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Physics · MeasurementCaesium-133 defining frequency

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

DefinitionMathematics & logic · InformationClassical propositions and connectives

Classical logic combines truth-valued propositions using defined connectives.

DefinitionMathematics & logicAxioms, deduction and mathematical proof

A mathematical proof derives a conclusion within stated assumptions and rules.

MethodMathematics & logic · InformationSets, membership and basic operations

A set specifies membership without counting duplicate listings.

DefinitionMathematics & logic · InformationFunctions, domain and codomain

A function assigns exactly one output to each input in its domain.

DefinitionMathematics & logic · InformationMathematical induction

A base case and general successor step establish a predicate on all nonnegative integers.

MethodMathematics & logic · MeasurementEuclidean right triangles and the Pythagorean theorem

In a Euclidean right triangle, squared leg lengths sum to the squared hypotenuse length.

Mathematical statementMathematics & logic · PhysicsSine, cosine and the unit circle

Sine and cosine are unit-circle coordinates whose squared values sum to one.

Mathematical statementMathematics & logic · InformationComplex numbers

A complex number has real coordinates a and b and an imaginary unit satisfying i²=−1.

DefinitionMathematics & logic · Information · PhysicsLinear maps and matrix representation

A linear map preserves linear combinations and has a matrix once bases are chosen.

DefinitionMathematics & logicLimit of a real function

A finite limit controls output error through sufficiently small input distance.

DefinitionMathematics & logic · PhysicsDerivative at a point

A derivative is a finite limit of local difference quotients.

DefinitionMathematics & logic · PhysicsDefinite integral and signed accumulation

A definite integral is the limiting signed accumulation of small contributions.

DefinitionMathematics & logic · PhysicsFundamental theorem of calculus

Continuity connects differentiation with integration.

Mathematical statementMathematics & logic · InformationProbability space and axioms

A probability assigns nonnegative, normalised, countably additive weights to events.

DefinitionMathematics & logic · InformationConditional probability and independence

Conditioning restricts attention to an event of positive probability.

DefinitionMathematics & logic · InformationExpected value of a discrete random variable

Expected value weights possible values by their probabilities.

DefinitionMathematics & logic · MeasurementConfidence interval for a population mean

A confidence level describes repeated-sampling coverage of an interval procedure.

MethodInformation · Mathematics & logicBits and unsigned binary encoding

A bit has two possible states; a fixed-width unsigned binary word encodes an integer.

DefinitionInformation · Mathematics & logicShannon entropy of a discrete distribution

Shannon entropy measures uncertainty in a specified probability distribution.

DefinitionInformationAlgorithm and decision procedure

An algorithm specifies effective steps; a decision procedure must terminate on every permitted input.

MethodInformation · Mathematics & logicUndecidability of the halting problem

No total algorithm decides halting for every program and input in a general computation model.

Mathematical statementInformation · Mathematics & logicAsymptotic upper bounds and big O

Big O bounds eventual growth up to a fixed constant factor.

DefinitionMeasurementSI base units

Seven named base units organize the SI quantity system.

DefinitionMeasurementSI decimal prefixes

Prefix symbols specify decimal scale factors.

DefinitionMeasurementMetrological traceability

Connect a result to a reference through documented calibrations.

DefinitionMeasurement · Mathematics & logicFirst-order uncertainty propagation

Combine input uncertainty through a measurement model.

MethodMeasurement · Physics · Mathematics & logicDimensional consistency

Use dimensions to detect impossible quantity equations.

MethodPhysics · Earth & cosmosNewtonian gravitation

An inverse-square force models attraction between point masses.

ModelPhysicsFrequency, wavelength and phase speed

Relate a periodic wave's spatial and temporal repetition.

Definition
DefinitionSource checked

Caesium-133 defining frequency

PhysicsMeasurement

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

Key knowledge

ΔνCs = 9 192 631 770 Hz, exactly by the SI definition.

Reference values

ΔνCs9192631770Hz

Exact value · SI definition

Values and equations

ΔνCs = 9 192 631 770 Hz

ΔνCs
ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Hz

Conditions and scope

  • Refers to the specified unperturbed atomic transition used to define the second.

Exact definitions do not remove uncertainty from practical measurements.

Sources · 5

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Bureau International des Poids et Mesures (BIPM)3 sources
    1. SI defining constantsBureau International des Poids et Mesures (BIPM)Reference guidebipm.orgRead source
    2. The International System of UnitsBureau International des Poids et Mesures (BIPM)Reference guidebipm.orgRead source
    3. The International System of Units, 9th edition, version 4.01 (2026)Bureau International des Poids et Mesures (BIPM)Reference guidebipm.orgRead source
  2. Meet the ConstantsNational Institute of Standards and Technology (NIST)Reference guidenist.govRead source
  3. 国際単位系（SI）第9版 · Japanese translation, V3.01National Metrology Institute of Japan, AISTReference guide · PDFunit.aist.go.jpRead source

Evidence and review

Exact SI value, symbol, unit and defining scope.

2026-10-09 · English value and scope checked against BIPM; value compared with NIST. This review covers the definition only.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Agreement within this scope

The unperturbed caesium133 ground-state hyperfine transition defines the second through exactly 9192631770 Hz.

The unperturbed transition is the reference; actual clocks need corrections and carry uncertainty.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–2 of 2 relationships

Scientific relationships · 2 / 2

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 1

    Linked statements

    • A primary caesium frequency standard relates its oscillator to the defining unperturbed Cs-133 hyperfine transition by estimating and correcting design-dependent shifts, including atomic-motion Doppler and thermal blackbody effects. The realized unit is local proper time with a finite uncertainty; transfer and comparison introduce additional effects.

    A corrected unperturbed caesium transition realizes the defining second with stated systematic uncertainties.

  2. Related to
    Relationship sources · 3

    Linked statements

    • Optical transition standards on the CIPM list are secondary representations of the second; their improved instrument performance does not itself change the SI definition. As checked 10 October 2026, the BIPM roadmap describes a conditional 2030 decision and competing single-transition versus weighted-optical-frequency options, contingent on criteria and consensus.

    Fixed defining values differ from measured/recommended transition values.

Entry detailsPermanent link to this entry ↗
Record identity
si-caesium-frequency
Revision
1
Structured reference record
SI