Kochen–Specker theorem
E645528
The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Kochen–Specker theorem canonical | 3 |
| Peres–Kochen–Specker theorem formulation | 1 |
| Peres–Mermin magic square | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7165017 — 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: Kochen–Specker theorem Context triple: [Ernst Specker, knownFor, Kochen–Specker theorem]
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A.
Gleason’s theorem
Gleason’s theorem is a foundational result in the mathematical formulation of quantum mechanics that characterizes all probability measures on the lattice of projection operators in a Hilbert space, effectively justifying the Born rule.
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B.
Clauser–Horne–Shimony–Holt inequality
The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
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C.
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.
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D.
Einstein–Podolsky–Rosen paradox
The Einstein–Podolsky–Rosen paradox is a thought experiment that challenges the completeness of quantum mechanics by highlighting the strange, nonlocal correlations predicted for entangled particles.
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E.
Clauser–Horne inequality
The Clauser–Horne inequality is a fundamental Bell-type inequality in quantum mechanics used to experimentally test local realism against the predictions of quantum entanglement.
- 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: Kochen–Specker theorem Target entity description: The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
-
A.
Gleason’s theorem
Gleason’s theorem is a foundational result in the mathematical formulation of quantum mechanics that characterizes all probability measures on the lattice of projection operators in a Hilbert space, effectively justifying the Born rule.
-
B.
Clauser–Horne–Shimony–Holt inequality
The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
-
C.
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.
-
D.
Einstein–Podolsky–Rosen paradox
The Einstein–Podolsky–Rosen paradox is a thought experiment that challenges the completeness of quantum mechanics by highlighting the strange, nonlocal correlations predicted for entangled particles.
-
E.
Clauser–Horne inequality
The Clauser–Horne inequality is a fundamental Bell-type inequality in quantum mechanics used to experimentally test local realism against the predictions of quantum entanglement.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
no-go theorem
ⓘ
result in quantum foundations ⓘ theorem in quantum mechanics ⓘ |
| appliesTo | Hilbert spaces of dimension at least three ⓘ |
| assumes |
functional composition principle for value assignments
ⓘ
noncontextuality of hidden variables ⓘ |
| citation | S. Kochen and E. P. Specker, Journal of Mathematics and Mechanics 17, 59–87 (1967) NERFINISHED ⓘ |
| concerns |
contextuality
ⓘ
hidden-variable theories ⓘ projection operators on Hilbert space ⓘ quantum observables ⓘ value definiteness ⓘ |
| countryOfOrigin | Switzerland ⓘ |
| doesNotApplyTo | two-dimensional Hilbert spaces ⓘ |
| field |
mathematical physics
ⓘ
philosophy of physics ⓘ quantum foundations ⓘ quantum logic ⓘ quantum mechanics ⓘ |
| hasConsequence |
measurement outcomes in quantum mechanics cannot be explained by noncontextual hidden parameters
ⓘ
motivates experimental tests of quantum contextuality ⓘ no global assignment of predetermined outcomes to all measurements is compatible with quantum predictions ⓘ supports contextual interpretations of quantum theory ⓘ |
| hasVariant |
finite-precision versions of the Kochen–Specker theorem
ⓘ
state-independent contextuality proofs ⓘ |
| implies |
impossibility of assigning noncontextual definite values to all quantum observables
ⓘ
value assignments to observables must be contextual ⓘ |
| influenced |
development of contextuality-based quantum information protocols
ⓘ
philosophical debates on realism in quantum mechanics ⓘ |
| isTypeOf | no-hidden-variables theorem NERFINISHED ⓘ |
| mainClaim | Noncontextual hidden-variable theories are incompatible with quantum mechanics in Hilbert spaces of dimension three or greater ⓘ |
| mathematicalFormulation | impossibility of a noncontextual 0–1 valuation on all projections preserving functional relations ⓘ |
| namedAfter |
Ernst Specker
NERFINISHED
ⓘ
Simon Kochen NERFINISHED ⓘ |
| originalTitle | The problem of hidden variables in quantum mechanics NERFINISHED ⓘ |
| publicationYear | 1967 ⓘ |
| publishedIn | Journal of Mathematics and Mechanics NERFINISHED ⓘ |
| relatedTo |
Bell's theorem
NERFINISHED
ⓘ
Gleason's theorem NERFINISHED ⓘ contextuality in quantum mechanics ⓘ nonlocality ⓘ quantum logic no-go theorems ⓘ |
| rulesOut |
global two-valued measures on the projection lattice of a Hilbert space of dimension at least three
ⓘ
noncontextual hidden-variable theories ⓘ |
| status | proven ⓘ |
| usesConcept |
Boolean homomorphisms on projection lattices
ⓘ
lattice of projections of a Hilbert space ⓘ orthogonality of vectors ⓘ projection-valued measures ⓘ |
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: Kochen–Specker theorem Description of subject: The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Peres–Mermin magic square
this entity surface form:
Peres–Kochen–Specker theorem formulation