Measurements"redirectshere.ForthedisusedrailwaystationinOldham,seeMeasurementsrailwaystation.
Forbust/waist/hipmeasurement,seeBWH.
Inscience,measurementistheprocessofobtainingthemagnitudeofaquantity,suchaslengthormass,relativetoaunitofmeasurement,suchasameterorakilogram.Ameasurementanswersthegeneralquestion,"howmany?",asinhowmanymiles,ormillimeters,orgigahertz.Asmeasurementisbasicallyaboutcounting,measurementisconductedinnumbersandisquantitative,incomparisontootherobservationswhichmaybemadeinwordsandarequalitative.Thetermmeasurementcanalsobeusedtorefertoaspecificresultobtainedfromthemeasurementprocess.
History
Mainarticle:Historyofmeasurement
Theword"measurement"isderivedfromtheGreekword"metron"whichmeansalimitedproportion.
Thehistoryofmeasurementsisatopicwithinthehistoryofscienceandtechnology.
目录
Standards
Unitsandsystems
Imperialsystem
Metricsystem
SI
Convertingprefixes
Distance
Somespecialnames
Time
Economics
Difficulties
Classicaldefinition
Representationaltheory
Informationtheory
Quantummechanics
Standards
data/attachment/portal/201111/06/091202rsrkg597k3wg2trm.jpgAbabybottlethatmeasuresinallthreemeasurementsystems,Imperial(U.K.),U.S.Customary,andmetric.
Withtheexceptionofafewseeminglyfundamentalquantumconstants,unitsofmeasurementareessentiallyarbitrary;inotherwords,peoplemakethemupandthenagreetousethem.Thereisnothinginherentinnaturewhichdictatesthataninchhastobeacertainlength,orthatamileisabettermeasureofdistancethanakilometer.Overthecourseofhumanhistory,however,firstforconvenienceandthenfornecessity,standardsofmeasurementevolvedsothatpeoplewouldhavecommonbenchmarks.Lawsregulatingmeasurementwereoriginallydevelopedtopreventfraudincommerce.Today,unitsofmeasurementarenowgenerallydefinedonascientificbasis,overseenbygovernmentalorsupra-governmentalagencies,andestablishedininternationaltreaties.Themeter,forexample,wasredefinedin1983asthedistancetraveledbylightinfreespacein1D299,792,458ofasecond.IntheUnitedStates,theNationalInstituteofStandardsandTechnology(NIST),adivisionoftheUnitedStatesDepartmentofCommerce,regulatescommercialmeasurements.IntheUnitedKingdom,theroleisperformedbytheNationalPhysicalLaboratory(NPL).
Unitsandsystems
Mainarticles:UnitsofmeasurementandSystemsofmeasurement
Ababybottlethatmeasuresinallthreemeasurementsystems,Imperial(U.K.),U.S.Customary,andmetric.Thedefinitionorspecificationofprecisestandardsofmeasurementinvolvestwokeyfeatures,whichareevidentintheInternationalSystemofUnits(SI).Specifically,inthissystemthedefinitionofeachofthebaseunitsrefertospecificempiricalconditionsand,withtheexceptionofthekilogram,alsotootherquantitativeattributes.EachderivedSIunitisdefinedpurelyintermsofarelationshipinvolvingitandotherunits;forexample,theunitofvelocityis1m/s.Becausederivedunitsrefertobaseunits,thespecificationofempiricalconditionsisanimpliedcomponentofthedefinitionofallunits.
Imperialsystem
Mainarticle:ImperialUnit
BeforeSIunitswerewidelyadoptedaroundtheworld,theBritishsystemsofEnglishunitsandlaterImperialunitswereusedinBritain,theCommonwealthandtheUnitedStates.ThesystemcametobeknownasU.S.customaryunitsintheUnitedStatesandisstillinusethereandinafewCaribbeancountries.Thesevarioussystemsofmeasurementhaveattimesbeencalledfoot-pound-secondsystemsaftertheImperialunitsfordistance,weightandtimeeventhoughthetons,hundredweights,gallons,andnauticalmiles,forexample,aredifferentfortheU.S.units.ManyImperialunitsremaininuseinBritaindespitethefactthatithasofficiallyswitchedtotheSIsystem.Roadsignsarestillinmiles,yards,milesperhour,andsoon,peopletendtomeasuretheirownheightinfeetandinchesandmilkissoldinpints,togivejustafewexamples.Imperialunitsareusedinmanyotherplaces,forexample,inmanyCommonwealthcountriesthatareconsideredmetricated,landareaismeasuredinacresandfloorspaceinsquarefeet,particularlyforcommercialtransactions(ratherthangovernmentstatistics).Similarly,gasolineissoldbythegalloninmanycountriesthatareconsideredmetricated.
Metricsystem
Mainarticle:Metricsystem
Themetricsystemisadecimalizedsystemofmeasurementbasedonthemetreandthegramme.Itexistsinseveralvariations,withdifferentchoicesofbaseunits,thoughthesedonotaffectitsday-to-dayuse.Sincethe1960s,theInternationalSystemofUnits(SI),explainedfurtherbelow,istheinternationallyrecognizedstandardmetricsystem.Metricunitsofmass,length,andelectricityarewidelyusedaroundtheworldforbotheverydayandscientificpurposes.Themainadvantageofthemetricsystemisthatithasasinglebaseunitforeachphysicalquantity.Allotherunitsarepowersoftenormultiplesoftenofthisbaseunit.Unitconversionsarealwayssimplebecausetheywillbeintheratiooften,onehundred,onethousand,etc.Alllengthsanddistances,forexample,aremeasuredinmeters,orthousandthsofameter(millimeters),orthousandsofmeters(kilometers),andsoon.ThereisnoprofusionofdifferentunitswithdifferentconversionfactorsasintheImperialsystem(e.g.inches,feet,yards,fathoms,rods).Multiplesandsubmultiplesarerelatedtothefundamentalunitbyfactorsofpowersoften,sothatonecanconvertbysimplymovingthedecimalplace:1.234metersis1234millimetersor0.001234kilometers.Theuseoffractions,suchas2/5ofametre,isnotprohibited,butuncommon.
SI
Mainarticle:InternationalSystemofUnits
TheInternationalSystemofUnits(abbreviatedSIfromtheFrenchlanguagenameSystèmeInternationald'Unités)isthemodern,revisedformofthemetricsystem.Itistheworld'smostwidelyusedsystemofunits,bothineverydaycommerceandinscience.TheSIwasdevelopedin1960fromthemetre-kilogram-second(MKS)system,ratherthanthecentimetre-gram-second(CGS)system,which,inturn,hadmanyvariants.AtitsdevelopmenttheSIalsointroducedseveralnewlynamedunitsthatwerepreviouslynotapartofthemetricsystem.TheSIunitsforthefourbasicphysicalquantities:length,time,mass,andtemperatureare:
meter(m):SIunitoflength
second(s):SIunitoftime
kilogram(kg):SIunitofmass
kelvin(K):SIunitoftemperature
TherearetwotypesofSIunits,baseandderivedunits.Baseunitsarethesimplemeasurementsfortime,length,mass,temperature,amountofsubstance,electriccurrentandlightintensity.Derivedunitsaremadeupofbaseunits,forexample,densityiskg/m3.
Convertingprefixes
TheSIallowseasymultiplicationwhenswitchingamongunitshavingthesamebasebutdifferentprefixes.Toconvertfrommeterstocentimetersitisonlynecessarytomultiplythenumberofmetersby100,sincethereare100centimetresinametre.Inversely,toswitchfromcentimetrestometersonemultipliesthenumberofcentimetersby0.01ordividecentimetersby100.
Distance
A2-metrecarpenter'srulerArulerorruleisatoolusedin,forexample,geometry,technicaldrawing,engineering,andcarpentry,tomeasuredistancesortodrawstraightlines.Strictlyspeaking,theruleristheinstrumentusedtorulestraightlinesandthecalibratedinstrumentusedfordetermininglengthiscalledameasure,howevercommonusagecallsbothinstrumentsrulersandthespecialnamestraightedgeisusedforanunmarkedrule.Theuseofthewordmeasure,inthesenseofameasuringinstrument,onlysurvivesinthephrasetapemeasure,aninstrumentthatcanbeusedtomeasurebutcannotbeusedtodrawstraightlines.Ascanbeseeninthephotographsonthispage,atwo-metrecarpenter'srulecanbefoldeddowntoalengthofonly20centimetres,toeasilyfitinapocket,andafive-metrelongtapemeasureeasilyretractstofitwithinasmallhousing.
Somespecialnames
Wealsousesomespecialnamesforsomemultiplesofsomeunits.
100kilograms=1quintal;1000kilogram=1metrictonne;
10years=1decade;100years=1century;1000years=1millennium
Buildingtrades
TheAustralianbuildingtradesadoptedthemetricsystemin1966andtheunitsusedformeasurementoflengtharemetres(m)andmillimetres(mm).Centimetres(cm)areavoidedastheycauseconfusionwhenreadingplans,thelengthtwoandahalfmetresisusuallyrecordedas2500mmor2.5m.
Time
Mainarticle:Time
Mass
Mainarticle:Weighingscale
Massreferstotheintrinsicpropertyofallmaterialobjectstoresistchangesintheirmomentum.Weight,ontheotherhand,referstothedownwardforceproducedwhenamassisinagravitationalfield.Infreefall,objectslackweightbutretaintheirmass.TheImperialunitsofmassincludetheounce,pound,andton.Themetricunitsgramandkilogramareunitsofmass.
Aunitformeasuringweightormassiscalledaweighingscaleor,often,simplyascale.Aspringscalemeasuresforcebutnotmass,abalancecomparesmasses,butrequiresagravitationalfieldtooperate.Themostaccurateinstrumentformeasuringweightormassisthedigitalscale,butitalsorequiresagravitationalfield,andwouldnotworkinfreefall.
Economics
Mainarticle:Measurementineconomics
Themeasuresusedineconomicsarephysicalmeasures,nominalpricevaluemeasuresandfixedpricevaluemeasures.Thesemeasuresdifferfromoneanotherbythevariablestheymeasureandbythevariablesexcludedfrommeasurements.Themeasurablevariablesineconomicsarequantity,qualityanddistribution.Byexcludingvariablesfrommeasurementmakesitpossibletobetterfocusthemeasurementonagivenvariable,yet,thismeansanarrowerapproach.
Difficulties
Sinceaccuratemeasurementisessentialinmanyfields,andsinceallmeasurementsarenecessarilyapproximations,agreatdealofeffortmustbetakentomakemeasurementsasaccurateaspossible.Forexample,considertheproblemofmeasuringthetimeittakesanobjecttofalladistanceofonemetre(39in).Usingphysics,itcanbeshownthat,inthegravitationalfieldoftheEarth,itshouldtakeanyobjectabout0.45secondtofallonemetre.However,thefollowingarejustsomeofthesourcesoferrorthatarise.First,thiscomputationusedfortheaccelerationofgravity9.8metrespersecondpersecond(32.2ft/s²).Butthismeasurementisnotexact,butonlyprecisetotwosignificantdigits.Also,theEarth'sgravitationalfieldvariesslightlydependingonheightabovesealevelandotherfactors.Next,thecomputationof.45secondsinvolvedextractingasquareroot,amathematicaloperationthatrequiredroundingofftosomenumberofsignificantdigits,inthiscasetwosignificantdigits.
Sofar,wehaveonlyconsideredscientificsourcesoferror.Inactualpractice,droppinganobjectfromaheightofametrestickandusingastopwatchtotimeitsfall,wehaveothersourcesoferror.First,andmostcommon,issimplecarelessness.Thenthereistheproblemofdeterminingtheexacttimeatwhichtheobjectisreleasedandtheexacttimeithitstheground.Thereisalsotheproblemthatthemeasurementoftheheightandthemeasurementofthetimebothinvolvesomeerror.Finally,thereistheproblemofairresistance.
Scientificmeasurementsmustbecarriedoutwithgreatcaretoeliminateasmucherroraspossible,andtokeeperrorestimatesrealistic.
Definitionsandtheories
Classicaldefinition
Intheclassicaldefinition,whichisstandardthroughoutthephysicalsciences,measurementisthedeterminationorestimationofratiosofquantities.Quantityandmeasurementaremutuallydefined:quantitativeattributesarethosewhichitispossibletomeasure,atleastinprinciple.TheclassicalconceptofquantitycanbetracedbacktoJohnWallisandIsaacNewton,andwasforeshadowedinEuclid'sElements.
Representationaltheory
Intherepresentationaltheory,measurementisdefinedas"thecorrelationofnumberswithentitiesthatarenotnumbers".Thestrongestformofrepresentationaltheoryisalsoknownasadditiveconjointmeasurement.Inthisformofrepresentationaltheory,numbersareassignedbasedoncorrespondencesorsimilaritiesbetweenthestructureofnumbersystemsandthestructureofqualitativesystems.Apropertyisquantitativeifsuchstructuralsimilaritiescanbeestablished.Inweakerformsofrepresentationaltheory,suchasthatimplicitwithintheworkofStanleySmithStevens,numbersneedonlybeassignedaccordingtoarule.
Theconceptofmeasurementisoftenmisunderstoodasmerelytheassignmentofavalue,butitispossibletoassignavalueinawaythatisnotameasurementintermsoftherequirementsofadditiveconjointmeasurement.Onemayassignavaluetoaperson'sheight,butunlessitcanbeestablishedthatthereisacorrelationbetweenmeasurementsofheightandempiricalrelations,itisnotameasurementaccordingtoadditiveconjointmeasurementtheory.Likewise,computingandassigningarbitraryvalues,likethe"bookvalue"ofanassetinaccounting,isnotameasurementbecauseitdoesnotsatisfythenecessarycriteria.
Informationtheory
Informationtheoryrecognizesthatalldataareinexactandstatisticalinnature.Thusthedefinitionofmeasurementis:"Asetofobservationsthatreduceuncertaintywheretheresultisexpressedasaquantity.".Thisdefinitionisimpliedinwhatscientistsactuallydowhentheymeasuresomethingandreportboththemeanandstatisticsofthemeasurements.Inpracticalterms,onebeginswithaninitialguessastothevalueofaquantity,andthen,usingvariousmethodsandinstruments,reducestheuncertaintyinthevalue.Notethatinthisview,unlikethepositivistrepresentationaltheory,allmeasurementsareuncertain,soinsteadofassigningonevalue,arangeofvaluesisassignedtoameasurement.Thisalsoimpliesthatthereisacontinuumbetweenestimationandmeasurement.
Quantummechanics
Inquantummechanics,ameasurementisthe"collapseofthewavefunction".Theunambiguousmeaningofthemeasurementproblemisanunresolvedfundamentalprobleminquantummechanics.