations can increase uncertainty lower bound
ⓘ
non-commutativity leads to measurement limits ⓘ |
| includes |
commutator term
ⓘ
covariance term ⓘ statistical correlations between observables ⓘ |
| mathematicallyBasedOn |
inner product spaces
ⓘ
operator algebra ⓘ |
| namedAfter |
Erwin Schrödinger
ⓘ
Howard Percy Robertson ⓘ
linked to:
Howard P. Robertson
|
| relatedTo |
Cauchy–Schwarz inequality
ⓘ
variance–covariance matrix positivity ⓘ |
| specialCase |
Heisenberg position–momentum uncertainty relation
ⓘ
linked to:
uncertainty principle
|
| usedIn |
continuous-variable quantum information
ⓘ
entanglement criteria ⓘ quantum optics ⓘ quantum state characterization ⓘ |
| usesConcept |
Hermitian operators
ⓘ
commutator of operators ⓘ covariance matrix ⓘ standard deviation ⓘ |
| validFor |
mixed states
ⓘ
pure states ⓘ |
| yearProposed |
1929
ⓘ
1930 ⓘ |
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: Robertson–Schrödinger uncertainty relation Description of subject: The Robertson–Schrödinger uncertainty relation is a generalized quantum mechanical inequality that extends Heisenberg’s uncertainty principle to arbitrary pairs of observables, incorporating both their commutator and statistical correlations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.